Site Saturation Nucleation Research Articles

Effect of solute concentration on microstructure evolution during static recrystallization in Mg-0.2%Ce alloy using cellular automata

A new cellular automata model has been developed to evaluate the effect of solute drag on the microstructure and texture evolution during static recrystallization of Mg and its alloys in the temperature range of 200 – 400 °C. In the present model, the site saturation nucleation was assumed and all the nuclei are present at the grain boundaries. The growth of each nucleus depends on the solute concentration and dislocation density difference between neighboring grains. The microstructural analysis of the newly developed cellular automata model showed the evolution of grain size at different temperatures compared to the equilibrium microstructure containing the equilibrium concentration of solute atoms at the grain boundaries. Further, the texture evolution showed that there is an increase in the texture strength with an increase in the annealing temperature when the solute concentration was lower than the equilibrium concentration at the boundaries, whereas the texture strength decreased with increasing the annealing temperature when the solute concentration was higher than the equilibrium solute concentration at the boundaries. The present model shows that solute drag pressure increased continuously with increasing the annealing temperature when the solute concentration was lower than the equilibrium concentration at the boundaries. However, the solute drag pressure decreased with an increase in the annealing temperature when the solute concentration was higher than the equilibrium solute concentration at the boundaries.

Nucleation Sites in the Static Recrystallization of a Hot-Deformed Ni-30 Pct Fe Austenite Model Alloy

In the present study, the nucleation of static recrystallization (SRX) in austenite after hot deformation is experimentally analyzed using a Ni-30 pct Fe model alloy. In agreement with the predictions by current models, nucleation rate exhibits a strong peak, early during SRX. Whereas such an early peak is explained by current models by the saturation of nucleation sites, this condition is far from reached, even after the peak declines. In addition, triple-junction and grain-boundary sites are shown to make a quantitatively similar contribution to nucleation. However, for a given boundary between deformed grains, nucleation predominantly starts at one of the triple junctions. Triple-junction nucleation initiates by strain-induced boundary migration of the nucleus (bulging) along one of the boundaries at the junction. Annealing twin boundaries contribute negligibly to nucleation through their grain-boundary sites. By contrast, their junctions with the boundaries of the parent grains do play a relevant role. The earlier nucleation at the triple junctions is attributed to the higher dislocation density observed around them, and the energy of the boundary consumed by the bulge. Both the maximum and average number of nuclei formed per boundary between deformed grains increase with increasing boundary length.

Mechanistic insights into the crystallization of coamorphous drug systems.

In our previous study, the coamorphous formulation of lurasidone hydrochloride (LH) with saccharin (SAC) showed significantly enhanced dissolution and physical stability compared to crystalline/amorphous LH. However, the coamorphous system is still in amorphous state, and has the tendency to recrystallization, which will in turn result in the loss of above advantages. In this study, the crystallization kinetics under isothermal and non-isothermal conditions was investigated. Compared to amorphous LH, coamorphous LH-SAC showed 68.3-361.2 and 2.6-6.1 times lower crystallization rates in glassy state and supercooled liquid state, respectively. After co-amorphization, the addition of SAC changed the crystallization mechanism of amorphous LH from nucleation-controlled to diffusion-controlled manner. Amorphous LH followed the site-saturated nucleation, whereas the coamorphous system exhibited a fixed number of nuclei. The non-isothermal crystallization indicated amorphous LH and coamorphous LH-SAC showed two-dimensional (JMAEK 2) and three-dimensional (JMAEK 3) growth of nuclei, respectively. Furthermore, coamorphous LH-SAC exhibited higher molecular mobility and dynamic fragility (mD) than amorphous LH, which is kinetically unfavorable for its physical stability. However, from thermodynamic perspective, coamorphous LH-SAC had a higher configurational entropy, i.e., a higher entropy barrier for crystallization, which is beneficial to hinder its crystallization. Therefore, it was concluded that the higher configurational entropy rather than the molecular mobility was proposed to be responsible for its improved stability. In addition, molecular dynamics simulations with miscibility, radial distribution function and binding energy calculations suggested coamorphous components exhibited good miscibility and strong intermolecular interactions, which was also conductive to the enhancement in its stability. This study offers an in-depth understanding about the effect of the coformer on the crystallization kinetics of coamorphous systems, and points out the important contribution of the configurational entropy in stabilizing the coamorphous systems.

