Radius Of Critical Nucleus Research Articles

Crystallization Kinetics of Tacrolimus Monohydrate in an Ethanol–Water System

Nucleation and growth during the crystallization process are crucial steps that determine the crystal structure, size, morphology, and purity. A thorough understanding of these mechanisms is essential for producing crystalline products with consistent properties. This study investigates the solubility of tacrolimus (FK506) in an ethanol–water system (1:1, v/v) and examines its crystallization kinetics using batch crystallization experiments. Initially, the solubility of FK506 was measured, and classical nucleation theory was employed to analyze the induction period to determine interfacial free energy (γ) and other nucleation parameters, including the critical nucleus radius (r*), critical free energy (∆G*), and the molecular count of the critical nucleus (i*). Crystallization kinetics under seeded conditions were also measured, and the parameters of the kinetic model were analyzed to understand the effects of process states such as temperature on the crystallization process. The results suggested that increasing temperature and supersaturation promotes nucleation. The surface entropy factor (f) indicates that the tacrolimus crystal growth mechanism is a two-dimensional nucleation growth. The growth process follows the particle size-independent growth law proposed by McCabe. The estimated kinetic parameters reveal the effects of supersaturation, temperature, and suspension density on the nucleation and growth rates.

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.

Investigation of nucleation parameters and third order nonlinear optical properties of triglycine sodiummolybdate single crystals

In this paper, nucleation parameters such as induction period, interfacial tension, metastable zone width, radius of critical nucleus and Gibbs free energy change in solution- grown triglycine sodium molybdate (TGSM) single crystals are studied. The solubility of TGSM at different temperatures has been determined. The induction period and metastable zone width have been experimentally found for optimizing the growth process. Various critical nucleation parameters have been calculated from the experimentally obtained values based on the classical nucleation theory. The nucleation rate is found to increase with the growth of the supersaturation value. The third order non-linear parameters such as absorption coefficient (β), susceptibility (χ (3) ) and refractive index (n 2 ) obtained from the Z-scan analysis confirm the self focusing and reverse saturation absorption nature of the grown crystals.

Origin of thermal deformation induced crystallization and microstructure formation in additive manufactured FCC, BCC, HCP metals and its alloys

The additive manufacturing (AM) technology has received the widespread attention in the industrial application because of its unique ability to achieve the complex shape and ideal performance. Unfortunately, the impact of the material natural characteristics, such as the crystal structure and alloying, on the microstructure formation at the nanoscale has never been revealed in AM metals. Here, we use large-scale molecular-dynamics simulations to study the rapid thermal deformation processes of additively-manufactured face-centered-cubic (FCC), body-centered-cubic (BCC), hexagonal close-packed (HCP) metals and their alloys (FCC Cu, CuAl0.1, BCC Fe, FeAl0.1, and HCP Mg, MgAl0.1) in the molten pool, in an attempt to elucidate the intrinsic physical mechanisms controlling the crystal nucleation and growth under the complex thermal stress. The results show that the arcuate solid-liquid interface migrates towards the liquid phase until the complete crystallization, in good agreement with the experimental observation. The solidification rate follows a unified slow-to-fast law in the three types of metals, due to the competition between the compressive thermal stress and fast atomic motion. It is noteworthy that the critical radius of the crystal nucleus in the FCC and BCC metals is smaller than that in the HCP metal. The FCC metal exhibits the weak nucleation ability and growth rate, and yet the HCP metal shows the fast growth rate and stable columnar crystal nucleation. Especially, due to the dual regulation of the steep thermal gradient and solute redistribution on the growth driving force, the alloying increases the constitutive supercooling of the solidification front and inhibits the growth of columnar crystals. This trend is particularly prominent in FCC alloys, which is manifested by the obvious amorphous phase and discrete nucleation point in the upper part of the melt pool. The nucleation barrier free energy descends in order of FCC, BCC, and HCP pure metals, but the alloying would increase this energy in the corresponding alloys. The current work gives an insight into the atomic mechanism of the nucleation and growth in AM FCC, BCC, and HCP metals.

