Activation Energy For Nucleation Research Articles

Experimental and Modelling Research on the Effect of Prior Ferrite on Bainitic Transformation in Medium-Carbon Bainitic Steel

In this study, we investigate the impact of prior ferrite on the bainite transformation kinetics and microstructure of medium-carbon steel interrupted by an intercritical annealing (IAA) process. It was found that the incubation time and completion time decreased from 687 s and 6018 s to 20 s and 4680 s, with the volume fraction of ferrite increasing from 9.5% to 28.6%, while the maximum transformation rate increased from 00271 μm/s to 0.0436 μm/s. The ferrite/austenite interface is introduced, and the nucleation sites are increased to accelerate the subsequent bainite transformation due to the formation of prior ferrite. However, there is a competitive relationship between the number and activation energy of bainite nucleation. According to the experimental results and theoretical calculations, the activation energy of the bainite transformation in the medium-carbon bainite steel decreases gradually with an increase in the volume fraction of prior ferrite.

Microstructure and mechanical properties of Al-Cu alloy during wire and arc additive manufacturing by adding micron TiB2 particles

ABSTRACT Micron TiB2 particles were added to the 2319 aluminum alloy using a surface coating method during the additive process. The study focused on the formation, microstructure, and properties in order to achieve deposited components with a uniform microstructure and enhancing strength and plasticity. The critical migration velocity (Vcr = 335 μm/s) of with micron-sized TiB2 particles addition was larger than the solidification rate, which caused particles to be pushed by the solid-liquid interface and ultimately reside at the grain boundary position. The micron-sized TiB2 particles reduced the activation energy for nucleation of the precipitation of the θ’ phase, lowered the energy barrier for nucleation, and introduced dislocations to create lattice distortion channels. This enabled rapid diffusion of solute atoms and facilitated the precipitation and growth of the θ’ phase. Finally, the transverse strength and elongation were higher, reaching 339.07 MPa and 21.3%, which increased by 45% and 60% respectively.

Sustainable Thermal Regulation of Electronics via Mitigated Supercooling of Porous Gallium-Based Phase Change Materials.

Gallium liquid metal is one of the promising phase change materials for passive thermal management of electronics due to their high thermal conductivity and latent heat per volume. However, it suffers from severe supercooling, in which molten gallium does not return to solid due to the lack of nucleation. It may require 28.2 °C lower temperature than the original freezing point to address supercooling, leading to unstable thermal regulation performance along fluctuations of cooling condition. Here, gallium is infused into porous copper in an oxide-free environment, forming intermetallic compound impurities at the interfaces to reduce the activation energy for heterogeneous nucleation. The porous-shaped gallium provides ≈63% smaller supercooling than that of the bulk type due to large specific surface area (≈9,070 cm2 per cm3) and high wetting characteristics (≈16° of contact angle) on CuGa2 intermetallic layer. During repetitive heating-cooling cycles, porous-shaped gallium consistently shows propagation of crystallization at even near room temperature (≈25 °C) while maintaining stable performance as thermal buffer, whereas droplet-shaped gallium is gradually degraded due to partial-supercooled state. The findings will improve the responsive thermal regulation performance to relieve a rapid increase in temperature of semiconductors/batteries, and also have a potential for energy storage applications.

Heterogeneous nucleation and dendritic growth of niobium under containerless electrostatic levitation

With the containerless electrostatic levitation method, the undercooling level and nucleation solidification mechanism of niobium samples of 99.7% and 99.95% in purity were comprehensively studied. The classical nucleation theory was used to measure and calculate the thermophysical and thermodynamic characteristics associated with the nucleation and solidification procedure. The measurement results show that the maximum undercooling of experimental samples is 455.7 K, while the hyper cooling limit of the niobium is derived at 739 K. The most probable nucleation undercooling, pre-exponential factor, nucleation activation energy, solid/liquid interface free energy, and the critical nucleus radius are determined. The dendrite growth velocity has a powerful relationship with undercooling, and the dendritic growth velocity of liquid niobium reaches 42.1 m/s at the undercooling of 454 K. The effect of the anisotropy of surface energy is taken into account, and the forecast results display excellent consistency with the experimental ones.

