Thermodynamic stability of binary compounds: A comprehensive computational and machine learning approach

Abstract

Exploration and exhaustive comprehension of novel materials are the main objectives of materials science. Laboratory evaluations have been the primary method by which substantial advancements have been achieved throughout the development of this scientific field. The contributions of density functional theory (DFT) algorithms have significantly altered the field of materials science over the past twenty years. These algorithms balance accuracy and efficiency. Supercomputers have enabled substantial breakthroughs in predicting electrical properties of crystal formations, facilitating a fundamental transition in the discipline. Developments of robust algorithms and lower computing costs have made data-driven approaches in materials research more widely adopted. Researchers can now analyze enormous datasets to guide experiments and uncover novel materials. Although databases are frequently used in contemporary materials science, there are some gaps regarding phonon calculations and the thermal properties of compounds. To address this deficiency, this thesis calculates the phonon stability, heat capacities at 298.15 K, formation enthalpies, formation entropies, and Gibbs free energies of binary structures. A total of 879 binary structures were examined, and the results of these calculations were compiled into a data set. In a recent study by my research team, the formation enthalpies and mechanical strengths of binary structures at absolute zero were investigated. This thesis contributes to this work by providing detailed analyses of the dynamic stability and thermodynamic properties of the same binary structures, supporting the findings of my team's prior research. In the initial phase of this thesis, the thermodynamic properties and phonon stabilities of the compounds were calculated. Subsequently, inspired by the PN-PN table model proposed and utilized in our team's recent work, this data set was mapped and visualized on a PN-PN table according to the periodic numbers (PN) assigned to the elements in the structures. This approach enabled the integrated visualization of phonon stability and other thermodynamic properties. Consequently, the chemical similarities between structures were more easily comprehended through the groups in the map, and the so-called forbidden regions were highlighted. Forbidden regions are regions in which specific pairings of elements are unable to form stable phases, which provides critical information on stability based on the PN numbers of the elements. The basic principle of the periodic numbering approach is as follows: First, periodic numbers (PN) are assigned to the elements with respect to their electronegativity, principal quantum number, and valence shell configuration, and then this numbering is extended to binary systems. This makes it easier to understand the chemical trends in the compounds formed by the elements and to predict phase formation. Although there are some exceptions in this mapping, it clearly shows the structures where phase formation is not expected. In our team's previous work, the PN-PN table significantly facilitated the identification of critical regions in different chemical systems and allowed for the analysis of trends in the chemical properties of equiatomic binary phases. Based on this, density functional theory-based thermodynamic calculations were performed in this thesis, providing thermodynamic data supporting the inferences of formation enthalpy and crystal structure stability calculated in our team's previous studies. A total of 879 structures' phonon stabilities were determined, and heat contribution values were calculated. Thus, the phonon stability and heat contribution data obtained from this thesis can be integrated with the mechanical strength properties of the structures from our team's previous findings. This allows for a more detailed interpretation of the relationship between phonon and mechanical stability. Additionally, using the elemental and structural properties of the compounds, machine learning techniques were applied to the current data set. Random Forest, Support Vector Machines (SVM), Gradient Boosting, and Decision Trees were assessed for their capacity to predict phonon stability. The Decision Tree model exhibited the highest performance, with an accuracy rate of 80\%. These models' accuracy was significantly enhanced by elemental descriptors such as band center, mean covalent radius, and mean electronegativity. The band center indicates the effect of the position in the electronic band structure on phonon stability, the mean covalent radius reflects the bonding properties of atoms, and the mean electronegativity determines the atoms' tendencies to attract electrons, thus affecting phonon stability. For predicting Gibbs free energy, Random Forest Regression, K-Nearest Neighbors (KNN) Regression, Support Vector Regression (SVR), and Linear Regression models were used. The performance of these models was evaluated using a 5-fold cross-validation method. The Random Forest Regression model exhibited the highest performance with an average score of 0.846. This result indicates that Random Forest Regression is the most effective model for predicting Gibbs free energy. These findings may encourage the broader application of machine learning techniques in future research. This significant step in understanding and modeling thermodynamic properties plays a critical role in optimizing material structures. In the future, it is expected that the methods of this study will be adapted and developed more specifically for certain material classes or other academic applications. This approach also serves as an efficient example of the discovery and design planning processes in materials science.