Process And Mechanism Of Bi-crystal Competitive Growth During Directional Solidification

How to control the competitive grain growth during directional solidification precisely is a key issue encountered during the preparation of advanced single-crystal materials.However,the traditional mechanism of competitive grain growth based on Walton-Chalmers model not only cannot supply enough theoretical supports to solve this issue perfectly,but also faces serious challenges.In this study,the microstructual evolution and solute distribution during bi-crystal directional solidification were analyzed by phase field simulations and in-situ observations of a transparent alloy.The dendritic growth,evolution of grain boundary(GB)and grain elimination under different growth modes,growth dimensions and crystal orientations were studied in a systematic way.The mechanisms of the competitive grain growth during directional solidification were clarified,and the model for grain boundary selection was improved.Main conclusions are as follows:(1)For the multi-phase-field model which is suitable for the competitive growth of various grains with different orientations,the code was developed by combining CUDA performed in Graphics Processing Unit(GPU)and MPI performed in Central Processing Unit(CPU),and then large-scale simulations using multiple GPUs in parallel were achieved.The calculating efficiency was greatly improved compared to the computation in CPU.A tansparent alloy sample of the bi-crystal diverging growth with specific orientations was prepared,and branching behaviors and the evolution rule of GBs during bi-crystal directional solidification were observed.Phase field simulations were proved to be reliable by comparing experimental results to simulation results.(2)The branching behaviors and the modulation of dendritic morphologies during directional solidification were studied.It is found that side branches from the primary dendrite at diverging GBs are packed by bursts.Side branches appear periodically and are strongly phase correlated inside a burst,while there is a suddenly jump in the side-branching phase at burst transitions.Side branches were found to be formed within a suitable range of frequencies,and regular dendritic side branches could be induced by introducing a periodic external force within this range;however,there is no obvious effect on the dendritic growth by introducing a periodic external force outside this range.(3)Origins of the stochasticity of new primary arm generation at diverging GBs were clarified.On the one hand,the well-developed side branches at GBs were found to be preferentially adjacent to the transitions between bursts during the diverging growth;but the length of the burst is irregular;moreover,not every side branch adjacent to the burst transitions can grow long enough to generate tertiary branches because of the obstruction of neighboring side branches,so tertiary branch generation fluctuates.On the other hand,tertiary branches generated from these well-developed side branches were blocked stochastically by surrounding side branches and the occurrence of blocking was also stochastic,which also contributes to the stochasticity of new primary arm generation.(4)The converging competitive growth of bi-crystals in both two dimensions(2Ds)and three dimensions(3Ds)were analyzed.It was found that the overgrowth was realized by the blocking of primary dendrite arms.During the bi-crystal converging growth in 2D,when favorably oriented(FO)dendrites were parallel to the thermal gradient direction or unfavorably oriented(UO)dendrites and FO dendrites orient in opposite lateral directions,the FO dendrite could block the UO dendrite(which is called the usual overgrowth)and the UO dendrite could also block the FO dendrite(which is called the unusual overgrowth)with a small difference in the crystal directions of two grains;however,with a large difference in the crystal directions of two grains,the unusual overgrowth could not occur.When UO dendrites and FO dendrites oriented in the same lateral direction during 2D bi-crystal converging growth,the unusual overgrowth hardly occurred.During 3D bi-crystal converging growth,when primary arms of two converging grains were face-to-face,the rotation of secondary arms in the FO grain can enhance the competitiveness of the FO grain and make the unusual overgrowth harder than that in which there is no rotation of secondary arms in the FO grain;however,if primary arms of two converging grains are staggered,the rotation of secondary arms in the FO grain can make the unusual overgrowth easier.(5)The diverging competitive growth of bi-crystals in both 2D and 3D were investigated.It was found that the overgrowth was realized by new primary arm generation.For 2D diverging grains,primary dendrite arms of two grains are face-to-face,and the competition between secondary arms at the GB is direct.When FO dendrites are parallel to the thermal gradient direction or UO dendrites and FO dendrites oriented in opposite lateral directions,the statistically averaged GB angle shows a non-monotonic variation with the angle between two grains.When UO dendrites and FO dendrites oriented in the same lateral direction,the GB will be parallel to the growth direction of FO dendrites.For 3D diverging grains,primary dendrite arms of two grains are usually staggered,and the competition between secondary arms at the GB is indirect,so new primary arms are generated easier.When FO dendrites were parallel to the thermal gradient direction,unlike the non-monotonic variation of the grain elimination rate in 2D,the elimination rate of the UO grain by the FO grain increased monotonically with the increase in the angle between two grains.(6)The non-uniplanar competitive growth of bi-crystals in both thin samples and large-scale samples were studied.It was found that the overgrowth was also realized by new primary arm generation.During the non-uniplanar growth of bi-crystals in thin samples,the secondary arm growth of UO dendrites was blocked by the sample wall,which caused difficulty in the generation of new primary arms from the UO grain.Therefore,even though the bi-crystal configuration observed in the thin-sample plane appeared similar to the 2D diverging growth,the new primary arm generation was obviously different in these two cases,and the GB orientation selection in thin samples also deviated significantly from that during the 2D diverging growth.During the non-uniplanar growth of bi-crystals in large-scale samples,the new primary arms developed from the FO grain along two directions,leading to a spiral shape of the GB morphology.The overgrowth rate of the UO grain by the FO grain shows a non-monotonic variation with the inclination angle in the UO grain.As the new primary arms could develop from the FO dendrites along two directions,the overgrowth rate is faster than that in the case of diverging growth in 2D.(7)Combining simulations and experiments of the diverging competitive growth of bi-crystals in 2D,we found that results from different alloy systems and different parameter conditions exhibit a uniform relation between the percentage of the whole gap region occupied by the FO grain and the difference in the absolute values of the secondary arm growth directions of the FO and UO grains.This uniform relation indicates that the competition of two diverging grains is actually the competition between side branches of two grains at the diverging GB,and the competitive outcome is determined by the growth direction of side branches at the GB.By describing such a uniform relation with a simple fitting equation,a simple formula for the diverging GB orientation was proposed,which is more consistent with the actual situation than the existing models.