Athermal Nucleation Research Articles

A note on the kinetics of non-isothermal crystallization of polymers

On the kinetics of non-isothermal crystallization of polymers, the reinterpreted Ozawa method proposed in a previous report is studied further to generate valuable information. The Ozawa method is used to investigate the crystallization kinetics with constant temperature scanning rates β and is concerned with the basic formula for apparent crystallinity, from which the true crystallinity is derived using the concept of an extended volume of the Kolmogorov–Johnson–Mehl–Avrami model. The formula is expressed by the temperature scanning rate β and a function of temperature T, βOz(T). This study investigates the temperature derivative of βOz(T), which represents the crystal growth rate in the presence of athermal nucleation from foreign heterogeneities including nucleating agents; this case is applicable to most polymer crystallization processes. The validity of this relationship was verified by comparing it directly to the crystal growth rate in numerical simulations and by comparing it to the crystallization peak and half times of isothermal crystallization for experimental results of poly(butylene terephthalate). This evaluation provides basic information on the crystal growth rate, which is necessary for understanding polymer crystallization. As is well known, the temperature derivative of βOz(T) also corresponds to the function required to derive Nakamura et al. model's suggested equation for polymer processing.

Revealing thermally-activated nucleation pathways of diffusionless solid-to-solid transition

Solid-to-solid transitions usually occur via athermal nucleation pathways on pre-existing defects due to immense strain energy. However, the extent to which athermal nucleation persists under low strain energy comparable to the interface energy, and whether thermally-activated nucleation is still possible are mostly unknown. To address these questions, the microscopic observation of the transformation dynamics is a prerequisite. Using a charged colloidal system that allows the triggering of an fcc-to-bcc transition while enabling in-situ single-particle-level observation, we experimentally find both athermal and thermally-activated pathways controlled by the softness of the parent crystal. In particular, we reveal three new transition pathways: ingrain homogeneous nucleation driven by spontaneous dislocation generation, heterogeneous nucleation assisted by premelting grain boundaries, and wall-assisted growth. Our findings reveal the physical principles behind the system-dependent pathway selection and shed light on the control of solid-to-solid transitions through the parent phase’s softness and defect landscape.

Analysis of non-isothermal polymer crystallization at constant scan rates based on the Avrami model

When polymer crystallization is initiated by an instantaneous athermal nucleation and controlled by two-dimensional secondary nucleation on the growth face, for crystallization from the melt upon cooling at a constant scan rate β, an analysis based on the Avrami model reveals that a plot of β/(ΔTpeak)2=β/(TM0−Tpeak)2, in which Tpeak represents the peak temperature of crystallization rate and TM0 the equilibrium melting point, is nearly equivalent to that of the inverse of crystallization half-time τ1/2 and peak time τpeak, which are obtained from isothermal crystallization and used as a measure of crystal growth rate. Therefore, a plot of β/(ΔTpeak)2 against Tpeak at different scan rates can be utilized to examine the temperature dependence of the crystal growth rate in the same way as that of τ1/2 and τpeak obtained under isothermal conditions at different temperatures. The applicability was confirmed via numerical calculations and experiments using poly(vinylidene fluoride) and poly(butylene terephthalate). The agreement of the temperature dependence estimated by the plot of β/(ΔTpeak)2 was much better than that of β/(Tpeak)2 used in the well-known Kissinger plot.

Phase field benchmark problems for nucleation

We present nucleation phase field model benchmark problems, expanding on our previous benchmark problems on diffusion, precipitation, dendritic growth, linear elasticity, fluid flow and electrochemistry. Nucleation is the process in which either a new thermodynamic phase or a new structure is created, such as solidification from the melt, or self-assembly of particulates. Based on where the nucleation occurs, it can be divided into two main categories: homogeneous nucleation and heterogeneous nucleation. In the first nucleation benchmark problem, we focus on homogeneous nucleation for both single seed under different initial conditions and multiple seeds. The second nucleation benchmark problem focuses on athermal heterogeneous nucleation and nucleation behavior near the free growth limit with different undercooling driving forces.