Effect of 0.5 at. % Cu addition on the crystallization behavior and soft magnetic properties of Fe83B11C1Si2P3 alloy

In order to gain insight into how the addition of Cu element affects the crystallization mechanism of amorphous nanocrystalline alloys and soft magnetic properties, the crystallization behavior of (Fe0.83B0.11Si0.02P0.03C0.01)100-xCux (x = 0 and 0.5) amorphous ribbons was investigated based on kinetic and thermodynamic behavior under non-isothermal and isothermal annealing conditions. The results show that under non-isothermal annealing conditions, the Cu0.5 amorphous ribbon not only favors the formation of the amorphous structure, but also enlarges the temperature window for annealing and improves the thermal stability of the α-Fe(Si) phase. At the same time, the Cu0.5 amorphous ribbon shows slow kinetic and is insensitive to heating rate change during annealing treatment. Under isothermal conditions, the addition of Cu decreases the nucleation activation energy (En) and increases the growth activation energy (Eg). This further indicates that the nucleation of α-Fe(Si) grains is easier than the growth process, which is conducive to the formation of a homogeneous nanostructure and improves the soft magnetic properties of the alloy. Compared to Cu0 amorphous ribbon, it is also shown that the Cu0.5 amorphous ribbon changes the crystallization mechanism from diffusion-controlled one-dimensional to two-dimensional growth when the crystallization volume fraction x is 10–30 vol%. While three-dimensional growth become dominated when x is reaches 60 vol% for both ribbons. Therefore, the kinetics of crystallization as well as microstructure supports that the Cu0.5 ribbon is able to exhibit uniformly fine nanocrystalline structures. Further, the Cu0.5 nanocrystalline ribbon shows a higher Bs of 1.85 T and a lower Hc of 2.55 A/m, respectively, and the favorable (100) orientation of α-Fe(Si) grains formed after annealing is another factor to increase Bs.

Graphene synthesis by electromagnetic induction heating: Domain size and morphology control

In this paper we discuss the effect of hydrogen and methane content during low-pressure chemical vapor deposition (LPCVD) of graphene on inductively heated copper foils. By increasing the H2/CH4 ratio by a factor of 5 from 25 to 125, different graphene morphologies ranging from dendritic fractals to compact hexagonal islands are obtained. In addition, increasing the hydrogen concentration allows the nucleation rate to be slowed down by a factor of ∼10 thereby high-quality regular hexagonal graphene single crystals of significant size of 0.1 mm are found. From these measurements, we estimate the activation energy for graphene nucleation in low-pressure CVD (2 eV) and propose a phenomenological law for graphene nucleation. As compared to conventional CVD methods, considerable advantages of inductive heating are outlined, and some fundamental aspects of this approach are discussed.

Thermal deformation behavior and microstructure analysis of the as-cast super austenitic stainless steel Sanicro35

Thermal compression experiments on the super austenitic stainless steel Sanicro35 were carried out using a Gleeble 3800 thermal simulation laboratory machine to investigate its thermal deformation behavior at different deformation temperatures (900 °C–1150 °C) and strain rates (0.001–10 s−1). The microstructure of the large deformation zone of the specimen was investigated using electron backscatter diffraction (EBSD). The results show that the thermal compression rheological stress of the super austenitic stainless steel Sanicro35 decreases with increasing temperature and decreasing strain rate. Dynamic recrystallization (DRX) is the main softening mechanism for this material. The morphology characteristics, recrystallization fraction, dislocation density and twin grain boundary distribution of the microstructure were analyzed by EBSD. With the increase of deformation temperature, the higher grain boundary mobility contributed to the growing of DRX grains. As the strain rate increases, the larger deformation storage energy provides sufficient activation energy for DRX grain nucleation, and the nucleation of DRX grains becomes denser. The twin boundaries are mainly distributed within the DRX grains. The smaller the grain size of DRX, the denser the nucleation of twin boundaries, and the generation of twins can promote the development of DRX. The softening mechanism under most deformation conditions is discontinuous dynamic recrystallization (DDRX). However, at 10 s−1, the high strain rate causes microbands to be generated within the deformed grains, and the microband boundaries evolve toward the high-angle grain boundaries (HAGBs) with increasing temperature, which promotes the occurrence of Continuous dynamic recrystallization (CDRX).

