Surface Supersaturation Research Articles

Optimal operating conditions for the rapid growth of KH2PO4 crystal by numerical simulation

Numerical simulations of the turbulent hydrodynamics and concentration in the rapid growth of potassium dihydrogen phosphate (KH2PO4 or KDP) crystals have been performed. In this work, a quadratic power-law growth model is applied, concerning the mass transfer occurring at the crystal surface during the growth process under low supersaturations. The mass transfer boundary condition is discretized by using the Over-Relaxed approach. The effects of the growth temperature and rotation rate on surface supersaturation distribution and the diffusion layer are investigated, which are critically involved in the processes of surface morphological instability and inclusion formation. Due to the kinetic limitation, the response of different types of crystal surfaces to temperature varies, with a pyramidal surface about twice as high as a prismatic face. In addition, the contour map of the growth rate combined with the coefficient of variation (C.V) for various temperatures and rotation rates is used. Uniformity of surface supersaturation is provided by lowering the growth temperature and increasing the rotation rate. Furthermore, the criteria of crystal growth strategies are proposed to optimize the process parameters and obtain favorable conditions for crystal growth, thereby facilitating defect-free and high-quality crystal formation at an appropriate growth rate.

Selective anomer crystallization from aqueous solution: Monitoring lactose recovery under mutarotation limitation via attenuated total reflection Fourier-transform spectroscopy and theoretical rate analysis

Lactose is typically produced via cooling crystallization either from whey or whey permeate (edible grade) or from aqueous solution (pharmaceutical grade). While in solution, lactose is present in 2 anomeric forms, α- and β-lactose. During cooling crystallization under standard process conditions, only α-lactose crystallizes, depleting the solution of α-anomer. In practice, mutarotation kinetics are often assumed to be much faster than crystallization. However, some literature reports limitation of crystallization by mutarotation. In the present research, we investigate the influence of operating conditions on mutarotation in lactose crystallization and explore the existence of an operation regimen where mutarotation can be disregarded in the crystallization process. Therefore, we study crystallization from aqueous lactose solutions by inline monitoring of concentrations of α- and β-lactose via attenuated total reflection Fourier-transform spectroscopy. By implementing a linear cooling profile of 9 K/h to a minimum temperature of 10°C, we measured a remarkable increase in β/α ratio, reaching a maximum of 2.19. This ratio exceeds the equilibrium level by 36%. However, when the same cooling profile was applied to a minimum temperature of 25°C, the deviation was significantly lower, with a maximum β/α ratio of 1.72, representing only an 8% deviation from equilibrium. We also performed a theoretical assessment of the influence of process parameters on crystallization kinetics. We conclude that mutarotation needs to be taken into consideration for efficient crystallization control if the crystal surface area and supersaturation are sufficiently high.

Numerical simulation of flow and mass transfer during growth of the long seed KDP crystals under 2D translation method

A novel motion method, namely, the two-dimensional translation method (2D TM) had been proposed by our team to effectively utilize convection to enhance morphological stability and mass transfer. To evaluate this new method and apply it to the long seed KDP crystals growth, numerical simulations on the hydrodynamics and mass transfer involved in the growth of the long seed KDP crystals through this new method have been performed. Comparisons with the rotating crystal method (RCM) indicates that 2D TM improves the value and distribution homogeneity of the surface supersaturation. As the translational velocity increases, the value of the surface supersaturation on the prismatic faces increases. However, as the translational distance becomes long, there is a decrease in the value of the prismatic surface supersaturation, but the homogeneity of the surface supersaturation is improved. Moreover, the increase of the crystal size not only reduces the value of the surface supersaturation on the prismatic faces, but also degrades the homogeneity of the surface supersaturation. A further improvement in the magnitude and distribution homogeneity of the prismatic face supersaturation can be observed through modifying the crystal mounting method.

