GPU parallel computation of dendrite growth competition in forced convection using the multi-phase-field-lattice Boltzmann model

A graphics-processing-unit(GPU)-parallel-based computational scheme is developed to realize the competitive growth process of converging bi-crystal in two-dimensional states in the presence of forced convection conditions by coupling a multi-phase field model and a lattice Boltzmann model.The elimination mechanism in the evolution process is analyzed for the three conformational schemes constituting converging bi-crystals under pure diffusion and forced convection conditions,respectively,expanding the research of the competitive growth of columnar dendrites under melt convection conditions.The results show that the elimination mechanism for the competitive growth of converging bi-crystals of all three configurations under pure diffusion conditions follows the conventional Walton-Chalmers model.When there is forced convection with lateral flow in the liquid phase,the anomalous elimination phenomenon of unfavorable dendrites eliminating favorable dendrites occurs in the grain boundaries.In particular,the anomalous elimination phenomenon is relatively strong in conformation 1 and conformation 2 when the orientation angle of unfavorable dendrites is small,and relatively weak in conformation 3.Moreover,the presence of convection increases the tip growth rate of both favorable and unfavorable dendrites in the grain boundary.In addition,the parallelization of the multi-phase-field-lattice Boltzmann model is achieved by designing the parallel computation of the model on the GPU platform concerning the computerunified-device-architecture parallel technique,and the results show that the parallel computation of this model based on the GPU has absolute advantages,and the parallel acceleration is more obvious as the computation area increases.

Numerical study of growth competition between twin grains during directional solidification by using multi-phase field method

A multi-phase field model is established to simulate the growth competition and evolution behavior between seaweed and columnar dendrites during directional solidification.According to the effects of surface tension and interfacial energy,we quantitatively analyze the influences of factors such as inclination angles,pulling velocity,and anisotropic strength on twin growth.The results demonstrate that the pulling velocity and anisotropic strength have an important influence on the morphology and evolution of the seaweed and dendritic growth.The low pulling velocity and anisotropic strength are both key parameters for maintaining the stable morphology of seaweed during competitive growth in a bicrystal,showing that the lateral branching behavior is the root of the dendrites that can ultimately dominate the growth.And it is clarified that the lateral branching behavior and lateral blocking are the root causes of the final dominant growth of dendrites.With the increase of anisotropy strength,the seaweed is eliminated fastest in case 1,the seaweed is transformed into degenerate dendritic morphology,and eliminates the seaweed by promoting the generation and lateral growth of the lateral branches of the dendrites.The increase of pulling velocity is to increase the undercooling of favorable oriented grain and accelerate the growth rate of dendrites,thus producing more new primary dendrites for lateral expansion and accelerating the elimination rate of unfavorable oriented grain.

Control of GaN inverted pyramids growth on c-plane patterned sapphire substrates

Growth of gallium nitride(GaN)inverted pyramids on c-plane sapphire substrates is benefit for fabricating novel devices as it forms the semipolar facets.In this work,GaN inverted pyramids are directly grown on c-plane patterned sapphire substrates(PSS)by metal organic vapor phase epitaxy(MOVPE).The influences of growth conditions on the surface morphol-ogy are experimentally studied and explained by Wulff constructions.The competition of growth rate among{0001},{1011},and{1122}facets results in the various surface morphologies of GaN.A higher growth temperature of 985 ℃ and a lowerⅤ/Ⅲratio of 25 can expand the area of{}facets in GaN inverted pyramids.On the other hand,GaN inverted pyramids with almost pure{}facets are obtained by using a lower growth temperature of 930℃,a higherⅤ/Ⅲratio of 100,and PSS with pattern arrangement perpendicular to the substrate primary flat.