Synergistic Enhancement of Stability and Performance for Perovskite Solar Cells Using Fluorinated Benzoic Acids as Additives

The introduction of additives with specific functional groups is an important approach to extend the operational lifetime of perovskite solar cells (PSCs). Herein, the effect of the additives of benzoic acid (0F‐B), 4‐fluorobenzoic acid (1F‐B), and 2,3,4,5,6‐pentafluorobenzoic acid (5F‐B) on the performance and stability of MAPbI3‐based PSCs is systematically investigated. These additives can both chelate onto lead ions and form hydrogen bond with methyl ammonium ions. These combined interactions result in an increased activation energy for nucleation of perovskite crystals, thereby, increasing crystal size, reducing defect formation, improving electronic properties, as well as reducing ion migration. As a result, PSCs added with 5F‐B achieve the highest power conversion efficiency (PCE) of 20.50% with a narrow distribution compared to those PSC devices added with 1F‐B (19.25 %), 0F‐B (18.80 %), and pristine devices (18.53 %). Notably, 5F‐B‐added PSCs retain 80% of their initial PCE after ≈100‐day humidity test (at 25 °C and 50% relative humidity), 30‐day thermal stability test (at 85 °C in nitrogen environment), and 12‐day light illumination test (under continuous simulated solar radiation).

Modeling the effect of prior austenite grain size on bainite formation kinetics

While experiments show that refining the prior austenite grain size can either accelerate or decelerate bainite formation in steels, kinetic models based on the successive nucleation of bainitic ferrite subunits can only predict an acceleration. In this work we develop a physically-based model for bainite kinetics assuming a displacive growth mechanism which is able to reproduce both faster and slower bainite formation kinetics induced by austenite grain refinement. A theoretical analysis of the model and comparison against published experimental data show that slower kinetics for smaller grains is favored as the difference between the activation energy for grain boundary and autocatalytic nucleation of bainite increases, and as the austenite grain refinement results in finer bainite sub-units. We also theoretically analyze the density of initially present potential nucleation sites for bainite and show that the values of density used in other published bainite nucleation models are mostly underestimated. After using physically consistent values for the density of potential nucleation sites, we were able to calculate the apparent lengthening rate of bainite sheaves which were in line with experimentally measured lengthening rates.

Enhanced electrolytic immersion cooling for thermal crisis mitigation in high-energy–density systems

Motivated by the increasing need for effective cooling solutions in high-energy–density systems, this experimental study presents the two-phase cooling of a superheated SS 316L sample via immersion quenching in saturated deionized (DI) water at atmospheric pressure conditions with and without a DC electric field. We investigate the effect of the applied electric field, electrode polarity, and in-situ oxidation on quenching characteristics such as the cooling profile, vapour layer behaviour, minimum film boiling temperature (Tmin), and heat transfer rate. The cooling curves of samples quenched with the application of an electric field shift towards the left compared to the sample quenched without an electric field. The cathode sample at 200 V exhibits 33 % faster cooling than the bare sample (0 V). Overall, the in-situ oxidised SS 316L cathode sample at 200 V exhibits a 55 % reduction in film boiling duration, and Tmin increased from 268 °C to 322 °C compared to the bare sample (0 V). The visualisation studies highlight that the liquid–vapour interface experiences a series of oscillations followed by temporal collapse due to electrostatic attraction and electrolytic activity. The obtained results show that hydrogen-rich vapour bubbles increase heat transfer performance. The evolution of hydrogen and its adsorption at the sample surface reduces the activation energy for bubble nucleation and improves the bubble density via liquid pumping. These insights open the pathway for employing hydrogen bubbles for handling ultra-high thermal loads in high-energy density systems, and the specific case of a revised design of concentrating solar receiver is considered based on the present findings.

Reliable Accessibility of Intermediate Polarization States in Textured Ferroelectric Al0.66Sc0.34N Thin Film

AbstractFerroelectric materials are promising candidates for neuromorphic computing synaptic devices due to the nonvolatile multiplicity of spontaneous polarization. To ensure a sufficient memory window, ferroelectric materials with a large coercivity are urgently required for practical applications in highly scaled multi‐bit memory devices. Herein, a remarkable reliability of intermediate ferroelectric polarization states is demonstrated in a textured Al0.66Sc0.34N thin film with a coercive field of 2.4 MV cm−1. Al0.66Sc0.34N thin films are prepared at 300 °C on Pt (111)/Ti/SiO2/Si substrates using a radio frequency reactive sputtering method. Al0.66Sc0.34N thin films exhibit viable ferroelectricity with a large remanent polarization value of >100 µC cm−2. Through the conventional current–voltage characteristics, polarization switching kinetics, and temperature dependence of coercivity, the reproducibility of multiple polarization states with apparent accuracy is attributed to a small critical volume (3.7 × 10−28 m3) and a large activation energy (3.3 × 1027 eV m−3) for nucleation of the ferroelectric domain. This study demonstrates the potential of ferroelectric Al1‐xScxN for synaptic weight elements in neural network hardware.

