Computational Exploration of RE-Si-O Chemical Space using Density Functional Theory and Trustworthy Machine Learning

The coefficient of thermal expansion (CTE) is a critical material property that quantifies the degree to which a material expands or contracts upon heating. Despite progress in theory, computations and empirical model development, existing knowledge has limitations in predicting the CTE of complex materials such as the compounds that form in the rare earth-silicon-oxygen (RE-Si-O) ternary space, which are candidate materials for environmental barrier coatings (EBCs). This thesis aims to bridge this gap by leveraging computational methods based on density functional theory (DFT) calculations and machine learning (ML) techniques. While well-trained ML models are good at generating predictions, they often serve as black boxes that limit their interpretability. This limitation is particularly problematic in materials science, where the available data sets are often limited and sparse.

To address these challenges, this dissertation targets three key goals: (1) Accelerating the design of novel compounds in the complex RE-Si-O chemical space with targeted CTE values by establishing previously unknown quantitative structure-property relationships using DFT and ML; (2) Building trust in ML models (in a narrow sense) by accurately gauging when and where they can succeed or fail, thereby facilitating well-informed design choices; and (3) Uncovering the insights behind ML model predictions to better comprehend the science underlying the quantified structure-property relationships. This integrated approach was applied to three major material classes in the RE-Si-O chemical space: RE disilicates, RE monosilicates, and RE silicate apatites. Finally, a holistic CTE model was developed that quantitatively captures the relationship between structure and volumetric CTE across these diverse material classes, including some of the high entropy variants.

Throughout the thesis, I focused on two critical attributes of RE-Si-O systems that are essential for the development of EBCs: the DFT total energies and the polyhedral description of the crystal structures. Key findings are summarized below:

In RE disilicates, I used DFT calculations to generate the total energy difference (∆E) data that offered key insights into the energetics favoring polymorph formation. The calculations also provide optimized crystal
structures from which one can generate two types of descriptors: (1) Unit cell parameters (more accessible to the experimental community) and (2) Polyhedral descriptors

(may carry mechanistic insights that can be correlated with CTE). I trained an ensemble of ML models to rapidly predict the volumetric CTE, along with the associated uncertainties. Experiments from our collaborators validated the CTE predictions for the Sm2Si2O7 compound in P41 space group.

In RE monosilicates, I focused on CTE anisotropy. Using DFT and density of states calculations, I uncovered a previously unidentified trend that correlated the d-orbital bandwidth and RE-O effective coordination numbers in isoelectronic Sc2SiO5, Y2SiO5, and La2SiO5 compounds with the measured CTE anisotropy data (taken from the literature). The crystal structures were constrained to the
C2/c space group in these calculations.

In RE silicate apatites, I calculated ∆E from DFT to reveal the energetics trend across the different RE silicate apatites: non-stoichiometric (RE9.33Si6O26) and RE silicate apatite bearing alkali metals (RE9A1Si6O26, where A=Li, Na, K, Rb, and Cs monovalent cations) and alkaline earth metals (RE8AE2Si6O26, where AE=Be, Mg, Ca, Sr, and Ba divalent cations). Unlike the disilicates and monosilicates, the literature data on CTE for this materials class is sparse. Therefore, I did not investigate the CTE property for this materials class. Nonetheless, my calculations led to the development of polyhedral descriptors which I hypothesize as a more meaningful representation of the crystal chemistry when compared to the traditional ionic radii description.

I built a holistic model that has the capability to predict the volumetric CTE of RE disilicate, RE monosilicate and RE silicate apatites as a function of chemical composition and crystal structure. Intriguingly, the model that was trained only using single-component compounds was also able to predict the CTE trend for two four-component systems: β-C2/m (Y, Yb, Lu, La)2Si2O2 and β-C2/m (Y,Yb, Er, Dy)2Si2O2 that were not part of the training data. Post hoc model interpretation of the trained model revealed the critical role of RE-O bond length, SiO4 polyhedral volume and bond angle variance within SiO4 polyhedral units.

This thesis lays the foundation for rational design of volumetric CTE in RE-Si-O compounds.