Eutectic-Dendrite Growth In Undercooled Binary Alloys

The technique of rapid solidification of undercooled melts has been widely applied to study the solidification process of eutectic alloys.Abundant of achievements have been obtained in this field,e.g.on the pattern formation and evolution,formation of anomalous eutectic structures,phase selections and so on.However,a qualitative analysis or a quantitative description of the above non-equilibrium phenomena is not satisfied,thus needing the development of non-equilibrium theory.In fact,the coupling growth of two phases always occurs at high undercooling,and thus the interface condition considerably deviates from equilibrium condition.In this case,the non-equilibrium interface kinetics,non-equilibrium solute diffusion and non-equilibrium triple-junction（TJ）kinetics play important roles in eutectic-dendrite growth.However,the previous eutectic dendrite growth models were established based on the assumption of dilute alloys and linear phase diagram,and did not consider completely the above non-equilibrium kinetic effects,which is the reason why the previous models cannot describe the practical solidification process accurately.To solve these problems,a new eutectic dendrite growth model was proposed currently from the thermodynamic extreme principle.It considers all the non-equilibrium effects above and is applicable to concentrated alloys.It predicts reasonably the non-equilibrium eutectic-dendrite growth of undercooled Fe₈₃B₁₇,Ag-39.4at.%Cu and Ni-Zr alloys,according to the calculation results of which the physical mechanisms for the failure of the coupling growth of two phases and the diffusion-controlled mode of eutectic-dendrite growth are shown clearly.The main results and conclusions are as follows.1.A kinetic eutectic model was proposed from the thermodynamic extreme principle.This model is applicable to concentrated alloys and considers the non-equilibrium interface kinetics,non-equilibrium solute diffusion and non-equilibrium TJ kinetics.A general eutectic dendrite growth model is then proposed in which the kinetic eutectic model is applied to describe the eutectic growth and the solvability theory is used to describe the thermal dendrite growth.2.The current model describes well the eutectic-dendrite growth of undercooled Fe₈₃B₁₇ alloys.By a comparison with the previous models based on the assumptions of dilute alloys and linear phase-diagram,the necessity to extend the models to concentrated alloys with non-linear phase diagram is shown.For example,there is no difference between the current model and the previous model predictions at low undercooling,which means that the assumptions of dilute alloys and linear phase-diagram are applicable.A high undercooling,however,the adoption of dilute alloys assumption introduces unreasonably the non-equilibrium effects and thus leads to significant deviation from the experimental results.3.The Ag-39.4at.%Cu eutectic alloy is chosen to show quantificationally each non-equilibrium effect during eutectic dendrite growth by different combination of non-equilibrium effects.The growth of eutectic dendrite ceases when the undercooling（or growth velocity）reaches the critical value.For the concentrated alloy,the reason is that the migration of TJ could not be kinetically possible at high undercooling,while for the dilute alloy,there is a transition from co-operative eutectic growth to single-phase growth.4.The growth modes of rapid solidification of undercooled NiZr and NiZr₂ alloys are concluded to be diffusion-controlled according to the simulation results from the thermal dendrite growth model,while for the Ni₃₆Zr₆₄ alloy,the diffusion-controlled growth mode is also verified for such cooperative growth of two phases.A transition from thermodynamic-controlled growth to kinetic-controlled growth happens in diffusion-controlled growth mode.The growth velocity therefore increases firstly and then decreases as undercooling and thus there is a maximal growth velocity.