An eco-friendly method for the scale-up synthesis of ZSM-5 Zeolite

Scaling-up is the key step of the commercialisation of ZSM-5 zeolite, and the cost-effectiveness and greenness of the synthesis strategy is a decisive factor that cannot be ignored in the scale-up process. Herein, we present a template-free and solid-state-like crystallisation method for the synthesis of ZSM-5 zeolite by mechanical mixing of starting material components, which can be used for the scale-up production of ZSM-5 zeolite. The crystallisation range of ZSM-5 zeolite was obtained by this mechanical mixing of anhydrous starting materials. We have analyzed the kinetics study of three different Na2O/Al2O3/SiO2 systems in the range, and obtained the trends of nucleation and growth activation energy. The results show that mechanical mixing can effectively achieve a high degree of homogenous dispersion of the starting material, which is conducive to obtaining ZSM-5 with high crystallinity and size uniformity. We have synthesised monolithic ZSM-5 with high crystallinity and uniform grain size of about 2 g, 30 g and 120 g in different sizes (2.5 ml/50 ml/200 ml) of Teflon lined high pressure reactors in a single synthesis method. This study affirms the possibility of achieving the scale-up of ZSM-5 zeolite synthesis through the synthetic pathway proposed, presenting a cost-effective, eco-friendly strategy for the industrial preparation of ZSM-5 zeolite.

Charge-transfer interatomic potential to reproduce 30° partial dislocation movements for 4H-SiC in the surface vicinity and its application to BPD-TED conversion

4H-SiC has recently attracted attention as a new power semiconductor material to replace silicon. One of the challenges impeding its practical use is the elimination of killer defects in its epitaxial layer, such as dislocations and stacking faults. The conversion of basal plane dislocations (BPDs) into threading edge dislocations (TEDs) is crucial for reducing harmful mobile dislocations. However, the atomistic mechanism underlying the process remains elusive. To clarify the BPD–TED conversion mechanism, we developed a charge-transfer interatomic potential to reproduce 30° partial dislocation dynamics in the surface vicinity of 4H-SiC. The proposed potential significantly improved the accuracy of estimating the stacking fault energy and dislocation mobility in the regions where the dislocation core and surface overlap. Using the developed potential, we investigated the mechanism underlying the contraction of a pair of 30° partial dislocations in the vicinity of the surface. From the energy landscape, the equilibrium distance between the two partials decreased as the depth from the surface decreased because of the strong image force near the surface. The equilibrium distance decreased to zero when the depth reached 0.25 nm. This result is qualitatively consistent with the dislocation theory and the known effect of image force. From the viewpoint of the activation energies of kink nucleation and migrations, the activation energy for C-core and Si-core partial contractions decreased below a depth of 1 nm from the C-face and S-face surfaces, respectively, and became almost equal to that of C-core and Si-core expansions, respectively, when the depth reached 0.25 nm. Therefore, the partial BPDs can contract easily in the corresponding structures, particularly when the depth from the surface is less than 1 nm.

Graphitization modified three-dimensional fully interconnected high porous TiO2 ceramics: A promising carrier material for thermal storage and thermal conductivity enhancement

In this work, porous TiO2 ceramics (PTC) and the graphitization modification of PTC (GPTC) with three-dimensional fully interconnected and uniform pore structure as a carrier for PCM was prepared by the Pickering emulsion method. Compared with PTC, the thermal conductivity and porosity of GPTCs were further improved and the specific surface area of GPTCs was increased by 5.7 times. The results of DSC curves showed that the melting and solidification enthalpy of PEG-GPTC20 were 143.8 J/g and 139.0 J/g, respectively, which only decrease by 0.68 % and 0.35 % after 100 phase change cycles. The experimental thermal conductivity of PEG-GPTC20 composites improved by 3.2 times. The results of non-isothermal crystallization kinetics revealed that the nucleation activation energy: PEG>PEG-PTC > PEG-GPTC, which indicated that GPTCs porous carrier encapsulation was beneficial to the nucleation process of PEG. The PEG-GPTCs composite phase change material designed in this paper has significant advantages in maintaining high thermal conductivity and heat storage performance at the same time while comparing other composites. Therefore, GPTCs are a promising carrier material for thermal storage and thermal conductivity enhancement.