Prediction of effective elastic properties of a polypropylene component by an enhanced multiscale simulation of the injection molding process

In the injection molding process of semi-crystalline polymers, the melt undergoes a complex deformation and cooling history which results in an inhomogeneous distribution of spherulites in the component. To evaluate these inhomogeneities in an isotactic polypropylene (α-iPP) part, an integrated multi-scale simulation approach has been developed in Laschet et al. (2017a). This approach combines a macroscale mold filling and heat transfer analysis with a crystallization model at the microscale and a two-scale homogenization scheme in order to calculate microstructure dependent elastic properties of the PP component. This approach is extended here by adding some features improving the local Hooke matrix predictions. A link between Molecular Dynamics (MD) simulations and the homogenization scheme is achieved in order to obtain unknown properties of the pure amorphous and crystalline phases. Next, the accuracy of the crystallization model is improved by considering not only isothermal but also athermal nucleation. The spherulite growth is now evaluated by a continuous cellular growth algorithm. Then, several numerical improvements have been integrated in the homogenization tool. The main ones are the implementation of stabilized mixed finite elements to handle accurately the quasi-incompressibility of the amorphous phase and the application of periodic boundary conditions via a master-slave projection algorithm. Eventually, the distribution of effective mechanical properties over the component thickness is compared for different crystallization scenarios with measured elastic moduli.

Molecular dynamics simulation of athermal heterogeneous nucleation of solidification

Athermal heterogeneous nucleation via grain refiners inoculated in undercooled Al melt is investigated by molecular dynamics (MD) simulations. A thin solid Al layer appears on close-packed surfaces of a cubic Ti particle and it grows to a spherical cap consisting of face-centered-cubic (FCC) Al, whereas no cap structure appears on the other surfaces. There is a threshold undercooling temperature dividing growth modes between stagnation and free growth. Since threshold undercooling temperature is proportional to the inverse of effective particle radius, cap formation at the surface of the Ti particle is regarded as athermal heterogeneous nucleation. Additional calculation of a solid growth of undercooled melt Al on the flat Ti surface reveals that initial solid formation on the Ti surface is caused by adsorption rather than classical (i.e., thermally–activated) heterogeneous nucleation. It is significant in this study to shed light on the mechanism of athermal heterogeneous nucleation from atomistic viewpoint since there is no atomistic description in an existing theoretical model of free growth.

Effect of surface nature of carbonaceous nanosized fillers on properties of polyurethane based nanocomposites

Polyurethane (PU) composites containing uniformly dispersed nanosized and macrosized carbonaceous fillers (fullerene C60, fullerene soot, detonation nanodiamonds, and nanodiamonds soot) with loadings varying from 0.1 to 0.5 wt.% were prepared by in situ polymerization. The kinetics of PU synthesis catalyzed by dibutyltin dilaurate was studied as a function of amount of nanosized filler. It was found that the reaction is zero-order. The kinetics of the hard domain growth of the PU matrix was studied and described successfully using the two-parameter Avrami model for isothermal crystallization. It was found that the growth of polymers induces athermal primary nucleation for hard domain growth, and that nanosized fillers do not change the nucleation mechanism. Our results show that the mechanical strength of PU composites increases in the presence of all types of nanoparticles under study. This can be related to the antiplasticization effect of the nanoparticles on the polymer matrix. The dielectric spectroscopy demonstrated that Tg values of the composites increase in comparison with neat PU. However, the effects of hydrophilic/hydrophobic properties of nanoparticles on the secondary relaxations are not obvious Microphase separation in these nanocomposites was studied using FTIR spectroscopy, but no effect of surface properties of the nanoadditives on this phenomenon has been observed.

Effect of Magnetic state of Austenite on Martensitic transformation in Fe–Ni Alloys in High and Zero Magnetic Fields

The effect of high pulsed magnetic fields on the martensitic γ → α transformation in Fe–Ni and Fe–Ni–Mn alloys characterized by dual kinetics has been analyzed. It has been shown that the higher the iron content and the lower the martensitic transformation temperature, the more substantial the effect of pulsed magnetic field on the athermal martensitic transformation (MT) in the Fe–Ni alloys. The possibility of athermal martensite nucleation at magnetic inhomogenities of austenite, which is characterized by disordered magnetic moments (antiferromagnetic contribution) within a local area that assumes coherent conjugation at the interface, has been discussed. It has been suggested that athermal MT in Invar Fe–Ni alloys characterized by dual kinetics occurs in a pulsed magnetic field via a first-order magnetic phase transformation.