Extensive numerical simulations on competitive growth between the Edwards–Wilkinson and Kardar–Parisi–Zhang universality classes

Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards–Wilkinson(EW) and Kardar–Parisi–Zhang(KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation(RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition(BD), etching, and restricted solid on solid(RSOS). The scaling exponents are obtained in both the(1 + 1)-and(2 + 1)-dimensional competitive growth with the nonlinear growth probability p and the linear proportion 1-p. Our results show that, when p changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

Phase-field numerical simulation of three-dimensional competitive growth of dendrites in a binary alloy

The normal vector of migration direction in the solid-liquid interface of dendrites was used to describe the phase-field governing equation. By using the three angles formed by the normal vector for the migration direction of the dendritic growth interface and the coordinate axes of the simulation region, the authors expressed the interfacial anisotropy equation, and built a phase-field model for the competitive growth of multiple grains. Taking a Al-2%mole-Cu binary alloy as an example, the competitive growth of multiple grains during isothermal solidification was simulated by applying parallel computing techniques. In addition, the phase field simulation results were verified by the experimental method. The simulation results show that the competitive growth of equiaxed dendrite is divided into two types: the first occurs during the process of competitive growth, the tips of primary dendrite on different grains taking part in the competition stop growing in their optimal growth direction; the second also occurs during competitive growth, the tips of primary dendrite which participate in the competition on different grains never stop growing in their optimal growth direction. The dendritic morphologies of the first competition growth type are divided into two types. Primary dendrites of grains taking part in the competition stop growing in their optimal growth direction and the competition plane enlarges when neither one wins the competition. However, when one wins the competition, the primary dendrites of grains with superiority go through the blocking grains and continue to grow in their optimal growth direction. The primary dendrites of inferior grains stop growing in their optimal growth direction and then instead grow in those areas without obstacles. The dendritic morphology of the second competition-growth type is shown to be the deformation of primary dendrites, which are mainly represented as the deflection and bending observed from different views. Compared with the metallographic picture, the simulation results can show the morphology of the competitive growth in all directions, so this simulation method can better characterize the competitive growth process.

Multi-phase field simulation of competitive grain growth for directional solidification

The multi-phase field model of grain competitive growth during directional solidification of alloy is established.Solving multi-phase field models for thin interface layer thickness conditions,the grain boundary evolution and grain elimination during the competitive growth of SCN-0.24-wt%camphor model alloy bi-crystals are investigated.The effects of different crystal orientations and pulling velocities on grain boundary microstructure evolution are quantitatively analyzed.The obtained results are shown below.In the competitive growth of convergent bi-crystals,when favorably oriented dendrites are in the same direction as the heat flow and the pulling speed is too large,the orientation angle of the bi-crystal from small to large size is the normal elimination phenomenon of the favorably oriented dendrite,blocking the unfavorably oriented dendrite,and the grain boundary is along the growth direction of the favorably oriented dendrite.When the pulling speed becomes small,the grain boundary shows the anomalous elimination phenomenon of the unfavorably oriented dendrite,eliminating the favorably oriented dendrite.In the process of competitive growth of divergent bi-crystal,when the growth direction of favorably oriented dendrites is the same as the heat flow direction and the orientation angle of unfavorably oriented grains is small,the frequency of new spindles of favorably oriented grains is significantly higher than that of unfavorably oriented grains,and as the orientation angle of unfavorably oriented dendrites becomes larger,the unfavorably oriented grains are more likely to have stable secondary dendritic arms,which in turn develop new primary dendritic arms to occupy the liquid phase grain boundary space,but the grain boundary direction is still parallel to favorably oriented dendrites.In addition,the tertiary dendritic arms on the developed secondary dendritic arms may also be blocked by the surrounding lateral branches from further developing into nascent main axes,this blocking of the tertiary dendritic arms has a random nature,which can have aninfluence on the generation of nascent primary main axes in the grain boundaries.

Competition Growth of α and β Phases in Ti-50 at.%Al Peritectic Alloy during the Rapid Solidification by Laser Melting Technique

Rapid solidification of Ti-50 at.%Al peritectic alloy is realized by laser melting technique at diferent conditions of laser power and scanning speed. The temperature field and the cooling rate under the corresponding conditions are derived from the finite element simulation.℃omparing the measured pool size with the simulated result, the laser absorptivity of Ti-50 at.%Al peritectic alloy at diferent conditions can be deduced to establish the relationships between the laser absorptivity, the laser power and the scanning speed. The morphology evolution and the phase selection of Ti-50 at.%Al peritectic alloy are described by the temperature gradient and the cooling rate. With the increase of temperature gradient and cooling rate, β phase replaces α phase to become the leading growth phase. And the growth of α phase experiences the transition from facet to non-facet manner, while β phase is refined. To understand the underlying mechanism of the competition growth can bring benefit to the industrial application of Ti-Al alloy.

