修正的似化学模型在熔渣体系中的应用
摘要
本文通过文献报道的二元渣系的活度实验值,应用变通的Gibbs-Duhem方程结合α函数法检验了8个全浓度及4个存在饱和浓度的二元渣系在不同温度下两组元活度的可靠性,得出两组元的总平均相对偏差分别为7%和13%,其中2个全浓度的二元渣系B2O3-SiO2(1450℃,1550℃)、FeO-TiO2(1400℃)及4个存在饱和浓度的熔渣体系误差较大,误差大的原因可能是由于实验数据太少或测量数据不太准确所致。其它6个全浓度的二元渣系在不同温度下的平均标准偏差在5%以下,因此通过变通的Gibbs-Duhem方程结合α函数法验证,除B2O3-SiO2(1450℃、1550℃)、FeO—TiO2(1400℃)及4个存在饱和浓度的渣系以外,其余6个全浓度二元渣系在不同温度下的实验数据较可靠。由于无限稀活度系数是冶金热力学重要的参数之一,因此本文计算出8个渣系中,不同温度下各组元的无限稀活度系数,仅作参考。
通过二分法及泰勒展开式对过量吉布斯能的优化拟合得到二元熔渣体系的键能参数ω,η多项表达式,应用修正的似化学模型计算了18个二元熔渣体系在不同温度下的活度值,与实验数据比较得出两组元的总平均相对偏差为：13%和12%,可以看出活度计算值与实验值吻合较好,所以应用半经验模型(修正的似化学模型)对计算熔渣体系的热力学量较为可靠,只是由于该模型中的配位数的物理意义相对比较模糊,因此有待于进一步改进。修正的似化学模型虽没有考虑体系的内部结构特征,但体系的最大有序一般是在体系离子间缔合(或络合)最强的成分附近,这相当于近似考虑了离子键的缔合,且该模型中比当量分数的ω,η多项表达式只考虑独立离子间的相互作用,这样更接近真实情况。
借助几何模型的方法(非对称近似),将修正的似化学模型推广到三元熔渣体系。并将该模型应用到SiO2-CaO-FeO(1600℃,1550℃)体系,计算得到该体系下aFeo活度值,且与实验值比较得出平均相对偏差为：S*FeO(1600℃)=±40％, S*FeO(1550℃)=±45％,可看出计算值与实验数据吻合的较好,而Si02-CaO-FeO体系(1550℃)的aCaO活度值和SiO2-CaO-FeO体系(1550℃)的asiO2活度值,与实验值的平均相对偏差分别为：S*CaO=±1497％,s*SiO2=±681％,可看出活度计算值与实验值吻合不是很好,并用Pelton的键能参数计算该体系下的aFeo' aCaO' aSi02活度值,与作者的计算结果基本一致。同时应用相同方法计算了SiO2-CaO-MnO(1550℃,1500℃)熔渣体系,通过非对称近似计算得到该体系组元aMnO活度值,得到与实验数据的平均相对偏差分别为：S*MnnO(1550℃)=±22％,SMnO(1500℃)=±41%,可看出计算值与实验值的吻合较好,同Pelton计算结果基本一致,因此利用该模型计算三元系中某组分活度值是可行的,对于预测冶金熔渣的热力学性质具有一定优势。
The reliability of the two components activity value of 8 entire-concentration and 4 existing-saturation-concentration binary systems at different temperature was tested by using Gibbs-Duhem equation combine withα-function, the general average relative deviation of the two components are 7% and 13% respectively. which two binary slag system-wide concentrations of B2O3-SiO2 (1450℃,1550℃) and FeO-TiO2 (1400℃) and the existence of four concentrations of slag saturated system error is larger.The reason induced this results may be the few experiment data or less accuracy of measurement data.The average relative deviations of the other 6 entire-concentration binary systems are all less than 5% at different temperature. Thereby, the results of the test which made by using Gibbs-Duhem equation combine withα-function show that the experimental data of the 6 binary slag systems at different temperatures, except B2O3-SiO2 (1450℃,1550℃),FeO-TiO2(1400℃) and the existence of four existing-saturation-concentration of slag system are reliable. Infinite dilution activity coefficient, one of the most important parameters of metallurgical thermodynamics, of each component of 8 entire-concentration the slag systems was calculated and the results could apply some reference.