Ecosystem Metabolism and Gradients of Temperature, Oxygen and Dissolved Inorganic Carbon in the Littoral Zone of a Macrophyte‐Dominated Lake

AbstractDense submerged macrophyte stands in lakes may promote alternating daytime stratification and nighttime convective mixing, driving extensive spatiotemporal variations in water temperature, oxygen, pH, and inorganic carbon (DIC). We set out to investigate environmental conditions and ecosystem metabolism in the macrophyte‐dominated littoral zone (0.6 m depth) of a shallow, mesotrophic lake and compared this with the pelagic zone (3.0 m deep). We found that, during summer, vertical water column gradients only occasionally occurred and were weak in the pelagic zone, while dense littoral macrophyte stands of charophytes exhibited strong diel changes and steep daytime temperature and oxygen depth gradients. Oxygen showed daytime surface supersaturation and bottom anoxia, alternating with nighttime mixing. In spring, before charophytes appeared, the vertical gradients were largely absent. Ecosystem metabolism was primarily positive in spring, but areal rates of daily gross primary production (GPP) and closely related respiration increased 6‐fold in summer. Ecosystem metabolism calculated based on oxygen or DIC was very similar, with a 1:1 M basis. Daytime DIC loss by CaCO3precipitation on charophyte surfaces averaged 6.3% of total DIC loss, and this loss was restored during nighttime. The contribution of shallow littoral macrophyte communities to whole‐lake summer GPP exceeded that estimated for phytoplankton. Environmental conditions in the macrophyte‐covered littoral zone differed markedly from pelagic waters with steep vertical gradients in temperature and chemistry during daytime including anoxic micro‐habitats in stark contrast to deep pelagic waters. The study highlights the significant influence of the littoral zone and macrophytes on whole‐lake ecosystem processes.

Estimation of supersaturation at steps during chemical vapor deposition of 4H-SiC () from reported growth rate and cross-sectional profile of spiral hillock

Based on the Burton–Cabrera–Frank (BCF) and Cabrera–Levine theories, supersaturation at steps (σ step) during chemical vapor deposition of 4H-SiC (0001̄) at 1570 °C under the condition of C/Si ratio of unity was estimated from the reported growth rate and cross-sectional profile of a spiral hillock, as a function of surface diffusion length of C2H2 molecules (λC2H2). The previously assumed zero σ step in the BCF theory was found to be a possible source of error in the case λC2H2 > 0.63 μm because of the estimated ratio of σ step to the surface supersaturation exceeding 0.1.

Cloud Droplet Nucleation Simulation and Parameterization

Abstract Cloud droplet nucleation is classically defined as a droplet growing to a size such that its ambient supersaturation exceeds its surface equilibrium water vapor pressure. Unactivated particles are always in equilibrium with the ambient vapor pressure. Further studies showed that such an equilibrium assumption leads to many more cloud droplets being nucleated due to neglecting kinetic growth limitations, including the inertial mechanism, evaporation mechanism, and deactivation mechanism. Moreover, the inertial mechanism results in great discrepancy between the actual size and the critical size of nucleation for large aerosol particles. These issues complicate cloud droplet nucleation parameterization for applications in cloud modeling. To establish a physically based nucleation scheme, we established a highly size-resolved Lagrangian parcel model. Vapor diffusion and heat conduction were calculated according to Maxwell theory, and the surface vapor density and temperature were explicitly simulated. The surface temperature variation of a droplet with its size was considered. The surface supersaturation of a droplet, taking into account the surface temperature variation, is different from its equilibrium supersaturation at its large sizes. The nucleation simulation showed that the inertial and deactivation mechanisms can impact droplet nucleation. Moreover, very large nuclei can trigger rain embryo formation in a short time period. Even though there are kinetic limitations, the classical equilibrium assumption can be applied to determine the primary nucleation number of cloud droplets. Meanwhile, a regression formula for the size of a nucleated droplet and its dry aerosol size was established.

Steps behaving badly: Nonlinear dynamics and a terrace-loading instability during solution growth of lysozyme crystals

A detailed finite-element model for step motion during solution crystal growth is applied to analyze the nonlinear growth dynamics of lysozyme. Insights from this model are applied to develop a much simpler, lumped-parameter model to describe step motion for this growth system. Bifurcation analysis applied to the lumped-parameter model demonstrates a critical bulk supersaturation at which an equidistant step train loses stability, via a supercritical Hopf bifurcation, to a stable, time-periodic system that exhibits a single step bunch. As supersaturation is further increased, additional bifurcations lead to more complicated behaviors, such as quasi-periodic patterns, multiple step bunches, and period doubling. The initial instability of the step train arises from the dynamics of terrace loading due to slow adsorption and step incorporation kinetics under high bulk supersaturation. These effects cause a time lag in the surface supersaturation level with respect to changes in terrace width, producing a phase shift of the surface supersaturation field in the direction of step motion and driving the formation of step bunches.

Calcite Kinetics for Spiral Growth and Two-Dimensional Nucleation.