Phase growth patterns for Al_(2)O_(3)/GdAlO_(3)eutectics over wide ranges of compositions and solidification rates

Phase selection and growth characteristics of directionally solidified Al_(2)O_(3)/GdAlO_3(GAP)faceted eutectic ce ramics are investigated over wide ranges of compositions and solidification rates to explore the eutectic coupled zone.Through the obse rvation of the quenched solid-liquid interface,the competitive growth of primary faceted Al_(2)O_(3)phase,prima ry non-faceted GAP phase and Al_(2)O_(3)/GAP eutectic with diffe rent morphologies is detected.Microstructure transitions from wholly eutectic to primary Al_(2)O_(3)(GAP)dendrite plus eutectic and then to wholly eutectic are found in Al_(2)O_(3)-2 O mol%Gd_(2)O_(3)hypoeutectic(Al_(2)O_(3)-26 mol%Gd_(2)O_(3)hypereutectic)ceramics with the increase of solidification rate.The dendrite growth of faceted Al_(2)O_(3)and non-faceted GAP phases are well predicted by KGT model,which have introduced appro p riate dimensionless supersaturationΩto characterize the anisotropic growth of dendrites.Based on the maximum interface temperature criterion,the competitive growth of primary phase and eutectic is analyzed theoretically and the predicted coupled zone of Al_(2)O_(3)/GAP eutectic ceramics is in good agreement with the experimental results.Besides,the influence of microstructure with these different morphologies on the flexural strength of Al_(2)O_(3)/GAP eutectic ceramics is studied.

Effect of solidification rate on competitive grain growth in directional solidification of a nickel-base superalloy

The mechanism of grain structure evolution during directional solidification is a fundamental subject in material science. Within the published research there exist conflicting views on the mechanism of grain overgrowth. To study the effect of solidification rate on grain structure evolution, bi-crystals samples were produced in a nickel-base superalloy at different solidification rates. It was found that at the convergent grain boundaries those grains better aligned with respect to the heat flux more readily overgrew neighbouring grains with misaligned orientations and the effect became more pronounced as solidification rate was increased. However, at diverging grain boundaries the rate of overgrowth was invariant to the solidification rate. These experimental results were compared with models in the literature. Thus, a better insight into competitive grain growth in directional solidification processes was obtained.

Misorientation dependent thermal condition-solute field cooperative effect on competitive grain growth in the converging case during directional solidification of a nickel-base superalloy

Nowadays,thermal condition and solute field are considered as the potential dominant factors controlling competitive grain growth during directional solidification process.However,the controlling modes and critical conditions of competitive grain growth have been drastically debated over the past two decades.In this work,thermal condition and solute field are combined to study the competitive grain growth in the converging case by experimental observation and numerical simulation of bicrystal samples.We find the competitive grain growth is controlled by the cooperative effect of thermal condition and solute field,and the controlling modes are related to the bicrystal misorientation between favorably and unfavorably oriented grains.When the unfavorably oriented grain is low misoriented,unfavorably oriented grain dominates grain selection,and the competitive grain growth performs as solute field domination.However,with the increase of unfavorably oriented grain’s misorientation,the grain selection converts into favorably oriented grain domination,and the competitive grain growth changes to thermal condition domination.To explain these abnormal transformation phenomena,we propose a misorientation dependent thermal condition-solute field cooperative domination model and identify the critical conditions by a critical misorientation(θ_(cm)).According to dynamic equation of dendrite growth,we calculate the critical misorientationθ;to prove this model.The theoretical calculation results agree well with the experimental results.