Thermal properties, phase morphology and stability of biodegradable PLA/PBSL/HAp composites

Blends/composites of poly(lactic acid) (PLA) with poly(butylene succinate-co-lactate) (PBSL) and hydroxyapatite (HAp) were successfully prepared by a conventional melt-mixing process. The thermal properties, phase morphology, crystal structure, and in vitro hydro-degradability of the prepared samples were characterized and compared. Thermogravimetric analysis confirmed that adding HAp increased the thermal stability of PLA/PBSL blends in both air and nitrogen environments. The activation energy for PLA thermal degradation increased with increasing HAp content in the samples. Scanning electron microscopy results showed that HAp was uniformly distributed within the composites. HAp also played a compatibilizer role for the PLA/PBSL blends, leading to evidently reduced size of dispersed PBSL domains. The Avrami crystallization analysis revealed that the n values of PLA in different samples ranged within 2.1–3.9, and the presence of HAp caused athermal nucleation process of PLA crystallization. The activation energy for non-isothermal crystallization of PLA decreased from 136 kJ/mol in neat state to 86 kJ/mol in PLA(70)/PBSL(30)/HAp(20 phr) composite. Melting behavior study revealed that the presence of HAp increased the original crystals stability of PLA in the composites. X-ray diffraction results confirmed that the crystal structures of PLA and PBSL remained in the blends and composites. Finally, in vitro hydrolytic degradation tests showed that the HAp addition facilitated the degradation of the prepared samples.

Numerical investigation of heterogeneous nucleation of water vapour on PM10 for particulate abatement

A heterogeneous nucleation model with inclusions of the line tension effect, the particle roughness effect, and the surface diffusion mechanism was presented. Effects of the particle roughness and the wetting agent on the heterogeneous nucleation behaviour were examined. The scaled nucleation barrier was analyzed and subsequently implications of the nucleation behaviour in the particulate abatement by vapour condensation were discussed. It was found that the effect of particle roughness on the nucleation behaviour was greatly affected by the line tension. There existed an optimal concentration of wetting agent at which the lowest nucleation barrier and critical saturation ratio could be obtained. The surface diffusion mechanism played an overwhelmingly important role in governing the embryo growth for hydrophilic particles with a diameter Dp > 0.1 µm and an embryo size smaller than the critical size, otherwise the contribution of direct vapour deposition mechanism could be significant. Based on the scaled nucleation barrier, three distinct nucleation regimes, i.e. athermal heterogeneous nucleation, thermal heterogeneous‐dominant nucleation, and homogeneous‐dominant nucleation, have been identified. When the contact angle was large, the wetting agent might need to be added to reduce the contact angle so as to reach the athermal heterogeneous and thermal heterogeneous‐dominant nucleation regimes, thus achieving efficient particulate abatement at low cost. The prediction results matched reasonably with the experimental data.

A Nucleation Progenitor Function approach to polycrystalline equiaxed solidification modelling with application to a microgravity transparent alloy experiment observed in-situ

A Nucleation Progenitor Function (NPF) approach that accounts for the interdependence between nucleation and growth during equiaxed solidification is proposed. An athermal nucleation density distribution, based on undercooling, is identified as a progenitor function. A Kolmogorov statistical approach is applied assuming continuous nucleation and growth conditions. The derived progeny functions describe the (supressed) distribution of actual nucleation events. The approach offers the significant advantage of generating progeny functions for volumetric (3D) data and projected image (2D) data. The main difference between 3D and 2D data in transparent alloy experiments is due to a stereological correction for over-projection. Progeny functions can be analysed to obtain statistical output information, e.g., nucleation counts, average nucleation undercooling and standard deviation. The statistical output data may be calculated in a formative (running) or a summative (final) mode. The NPF kinetics have been incorporated into a transient thermal model of equiaxed solidification. The model has been applied to characterise a microgravity solidification experiment with the transparent alloy system Neopentylgycol-30 wt%(d)Camphor. The model predicted thermal and observed nucleation and growth data with a good level of agreement.