Effects of Vanadium on the Kinetics of Austenitization from Pearlite in Fe–V–C Alloys

Vanadium effects on the kinetic characteristics of the austenit transformation in Fe-V-C ternary alloys were investigated by microstructure analysis, differential scanning calorimetry (DSC) and the Johnson-Mehl-Avrami-Kolmogorov model (JMAK). The results show that the vanadium gives rise to the refinement of pearlite lamellar spacing before transformation, the original austenite grain size decreases after transformation, and and the increase of the amount of carbide at the grain boundarsy. Studies on kinetics showed that the austenization of the Fe-V-C ternary alloys is characterized by JMAK model involving site saturation nucleation, diffusion-controlled growth, and impingement correction. V increases the diffusion activation energy and decreases the pre-exponential factor for diffusion.

Kinetics of Reordering in Quenched Ni2Mn0.8Cu0.2Ga Ferromagnetic Shape Memory Alloys

Quenched Ni2Mn1−xCuxGa ferromagnetic shape memory alloys undergo two consecutive post-quench ordering processes. The kinetics of order recovery has been analysed in detail for Ni2Mn0.8Cu0.2Ga, based on the calorimetric curves obtained during post-quench heating at constant rates. Isoconversional methods have been used to determine the activation energy, the pre-exponential factor, and the reaction model that best fits the two reordering processes. The kinetic analysis has been extended to samples quenched from different temperatures. The kinetic study shows that order improvement processes in quenched Ni2Mn0.8Cu0.2Ga alloys can be described by a first order reaction model, consistent with site-saturation nucleation and homogeneous diffusion-controlled growth, with apparent activation energies around 1.1 eV. The pre-exponential factors, especially those obtained for samples quenched from different temperatures, highlight the crucial role of the vacancies retained by high temperature quenching on the atomic reordering underlying the observed processes.

Atomistic mechanisms of the initial oxidation of stepped Cu3Au(100)

Alloy oxidation is complex and involves several critical processes that lack understanding on the atomic level. Here, we report an atomistic picture of the initial-stage oxidation of stepped ${\mathrm{Cu}}_{3}\mathrm{Au}(100)$ using a combination of surface science tools and modeling to illuminate the microscopic processes underlying oxygen-adsorption-induced structural and compositional changes. Pristine ${\mathrm{Cu}}_{3}\mathrm{Au}(100)$ consists of wide CuAu-terminated terraces and narrow Cu-terminated terraces separated by monatomic steps. Counterintuitive to the common expectations of the adsorbate-induced surface segregation of the more reactive alloy component, our observations demonstrate that the oxygen adsorption leads to the exfoliation of the outermost CuAu layer, thereby exposing the inner Cu plane to O attack. This occurs via the oxygen-assisted abstraction of Au and Cu atoms from step edges and CuAu terraces, which generates many Cu adatoms aggregating into Cu clusters and Au adatoms dissolving into the bulk. The oxygen adsorption onto fourfold hollow sites of the exposed Cu plane results in nucleation and growth of the $c(2\ifmmode\times\else\texttimes\fi{}2)\text{\ensuremath{-}}\mathrm{O}$ superstructure, which can be fit well by the Johnson-Mehl-Avrami-Kolmogorov theory with a site-saturated nucleation mechanism.

On the grain size distribution function in KJMA compliant growth

The temporal evolution of the probability density function (PDF) of grain size in phase transformations by nucleation and growth has been computed by means of Kolmogorov’s second equation. The transformation is modeled in accord with the classical KJMA (Kolmogorov-Johnson-Mehl-Avrami) theory for linear growth of nuclei and either simultaneous or progressive nucleation. For 3D growth, it is shown that for progressive nucleation, second order term can be neglected in the differential equation for the PDF of grain volume. For site-saturated nucleation the variance of the distribution increases with time to attain the value of the Gamma distribution at the end of the transformation. It is demonstrated that in this case the PDF is given by convolution of Gaussian-like solutions of Kolmogorov’s equation with Gamma distribution. The validity of the model is checked by computer simulations available in literature.