Tuning the growth of intermetallic compounds at Sn-0.7Cu solder/Cu substrate interface by adding small amounts of indium

The void defect in intermetallic compounds (IMCs) layer at the joints caused by inhomogeneous atomic diffusion is one of the most important factors limiting the further development of Sn-based solders. In this work, the thermodynamic stability of IMCs (high-temperature η-Cu6Sn5 and o-Cu3Sn phases) was improved by adding small amounts of indium (In), and the IMCs layers with moderate thickness, low defect concentrations and stable interface bonding were successfully obtained. The formation order of compounds and the interfacial orientation relationships in IMCs layers, the atomic diffusion mechanism, and the growth tuning mechanism of In on η-Cu6Sn5 and Cu3Sn, after In adding, were discussed comprehensively by combining calculations and experiments. It is the first time that the classic heterogeneous nucleation theory and CALPHAD data were used to obtain the critical nucleus radius of η-Cu6Sn5 and Cu3Sn, and to explain in detail the main factors affecting the formation order and location of IMCs at joints during the welding process. A novel and systematic growth model about IMCs layers in the case of doping with alloying elements was proposed. The growth tuning mechanism of In doping on η-Cu6Sn5 and Cu3Sn was further clarified based on the proposed model using first-principles calculations. The growth model used in this study can provide insights into the development and design of multielement Sn-based solders.

The Influence of Solvent Selection upon the Crystallizability and Nucleation Kinetics of Tolfenamic Acid Form II.

The influence of the solution environment on the solution thermodynamics, crystallizability, and nucleation of tolfenamic acid (TFA) in five different solvents (isopropanol, ethanol, methanol, toluene, and acetonitrile) is examined using an integrated workflow encompassing both experimental studies and intermolecular modeling. The solubility of TFA in isopropanol is found to be the highest, consistent with the strongest solvent-solute interactions, and a concomitantly higher than ideal solubility. The crystallizability is found to be highly dependent on the solvent type with the overall order being isopropanol < ethanol < methanol < toluene < acetonitrile with the widest solution metastable zone width in isopropanol (24.49 to 47.41 °C) and the narrowest in acetonitrile (8.23 to 16.17 °C). Nucleation is found to occur via progressive mechanism in all the solvents studied. The calculated nucleation parameters reveal a considerably higher interfacial tension and larger critical nucleus radius in the isopropanol solutions, indicating the higher energy barrier hindering nucleation and hence lowering the nucleation rate. This is supported by diffusion coefficient measurements which are lowest in isopropanol, highlighting the lower molecular diffusion in the bulk of solution compared to the other solutions. The TFA concentration and critical supersaturation at the crystallization onset is found to be directly correlated with TFA/isopropanol solutions having the highest values of solubility and critical supersaturation. Intermolecular modeling of solute-solvent interactions supports the experimental observations of the solubility and crystallizability, highlighting the importance of understanding solvent selection and solution state structure at the molecular level in directing the solubility, solute mass transfer, crystallizability, and nucleation kinetics.

Large‐scale synthesis of CuS nanoparticles for photothermal materials using high‐concentration Cu complex ion precursor

AbstractCopper sulfide (CuS), a copper‐deficient p‐type semiconductor material, has been widely utilized due to its unique optical properties, low toxicity, and cost‐effectiveness. Although many studies have been conducted on synthesizing CuS nanoparticles, harsh synthetic conditions and low yield must be solved. This study presents a new methodology that can synthesize CuS nanoparticles in large quantities at room temperature and pressure using high‐concentration Cu complex ion precursors. This methodology is based on the theory that the critical nucleus radius and the critical nucleation free energy decrease as the concentration of the precursor increases to synthesize a large number of nanoparticles by applying low energy. In addition, it is possible to minimize the aggregation of nanoparticles, which is a problem of nanoparticles synthesized at a high precursor concentration through complex ions in the solution. We synthesized nanoparticles by controlling the precursor concentration from 0.1 to 2.5 M to confirm the effect of the precursor concentration on the size, shape, and yield of nanoparticles. As the precursor concentration increased, the particle size decreased, and the yield improved. The CuS nanoparticles synthesized at the highest concentration had a size of about 17 nm without a strong agglomeration and a yield of about 213.9 g/L. Furthermore, the nanoparticles showed excellent photothermal performance due to their high near‐infrared absorption. When about 0.1 g of the nanoparticles were irradiated with a Xenon lamp and an 808 nm laser, the maximum temperatures and rising rates were 53.7°C and 172.1°C and 13.8°C/mg and 33°C/mg, respectively. The excellent photothermal properties of CuS nanoparticles suggest the potential of this material for various applications.

