Gaussian Function Fitting Of The First Peak Of The Radial Distribution Function Of Binary Liquid Alloys And Estimation Of Thermodynamic Propertie

Thermodynamic models are widely used in the calculation of the phase equilibrium of gas-liquid reactions of solution mixtures,and it is common for technicians to obtain model parameters by fitting to thermodynamic experimental values,and then use the models to describe the phase equilibrium changes.It is a consistent goal of researchers to propose methods with rigorous physical meaning,simple methods for parameter determination,stable numerical calculations,and good performance of model prediction.In this work,the parameters of the thermodynamic model are expressed using the pair distribution function to realize the estimation of the activity and excess Gibbs free energy,and the main work is as follows:（1）In order to match the local composition thermodynamic model,it is necessary to construct the local pair distribution function that represents the local structure of the solution,and the first peak of the distribution function is used to represent the local pair distribution function.There are seven construction methods,namely g_a（r）,g_b（r）,g_c（r）,g_d（r）,g_e（r）,g_f（r）,g_g（r）.The formula of various coordination shells is given by the Gaussian function to offer the convenience of applying the numerical calculation of local coordination shell.The analytical formula form of g_b（r）is applied to do the explanation of the derivation of Tao Dongping’s coordination number formula,and the combination of g_g（r）and Tao’s coordination number formula is used to derive the asymmetric form of Tao’s coordination formula,and to obtain the peak position of g（r）with the peak relation formula.The 27 liquid metal coordination numbers were calculated.The ARD of the coordination number obtained by Gaussian extrapolation is±6.49%,the ARD of the Tao coordination number model is±14.45%,and the ARD of the modified Tao coordination number model is±18.74.84%for the classical calculation method（±15.13%～±38.27%）.（2）The pair potential function is calculated by the pair distribution function,and gives the average pair potential of molecular pairs according to the expectation principle.The pair potential function and the pair distribution function are the main parameters for calculating the microscopic properties of solutions.The mean pair potential and coordination number are taken into the thermodynamic models（MIVM,RSM,NRTL,Wilson）based on the local structure theory of the liquid solution.and the expressions for the local structure parameters representing the parameters of each model are derived.Based on the understanding of the two-fluid theory of solutions,the assumptions of MIVM,RSM,and NRTL derivation process are modified to be more consistent with the theoretical constraints,and a new form of the model is obtained.Validation of Wilson,NRTL,and MIVM hypothetical equations by applying molecular pair potentials and local molar fractions.The correlation（R）of variables on both sides of Wilson’s equations was 0.863,0.9511 and R>0.88 for NRTL.The correlations of the local coordination number equations for MIVM are low,Z_ii～ε_ii:0.52,Z_ij～ε_ij:0.67,Z_jj～ε_jj:0.44,Z_ji～ε_ij:0.49,respectively.It is not recommended to use the local coordination number formula in MIVM work,and the ratio formula of Wislon’s local molar fraction can be used instead.（3）Describe specific methods for distribution function calculations of MIVM,RSM,NRTL,Wilson,and Quasi-chemical Model（QCM）parameters to estimate excess Gibbs free energy and activity for 66 liquid alloys.The fitted parameters and calculated parameter relationships of MIVM and RSM for 66 alloys were analyzed to demonstrate the scientific validity of the estimation method from the parameter perspective.The 66 alloys were classified according to their characteristics to explore the applicability of the estimation method.New method has better performance in positive deviation alloys.QCM is a very good choice for weak deviation systems,and MIVM performs better for alloys with medium deviation strength.（4）Different parameters for the calculation of the partial pair distribution function at different molar compositions.The 16 alloys with multi-group partial pair distribution functions were selected to analyze the relationship between the model parameters and the molar composition.The correlation coefficient（R）and coefficient of variation（Cv）were used as quantitative indicators in order to provide statistical support for the constant and functionalization of the model parameters.In the process of analyzing the relationship between parameters and x_jof QCM,the relationship between B_ij,B_ji,β,σwas studied.It was found that B_ij,B_jican characterize ii,jj,ij molecules on the meaning of the strong or weak formation ability.The estimation of excess Gibbs free energy and activity was done with 16 alloys brought into the model parameter first-order functionalized model.After the first-order functionalization of the parameters,the best performance of the QCM estimation was achieved with 10alloys having an ARD less than±20%and 3 alloys having an ARD greater than±60%.RSM has 6 alloys with ARD less than±20%and 4 alloys with ARD less than±60%.The rest of the models have significantly poorer estimation performance.The model is significantly affected by the functionalization of the parameter,and the estimation ability deteriorates after parameterization,because the parameter changes are large after parameterization,and the model is poorly adapted to the parameter changes.（5）The model parameters are simplified to build a computationally convenient basis for its application.Applying the phase diagram to extract the activity and estimation method to give the activity of rare earth alloys,the estimation method in this work has obvious mathematical superiority compared to the complex calculation of the activity extracted from the phase diagram.Estimating the thermodynamic properties of methanol-methacrylate organic mixtures by RSM,NRTL.The method proposed in this work for calculating NRTL parameters is significantly simpler and clearer than the Ravichandran method.The deviations of the NRTL estimated free energy of mixing and the fitted values of NRTL are at the same level of deviation as that of Ravichandran’s estimation.The RSM estimation performs better than Ravichandran’s method,which proves that the estimation method has the potential to be applied in organic mixtures.