Prediction of Lattice Constant of A₂XY₆ Cubic Crystals Using Gene Expression Programming

Abstract

Lattice constant is one of the paramount parameters that mark the quality of thin film fabrication. Numerous research efforts have been made to calculate and measure lattice constant, including experimental and empirical approaches. Not withstanding these efforts, a reliable and simple-to-use model is still needed to predict accurately this vital parameter. In this study, gene expression programming (GEP) approach was implemented to establish trustworthy model for prediction of the lattice constant of A2XY6 (A = K, Cs, Rb, TI; X = tetravalent cation; and Y = F, Cl, Br, I) cubic crystals based on a comprehensive experimental database. The obtained results showed that the proposed GEP correlation provides excellent prediction performance with an overall average absolute relative deviation (AARD%) of 0.3596% and a coefficient of determination (R 2) of 0.9965. Moreover, the comparison of the performance between the newly proposed correlation and the best pre-existing paradigms demonstrated that the established GEP correlation is more robust, reliable, and efficient than the prior models for prediction of lattice constant of A2XY6 cubic crystals.

Mlatticeabc: Generic Lattice Constant Prediction of Crystal Materials Using Machine Learning

“…Computational prediction of lattice constants of crystal materials has wide applications in both materials property prediction and discovery, 5 crystal structure prediction, 6 , 7 and large screening of materials for materials fabrication. 8 Lattice prediction models are very helpful for the crystal structure prediction algorithms, which can allow conducting mutagenesis experiments to examine how composition changes may affect the structural mutations in terms of lattice constant changes or symmetry breaking. Crystal structure prediction can also be used to augment the X-ray diffraction (XRD)-based crystal structure determination via space group identification or providing initial parameters for the XRD-based Rietveld refinement method for structure determination.…”

“… 9 While the majority of methods are based on composition information, the structure-based approaches can also bring interesting insights. 8 In this paper, 9 a deep learning method is proposed to predict lattice parameters in cubic inorganic perovskites based on Hirshfeld surface representations of crystal structures. They showed that two-dimensional Hirshfeld surface fingerprints contain rich information encoding the relationships between chemical bonding and bond geometry characteristics of perovskites.…”

“…Lattice prediction methods can also be classified by the machine learning models used. A variety of machine learning models have been applied for lattice constant prediction including conventional machine learning methods in the early stage such as linear regression, 4 , 10 support vector machines, 11 , 12 neural networks (NNs), 10 , 13 gene expression programming, 8 random forests (RFs), 14 and Gaussian process regression. 15 However, the performance difference among different machine learning algorithms has not been thoroughly evaluated.…”

“…A major difference among different lattice constant prediction studies is the chemical systems or materials families they focus on. The majority of the studies are focused on a special category of materials with fixed mole ratios, including the cubic perovskites ABX 3 , 4 , 11 , 16 − 19 A 2 XY 6 , 8 half-Heusler ternary compounds (XYZ), 20 and binary body-centered cubic crystals. 12 Most of such studies use an extremely small data set (<200 samples) coupled with selected elemental properties to achieve high accuracy (coefficient of determination ( R 2 ) > 0.95) as evaluated by the random hold-out or cross-validation methods.…”

“…A large number of descriptors have been used for lattice constant prediction even though some of them may be specific to the form of the chemical compositions. For perovskite lattice constant prediction, the following descriptors have been used: valence electron, 10 , 23 ionic radii (which reflects bond lengths), 8 , 23 tolerance factor ( ) calculated from ionic radii of the A-site and B-site cations and r X , the ionic radius of the anion, 4 electronegativity, 24 , 25 and ionic charge. 26 In terms of ionic radii, there are several ways to combine the values of the component elements such as the sum, differences, or ratios.…”