Calcite crystals grow by means of molecular steps that develop on {10.4} faces. These steps can arise stochastically via two-dimensional (2D) nucleation or emerge steadily from dislocations to form spiral hillocks. Here, we determine the kinetics of these two growth mechanisms as a function of supersaturation. We show that calcite crystals larger than ∼1 μm favor spiral growth over 2D nucleation, irrespective of the supersaturation. Spirals prevail beyond this length scale because slow boundary layer diffusion creates a low surface supersaturation that favors the spiral mechanism. Sub-micron crystals favor 2D nucleation at high supersaturations, although diffusion can still limit the growth of nanoscopic crystals. Additives can change the dominant mechanism by impeding spiral growth or by directly promoting 2D nucleation.

Effect of V/III ratio and growth pressure on surface and crystal quality of AlN grown on sapphire by metal-organic chemical vapor deposition

The epitaxial growth of high-quality AlN on sapphire substrates is challenging due to high lattice and thermal mismatch and low Al-adatom mobility, which cause high dislocation density and rough surface morphology. High-temperature AlN (deposited at 1130 °C) was grown on low-temperature AlN nucleation layers (880 °C) with different V/III ratios and reactor pressures by metal-organic chemical vapor deposition. Surface and crystal quality was optimized using high V/III ratios. Thereby, slow layer-by-layer growth at high V/III laterally overgrows the 3D nucleation layer reducing the dislocation density, twist, and tilt in the crystal. This was as effective as multistep growth with increasing V/III. At high pressure of 95 mbar, step-bunching occurred. This indicates low surface supersaturation due to parasitic reactions in the gas phase. This was suppressed by low growth pressure of 50 mbar, while the crystal quality worsened.

Critical Step Length as an Indicator of Surface Supersaturation during Crystal Growth from Solution.

The surface processes that control crystal growth from solution can be probed in real-time by in situ microscopy. However, when mass transport (partly) limits growth, the interfacial solution conditions are difficult to determine, precluding quantitative measurement. Here, we demonstrate the use of a thermodynamic feature of crystal surfaces—the critical step length—to convey the local supersaturation, allowing the surface-controlled kinetics to be obtained. Applying this method to atomic force microscopy measurements of calcite, which are shown to fall within the regime of mixed surface/transport control, unites calcite step velocities with the Kossel–Stranski model, resolves disparities between growth rates measured under different mass transport conditions, and reveals why the Gibbs–Thomson effect in calcite departs from classical theory. Our approach expands the scope of in situ microscopy by decoupling quantitative measurement from the influence of mass transport.

Numerical simulation of heat, mass and momentum transfer during NH4H2PO4 crystal growth by solution circulating method

Three-dimensional unsteady numerical simulations are carried out to study the interactions of heat, species transport and fluid flow during the ADP crystal growth by solution circulating method (SCM). The supersaturation distribution on the crystal surface under different conditions is investigated and the effects of temperature and flow fields on the surface supersaturation are analyzed in detail. The results show that the magnitude and distribution of the surface supersaturation are improved when the rotation rate gets high. With an increase of the inlet velocity, there is a reduction in the magnitude of the surface supersaturation, while the uniformity of the supersaturation distribution is improved slightly. Besides, the increase of the inlet temperature decreases the magnitude of the surface supersaturation. As the crystal size gets large from 50 to 70 mm, the magnitude of the supersaturation on the crystal surfaces reduces obviously, but a little improvement can be seen in the uniformity of the supersaturation distribution on the prismatic faces.

An analysis of flow and mass transfer of solution growth of NH4H2PO4 crystals by the modified seed mounting geometries

A modified seed mounting geometry is proposed, aiming to improve the distribution homogeneity of the supersaturation on the crystal face during the growth of ammonium dihydrogen phosphate (NH4H2PO4, ADP) crystals. To evaluate the modification, three dimension transient numerical simulation of flow and solute transfer involved in the growth of ADP crystals have been performed. The effects of flow on the surface supersaturation distribution is analyzed in detail. Compared with the ordinary seed mounting geometry, the modified geometry is able to suppress the formation of flow stagnation regions near the prismatic surface and improve the magnitude and the distribution homogeneity of the supersaturation. Particularly even at a lower rotation rate (ω = 30 rpm), the distribution of the surface supersaturation still possesses a better uniformity under the modified geometry. Meanwhile, with the increase of rotation rate, there is an improvement in the magnitude and the distribution of the supersaturation on the crystal surfaces. The effects of natural convection adjacent to prismatic faces can be ignored when rotation rate is equal to or greater than 50 rpm. Moreover, as the crystal size increases, the magnitude of the supersaturation on the prismatic surface declines a little, and its uniformity deteriorates gradually. Consequently, as the crystal growing, it should increase the rotation rate appropriately. Finally, etching studies reveal that the ADP crystals with higher quality can be obtained by modifying the seed mounting geometry simply.

