Isothermal Growth Research Articles

The non-steady-state growth of divergent pearlite in Fe–C–Mn steels: a phase-field investigation

The eutectoid decomposition of austenite is generally analysed as a steady-state transformation. Although such a time-invariant framework is appropriate for binary systems, in ternary Fe–C–Mn alloys, particularly in the three-phase regime, a characteristic non-stationary equilibrium condition results in the formation of a unique microstructure, called ‘divergent pearlite’. In the present work, the isothermal growth of the divergent pearlite, under different transformation temperatures; $$605\,^{\circ }\hbox {C}$$, $$625\,^{\circ }\hbox {C}$$ and $$650\,^{\circ }\hbox {C}$$, is investigated by adopting a phase-field approach which establishes local-equilibrium (LE) condition across the interface. Though most theoretical approaches intend to setup such condition, the current numerical technique elegantly recovers the non-stationary partitioning equilibrium (P-LE). The thermodynamical framework, which dictates this unique equilibrium condition, is introduced by incorporating the CALPHAD-based data. In addition to rendering the microstructure which is consistent with the observed divergent pearlite, the factors governing the characteristic kinetics and phase distributions are analysed. In complete agreement with the existing studies, it is recognised that the non-steady-state growth is induced by a proportional decrease in the matrix carbon-content, which reduces the transformation kinetics, by influencing the Mn partitioning driving force. The characteristic proportionality which exists between these governing factors is unravelled in the current investigation. Moreover, it is also identified that the transition from the non-steady-state evolution in three-phase regime to predominantly steady state in two-phase regime is continuous. In other words, at higher undercooling, a resolvable segment of time-invariant growth is observed in the initial stages, which is subsequently followed by the divergent evolution.

Intermetallic growth kinetics in gold ball bonds on Al-1%Si-0.5%Cu bond pads at 175∘C

Purpose The purpose of this study is to demonstrate that isothermal intermetallic growth data for gold ball bonds can be non-parabolic with explanations of why deviation from parabolic kinetics may occur. Design/methodology/approach Intermetallic thickness measurements were made at the centre of cross-sectioned ball bonds that were isothermally annealed at 175°C. Intermetallic growth kinetics were modelled with a power law expression(x(t) − x0)2 = α1tα2. The parameters of the power law model were obtained by transformation of the response and explanatory variables followed by data fitting using simple linear regression (SLR). Findings Ball bonds made with 4 N (99.99%Au) and 3 N (99.9%Au) gold wires exhibited two consecutive time regimes of intermetallic growth denoted Regime I and Regime II. Regime I was characterised by reactive diffusion between the gold wire and the aluminium alloy bond pad, during which Al was completely consumed in the formation of Au–Al intermetallics with non-parabolic kinetics. In Regime II, the absence of a free supply of Al to sustain intermetallic growth led to the conclusion that thickening of intermetallics was caused by phase transformation of Au8Al3 to Au4Al. Ball bonds made with 2 N (99%Au) wire also exhibited non-parabolic kinetics in Regime I and negligible intermetallic thickening in Regime II. Research limitations/implications The analysis of intermetallic growth is limited to total intermetallic growth at a single temperature (175°C). Originality/value The value of this study lies in showing that the assumption that only parabolic intermetallic growth is observed in isothermally aged gold ball bonds is incorrect. Furthermore there is no need to assume parabolic growth kinetics because with an appropriate data transformation, followed by fitting the data to a power law model using SLR and with the use of statistical diagnostics, both the suitability of the kinetic model and the nature of the growth kinetics (parabolic or non-parabolic) can be determined.