Long-range Tersoff potential for silicon to reproduce 30° partial dislocation migration

Dislocation in silicon has been studied from atomistic viewpoints for many years. It is widely acknowledged that the bond-order Tersoff potential does not reproduce the dislocation dynamics. Addressing the abovementioned shortcoming remains challenging for over three decades. We have developed a new long-range Tersoff potential to reproduce the 30° dislocation dynamics in silicon. We also clarified that the first-neighbor cutoff distance of the original Tersoff potential inhibited the smooth breaking and formation of bonds within the dislocation cores, resulting in non-smooth reaction pathways during kink formation and migration. Consequently, we incorporated a long cutoff distance of 4.5 Å, corresponding to the third-neighbor distance. We also modified the distance-difference term of the Tersoff potential to eliminate an artificial energy increase attributed to the long-range cutoff. The developed potential accurately reproduced the stacking fault energy and the activation energies of kink nucleation and migration, leading to a smoother reaction pathway than the original Tersoff potential. The stacking fault energies of our potential and the original Tersoff potential were 74 and 0 mJ/m2, respectively. The activation energies of kink formation, left kink migration, and right kink migration were 1.09, 0.97, and 0.68 eV, which are closer to the experimental values than those of the original Tersoff. We also confirmed the smooth movement of partial 30° dislocations using molecular dynamics simulation. Our developed potential could contribute the microscopic studies of dislocation in silicon.

Effect of recrystallization on bainite transformation and mechanical properties of complex phase steel with high formability (CH steel)

Herein, the effect of recrystallization on the bainite transformation and mechanical properties of CH steel were investigated using SEM, TEM, EBSD, dilatometry, and tensile testing machine. First, precipitation was introduced to hinder recrystallization by batch annealing. Subsequently, the competitive relationship between austenite transformation and recrystallization was revealed using different annealing processes. Finally, the effect of recrystallization on bainite transformation was analyzed, mainly including bainite morphology, fraction, transformation rate, bainite nucleation rate of untransformed austenite and austenite-bainite orientation relationship, as well as the effect on the mechanical properties. After batch annealing, a large amount of cementite and nanoscale (Nb, Ti)C precipitated in the hot-rolled sheet, the austenite transformation start temperature (Ac1) and the pearlite to austenite transformation end temperature (Ac1f)of the cold-rolled sheet increased, and the austenite transformation end temperature (Ac3) of the cold-rolled sheet decreased, and the austenite transformation process accelerated. The microstructure of annealed sheets is consisted of ferrite, granular bainite, martensite, and a small fraction of retained austenite. Carbide hindered the recrystallization process during the annealing process, resulting in significant refining of the grains. The lower degree of recrystallization promoted bainite transformation, providing more nucleation sites, higher grain boundary and autocatalytic nucleation activation energy, improving bainite's fraction and transformation rate. The bainitic ferrite was mainly lathy in the recrystallized zone and polygonal in the non-recrystallized zone. Both a K-S and an N-W relationship between retained austenite and bainite, while the N-W relationship in the non-recrystallized zone was relatively higher. Without severe loss of plasticity, hindering recrystallization increased the dislocation, grain refinement, and precipitation strengthening values of the samples, and the strength significantly improved. However, with the increase of annealing temperature, recrystallization fraction increased gradually, and the increase in strength became less noticeable.