Numerical simulation of the flow and mass transport during the growth of ADP crystals by additional stirrer

Abstract A stirrer is added to the traditional rotating crystal growth system of ammonium dihydrogen phosphate (NH4H2PO4, ADP), aiming at effectively utilizing the convection to improve the mass transfer and the distribution homogeneity of the supersaturation on the crystal face. 3D numerical simulation on flow and surface supersaturation distribution under different conditions is performed employing the finite-volume method, and the effect of flow on the surface supersaturation distribution is analyzed in detail. Compared with the traditional rotating-crystal system, the introduction of a stirrer can produce stronger axial flow and accordingly improve the magnitude and distribution homogeneity of the surface supersaturation, which is favorable to grow high quality crystals. As the stirrer rotation rate increases, the magnitude of the axial flow velocity increases, resulting in a reduction of the thickness of the solute boundary layer and an increase of the supersaturation on the crystal faces. Meanwhile, the homogeneity of the surface supersaturation is also improved. The crystal rotation rate strongly influences the magnitude and distribution of the prismatic surface supersaturation. As the crystal size increases from 25 cm to 35 cm, the distribution homogeneity of the prismatic surface supersaturation improves significantly, which is beneficial to crystal growth. Additionally, the importance of natural and forced convections in mass transport are discussed. Results show that the effects of natural convection adjacent to crystal faces can be ignored when stirrer rotation rate is greater than 400 rpm.

Intergrowth of two aspirin polymorphism observed with Raman spectroscopy

Abstract Polymorphism of aspirin, one of the important pharmaceutical compounds, crystallizes in two similar structures (form I and form II). This similarity causes the intergrowth structure containing both form I domain and form II domains in the same crystal. The intergrown crystal is often observed, however, the crystallization process of the intergrown crystal was unclear. In order to reveal the crystallization process, we performed in situ observation of the growth using the crystal obtained immediately after the nucleation with Raman spectroscopy. The temporal change of Raman spectral pattern showed that form I grew on the surface of the form II seed crystal. In addition, we investigated spatially where the growth of form I was initiated. It was suggested that the crystal growth rate of form I on form II surface depends on the local surface supersaturation. We concluded that the crystallization of the intergrowth of aspirin was caused by the crystal that was form II at the nucleation being covered by form I as the growth proceeded.

Numerical simulation of the hydrodynamics and mass transfer in the capping of large size Z-cut plates

Numerical simulation of the hydrodynamics and mass transfer involved in the capping of large size Z-cut KDP plates has been performed. The variations of surface supersaturation with thin layer height, bulk supersaturation and rotation rate are analyzed. The results show that keeping still is very unfavorable for the growth of thin layer, a certain rotation rate should be applied to the Z-cut plate to increase the concentration gradient across the (0 0 1) face, thus making sure that thin layers can grow from the edges while small pyramids barely grow from the face center. Given the result that end faces of thin layers nearly bear a bulk supersaturation, a relative low bulk supersaturation will be better to ensure both the growth of thin layers and the good surface uniformity brought by low supersaturation. Moreover, as thin layers grow, rotation rate should be increased to make up the insufficient solute supply resulting from the decreasing linear speed. The optimal parameters for rapid and high-quality capping of large size Z-cut plates are suggested, the relevant simulation results are also presented.

Numerical simulation of the hydrodynamics and mass transfer in the growth of KH2PO4 crystal through a frustum platform

A frustum is added to the platform used in the rapid growth of the potassium dihydrogen phosphate crystal on point seed, aiming at improving the supersaturation distribution on crystal surfaces. To evaluate the modification, numerical simulations of the hydrodynamics and mass transfer involved in the aqueous solution growth of KH2PO4 with the new platform have been performed. The variations of surface supersaturation with frustum inclination, rotation rate and crystal size are analyzed. The results show that the existence of frustum eliminates the low-supersaturation area on the lower prismatic face and greatly promotes the supersaturation distribution uniformity. Moreover, the increases of rotation rate and crystal size not only help to improve the supersaturation distribution on the prismatic face, but also substantially reduce the low-supersaturation area on the pyramidal surface. Performance tests of small size crystals grown with ordinary and frustum platform confirms that frustum platform benefits crystal quality. Under optimum design and growth conditions, the simple frustum holds the potential for considerably improving the quality of large size crystal.

