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We developed an ML framework to predict Vickers hardness in RHEAs. Feature selection reduced descriptors, enabling Kernel Ridge Regression to achieve the highest accuracy. SHAP identified valence electron concentration as a key predictor, highlighting ML’s potential in alloy design. 

Multi-Principal Element Alloys (MPEAs) have emerged as an exciting area of research in materials science in the 2020s, owing to the vast potential for discovering alloys with unique and tailored properties enabled by the combinations of elements. 

The Cluster Expansion (CE) Method encounters significant computational challenges in multicomponent systems due to the computational expense of generating training data through density functional theory (DFT) calculations. This work aims to refine the cluster and structure selection processes to mitigate these challenges. We introduce a novel method that significantly reduces the computational load associated with the calculation of fitting parameters. This method employs a Graph Neural Network (GNN) model, leveraging the M3GNet network, which is trained using a select subset of DFT calculations at each ionic step. The trained surrogate model excels in predicting the volume and energy of the final structure for a relaxation run. By employing this model, we sample thousands of structures and fit a CE model to the energies of these GNN-relaxed structures. This approach, utilizing a large training dataset, effectively reduces the risk of overfitting, yielding a CE model with a root-mean-square error (RMSE) below 10 meV/atom. We validate our method’s effectiveness in two test cases: the (Ti, Cr, Zr, Mo, Hf, Ta)B2 diboride system and the Refractory High-Entropy Alloy (HEA) AlTiZrNbHfTa system. Our findings demonstrate the significant advantages of integrating a GNN model, specifically the M3GNet network, with CE methods for the efficient predictive analysis of chemical ordering in High Entropy Materials. The accelerating capabilities of the hybrid ML-CE approach to investigate the evolution of Short Range Ordering (SRO) in a large number of stoichiometric systems. Finally, we show how it is possible to correlate the strength of chemical ordering to easily accessible alloy parameters. 

In this work, a long-established but sparsely documented method of obtaining semi-analytic derivatives of thermodynamic properties with respect to equilibrium conditions is briefly reviewed and rigorously derived. This procedure is then leveraged to construct general forms of derivatives of the residual driving force, a metric for measuring phase stability used in CALPHAD model optimization, with respect to overall system and individual phase compositions. Applied examples – calculating heat capacity in the Al-Fe system, thermodynamic factors in the Nb-V-W system, and residual driving force derivatives in the Ni-Ti system – demonstrate the versatility, accuracy, and extensibility of this method. Using the developed method, residual driving force gradients can be applied directly in CALPHAD model optimizers, as well as in materials design frameworks, to identify regions of phase stability with an efficient, gradient-based approach. 

We consider the problem of crystal materials generation using language models (LMs). A key step is to convert 3D crystal structures into 1D sequences to be processed by LMs. Prior studies used the crystallographic information framework (CIF) file stream, which fails to ensure SE(3) and periodic invariance and may not lead to unique sequence representations for a given crystal structure. Here, we propose a novel method, known as Mat2Seq, to tackle this challenge. Mat2Seq converts 3D crystal structures into 1D sequences and ensures that different mathematical descriptions of the same crystal are represented in a single unique sequence, thereby provably achieving SE(3) and periodic invariance. Experimental results show that, with language models, Mat2Seq achieves promising performance in crystal structure generation as compared with prior methods. 

We consider the problem of crystal materials generation using language models (LMs). A key step is to convert 3D crystal structures into 1D sequences to be processed by LMs. Prior studies used the crystallographic information framework (CIF) file stream, which fails to ensure SE(3) and periodic invariance and may not lead to unique sequence representations for a given crystal structure. Here, we propose a novel method, known as Mat2Seq, to tackle this challenge. Mat2Seq converts 3D crystal structures into 1D sequences and ensures that different mathematical descriptions of the same crystal are represented in a single unique sequence, thereby provably achieving SE(3) and periodic invariance. Experimental results show that, with language models, Mat2Seq achieves promising performance in crystal structure generation as compared with prior methods.