Predictive Model of Listeria monocytogenes Growth in Queso Fresco

Listeria monocytogenes is a hardy psychrotrophic pathogen that has been linked to several cheese-related outbreaks in the United States, including a recent outbreak in which a fresh cheese (queso fresco) was implicated. The purpose of this study was to develop primary, secondary, and tertiary predictive models for the growth of L. monocytogenes in queso fresco and to validate these models using nonisothermal time and temperature profiles. A mixture of five strains of L. monocytogenes was used to inoculate pasteurized whole milk to prepare queso fresco. Ten grams of each fresh cheese sample was vacuum packaged and stored at 4, 10, 15, 20, 25, and 30°C. From samples at each storage temperature, subsamples were removed at various times and diluted in 0.1% peptone water, and bacteria were enumerated on Listeria selective agar. Growth data from each temperature were fitted using the Baranyi model as the primary model and the Ratkowsky model as the secondary model. Models were then validated using nonisothermal conditions. The Baranyi model was fitted to the isothermal growth data with acceptable goodness of fit statistics (R2 = 0.928; root mean square error = 0.317). The Ratkowsky square root model was fitted to the specific growth rates at different temperatures (R2 = 0.975). The tertiary model developed from these models was validated using the growth data with two nonisothermal time and temperature profiles (4 to 20°C for 19 days and 15 to 30°C for 11 days). Data for these two profiles were compared with the model prediction using an acceptable prediction zone analysis; >70% of the growth observations were within the acceptable prediction zone (between -1.0 and 0.5 log CFU/g). The model developed in this study will be useful for estimating the growth of L. monocytogenes in queso fresco. These predictions will help in estimation of the risk of listeriosis from queso fresco under extended storage and temperature abuse conditions.

Commencement of Ordering in Al–0.69Mg–0.31Si Alloy

Early stages of ordering in dilute Al–0.69(at.%)Mg–0.31(at.%)Si alloy, aged at 373 K for 120 h and 7200 h and at 453 K for 20 h, have been studied using scanning transmission electron microscopy techniques. Starting from the solute enrichment in (110)-type parallel planes, merely after 120 h of aging, isothermal growth at 373 K has been observed to lead to the formation of the small-ordered region after 7200 h of aging. Scanning transmission electron microscopy images from the aforesaid three varieties of samples and the corresponding Fourier-transformed images have been the basis to suggest the possible path of evolution of β″ ordering in this dilute alloy. Based on this, the present study reveals the mechanism of formation of silicon pillar, which is the early stage of β″ that transforms to a fully developed β″. This corroborates with the concept of getting the final β″-strengthened product from an under-aged alloy by a suitable heat treatment.

Synthesis, structural, dielectric, laser damage threshold, third order nonlinear optical and quantum chemical investigations on a novel organic crystalline material: Pyrrolidin-1-ium 2-chloro-4-nitrobenzoate 2-chloro-4-nitrobenzoic acid for opto-electronic applications

It is reported that a novel third order organic nonlinear optical material namely, Pyrrolidin-1-ium 2-chloro-4-nitrobenzoate 2-chloro-4-nitrobenzoic acid (PCNCN) has been synthesized and grown by isothermal solvent evaporation solution growth technique. Single crystal X-ray diffraction analysis revealed that PCNCN belonged to monoclinic crystal system with a centrosymmetric space group of P21/c. The morphology of the as grown PCNCN crystal compared well with that obtained by theoretically generated morphology. The molecular vibrations of PCNCN were analyzed through Fourier transform infrared and NMR spectrum analyses. Optical properties such as transmittance, photoluminescence, and laser damage threshold were studied. The thermal stability of PCNCN was measured through TG-DTA measurement. The dielectric properties such as dielectric constant, dielectric loss, ac conductivity and activation energy of PCNCN single crystal were studied as a function of frequency at different temperatures. The PCNCN single crystals were further characterized for their third order nonlinear optical properties such as nonlinear absorption coefficient, nonlinear refractive index and optical limiting behavior using continuous wave Nd: YAG laser. The quantum chemical investigations were performed using B3LYP/6-311++G(d, p) basis set.

Fundamentals of isothermal austenite reversion in a Ti-stabilized 12Cr – 6 Ni – 2 Mo super martensitic stainless steel: Thermodynamics versus experimental assessments