Exploring the Impact of Arp2/3 Concentration on Actomyosin Dynamics

Actin binding proteins facilitate the structural re-organization of actomyosin networks which underpins the shape changes in living cells. We explore the effect of actin-related proteins 2/3 (Arp2/3) complex, an actin nucleator, on actomyosin network structures and dynamics. Using a coarse-grained active network model, we show that such motor-driven networks with high concentrations of Arp2/3 complexes show inhibited dynamics because of the saturation of nucleation sites on actin filaments by the Arp2/3 complexes, while low Arp2/3 concentrations aggravate contractility of the networks with hallmarks of short contraction time and small actin clusters.

Precipitation kinetics of Ti3Ni4 and multistage martensitic transformation in an aged Ni–rich Ni–Ti shape memory alloy

The precipitation kinetics of Ti3Ni4 in a Ti–51.0 at.% Ni alloy was studied through the martensitic transformations temperatures and the JMAKE model. The influences of different aging temperatures and aging time on martensitic transformations temperatures were investigated using differencial scanning calorimetry and X–ray diffraction. The Ti3Ni4 precipitation is more preferred at aging temperatures between 350 and 450 °C for 1 h. At these aging temperatures, the martensitic transformation occurred in 4 stages due to Ti3Ni4 heterogeneous nucleation. The obtained Avrami exponents suggests that Ti3Ni4 precipitation has unidimensional growth, is diffusion controlled, and presents nucleation site saturation before complete precipitation. Also, heterogeneous nucleation explains why Avrami exponent values were lower than theoretically expected for JMAKE model. The apparent activation energy estimated for Ti3Ni4 precipitation was 108 (± 8) kJ/mol, and the frequency factor 5.1 (± 4.2) 104 s−1. MET and EDS techniques confirmed the presence of Ti3Ni4 precipitates through morphological and chemical characterization. The estimated Ti3Ni4 volumetric fractions at metastable equilibrium were 12.5, 11.4, and 9.2% for 350, 400, and 450 °C, respectively.

Sensitivity analysis of a phase field model for static recrystallization of deformed microstructures

Static recrystallization is a process whereby dislocation-free grains are nucleated in a deformed microstructure and then newly recrystallized grains grow and consume the previously existing grains. This paper describes a phase field model for static recrystallization, along with details of the implementation and simulation results. Recrystallized grains are seeded utilizing a probability-based method, including a hold time to allow the order parameters to adjust to seeded grains. The nominal simulation time is corrected to account for the nuclei hold and for the time required for a nucleus to grow from its critical size to the seeded size. Microstructural evolution was simulated for two- and three-dimensional systems and the fraction recrystallized was quantified via Avrami kinetics. The resulting Avrami time exponents were in agreement with the expected values for site-saturated nucleation. The variability in the Avrami parameters was quantified by simulating the recrystallization of the same underlying polycrystalline microstructure but using different seed locations. Additional simulations were performed to determine the influence of the deformed microstructure on recrystallization, specifically investigating the effects of the spatial distribution of the initial dislocation density within the microstructure as well as the morphologies of the polycrystalline microstructure. For the significantly deformed polycrystalline microstructures examined in this work, it is shown that microstructural evolution is primarily driven by stored energy in dislocations rather than grain boundary energy.

