Amending CALPHAD databases using a neural network for predicting mixing enthalpy of liquids

Abstract: In order to establish the thermodynamic stability of a system, knowledge of its Gibbs free energy is essential. Most often, the Gibbs free energy is predicted within the CALPHAD framework using models employing thermodynamic properties, such as the mixing enthalpy, heat capacity, and activity coefficients. Here, we present a deep-learning approach capable of predicting the mixing enthalpy of liquid phases of binary systems that were not present in the training dataset. Therefore, our model allows for a system-informed enhancement of the thermodynamic description to unknown binary systems based on information present in the available thermodynamic assessment. Thereby, significant experimental efforts in assessing new systems can be spared. We use an open database for steels containing 91 binary systems to generate our initial training (and validation) and amend it with several direct experimental reports. The model is thoroughly tested using different strategies, including a test of its predictive capabilities. The model shows excellent predictive capabilities outside of the training dataset as soon as some data containing species of the predicted system is included in the training dataset. The estimated uncertainty of the model is below 1 kJ/mol for the predicted mixing enthalpy. Subsequently, we used our model to predict the enthalpy of mixing of all binary systems not present in the original database and extracted the Redlich-Kister parameters, which can be readily reintegrated into the thermodynamic database file.