Mechanism study of synergistic effect of organic and inorganic foulants in membrane distillation

In this paper, we investigated the mechanism of membrane fouling during the membrane distillation (MD) process by using humic acid (HA) and calcium carbonate (CaCO3) as the model organic and inorganic foulants respectively. The aggregation induced crystallization theory was introduced to analyze the fouling process. Field emission scanning electron microscopy (FESEM) images and X-ray photoelectron spectroscopy (XPS) were used to examine the morphology and variation of foulants on membrane surfaces that treated different feeds at different concentration factors. The interface free energies of the membranes surfaces were calculated based on contact angles and surface tensions between the testing solutions and the membrane surfaces. The results indicated that the aggregations of HA onto the hydrophobic polyvinylidene fluoride (PVDF) membrane surface altered membrane surface properties, which reduced critical nucleus radius (R⁎) and facilitated the heterogeneous nucleation of CaCO3. Furthermore, the presence of calcium ion enhanced the aggregation of HA, which further promoted the crystallization of CaCO3.

Refining effect of an intermetallic inoculant on a Cu–Al–Mn shape memory alloy

Cu51Zr14 intermetallic inoculant was adopted to effectively decrease the grain size of a Cu–Al–Mn shape memory alloy (SMA), and key factors affecting the refining effect were systemically investigated. It is found that the important prerequisite for grain refinement of this alloy is that the Cu51Zr14 inoculant can provide effective heterogeneous nucleating centers, and the size of the spherical cap of the Cu–Al–Mn nuclei formed on these centers can reach the critical nucleus radius under a certain undercooling degree. The size of inoculant, the temperature and time of inoculation are all important factors affecting the refining effect. When the Cu51Zr14 inoculant was mechanically crushed into small pieces with the size ranged from 0.05 mm to 1 mm, and the temperature and time of inoculation are 1100 °C and 6 min, respectively, the best refining effect and the highest damping and mechanical properties can be achieved. The correlated mechanisms have been discussed in detail. The results of this work nicely provide an important theoretical base for the research, development as well as application of high damping performance alloys.

Investigation on pore formation in pulsed laser spot welding of AZ31 magnesium alloy

Micropores exist in the conduction-mode welds (depth/width < 0.4), while the keyhole-mode welds (depth/width ≥ 0.4) contain macropores. The equation of critical nucleus radius of the micropores is derived, which is related to the recoil pressure, atmospheric pressure, metal pressure and surface tension. After calculation, the critical nucleus radius is 3.51 μm, which is consistent with the measured radius in practice. The equation of the shortest floating time of the macropores with radius as variable is proposed, and the shortest time of bubble floating (tmin = 11.35 ms) is calculated, which is larger than the longest solidification time (tmax = 9.5 ms) of the welding pool, thus quantitatively demonstrates the formation mechanism of the macropores. The influence of pulse processing parameters on micropores is not significant, while the area percent of the macropores increases with the increase of pulse peak power density.