Effect of Cerium on the Austenitic Nucleation and Growth of High-Mo Austenitic Stainless Steel

The influence of small amounts of cerium on the solidification phenomena of S31254 high-Mo austenitic stainless steel was investigated by in situ observations and theoretical calculations. In situ observations indicate that cerium addition in molten steel can accelerate austenitic nucleation but inhibit primary austenite grain growth. The initial nucleation temperature occur 32.3 °C in advance and the nucleation site density increases to 176/mm after 2 seconds in S31254-Ce compared to S31254. The modified Ce-containing inclusions in S31254-Ce improve the ability for austenite heterogeneous nucleation, which would significantly reduce the energy barrier of nucleation. The nucleation mechanism obtained from Johnson–Mehl–Avrami–Kologoromov (JMAK) theory is changed from site saturation nucleation to site saturation plus Avrami nucleation after cerium addition. Furthermore, cerium addition also prolongs the whole solidification temperature range from 28 °C to 43.9 °C and limits the growth velocity of a single austenite grain from approximately 20 to 2 μm/s. The ratio of the solid phase decreases from 60 to 8.2 pct, but the grain density increases from 68.8 to 280/mm2, with the solidification time extended to 8 seconds after cerium addition. Thus, the main solidification behavior in the early solidification stage of S31254-Ce is nucleation instead of primary grain growth. The low growth velocity for austenite grains and significant high nucleation site density exhibit a low rate constant k during the solidification process. Moreover, cerium addition could significantly refine the solidified structure, and the grain density of the final solidified structure in S31254-Ce is 366.6/mm2.

Unique buoyancy-force-based kinetics determination of beta to alpha phase transformation in bulk tin plates

Reliable measurements of the kinetics of β → α allotropic transformation in Sn-based solder underlie the design and development of advanced interconnects for low-temperature electronics. In this paper, a highly-accessible and buoyancy-based method, but different from common dilatometry, was developed to consistently detect a change of the transformed fraction in bulk βSn plates (10 × 10 × 1mm) with time at −20, −40, and −60 °C. Due to the concurrent effects of undercooling temperature and interfacial atomic diffusion, the β → α transformation in Sn plates at −40 °C proceeded most rapidly up to around 70% αSn fraction after 168 h. The transformed fraction versus time curves yielded excellent fits to the classic Johnson-Mehl-Avrami-Kolmogorov model with a constant nucleation rate during transformation process (Avrami exponent, n of 4). Addition of nucleation agent accelerated the transformation by shortening the incubation period, but the nucleation rate decreased to zero in the following transformation (n = 3). Furthermore, coarsening grain size depressed β → α transformation and led to the saturation of nucleation sites in the vicinity of half transformation (n decreasing from 4 to 2). The simple, convenient, and reliable method proposed showed high sensitivity with detection limits of about 2%, and it could be a promising approach to study and predict solid-state phase transformation kinetics.

Computer simulation of site saturation and constant nucleation rate transformations on a network of Kelvin polyhedra

A crucial step of transformations in solids is that of nucleation. To model nucleation, one must specify nuclei location in space as well as how nuclei appear as a function of time. In the classical theory of Johnson–Mehl–Avrami–Kolmogorov (JMAK), there are two essential nucleation modes. One is site-saturation in which all nucleation sites are exhausted early in the transformation. Another is the so-called constant nucleation rate. JMAK theory considers that nuclei are located uniform randomly within the matrix both in the case of site-saturation and constant nucleation rate. Nonetheless, it is usually common in polycrystals to observe nucleation taking place on the grain surfaces, edges, and vertices. Cahn proposed analytical expression for such situations. In this work, we conduct a computer simulation considering that grains can be represented by a network of Kelvin polyhedra. We restrict nucleation to the grain boundaries of the Kelvin network. Grain boundary nucleation can be either site-saturated or a constant nucleation rate. We compare the effect of these two nucleation modes. JMAK theory and Cahn’s theory are applied to the simulated results. The microstructures are characterized by several quantitative metallographic parameters. We observed that the two nucleation modes exhibited similar behavior.