Insights from polymer crystallization： Chirality, recognition and competition

Crystallization of flexible polymer chains reveals distinct characters compared to small molecules, which provides a platform to study molecular self-assembly and morphogenesis. In this review, some examples, e.g., twisting chirality of polymer lamellar crystals, recognition of different chain units and competitive nucleation of different polymorphs and different lamellar thicknesses are briefly discussed. It is shown that the polymer crystallization process far from equilibrium is in practically minimization of the system free energy in local space and finite time, leading to formation of twisted crystals, metastable polymorphism and lamellar crystals with finite thickness. Though each molecule is blind to others, the peculiar ordered configurations with stronger long-range interactions are chosen from the enormous random trials. At the end, we list some remaining questions and outlook the perspectives.

Distribution of α-, β-, and γ-Phases in a Multi-flow Injection-molded Hierarchical Structure

In the current work, a custom-made vibration injection molding device that can provide oscillatory pressure was utilized to create an injection-molded hierarchical structure. Growth competition among α, β, and γ phases in the injection-molded structure can be studied because of the presence of this hierarchical structure, wherein shish-kebab and spherulite layers were arranged alternately along the thickness direction. The γ crystals only existed in layers subjected to high pressure and shear stress, whereas β crystals formed between the shear layers. The change in trend of the γ fraction was similar to that of parent-to-daughter ratio. In addition, this hierarchical and alternating crystal structure can sharply increase the mechanical properties.

Bacillus promotes invasiveness of exotic Flaveria bidentis by increasing its nitrogen and phosphorus uptake

The effect of exotic plants on Bacillus diversity in the rhizosphere and the role of Bacilli in exotic or native plant species remain poorly understood.Flaveria bidentis is an invasive grass in China.Setaria viridis is a native grass and occurs in areas invaded by F.bidentis.Our objectives were(i)to examine the differences in the Bacillus communities between F.bidentis and S.viridis rhizospheres soil,and(ii)to compare the effects of Bacilli from F.bidentis and S.viridis rhizospheres on the competitiveness of the invasive species.Flaveria bidentis monoculture,mixture of F.bidentis and S.viridis and S.viridis monoculture were designed in the field experiment.Bacillus diversity in their rhizosphere was analyzed using 16S rRNA.One of the dominant Bacilli in the rhizosphere soil of F.bidentis was selected to test its effect on the competitive growth of F.bidentis in a greenhouse experiment.Bacillus diversity differed in F.bidentis and S.viridis rhizosphere.Brevibacterium frigoritolerans was the dominant Bacilli in the rhizosphere of both F.bidentis and S.viridis;however,its relative abundance in the F.bidentis rhizosphere was much higher than that in the S.viridis rhizosphere.In addition,B.frigoritolerans in the F.bidentis rhizosphere enhanced the growth of the plant compared with that of S.viridis by improving the nitrogen and phosphorus levels.This study showed that F.bidentis invasion influenced Bacillus communities,especially B.frigoritolerans,which,in turn,facilitated F.bidentis growth by increasing the levels of available nitrogen and phosphorus.

Effect of Solidifcation Rate on Grain Structure Evolution During Directional Solidifcation of a Ni-based Superalloy

The effect of solidification rate on grain structure evolution during directional solidification （I J：5） ot a Ni-oasea superalloy was explored. It was found that a high solidification rate led to sharper 〈001〉 texture and smaller grain size in the DS samples. One of the most important findings in this work was that such result was not in accordance with the general concept, and the sharper 〈001〉 texture was accompanied by the larger grain size. To explain the contradiction, the modeling samples with five grains were produced and the effect of solidification rate on the evolution of grain texture was illustrated based on the modeling samples.

Modes of Grain Selection in Spiral Selector during Directional Solidification of Nickel-base Superalloys

The modes of grain selection in spiral selector were investigated by both a ProCAST simulation and experimental confirmation.The results show that the efficiency of grain selection in starter block is associated with the geometry shape.At the early stage of grain selection,the optimization of grain orientation is dominated by competitive grain growth,but the optimization of grain orientation in starter block is gradually dominated by geometry shape at the later stage of grain selection.Besides,the spiral part could also optimize the orientation of the selected single crystal when the initial angle is large enough,and the single crystal selection in spiral parts with different pitch lengths and initial angles is dominated by different modes.The simulation results agree well with experimental ones.