Optimization Of Geometrical Model For Systems With Limited Solubility And Its Application In Predicting The Properties Of Refining Slags

The physicochemical properties of molten slags are of great significance for optimizing metallurgical processes and controlling products quality.Experiment is the basic method to obtain this data of molten slag.However,due to the high melting points of slags and the difficulty of testing,the data those can be obtained through experiments are very limited.Therefore,model prediction based on limited experimental data becomes particularly important.At present,the calculation of the physicochemical properties of multicomponent melts is mainly based on geometrical models,which can calculate the internal properties based on limited boundary data.As an important part of the CALPHAD methods,geometrical models have been widely used in the calculation of systems with complete miscibility,and are expanding to systems with partial miscibility,such as molten slags.The development of geometrical model for systems with limited solubility has experienced two stages:Mass Triangle(MT)model and Double Line(DL)model.Double Line model overcomes the shortcomings of the linear weight probability of Mass Triangle model,and provides a new method for solving the calculation problems of systems with partial miscibility.However,Double Line model still has three problems in calculating the properties of multicomponent slags:1)How to optimize the calculation method of boundary properties within the limited miscibility area to improve the prediction accuracy;2)How to optimize the extension method for high-order systems to expand its application range;3)The property data of molten slags is scattered,which is difficult to verify the optimized model.In response to the problems above,firstly,some nonlinear interpolation methods are proposed to optimize the calculation of the boundary properties within the limited miscibility area.Secondly,optical alkalinity is introduced into the transformation of the pseudo-ternary systems for optimizing the high-order extension method of Double Line model.Finally,the surface tension of CaO-Al₂O₃-MgO-SiO₂ refining slag with the designed compositions are tested experimentally for verifying the optimized model.The specific research contents are as follows:(1)For the problem of"how to optimize the calculation method of boundary properties within the limited miscibility area",this paper introduces two nonlinear interpolation methods,Lagrange and Cubic Spline,to optimize the linear interpolation method used in Double Line model,which is verified in the viscosity prediction of CaO-Al₂O₃-SiO₂ ternary slag.The prediction results based on the boundary property by nonlinear interpolation methods are generally better than those by linear interpolation method,where the calculation results by Lagrange interpolation method are in the best agreement with experimental values.(2)For the problem of"how to optimize the extension method for high-order systems",optical alkalinity of oxides is introduced into the transformation of the pseudo-ternary systems,which is based on the classification method of Urbain model.The high-order extension method of Double Line model is optimized by quantifying the influence degree of different oxides on properties.The optimized Double Line model has achieved better agreement with the experimental values in predicting the viscosity,surface tension and conductivity of the refining slag systems,including CaO-Al₂O₃-MgO-SiO₂ and CaO-Al₂O₃-MgO-SiO₂-CaF₂,and the forecast errors are generally smaller than those by other models.(3)For the problem of"the property data of molten slags is scattered,which is difficult to verify the optimized model",the surface tension of CaO-Al₂O₃-MgO-SiO₂refining slag with 13 designed compositions at different temperatures are tested experimentally for verifying the optimized model.The prediction results by the optimized Double Line model at three temperature sections of 1723K,1698K and1673K are in good agreement with the experimental values.The feasibility of two types of optimization methods for Double Line model is verified.In summary,this paper optimizes the boundary calculation method and high-order extension method of Double Line model,which has been verified in calculating the physicochemical properties of different refining slags.The optimization of Double Line model is of help for the development of geometrical model for systems with limited solubility.