Effect of initial aluminium-oxygen concentration product on alumina-based inclusions in high carbon Al-killed steels during the ladle refining process

ABSTRACT The effect of different aluminium-oxygen concentration products at the start of deoxidation on the evolution of alumina-based inclusions in high carbon Al-killed steels during the ladle refining process was investigated. Results showed that the higher aluminium-oxygen concentration product at the start of deoxidation, the higher area fraction and the number density of large-sized inclusions before the slag melting, then clustered alumina-based inclusions gradually became ripening. Thermodynamic equilibrium results indicated that initial contents of the [O] were 100, 200, 300 and 400 ppm in the molten steel, then contents of the [O] at the final reaction equilibrium were 4.6, 4.9, 5.8 and 9.5 ppm, respectively. The relationship between oversaturation and size of Al2O3 inclusions showed that the larger the critical radius of nucleus, the lower the oversaturation. Meanwhile, the evolution mechanism of alumina-based inclusions during the LF refining process was also revealed.

Nucleation kinetics, Williamson-Hall analysis, hardness and dielectric properties of pyridine-2-carboxylictrichloroacetate single crystals

The single crystals of pyridine-2-carboxylictrichloroacetate (P2CT) were synthesized using standard method at room temperature. Nucleation parameters such as, radius of critical nucleus, nucleation rate, and interfacial and volume free energy has been estimated. The solubility of the crystal at different temperatures is analyzed. Thermodynamic parameters from vibration analysis are compared with the enthalpy obtained from solubility to predict the stability of the crystal. X-ray diffraction investigating the structural aspects establishes the crystal structure belonging to crystal system as monoclinic nature. Williamson–Hall approach assesses the structural characteristics of the grown crystal: average crystallite size along with lattice strain. In between 220 and 1000 nm wavelength range, the optical absorption spectra of P2CT are recorded. Based on derivation of absorption spectrum fitting method, optical energy band gap and nature of optical transitions in the crystal is determined. Vickers microhardness test estimates the hardness parameters and elastic stiffness is evaluated through Wooster's empirical relation.

Inhibition of calcium sulphate hemihydrate crystallization under simulated conditions of phosphoric acid evaporation

AbstractNucleation and crystal growth of CaSO4 ∙ 0.5H2O (calcium sulphate hemihydrate) was studied under conditions simulating scale formation in phosphoric acid production evaporators. Phosphoric acid, calcium hydrogen phosphate, and sulphuric acid were mixed at 88°C. The induction time was determined using a turbidimeter across a range of supersaturation from 1.3–3.5. Crystallization equations, taking as input the induction time and supersaturation, were used to calculate surface energy, nucleation rate, free energy, and the critical nucleus radius of CaSO4 ∙ 0.5H2O with and without the addition of 75 mg/L of various scale inhibitors: polyacrylic acid (PAA) 8000 g/mol, poly(diallyldimethylammonium chloride) (PDADMAC) &lt;100 000 g/mol, or polyethyleneimine (PEI) 60 000 g/mol. The results suggest that PEI is capable of inhibiting crystal growth through the impediment of crystal nucleation.

Effect of pulsed magneto oscillation and phosphorus on microstructure and tensile properties of as-cast Al-25% Si alloy

Abstract The effect of pulsed magneto oscillation (PMO) on the microstructure and tensile properties of Al-25% Si alloys with and without phosphorus addition was investigated. When PMO was applied to the melt during solidification, the results show that the PMO treatment is an effective method for refining the primary Si of Al-25% Si alloy with and without phosphorus addition. The morphology of primary Si was considerably refined via coarse dendritic and polygon shape to fine and regular block under the PMO treatment, and the average size of primary Si was refined to 30.8 μm and 45.3 μm under the optimal processing conditions for the alloy with and without phosphorus addition, respectively. The tensile strength and elongation of the alloys first increased and then decreased with rise of current. Analysis shows that application of PMO decreases Gibbs free energy and critical nucleus radius of the Al-25% Si alloy during solidification. The nucleation rate first increased and then decreased with increasing PMO intensity. The variation tendency of average number of primary Si per unit area is consistent with the theory analysis.