This work addresses the fundamentals of inter-critical austenite reversion in a Ti-stabilized 12Cr-6Ni-2Mo (at.%) supermartensitic stainless steel, combining thermodynamic and experimental assessments. The calculation of the temperature and composition at which ferrite and austenite phases have the same free energy, i.e. T0 and C0(T), respectively, is discussed as a methodology to understand the austenite reversion and stabilization mechanisms. An ultra-fast heating rate of 500 °C s−1 provided isothermal austenite nucleation and growth from a fully solubilized martensite, allowing direct comparison with the compositional tie-lines and the transformation paths described by the free energy calculations. Isothermal transformation temperatures below and above T0 (625 °C) were used. Below T0, massive reversion was suppressed since it would imply a free energy increase. The opposite occurred above T0, since the critical Ni concentration for austenite reversion was lower than for the solubilized case. Transmission electron microscopy and atom probe tomography evidenced that, in all cases, lath growth occurred by local equilibrium partitioning of Ni, along with co-segregation of ferrite-stabilizing elements (Cr and Mo) at the advancing interface. The complex interaction between Cr, Ni and Mo on the energy gain upon nucleation of austenite revealed that Cr segregation can be beneficial while the adverse effect of Mo can be quickly outbalanced by Ni. The most stable reverted laths were obtained for transformation temperatures at least 15 °C below T0 with average austenite/martensite Ni partitioning factors higher than 2.0.

Isothermal Crystallization of iPP in Environment-friendly Diluents: Effect of Binary Diluents and Crystallization Temperature on Crystallization Kinetics

The growing demand for non-toxic solvents for membrane preparation has motivated the studies for green and sustainable alternatives of solvents. The effect of droplet isothermal growth within the liquid-liquid phase separation region on isothermal spherulitic growth rate of isotactic polypropylene (iPP) was investigated. The results showed that the droplets grew up at a rate of 0.0172 μm·s−1. The larger droplets slowed down the isothermal spherulitic growth rate of iPP. Higher mass ratio of carnauba wax (Cwax)/soybean oil (SO) resulted in faster droplet growth due to weak interaction with polymers. The isothermal crystallization behaviors of iPP in environment-friendly binary diluents consisting of Cwax and SO mixture were further investigated experimentally using polarized optical microscopy. It was demonstrated that the isothermal spherulitic growth rate of iPP in diluents decreased nonlinearly with the increasing crystallization temperature. Compared with virgin iPP, isothermal spherulitic growth rate of iPP in SO diluent was significantly slowed down. The spherulitic growth was further retarded after the addition of Cwax in mixed diluents, resulting in a lower crystallization rate than that in SO. Moreover, the crystal form of iPP membranes was found to be α type through the characterization of small angle X-ray scattering and wide angle X-ray diffraction.

Growth dynamics of InAs/InP nanowire heterostructures by Au-assisted chemical beam epitaxy

The steady-state chemical composition of the In/Au alloy nanoparticles (NPs) during isothermal growth of Au-assisted InAs and InP nanowires (NWs) is different for the two materials. Therefore, when switching from one material to the other, to grow axial NW heterostructures, transient effects dominate during the time period of the NP reconfiguration. As a consequence, the precise control of the thickness of thin InP and InAs segments, which is fundamental for the realization of quantum dot (QD) structures and superlattices, can be very challenging. In this work, we present a study of the thickness/diameter dependence of two InP barriers and of the InAs short segment in between (QD), inserted into InAs NWs grown by means of Au-assisted chemical beam epitaxy. We found a broad variability of the InP segment thickness within the same as-grown sample, resulting in InAs NWs with asymmetric and non-homogeneous InP barriers. We explain the results by considering the NP reconfiguration dynamics which dominates at the early stages of the growth in both growth sequences. Moreover, we propose a strategy to control the growth rate and the dynamics of the barriers, by forcing the NP reconfiguration before starting the InP growth. This allows for the realization of InAs/InP NW heterostructures of different diameters, all having symmetric InP barriers with well controlled thickness, which are crucial parameters for the realization of advanced electronic quantum devices.

A Taylor approximation scheme for coupling thermodynamic data of multicomponent alloy in phase-field model

A phase-field model for multicomponent alloy coupling thermodynamic data is developed. Using a Taylor approximation scheme, the nonlinear calculation is converted into linear calculation when solving equal chemical potential constraint. 1D benchmark tests with the software DICTRA have been carried out, which demonstrate that the model reproduces the right growth kinetics of diffusion controlled phase transformations in multicomponent systems. 2D test of Gibbs-Thomas relationship is also carried out, and the results for phase-field simulation and theoretical analysis are consistent with each other. The application for the microsegregation and isothermal dendrite growth demonstrated feasibility of this model.