Austenite to Ferrite Transformation Kinetics in Fe-9 %Cr Alloys - I. General Kinetic Analysis

The paper considers theoretical aspects of the kinetics of austenite → ferrite transformation in an Fe–9 %Cr alloy, a common model of diffusionless transformation. In previous studies it was shown that this transformation under isothermal conditions shows a behaviour typical for nucleation site saturation, including the change of the Avrami exponentn(determined as the slow of transformation curve on double logarithmic scale) from 4 to 1. Activation energies determined in two ways: by the ‘nose’ temperature of the normal C-curve and by the slope of the C-curve re-drawn on a reverse temperature scale are unexpectedly similar (272–315 kJ/mole) and not temperature-dependent. But the complete TTT diagrams calculated using these values determined directly from experimental data and the precise formula of Cahn’s solution of grain face nucleated transformation problem do not provide good agreement with experiment in the whole temperature range. This may mean that the theory of site saturation needs some correction.

Level-set simulation of anisotropic phase transformations via faceted growth

Level-set method is used to simulate phase transformations with anisotropic kinetics where the transforming interface is faceted. The method overcomes previous limitation of this simulation methodology in tracking dynamic evolution of a large number of growing grains. The method is then used to simulate multi-grain phase transformations where the facets are three low-index ([1 0 0], [1 1 1], [1 1 0]) planes that yield morphologies including cube, octahedron and rhombic dodecahedron. The microstructure evolves under site-saturated nucleation and constant nucleation rate. The cube morphology undergoes fastest transformation followed by octahedron, rhombic dodecahedron and sphere. It is also shown that the Johnson-Mehl-Avrami-Kolmorgorov theory can be used to describe the kinetics of the faceted phase transformation. The resulting microstructure shows non-convex grain shapes with highly corrugated surfaces. The structures are also characterized using the average grain length along certain low index crystallographic directions, the coherent length. This measurement shows that for a cubic morphology, there is a significant difference in the coherent length for low index directions, while there is no meaningful difference in the coherent length for kinetic Wulff shapes of other anisotropies examined.

Kinetics of the fcc\xa0\u2192\xa0hcp Phase Transformation in Cu-Ge Solid Solutions Upon Isothermal Aging

The kinetics of the ζ-phase formation from a supersaturated α-Cu(Ge) solid solution (i.e., transformation from the fcc crystal structure to the hcp crystal structure) containing 10.8 at. pct Ge [at isothermal temperatures of 573 K, 613 K, and 653 K (300 °C, 340 °C, and 380 °C)] were studied by X-ray diffraction (XRD) for phase fraction determination. Both in situ and ex situ annealing experiments were performed. The transformation kinetics were modeled on the basis of a versatile modular model. The transformation kinetics complied with a site-saturation nucleation mode and strongly anisotropic interface-controlled growth mode in association with a corresponding impingement mode: diffusion of Ge (towards the stacking faults, SFs) does not control the transformation rate. Transmission electron microscopy (TEM) investigations showed that segregation of Ge at the stacking faults (SFs) takes place (relatively fast) prior to the structural transformation (fcc → hcp).

Influence of the Heterogeneous Nucleation Sites on the Kinetics of Intermetallic Phase Formation in Aged Duplex Stainless Steel

The aim of this work is to study the influence of the heterogeneous nucleation site quantity, observed in different ferrite and austenite grain size samples, on the phase transformations that result in intermetallic phases in a UNS S31803 duplex stainless steel (DSS). Solution treatment was conducted for 1, 24, 96, or 192 hours at 1373 K (1100 °C) to obtain different ferrite and austenite grain sizes. After solution treatment, isothermal aging treatments for 5, 8, 10, 20, 30, or 60 minutes at 1123 K (850 °C) were performed to verify the influence of different amounts of heterogeneous nucleation sites in the kinetics of intermetallic phase formation. The sample solution treated for 1 hour, with the highest surface area between matrix phases, was the one that presented, after 60 minutes at 1123 K (850 °C), the smaller volume fraction of ferrite (indicative of greater intermetallic phase formation), higher volume of sigma (that was present in coral-like and compact morphologies), and chi phase. It was not possible to identify which was the first nucleated phase, sigma or chi. It was also observed that the phase formation kinetics is higher for the sample solution treated for 1 hour. It was evidenced that, from a certain moment on, the chi phase begins to be consumed due to the sigma phase formation, and the austenite/ferrite interface presents higher S V for all solution treatment times. It was also observed that intermetallic phases form preferably in austenite-ferrite interfaces, although the higher occupation rate occurs at triple junction ferrite-ferrite-ferrite. It was verified that there was no saturation of nucleation sites in any interface type nor triple junction, and the equilibrium after 1 hour of aging at 1123 K (850 °C) was not achieved. It was then concluded that sigma phase formation is possibly controlled by diffusional processes, without saturation of nucleation sites.