Suppression of ice nucleation in supercooled water under temperature gradients

Understanding the behaviours of ice nucleation in non-isothermal conditions is of great importance for the preparation and retention of supercooled water. Here ice nucleation in supercooled water under temperature gradients is analyzed thermodynamically based on classical nucleation theory (CNT). Given that the free energy barrier for nucleation is dependent on temperature, different from a uniform temperature usually used in CNT, an assumption of linear temperature distribution in the ice nucleus was made and taken into consideration in analysis. The critical radius of the ice nucleus for nucleation and the corresponding nucleation model in the presence of a temperature gradient were obtained. It is observed that the critical radius is determined not only by the degree of supercooling, the only dependence in CNT, but also by the temperature gradient and even the Young’s contact angle. Effects of temperature gradient on the change in free energy, critical radius, nucleation barrier and nucleation rate with different contact angles and degrees of supercooling are illustrated successively. The results show that a temperature gradient will increase the nucleation barrier and decrease the nucleation rate, particularly in the cases of large contact angle and low degree of supercooling. In addition, there is a critical temperature gradient for a given degree of supercooling and contact angle, at the higher of which the nucleation can be suppressed completely.

ALÜMİNYUM HİDROKSİT KRİSTALİZASYONU ÜZERİNE LİTYUM SAFSIZLIĞININ ETKİSİ

Bu çalışmada, farklı modülb değerlerine (1,35; 1,41; 1,45; 1,49; 1,8; 2,0; 2,25; 2,50) sahip sodyum alüminat çözeltilerinin nükleasyon davranışları incelenmiştir. Bu amaçla, çözeltiye verilen farklı aşırı doygunluk değeri (1,321-1,785) ve farklı derişimde (5-20 ppm) lityum (Li) varlığı için bekleme zamanı ölçümleri yapılmıştır. Deneysel çalışmalar sonucu, kritik serbest enerji değişimi, kritik nüklei yarıçapı, kritik nükleide yer alan molekül sayısı ve nükleasyon hızı hesaplanmıştır. Katkısız sodyum alüminat çözeltisi için bekleme zamanının, farklı aşırı doygunluk değerlerine bağlı olarak 100-400 dk. aralığında değiştiği belirlenmiştir. Lityum varlığında ise, en yüksek bekleme zamanı 10 ppm lityum derişimi için 20 dk. olarak tespit edilmiştir. Klasik nükleasyon teorisine göre yapılan hesaplamalar sonucu, lityum varlığında, katkısız ortama kıyasla, kritik nüklei yarıçapının düştüğü, kritik nükleideki molekül sayısının azaldığı ve nükleasyon hızının arttığı belirlenmiştir. 5 ppm lityum katkısı için, katkısız ortama kıyasla, nükleasyon hızındaki artışın yaklaşık 100 kat, 20 ppm lityum katkısı için ise yaklaşık olarak 39 kat olduğu belirlenmiştir. Lityum varlığında, farklı modülb değerlerindeki sodyum alüminat çözeltilerinin bekleme zamanlarının düşük ve yüksek modülb değerine sahip çözeltiler için 6 – 7 dk. aralığında değiştiği tespit edilmiştir. Modülb 1,49 ve 1,8 için ise maksimum 10 dk’lık bekleme süreleri elde edilmiştir.

Phase-field modeling of irradiated void microstructure evolution of Fe-Cr alloy

As cladding materials, Fe-Cr alloys are used in the extreme environments of high temperature, high pressure, and energetic particle radiation, thus generating irradiation defects such as vacancies and interstitials. The clustering of irradiation defects leads the voids or dislocation loops to form, resulting in irradiation swelling and lattice distortion, and further radiation hardening or softening, finally, material failure. It is beneficial to tailor desired microstructures and obtain stable service performances by understanding defects cluster and voids formation process. In this paper, the phase-field method is employed to study the evolution of voids of Fe-Cr alloy. In the model the temperature effects on point defects and generation/recombination of vacancies and interstitials are taken into consideration. The 400–800 K temperature range and 0–16 dpa radiation dose range are selected, in which the voids’ formation process including generation and recombination, as well as vacancy clustering caused by vacancy diffusion, is studied for Fe-Cr alloy. The nucleation rate of the void cluster shows a trend of first increasing and then decreasing with temperature increasing from 400 to 800 K. This phenomenon is related to complex interactions among defects concentration, atomic diffusion, recombination, nucleation, and growth conditions. At a given temperature, the average radius and the volume fraction of the voids grow bigger as the radiation dose increases. With the increase of irradiation dose, the cascade collision reaction is strengthened, and the number of Frenkel defect pairs is also increases. A large number of vacancies and interstitial atoms are generated, and the rapid diffusion and accumulation of vacancies in the Fe-Cr alloy at high temperature form a larger number and larger size of voids. The incubation period of vacancy clusters and voids are quite different due to the influence of irradiation temperature and dose. The higher the irradiation dose, the shorter the incubation period is. The relationship between the incubation period and temperature is more complicated. When the temperature is relatively low, the incubation period is shortened as the temperature increases, and as the temperature continues to increase to a higher temperature, the incubation period is extended. This relates to the increase in the concentration of vacancies, the recombination of vacancies and interstitials, and the increase of the critical nucleus radius for the growth of voids when the temperature increases.