Fundamentals of Isothermal Austenite Reversion in a Ti-Stabilized 12cr - 6 Ni - 2 Mo Super Martensitic Stainless Steels: Thermodynamics Versus Experimental Assessments

This work addresses the fundamentals of inter-critical austenite reversion in a 12Cr-6Ni-2Mo supermartensitic stainless steel, combining thermodynamic and experimental assessments. The calculation of the temperature and composition at which ferrite and austenite phases have the same free energy, i.e. T0 and C0, is discussed as a methodology to understand the austenite reversion and stabilization mechanisms. An ultra-fast heating rate of 500 °C.s-1 provided isothermal nucleation and growth from a fully solubilized martensite, allowing direct comparison with the compositional tie-lines and the transformation paths described by the free energy calculations. Isothermal transformation temperatures below and above T0 (625 °C) were used. Below T0, massive reversion was suppressed since it would imply a free energy increase. The opposite occurred above T0, since the critical Ni concentration for austenite reversion (C0-Ni) was lower than the solubilized case. Nevertheless, transmission electron microscopy and Atom Probe Tomography evidenced that, in all cases, lath growth occurred by local equilibrium partitioning of Ni, along with co-segregation of ferrite-stabilizing elements (Cr and Mo) at the advancing interface. The complex interaction between Cr, Ni and Mo on the energy gain upon nucleation of austenite revealed that Cr segregation can be beneficial while the adverse effect of Mo can be quickly outbalanced by Ni. The concentration of Ni along the reverted laths was rather inhomogeneous due to isothermal coalescence and lack of redistribution. However, the most stable laths were obtained for transformations at least 15 °C below T0, with average austenite/martensite Ni partitioning factors higher than 2.0.

Moving Boundary Problems for Quasi-Steady Conduction Limited Melting

The problem of melting a crystal dendrite is modelled as a quasi-steady Stefan problem. By employing the Baiocchi transform, asymptotic results are derived in the limit that the crystal melts completely, extending previous results that hold for a special class of initial and boundary conditions. These new results, together with predictions for whether the crystal pinches off and breaks into two, are supported by numerical calculations using the level set method. The effects of surface tension are subsequently considered, leading to a canonical problem for near-complete-melting which is studied in linear stability terms and then solved numerically. Our study is motivated in part by experiments undertaken as part of the Isothermal Dendritic Growth Experiment, in which dendritic crystals of pivalic acid were melted in a microgravity environment: these crystals were found to be prolate spheroidal in shape, with an aspect ratio initially increasing with time then rather abruptly decreasing to unity. By including a kinetic undercooling-type boundary condition in addition to surface tension, our model suggests the aspect ratio of a melting crystal can reproduce the same non-monotonic behaviour as that which was observed experimentally.

Dendrite tip selection during isothermal free growth in multi-component alloys: Marginal stability theories and insights from phase-field simulations

The principal length scales associated with dendritic solidification, which being the dendritic tip-radius (Rtip) and the primary dendritic arm spacing, are functions of the relative solutal interdiffusivities of the different components in a multi-component alloy. In this paper, we firstly derive marginal stability based theories to predict Rtip during isothermal free growth in any generic multi-component alloy for any generic diffusivity matrix. Here, we extend the Ivanstov solution of the diffusion problem in the liquid with a parabolic solid-liquid interface and propose the closure conditions between the Rtip and the selected dendrite tip velocity (V) based on modification of the classical marginal stability criteria for multi-component situations. Additionally, we derive the constant Rtip2V from phase-field simulations and using the Ivantsov parabola as the approximate interface shape compute the Rtip and the V, which we term as “Approximate microsolvability prediction (AMP)”. Thereafter, we compare our predictions of Rtip,V as well as phase compositions with independent phase-field simulation results for different choices of the diffusivity matrix, where we show that the analytical theories based upon the marginal stability theory are unable to accurately predict variations of the dendrite tip velocity V and the Rtip. We thereby utilize the phase-field simulation results to investigate the tip selection in multi-component alloys and derive an appropriate solvability constant σ∗. We find that the σ∗ in a multi-component alloy is a function of the diffusivity ratios of the components for the case of a diagonal diffusivity matrix.