Effects of tantalum on austenitic transformation kinetics of RAFM steel

The RAFM (reduced activation ferritic/martensitic) steels containing different tantalum contents (0 wt. %, 0. 027 wt. %, 0. 073 wt. %) were designed and cast. Differential scanning calorimetry and optical microscopy were employed to explore the influence of tantalum content on the austenitic transformation of RAFM steels. The austenitic transformation kinetics was described by a phase-transformation model. The model, involving site saturation nucleation, diffusion-controlled growth and impingement correction, was established based on the classical Johnson-Mehl-Avrami-Kolmogorov model. The phase-transformation kinetics parameters, including D0 (pre-exponential factor for diffusion) and Qd (activation energy for diffusion), were calculated by fitting the experimental data and the kinetic model. The results indicated that the average grain size is decreased with the increase of tantalum. The values of Ac1 and Ac3 (onset and finish temperature of austenitic transformation, respectively) are increased by increasing the tantalum content. The increase of tantalum caused the decrease of D0. However, Qd is increased with the increase of tantalum. In addition, as a carbides forming element, tantalum would reduce the carbon diffusion coefficient and slow down the austenitic transformation rate.

Abnormal change of electrical resistivity in the Cu46Zr46Al8 bulk metallic glass during crystallization

The crystallization of bulk metallic glass occurs with heat release, volume shrinkage, and electrical resistivity decrease because of the differences in properties between the glass and crystalline phases. A standard four-probe electrical resistivity measurement during the crystallization of the Cu46Zr46Al8 bulk metallic glass shows an abnormal increase of resistivity at the initial stage before the normal declining stage. High-density nanocrystals emerged in the matrix, which enhanced electron scattering and resulted in increasing of resistivity. The subsequent normal declining of resistivity was dominated by the growth of the nanocrystals. This high-density site-saturated nucleation followed by slow growth crystallization kinetics was supported by microstructure analysis with SEM and TEM.

Kinetics of the olivine–ringwoodite transformation and seismic attenuation in the Earth's mantle transition zone

In regions of the mantle where multi-phases coexist like at the olivine–wadsleyite–ringwoodite transitions, the stress induced by the seismic waves may drive a mineralogical reaction between the low to high pressure phases, a possible source of dissipation. In such a situation, the amount of attenuation critically depends on the timescale for the phase transformations to reach equilibrium relative to the period of the seismic wave. Here we report synchrotron-based measurements of the kinetics of the olivine to ringwoodite transformation at pressure-temperature conditions of the co-stability loop, for iron-rich olivine compositions. Both microstructural and kinetic data suggest that the transformation rates are controlled by growth processes after the early saturation of nucleation sites along olivine grain boundaries. Transformation-time data show an increase of reaction rates with temperature and iron content, and have been fitted to a rate equation for interface-controlled transformation: G=k0⋅T⋅exp⁡[n⋅XFa]⋅exp⁡[−(ΔHa+PV⁎)/RT]×[1−exp⁡(ΔGr/RT)], where XFa is the fayalite fraction, the exponential factor n=9.7, ln⁡k0=−9.1 ms−1. XFa−1 and ΔHa=199 kJ/mol, assuming V⁎=0 cm3/mol. Including these new kinetic results in a micro-mechanical model of a two-phase loop (Ricard et al., 2009), we predict QK−1 and Qμ−1 significantly higher than the PREM values for both body waves and normal modes. This attests that the olivine–wadsleyite transition can significantly contribute to the attenuation of the Earth's mantle transition zone.