NUCLEATION AND CRYSTALS GROWTH IN THE VOLUME OF GLASS Li2O–Al2O3–SiO2 SYSTEM

By the Marotta et al method, temperature of 670 ?C at a holding time of 2 hours provides the maximum rate of nucleation the crystalline phase of ?-eucryptite-like solid solutions was found. The activation energy of nucleation and the Avrami parameter were measured by the DSC method, allowing to estimate the crystallization characteristics. The gradient crystallization method has established the temperature range of heat treatment, within which it is possible to obtain a transparent glass-ceramic. The refinement of regime the nucleation stage made it possible to reduce the time of the second stage crystallization required for the complete formation of the transparent glass-ceramic structure. Varying the holding time at a temperature of 710 ?C makes it possible to smoothly change the CTE in the range of ?(3…+41)?10–7 K?1 in the temperature range from ?120 to +500 ?C.

Electrochemical co-deposition of carbon nanotube/Ni composite layer

The type and content of particles in the plating solution greatly affect the electrodeposition process, making it important to study the effect of carbon nanotubes (CNTs) on the electrodeposition of nickel during the preparation of CNTs/Ni composites. In this paper, cyclic voltammetry (CV), linear sweep voltammetry (LSV), chronoamperometric analysis (CA), and electrochemical impedance spectroscopy (EIS) were adopted to study the nucleation mechanism in the early stage of electrocrystallization. Field emission scanning electron microscopy (FESEM) and X-ray diffraction (XRD) were used to reveal the electrocrystallization properties. The results showed that Ni was electrodeposited by 3D nucleation/growth and was controlled by diffusion and electrochemical kinetics. Increasing the CNTs concentration shortened the time required for 3D growth. Additionally, the polarizability of the electrodeposited nickel increased upon increasing the CNTs content, which helped increase the electro-crystallization probability of Ni. As the concentration of CNTs increased, the charge transfer resistance decreased, the Ni nucleation activation energy decreased, and the Ni nucleation became easier. The introduction of CNTs changed the preferred growth orientation of pure nickel, and the surface growth morphology was mainly a spiral in a stepwise pyramid.

Hydrodynamics (Reynolds number) determine scaling, nucleation and crystal growth kinetics in membrane distillation crystallisation

Reynolds number (Re) has been previously related to several scaling mitigation and crystallisation strategies that offer distinct hypotheses for how Re may regulate the kinetics of nucleation and crystal growth in membrane crystallisation. Such ambiguity has arisen from the present inability to discretely characterise induction time in membrane systems. This study therefore introduces techniques for the detection of induction time, with measurements used to develop a modified power-law relation between nucleation rate and supersaturation to establish how Re can be used to adjust nucleation kinetics. Increasing Re enhanced mass and heat transfer processes which raised permeate flux. The interfacial supersaturation set by the increase in flux, also modified the supersaturation rate at induction for crystals formed in the bulk solution, providing the first direct evidence that it is the supersaturation level set within the boundary layer which controls primary nucleation in the bulk solution. Bulk nucleation rate can therefore be adjusted in proportion to Re. While the extent of scaling was also determined by the interfacial supersaturation set by Re, its formation was shown to be more dependent on the interfacial diffusion coefficient which regulates solute backtransport and the activation energy for nucleation. Through this work we suggest that the nucleation mechanisms underlying scale formation and bulk crystallisation are distinct. The regulation of nucleation rate in the bulk solution by Re is described analytically through classical nucleation theory, while scaling can be mitigated through operation below a critical threshold supersaturation value that determines the rate and type of scaling that prevails. These seemingly distinct strategies can be combined through modifications to T and dT with Re to suppress scaling and offer refined control over the kinetics of nucleation and crystal growth.

Phase diagram and nucleation kinetics of barbituric acid – Urea Co-crystal: Focus on metastable zone width and activation energy

As an intermediate for preparing sedative drugs, barbituric acid (BA) is often used for anesthesia and hypnosis in clinical practice. Due to the poor solubility of BA, barbituric acid – urea co-crystal (BAUR) was prepared to improve the physicochemical properties and bioavailability of BA. Notely, urea is also required in the production process of BA, so selecting urea as the co-crystal former will not bring additional impurities. BAUR has three forms reported. In this paper, the phase diagram of BAUR-Ⅰ was measured to determine the limit concentration of urea. Further, the nucleation metastable zone experiments were conducted to investigate the effects of cooling rates and urea concentrations during the nucleation. The nucleation process was then simulated using two approaches: the self-consistent Nývlt-like approach and the classical 3D model approach. Combined with the calculation of nucleation activation energy Esat, it can conclude that increasing the concentration of urea widens the metastable region to inhibit the nucleation of form Ⅰ in the cooling crystallization.