Polynomial ofωandη(ωandηare bond energy parameters of binary slag systems) was obtained from optimization fitting of excess Gibbs energy with dichotomy and Taylor expansion. The activity values of 18 binary slag systems were calculated with the model of modified quasi-chemical model, and error analysis comparing with experiment data indicates that the general average relative deviation of the two components are 13% and 12% respectively. It could conclude that the activity values obtained from calculation fit better with experimental values, hence that the application of semi-empirical model (modified quasi-chemical model) on calculation and prediction of slag systems thermodynamic is reliable. However the physical meaning of the coordination number in this theory is rather ambiguous and further improvement need to be made. Inner structural features of the system had not been considered in modified quasi-chemical model, but the maximum ordering of the system occurs near at the component of the strongest association (or complexation) effect between ions in the system, and it could be taken for that the association effect of ionic bond has been considered.In this model only interaction of ions has been considered in multiterm expression ofωandη, and it will be more closer to the fact.
With the help of two methods of geometric model (symmetry approximate and non-symmetry approximate) modified quasi-chemical model has been extend to ternary slag systems.With the application of this model on the system of SiO2-CaO-FeO, the activity value aFeO of the system of SiO2-CaO-FeO (1600℃, 1550℃) was obtained, the average relative deviation compared with experiment data are S*FeO (1600℃)=±40%, S*FeO (1550℃)=±45%, it inosculates better with experimental data. The average relative deviation between activity value aCaO and aSiO2 of the system of SiO2-CaO-FeO (1550℃) and the system of SiO2-CaO-FeO (1550℃)and the experiment data are S*CaO=±1497%,S*SiO2=±681%, respectively, it inosculates not good with experimental data. Activity values of aFe0, aCaO, aSiO2 in this system was calculated with Pelton bond energy parameter, and it inosculates good with the calculation results obtained by the author.In the mean time the same method was applied on slag system of SiO2-CaO-MnO (1550℃,1500℃), Activity value of this system component aMnO was obtained with non-symmetry approximate calculation, the relative deviation compared with experimental data are S*MnO (1550℃) =±22%,S*MnO (1500℃)=±41%, Which are in accordance with Pelton's results. it inosculates better with experimental data.Thereby the modified quasi-chemical model has obviously advantage in ternary slag systems.
通过二分法及泰勒展开式对过量吉布斯能的优化拟合得到二元熔渣体系的键能参数ω,η多项表达式,应用修正的似化学模型计算了18个二元熔渣体系在不同温度下的活度值,与实验数据比较得出两组元的总平均相对偏差为：13%和12%,可以看出活度计算值与实验值吻合较好,所以应用半经验模型(修正的似化学模型)对计算熔渣体系的热力学量较为可靠,只是由于该模型中的配位数的物理意义相对比较模糊,因此有待于进一步改进。修正的似化学模型虽没有考虑体系的内部结构特征,但体系的最大有序一般是在体系离子间缔合(或络合)最强的成分附近,这相当于近似考虑了离子键的缔合,且该模型中比当量分数的ω,η多项表达式只考虑独立离子间的相互作用,这样更接近真实情况。
借助几何模型的方法(非对称近似),将修正的似化学模型推广到三元熔渣体系。并将该模型应用到SiO2-CaO-FeO(1600℃,1550℃)体系,计算得到该体系下aFeo活度值,且与实验值比较得出平均相对偏差为：S*FeO(1600℃)=±40％, S*FeO(1550℃)=±45％,可看出计算值与实验数据吻合的较好,而Si02-CaO-FeO体系(1550℃)的aCaO活度值和SiO2-CaO-FeO体系(1550℃)的asiO2活度值,与实验值的平均相对偏差分别为：S*CaO=±1497％,s*SiO2=±681％,可看出活度计算值与实验值吻合不是很好,并用Pelton的键能参数计算该体系下的aFeo' aCaO' aSi02活度值,与作者的计算结果基本一致。同时应用相同方法计算了SiO2-CaO-MnO(1550℃,1500℃)熔渣体系,通过非对称近似计算得到该体系组元aMnO活度值,得到与实验数据的平均相对偏差分别为：S*MnnO(1550℃)=±22％,SMnO(1500℃)=±41%,可看出计算值与实验值的吻合较好,同Pelton计算结果基本一致,因此利用该模型计算三元系中某组分活度值是可行的,对于预测冶金熔渣的热力学性质具有一定优势。