Analysis of crystal growth and viscosity in Ge-Sb-Se-Te undercooled melts

A comprehensive analysis on crystal growth and viscosity is presented for the Ge2Sb2Se5-xTex (x = 0.5 and 1) undercooled melts in this article. Temperature dependence of the measured viscosities (107.5–1012.5 Pa·s) can be described by a simple exponential Arrhenius type equation in the relatively narrow temperature region in which the measurements were performed. Fragility of the measured materials are all roughly equal to 43, which means that these materials belong to the so called “intermediate” liquids (lying in the middle between strong and fragile liquids) and cannot be described by simple Arrhenius type equation if the temperature region is expanded from glass transition to melting, which is important for description of crystal growth. Therefore, MYEGA equation is used to extrapolate the viscosity data into the temperature region of studied crystal growth. Nucleation and crystal growth started on a surface of studied samples. The isothermal growth rate of the formed surface crystalline layer was measured at various temperatures. Analysis of the growth data revealed a crystal growth driven by liquid-crystal interface kinetics. Therefore, the standard crystal growth models were used for description of crystal growth rates in the studied systems.

Mass transfer characteristics of pipeline leak-before-break in a nuclear power station

This paper aims to develop a correlation for pressure undershoot and revises the hypotheses of nucleation inception in the two-phase critical flow model. The theories of rapid depressurization and isothermal bubble growth were used to construct a modified two-phase critical flow model for leak-before-break analysis. The modified model predictions exhibit strong similarities with the experimental values compared with the Moody and Henry–Fauske models, with prediction deviations of less than 8.9% in the inter-granular stress corrosion crack. The effects of the inlet conditions on the nucleation inception point, as well as the distribution characteristics of the mass quality and void fraction along the channel, were investigated to explore the mass transfer process.

Use of modified Richards model to predict isothermal and non-isothermal microbial growth

Mathematical models are often used to predict microbial growth in food products. An important class of these models involves the adaptation of classical sigmoid functions, such as the Gompertz and logistic functions. This study aimed to validate the use of the modified Richards model in various situations, which have not previously been tested. The model was obtained through solving a system of two differential equations and could be applied to both isothermal and non-isothermal environments. To test and validate this model, we used published datasets containing data for the growth of Pseudomonas spp. in fish products. The results obtained after fitting the model showed that it could be effectively used to describe and predict the Pseudomonas growth curves under various temperature regimens. However, the influence of the shape parameter on the growth curve is an issue that needs further evaluation.

Growth of non-toxigenic Clostridium botulinum mutant LNT01 in cooked beef: One-step kinetic analysis and comparison with C. sporogenes and C. perfringens

The objective of this study was to investigate the growth kinetics of Clostridium botulinum LNT01, a non-toxigenic mutant of C. botulinum 62A, in cooked ground beef. The spores of C. botulinum LNT01 were inoculated to ground beef and incubated anaerobically under different temperature conditions to observe growth and develop growth curves. A one-step kinetic analysis method was used to analyze the growth curves simultaneously to minimize the global residual error. The data analysis was performed using the USDA IPMP-Global Fit, with the Huang model as the primary model and the cardinal parameters model as the secondary model.The results of data analysis showed that the minimum, optimum, and maximum growth temperatures of this mutant are 11.5, 36.4, and 44.3 °C, and the estimated optimum specific growth rate is 0.633 ln CFU/g per h, or 0.275 log CFU/g per h. The maximum cell density is 7.84 log CFU/g. The models and kinetic parameters were validated using additional isothermal and dynamic growth curves. The resulting residual errors of validation followed a Laplace distribution, with about 60% of the residual errors within ±0.5 log CFU/g of experimental observations, suggesting that the models could predict the growth of C. botulinum LNT01 in ground beef with reasonable accuracy.Comparing with C. perfringens, C. botulinum LNT01 grows at much slower rates and with much longer lag times. Its growth kinetics is also very similar to C. sporogenes in ground beef. The results of computer simulation using kinetic models showed that, while prolific growth of C. perfringens may occur in ground beef during cooling, no growth of C. botulinum LNT01 or C. sporogenes would occur under the same cooling conditions. The models developed in this study may be used for prediction of the growth and risk assessments of proteolytic C. botulinum in cooked meats.

