Kinetic Simulation Of Single Crystal Growth

A chemical bonding approach for kinetically predicting the growth shape of single crystals is proposed.An attempt was made to find the relation between crystal morphology and both internal and external factors.Here,we divide the crystal growth process into two sections:(â… )the volume diffusion of growth units from the bulk solution to the interface;(â…¡) the growth units on the interface binding with the ions on the crystal surface.When the supersaturation is not too high and viscidity is not too big,the volume diffusion process can be completed quickly and the binding process is the rate-limiting step.Thus,we can relate the growth process to the crystal structure.Furthermore,the binding process is related to the binding ability of the crystal face.Here,the binding ability of a particular face(hkl)can be considered as the combination of the deviation binding energy,which is defined by the binding energy difference between surface ions and crystals.In this model,the growth rate coefficient K,the supersaturation of the solutionσwhich can be taken as the driving force of the crystal growth and the growth rate order n are all successfully involved.On the basis of the chemical bond understanding,this novel kinetic model describes the microscopic behaviors of the crystal growth,by employing the deviation energy of surface ions within the crystallographic frame.It is found that the average growth rate of a particular face is related to its total deviation energy that divided by the area of the selected crystal face, and the differences of the growth rate among the center,edge,and comer of a face are related to different deviation energies at these sites.In this way,the influences of both adsorption effect and ion concentration gradient at the crystal surface on the crystal growth are investigated from these two aspects,respectively.Such model has been successfully used to predict the polymorphology formation of Cu₂O single crystal and the growth of Cu₂O dendritic crystal.This present method provides us a good understanding of the polymorphology formation and the branch phenomenon,which may be applicable to the estimation of the growth mechanisms of inorganic crystals.To validate this model,we applied it to potassium dihydrogen phosphate(KDP)and ammonium dihydrogen phosphate(ADP)crystals grown from aqueous solution.Because the growth rate order plays an important role in restricting the growth rate of the crystal face,we studied the factors which are related to the growth rate order n_hklin this section.Shape evolutions can be got by changing the habit-controlling factors.The simulated results closely match with experimental results.Furthermore,we elucidate the reason of the different morphology at the same supersaturation for KDP and ADP crystals.