Surface premelting of water ice

Frozen water has a quasi-liquid layer at its surface that exists even well below the bulk melting temperature; the formation of this layer is termed premelting. The nature of the premelted surface layer, its structure, thickness and how the layer changes with temperature have been debated for over 160 years, since Faraday first postulated the idea of a quasi-liquid layer on ice. Here, we briefly review current opinions and evidence on premelting at ice surfaces, gathering data from experiments and computer simulations. In particular, spectroscopy, microscopy and simulation have recently made important contributions to our understanding of this field. The identification of premelting inhomogeneities, in which portions of the surface are quasi-liquid-like and other parts of the surface are decorated with liquid droplets, is an intriguing recent development. Untangling the interplay of surface structure, supersaturation and surface defects is currently a major challenge. Similarly, understanding the coupling of surface structure with reactivity at the surface and crystal growth is a pressing problem in understanding the behaviour and formation of ice on Earth. A quasi-liquid layer on the surface of ice makes it slippery even below the bulk melting temperature. The nature of this premelted layer has long been debated, and this Review gathers experimental and theoretical data and discusses opinions and evidence on premelting at ice surfaces.

Morphological study of InGaN on GaN substrate by supersaturation

The morphology of thin InGaN layers grown on c-plane GaN substrates by metalorganic vapor phase epitaxy (MOVPE) has been studied by atomic force microscopy. Three different morphologies appeared, a stepped surface, large flat two-dimensional (2D) islands and small high three-dimensional (3D) dots. Low growth temperature and high growth rate (i.e. increased vapor supersaturation) changed the InGaN morphology from steps to 2D islands and then 3D dots (when exceeding the critical thickness for 3D dots). Larger miscut angle of GaN substrate changed the morphology from 2D islands to step by decreasing the surface supersaturation of individual terraces. InGaN layers with a stepped morphology had the highest internal quantum efficiency at similar InN mole fraction. InGaN grown on GaN substrate more easily achieved a stepped morphology compared to InGaN on GaN/sapphire templates.

Surface Diffusion Constants and Supersaturations in SmBCO Films Prepared by Pulsed Laser Deposition Method

REBa 2 Cu 3 Oy (REBCO, RE = rare earth) coated conductors are required for high current carrying capability. Self-organization of Ba-M-O (BMO, M = Zr, Sn, Hf...) is available to improve critical current density (J c ) in magnetic field, and suppression of a-axis grain growth contributes to enhance J c . The former and latter are affected by the surface diffusion of adatoms and supersaturation in the REBCO film growth, respectively. We focused on surface morphologies of SmBa 2 Cu 3 O y (SmBCO) films deposited by the pulsed laser deposition method in this paper, and estimated surface diffusion constant and supersaturation from the surface morphologies. As a result, an activation energy of the surface diffusion was approximately 2.2 eV and the value is somewhat smaller than 2.5 eV for YBCO films. Additionally, we found that a-axis grains appeared when supersaturation (Δμ) became higher than a threshold Δμ . Interestingly, a seed layer consisting of c-axis oriented SmBCO suppressed a -axis grain growth. These findings are useful to improve J c in REBCO coated conductors.

Numerical simulation of flow and mass transfer for large KDP crystal growth via solution-jet method

A novel technique of growing large crystals of potassium dihydrogen phosphate (KDP) named solution-jet method is proposed. The aim is to increase supersaturation on the pyramidal face, especially for crystal surface regions close to the rotation axis. The fluid flow and surface supersaturation distribution of crystals grown under different conditions were computed using the finite-volume method. Results indicate that the time-averaged supersaturation of the pyramidal face in the proposed method significantly increases and the supersaturation difference from the crystal center to edge clearly decreases compared with the rotating-crystal method. With increased jet velocity, supersaturation on the pyramidal face steadily increases. Rotation rate considerably affects the magnitude and distribution of the prismatic surface supersaturation. With increased crystal size, the mean value of surface supersaturation averaged over the pyramid gradually decreases; conversely, standard deviation increases, which is detrimental to crystal growth. Moreover, the significant roles played by natural and forced convection in the process of mass transport are discussed. Results show that further increased jet velocity to 0.6 m/s renders negligible the effects of natural convection around the pyramid. The simulation for step propagation indicates that solution-jet method can promote a steady step migration and enhance surface morphology stability, which can improve the crystal quality.