Using the particle swarm optimization technique, we proposed a cubic superhard phase of C₃N (c-C₃N) with an estimated Vicker’s hardness of 65 GPa, which is more energetically favorable than the recently proposed o-C₃N. The c-C₃N is the most stable phase in a pressure range of 6.5–15.4 GPa. Above 15.4 GPa, the most energetic favorable high pressure phase R3m-C₃N is uncovered. Phonon dispersion and elastic constant calculations confirm the dynamical and mechanical stability of c-C₃N and R3m-C₃N at ambient pressure. The electronic structure calculations indicate that both c-C₃N and R3m-C₃N are indirect semiconductor.

By combining first-principles calculations with the particle swarm optimization algorithm, we predicted a hexagonal structure for TcB, which is energetically more favorable than the previously reported WC-type and Cmcm structures. The new phase is mechanically and dynamically stable, as confirmed by its phonon and elastic constants calculations. The calculated mechanical properties show that it is an ultra-incompressible and hard material. Meanwhile, the elastic anisotropy is investigated by the shear anisotropic factors and ratio of the directional bulk modulus. Density of states analysis reveals that the strong covalent bonding between Tc and B atoms plays a leading role in forming a hard material. Additionally, the compressibility, bulk modulus, Debye temperature, Grüneisen parameter, specific heat, and thermal expansion coefficient of TcB are also successfully obtained by using the quasi-harmonic Debye model.

Amid global rural tourism growth and rural revitalization policies, traditional villages’ resource protection and tourism development have drawn international academic attention. To guide villages’ resource planning and management, this study constructed an evaluation index system of cultural, ecological, industrial, talent, and organizational amenities in traditional villages from the perspective of tourists’ perceptions using grounded theory and measured the spatial agglomeration differences, synergistic effects and their influencing factors of traditional village amenities by using location entropy, spatial autocorrelation, and gray correlation degree analysis. The results show that (1) the spatial distributions of cultural, ecological, industrial, and organizational amenities are more balanced, while talent amenities exhibit a more concentrated distribution. (2) The spatial concentration of amenities in traditional villages has a strong positive spatial correlation, the agglomeration level of the high-high type of concentration is distributed in clusters, the low–low type tends to be contiguous, and the low–high type is distributed sporadically around the high–high type; significant synergy between ecological and industrial amenities, and organizations play a supportive role in the spatial agglomeration of cultural, ecological, ecological and talent amenities. (3) Gross regional product, slope, and distance to 3A and above scenic spots significantly influence the spatial agglomeration of amenities. This study provides reference for the sustainable development of traditional villages from the perspectives of exerting agglomeration and radiation effects, synergistically promoting villages’ development, constructing the memory symbol system, and integrating the resource structural system based on the spatial agglomeration difference characteristics of traditional village amenities.