One type of two-dimensional diamonds that are derived from [111] direction, so-called diamane, has been previously shown to be stabilized by N-substitution, where the passivation of dangling bonds is no longer needed. In the present work, we theoretically demonstrated that another type of two-dimensional diamonds derived from [110] direction exhibiting a washboard conformation can also be stabilized by N-substitution. Three structural models of washboard-like carbon nitrides with compositions of C₆N₂, C₅N₃, and C₄N₄ are studied together with the fully hydrogenated washboard-like diamane (C₈H₄). The result shows that the band gap of this type structure is only open the dangling bonds that are entirely diminished through N-substitution. By increasing the N content, the C₁₁ and C₂₂ are softer and the C₃₃ is stiffer where their bulk modulus are in the same order, which is approximately 550 GPa. When comparing with the hydrogenated phase, the N-substituted phases have higher elastic constants and bulk modulus, suggesting that they are possibly harder than the fully hydrogenated diamane.

Determining whether a candidate crystalline material is thermodynamically stable depends on identifying its true ground-state structure, a central challenge in computational materials science. We introduce CrystalGRW, a diffusion-based generative model on Riemannian manifolds that proposes candidate crystal configurations in stable phases, validated through density functional theory calculations. Our model is designed for de novo generation, which creates crystal structures together with their compositions. The crystal properties, such as fractional coordinates, atomic types, and lattice matrices, are represented on suitable Riemannian manifolds, ensuring that new predictions generated through the diffusion process preserve the periodicity of crystal structures. We also incorporate an equivariant graph neural network to account for rotational and translational symmetries within the model. CrystalGRW generates crystal structures that are stable and closely resemble their density-functional-theory ground states. The model also supports conditional control, such as enforcing a specified crystallographic point group, thereby accelerating materials discovery and inverse design by providing symmetry-consistent, energetically stable candidate crystals for experimental validation.