The reliability of the two components activity value of 8 entire-concentration and 4 existing-saturation-concentration binary systems at different temperature was tested by using Gibbs-Duhem equation combine withα-function, the general average relative deviation of the two components are 7% and 13% respectively. which two binary slag system-wide concentrations of B2O3-SiO2 (1450℃,1550℃) and FeO-TiO2 (1400℃) and the existence of four concentrations of slag saturated system error is larger.The reason induced this results may be the few experiment data or less accuracy of measurement data.The average relative deviations of the other 6 entire-concentration binary systems are all less than 5% at different temperature. Thereby, the results of the test which made by using Gibbs-Duhem equation combine withα-function show that the experimental data of the 6 binary slag systems at different temperatures, except B2O3-SiO2 (1450℃,1550℃),FeO-TiO2(1400℃) and the existence of four existing-saturation-concentration of slag system are reliable. Infinite dilution activity coefficient, one of the most important parameters of metallurgical thermodynamics, of each component of 8 entire-concentration the slag systems was calculated and the results could apply some reference.
Polynomial ofωandη(ωandηare bond energy parameters of binary slag systems) was obtained from optimization fitting of excess Gibbs energy with dichotomy and Taylor expansion. The activity values of 18 binary slag systems were calculated with the model of modified quasi-chemical model, and error analysis comparing with experiment data indicates that the general average relative deviation of the two components are 13% and 12% respectively. It could conclude that the activity values obtained from calculation fit better with experimental values, hence that the application of semi-empirical model (modified quasi-chemical model) on calculation and prediction of slag systems thermodynamic is reliable. However the physical meaning of the coordination number in this theory is rather ambiguous and further improvement need to be made. Inner structural features of the system had not been considered in modified quasi-chemical model, but the maximum ordering of the system occurs near at the component of the strongest association (or complexation) effect between ions in the system, and it could be taken for that the association effect of ionic bond has been considered.In this model only interaction of ions has been considered in multiterm expression ofωandη, and it will be more closer to the fact.
With the help of two methods of geometric model (symmetry approximate and non-symmetry approximate) modified quasi-chemical model has been extend to ternary slag systems.With the application of this model on the system of SiO2-CaO-FeO, the activity value aFeO of the system of SiO2-CaO-FeO (1600℃, 1550℃) was obtained, the average relative deviation compared with experiment data are S*FeO (1600℃)=±40%, S*FeO (1550℃)=±45%, it inosculates better with experimental data. The average relative deviation between activity value aCaO and aSiO2 of the system of SiO2-CaO-FeO (1550℃) and the system of SiO2-CaO-FeO (1550℃)and the experiment data are S*CaO=±1497%,S*SiO2=±681%, respectively, it inosculates not good with experimental data. Activity values of aFe0, aCaO, aSiO2 in this system was calculated with Pelton bond energy parameter, and it inosculates good with the calculation results obtained by the author.In the mean time the same method was applied on slag system of SiO2-CaO-MnO (1550℃,1500℃), Activity value of this system component aMnO was obtained with non-symmetry approximate calculation, the relative deviation compared with experimental data are S*MnO (1550℃) =±22%,S*MnO (1500℃)=±41%, Which are in accordance with Pelton's results. it inosculates better with experimental data.Thereby the modified quasi-chemical model has obviously advantage in ternary slag systems.
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