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Low-dimensional materials have attracted significant attentions over the past decade. To discover new low-dimensional materials, high-throughout screening methods have been applied in different materials databases. For this purpose, the reliability of dimensionality identification is therefore highly important. In this work, we find that the existence of self-penetrating nets may lead to incorrect results by previous methods. In stead of this, we use the quotient graph to analysis the topologies of structures and compute their dimensionalities. Based on the quotient graph, we can calculate not only the dimensionality but also the multiplicity of self-penetrating structures. As a demonstration, we screened the Crystallography Open Database using our method and found hundreds of structures with different dimensionalities and high multiplicities up to eleven.
Variation of the geometrical and electronic properties of the gold materials in different dimensions has been investigated by $ab$ $initio$ method, taking into account the spin-orbit (SO) interaction. It is found that SO effects in different dimens
The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the elastic distorti
We propose an approach for exploiting machine learning to approximate electronic fields in crystalline solids subjected to deformation. Strain engineering is emerging as a widely used method for tuning the properties of materials, and this requires r
Lattice constants such as unit cell edge lengths and plane angles are important parameters of the periodic structures of crystal materials. Predicting crystal lattice constants has wide applications in crystal structure prediction and materials prope
Crystal structure prediction is now playing an increasingly important role in discovery of new materials. Global optimization methods such as genetic algorithms (GA) and particle swarm optimization (PSO) have been combined with first principle free e