Determination of metastable zone width, induction time and primary nucleation kinetics for cooling crystallization of sodium orthovanadate from NaOH solution

A systematic investigation was carried out to determine the metastable zone width (MSZW) and induction time of unseeded batch cooling crystallization of sodium orthovanadate from concentrated alkaline solutions using laser scattering method. Dependence of sodium orthovanadate MSZW on NaOH concentration, stirring speed, and cooling rate were measured at different temperatures. The induction time was measured at different NaOH concentrations and various supersaturation ratios. The experimental results revealed homogeneous nucleation regions at high supersaturation ratios, whereas heterogeneous nucleation dominated at low supersaturation ratios. Thus the classical primary nucleation kinetics were determined based on the obtained induction time data. Interfacial energy and various nucleation parameters, such as radius of critical nucleus and critical free energy of nucleus were subsequently calculated and analyzed. Moreover, the crystal shape changes of Na3VO4 at different ionic strengths and supersaturation ratios were analyzed and discussed in detail to provide fundamental information for optimizing and controlling of the crystallization process.

Isothermal by Design: An Accelerated Approach to the Prediction of the Crystallizability of Slowly Nucleating Systems

A route to the accelerated nucleation of α-para-aminobenzoic acid in ethanol/water (EtOH/H2O) mixed solvent solutions, using antisolvent crystallization, is presented. An isothermal by design approach is adopted, whereby the exothermic enthalpy of mixing associated with antisolvent addition is offset by the control of the temperature of the antisolvent added. Induction times (τ) are found to be reduced by 4 orders of magnitude using this methodology, consistent with the use of this approach as a nucleation acceleration technique. Calculation of the nucleation kinetic parameters for a range of solution concentrations, compositions, and supersaturations (S) reveal that effective interfacial tensions (γeff) vary from 8.4 to 2.3 mJ m–2 from solutions in H2O solvent and EtOH solvent, respectively, in line with the trend in solubility. The critical nucleus radius (r*) decreases from 1.98 to 0.40 nm associated with a decrease in the number of molecules in the critical nucleus (i*) from 196 to 2 molecules. A change in nucleation mechanism from heterogeneous nucleation to homogeneous nucleation is observed to take place at S ≈ 1.5. Limitations, particularly with focus toward larger-scale operation, are highlighted together with potential solutions to overcome such aspects.

Studies on nucleation kinetics of pyridoxal 5-phosphate monohydrate in water

With the change of pH, the metastable zone of PLP in water was measured at various temperatures by applying laser monitoring method under normal pressure. The metastable zone became wider as the pH increased within the studied scope, but it became narrower as the temperature increased within the studied scope. With the change of supersaturation ratio, the induction period of PLP in water was also measured at various temperatures. According to the classical homogeneous nucleation theory, the crystal-solution interfacial tensions at various temperatures were calculated which were then used to calculated the primary nucleation parameters containing per unit volume free energy change (ΔGv), critical free energy change for the formation of critical crystal nucleus (ΔG*), radius of critical crystal nucleus (r*) and the molecular number in the critical crystal nucleus.