(1−3) Lattice mismatch between the films and the growth substrates is also known to cause major issues in fabricating large and high quality of heteroepitaxial films of semiconductors such as GaAs, GaN, and InP. Lattice constants and their changes such as lattice distortion upon different pressures and temperatures are related to many interesting physical and chemical properties of the materials. The shape of the unit cell of a crystal material determines its crystal system out of seven possibilities: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. A unit cell is defined by six lattice parameters/constants including the lengths of three cell edges ( a, b, c) and the angles between them (α, β, γ).
The periodic structures of crystal materials can be summarized by their space group and the parallelepiped unit cell as shown in Figure 1.
Source code and trained models can be freely accessed at. Our results also show significant performance improvement for lattice angle predictions. The R 2 scores are between 0.498 and 0.757 over lattice b and c prediction performance of the model, which could be used by just inputting the molecular formula of the crystal material to get the lattice constants. Herein, we report MLatticeABC, a random forest machine learning model with a new descriptor set for lattice unit cell edge length ( a, b, c) prediction which achieves an R 2 score of 0.973 for lattice parameter a of cubic crystals with an average R 2 score of 0.80 for a prediction of all crystal systems. However, these models trained with small data sets are usually not applicable to generic lattice parameter prediction of materials with diverse compositions. Other models tailored for special materials family of a fixed form such as ABX 3 perovskites can achieve much higher performance due to the homogeneity of the structures. Previous work has used machine learning models such as neural networks and support vector machines combined with composition features for lattice constant prediction and has achieved a maximum performance for cubic structures with an average coefficient of determination ( R 2) of 0.82. Predicting crystal lattice constants has wide applications in crystal structure prediction and materials property prediction.
Lattice constants such as unit cell edge lengths and plane angles are important parameters of the periodic structures of crystal materials.
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