The density of Al₂O₃–CaO–MgO–SiO₂ system is calculated using a model for molar volume. The model is similar to the one used for enthalpy of a multicomponent solution in the CALPHAD approach. The expression for molar volume consists of two terms: one representing the volume contribution from pure components and the other the volume of mixing. The molar volume of mixing takes into account of the binary and the ternary interactions. A total of 565 experimental density data for the constituent unary, binary and ternary systems were collected from the literature. These were used as input to simultaneously optimise the model parameters describing the molar volume, after ensuring that the data belong to a fully molten state. During the optimisation 48 data points that showed significant deviation from the average trend were excluded. The optimised model parameters for the unary, binary and ternary subsystems were used to calculate the density of the quaternary system. The calculated results were compared with experimental data. Finally, it is shown that the volume of mixing of binary systems correlates well with the corresponding enthalpy of mixing.

Al ₂ O ₃ –CaO–MgO–SiO ₂的密度使用摩尔体积模型计算系统。该模型类似于CALPHAD方法中用于多组分溶液焓的模型。摩尔体积的表达包括两个术语：一个代表纯组分的体积贡献，另一个代表混合体积。混合的摩尔体积考虑了二元和三元相互作用。从文献中收集了总共565个构成一元，二元和三元系统的实验密度数据。在确保数据属于完全熔融状态之后，将这些用作输入以同时优化描述摩尔体积的模型参数。在优化过程中，排除了显示与平均趋势有明显偏差的48个数据点。一元模型的优化模型参数，二元和三元子系统用于计算四元系统的密度。将计算结果与实验数据进行比较。最后，表明二元体系的混合量与相应的混合焓很好地相关。