In-situ studies of multicrystalline silicon nucleation and growth on α- and β-Si3N4 coated substrates

The growth of silicon on various nitride coated quartz substrates were studied using in-situ observation of the solidification process. Three different coating types were used: One consisting entirely of α-Si3N4 particles, one of only β-Si3N4 particles, and a third of a 50/50 mixture of the above mentioned coating powders. The mean particle size of the α- and β-particles was about 0.3 μm and 5.7 μm, respectively. Three different cooling rates were used for each coating type: 2, 5 and 10 K/min. It was observed that the samples were similar at the lowest cooling rate, but at 5 K/min and higher the samples differed significantly. The biggest difference was seen in the α-particle coating, which showed significant dendritic growth, compared to the more faceted growth observed from the other coatings. All coatings containing the β-particles showed similar growth characteristics. These samples were also analyzed by electron-backscattered diffraction (EBSD) on both the vertical and horizontal planes. No clear trend in preferred crystal orientations was observed; however, it was seen that the density of Σ3 boundaries, especially parallel twins, increased with cooling rate. A gradual increase in the Σ3 grain boundary density was seen for the coatings containing β-Si3N4 particles, while the α-particle coating showed a faster increase. The grain sizes were also analyzed from the horizontal EBSD maps. Again there was a clear difference between the samples containing β-particles and the sample with α-particle coating. The ones containing β-particles showed a decrease in grain size with increasing cooling rate, while the opposite was true for the other α-particle coated samples. This was attributed to the rapid dendritic growth, which caused the grain structure to be dominated by one single grain. The difference in growth for the three coating types was explained using the athermal nucleation theory, which states that there is a correlation between particle sizes and nucleation undercooling.

Dislocation kinematics: a molecular dynamics study in Cu

The kinematics and kinetics of edge and screw dislocations in FCC materials were studied by molecular dynamics, with Cu as a case study. It was found that with increasing stress screw dislocations enter into the transonic regime continuously and that they remain stable up to a velocity of about 2.2 km s−1. Edge dislocations are limited by the transverse sound velocity at low stresses and discontinuously cross into the transonic regime at higher stresses. For sufficiently long edge dislocations, the subsonic–transonic transition is initiated by an athermal nucleation process. Finally, an expression for the velocity dependence of the dislocation mobility was derived.

Computer simulation of the dynamics of structural rearrangements in iron metallic glass in the process of its formation

Patterns of the generation of nanocluster icosahedral substructures of pure iron metallic glass upon quenching a melt with two competing processes, athermal nucleation and the growth of polytetrahedral local formations and their decomposition under the impact of thermal fluctuations, are investigated by means of molecular dynamic simulation.

Non-instantaneous growth characteristics of martensitic transformation in high Cr ferritic creep-resistant steel

Microstructural observation and high-resolution dilatometry were employed to investigate kinetics of martensitic transformation in high Cr ferritic creep-resistant steel upon different quenching/cooling rates. By incorporating the classical athermal nucleation and impingement correction, a non-instantaneous growth model for martensitic transformation has been developed. The developed model describes austenite/martensite interface mobility during martensite growth. The growth rate of martensite is found to be varied from 1 × 10−6 to 3 × 10−6 m/s. The low interface mobility suggests that it is not appropriate to presume the instantaneous growth behavior of martensite. Moreover, based on the proposed model, nucleation rate of martensite under different cooling rates is found to be nearly the same, while the growth rate of martensite is promoted by increasing the cooling rate.