Isothermal Growth of Spinel Crystals in Vanadium‐Chromium Slag

AbstractIn order to explore the isothermal growth crystallization mechanism of vanadium‐chromium slag, the growth behavior of spinel crystals in vanadium‐chromium slag is investigated in this paper by using SEM/EDS and crystal size distribution (CSD) theory. It is found that with the prolongation of holding time at 1523 K, the mean diameter of spinel crystals decrease in the initial 30 min and then increased to 60.34 µm. The area fraction of spinel crystals increases from 35.56 to 54.28%. While at 1623 K, expect for the transient decrease at 30 min, the mean diameter of spinel crystals also increases obviously with the prolongation of time. The area fraction of spinel crystals increase from 31.28 to 50%. The results reveal that low temperature befits the growth of spinel crystals. All CSD shapes of vanadium‐chromium slag are lognormal distribution, which implies that the growth of the spinel crystals is controlled by surface and supply, and more inclined to supply control.

Effect of Self-Poisoning on Crystallization Kinetics of Dimorphic Precision Polyethylenes with Bromine

High molar mass polyethylenes with bromine atoms placed on each and every 21st, 19th, 15th, or 9th backbone carbon crystallize into two distinctive layered polymorphs by changing undercooling. Crystallization at low temperatures produces Form I, a planar all-trans conformation, while at higher temperatures gauche conformers set for backbone bonds adjacent to the methine due to a close intermolecular staggering of bromines resulting in a herringbone Form II structure. In this work, the sharp range of isothermal crystallization temperatures for the transition between Form I and Form II is first identified via WAXD and melting behaviors for all members of the series. Furthermore, the temperature dependence of the isothermal linear spherulitic growth rates of Form II has been studied for a wide range of crystallization temperatures. The linear growth rates display a discrete minimum with decreasing temperature at a crystallization temperature near the melting point of Form I, a feature which is reminiscent of...

Reversible phase transformation phenomenon in titanium dioxide films: Evidence beyond interface-nucleation and dissolution-precipitation kinetics

The re-crystallization kinetics and rutile to anatase reversible phase transformation (PT) in nano-crystalline titanium dioxide (TiO2) are reported. Initially, an amorphous TiO2 film is used for the present study and in situ isothermal annealing dependent nucleation and growth kinetics of anatase and rutile phase is studied at low temperature (∼523 K) and well explained using Johnson–Mehl–Avrami-Kolmogorov (JMAK) model. The anatase nanocrystallite (NCs) transformation into rutile phase is reported with isothermal annealing for longer time and temperature dependent annealing in lower temperature range 523 K–673 K and explained using interface-nucleation mechanism. Furthermore, the thermodynamic stability of rutile NCs and lattice stress-induced reversible PT in nano-sized rutile TiO2 are confirmed in moderate temperature range (623 K - 973 K) and well explained using x-ray diffraction, micro-Raman spectroscopy and near edge x-ray absorption fine structure spectroscopy studies. However, annealing at higher temperature (1123 K - 1323 K) induces the growth of anatase NCs and their natural transform into rutile phase are explained by well-known dissolution–precipitation mechanism. Activation energy of rutile PT is quantified and found higher for dissolution-precipitation mechanism than that for interface nucleation at earlier stage. Thus, overall PT kinetics at different temperature range is well understood by invoking in three step mechanism: I) early stage anatase-to-rutile transformation is dominated by interface-nucleation, II) then intermediate stage reversible rutile-to-anatase PT and, III) at later stages, anatase-to-rutile PT is controlled by dissolution–precipitation mechanism.

Effects of Impurity Elements on Isothermal Grain Growth of Electroplated Copper

The grain growth of electroplated copper films implanted with individual impurity elements were studied with elements implanted separately. Sheet resistance evolution, focus ion beam imaging, and X-ray diffraction were used to characterize the grain growth along time at various annealing temperatures. While the incorporation of oxygen, sulfur, and chlorine impedes the grain growth, the oxygen has the weakest impact and chlorine has the strongest. Fully transformed films with coarse grains were obtained at temperatures up to 400 C. The presence of carbon resulted in a nucleation limited grain growth and the full transformation was not achieved until at 700 C. On the other hand, the presence of chlorine enhanced a preference of grain growth in [111] orientation. This study aims to provide a new perspective of improving grain structures of copper with engineered chemical additives.