Kinetic model of non-isothermal crystal nucleation with transient and athermal effects

A kinetic model of primary homogeneous non-isothermal crystal nucleation with transient and athermal effects is developed. For comparison, steady-state and transient isothermal nucleation rates are considered. Kinetic equation for the development of cluster size distribution provides the basis for the model. Transient effects are characterized by the longest relaxation time which increases with temperature at low and moderate undercooling. In isothermal conditions, nucleation rate is controlled by thermal mechanism; in non-isothermal conditions, there appears also athermal mechanism. Closed-form analytical formula for the development of transient cluster size distribution in single-relaxation-time approximation is derived for non-isothermal processes, as well as thermal and athermal nucleation rates and total number of nuclei produced in a cooling or heating run. The transient term contributes to isothermal nucleation kinetics the more the higher is temperature. Under non-isothermal conditions, the relaxation time contributes to the nucleation kinetics by the product with the cooling/heating rate. Considerable transient effects should be expected for the relaxation times as long as 102–105 s. Contribution of thermal nucleation to the concentration of nuclei is inversely proportional to the temperature rate, while the contribution of athermal nucleation depends on the temperature interval of cooling or heating. Our kinetic model indicates similarities in the nucleation mechanisms in polymers and metals undergoing crystallization. Example computations are presented for molten indium and a linear polymer—polyhydroxybutyrate (PHB). A low-temperature limit is predicted for the nucleation mechanism in PHB, while for indium the mechanism is active in the entire temperature range.

Primary and Secondary Crystallization Kinetic Analysis of Poly(Hexamethylene Succinate)

Isothermal crystallization kinetics of poly(hexamethylene succinate) (PHS) were investigated by using differential scanning calorimetry (DSC). Primary and secondary crystallization behaviors were described satisfactorily by a modified Avrami model. The obtained results suggest that primary crystallization under isothermal conditions involves three-dimensional spherulite growth with athermal nucleation, and secondary crystallization displays approximate one-dimensional crystal growth.

Micromechanics of the transition from intergrain to intragrain deformation in nanomaterials

A micromechanism of the transition from intergrain sliding to intragrain glide by nucleation and emission of lattice partial dislocations at grain-boundary dislocations is proposed and described theoretically. The energy characteristics of this process are calculated. It is shown that the nucleation of lattice partial dislocations is energetically efficient and can occur athermally (without the energy barrier) under conditions of the action of ultrahigh mechanical stresses. The critical stresses required for the athermal nucleation and emission of dislocations are calculated.

Anomalous kinetics of lath martensite formation in stainless steel

The kinetics of lath martensite formation in Fe–17·3 wt-%Cr–7·1 wt-%Ni–1·1 wt-%Al–0·08 wt-%C stainless steel was investigated with magnetometry and microscopy. Lath martensite forms during cooling, heating and isothermally. For the first time, it is shown by magnetometry during extremely slow isochronal cooling that transformation rate maxima occur, which are interrupted by virtually transformation free temperature regions. Microscopy confirms martensite formation after athermal nucleation of clusters followed by their time dependent growth. The observations are interpreted in terms of time dependent autocatalytic lath martensite formation followed by mechanical stabilisation of austenite during the transformation process.

Martensite formation kinetics of substitutional Fe–0.7 at.%Al alloy under uniaxial compressive stress

Differential dilatometry was applied to investigate the effect of an applied constant uniaxial compressive stress on the kinetics of the austenite (γ)→martensite (α′) transformation in the substitutional Fe–0.7at.%Al alloy upon isochronal cooling/quenching with constant rate. All imposed stress levels are below the yield stresses of γ and α′ phases in the temperature range of the martensite formation. Albeit the start temperature of the γ→α′ transformation remains approximately constant in the range of stress explored, the overall transformation temperature range increases significantly with the increase of the uniaxial compressive stress. A modular phase transformation model, adopting a model for continuous nucleation and an anisotropic thermally-activated growth model, yielding a corresponding impingement correction, was employed to extract the nucleation rate and the γ/α′-interface velocity during the transformation. The kinetic analysis suggests that athermal nucleation and thermally activated growth govern the martensite transformation under the uniaxial compressive stress. More driving force is required when a larger uniaxial compressive stress is imposed, and the thus obtained velocity of the γ/α′-interface as function of temperature indicates a thermally activated growth governed by a relatively low activation energy.