Strength, as an important indicator of structural materials, has always been an important research topic in materials science. Theoretically, building a strength model is a rewarding method to understand the relationship between the mechanical properties and microstructure of materials. Although many strength models can reduplicate experimental values very well, they are empirical models, and their applicability is limited to materials for which empirical parameters have been obtained. Here, a nonempirical strength model is proposed based on the two-dimensional (2D) displacement potential of dislocation slipping, which can be applied to different chemically bonded crystals. Owing to the large electron localization function (ELF), covalent and ionic crystals have a high 2D displacement potential of dislocation slipping, and their dislocation slip mode prefers the kink-pair mode, further exhibiting a high critical resolved shear stress (CRSS). In contrast, metallic crystals with a small ELF have a low 2D displacement potential of dislocation slipping, and their dislocation slip mode is more inclined to the string mode, showing a low CRSS. This work provides new insights into dislocation-slipping configurations that will be useful for the development of new high-performance structural materials.

Multi-path (or multi-mode) entanglement has been proved to be a useful resource for sub-shot-noise sensitivity of phase estimation, which has aroused much research interest inquantum metrology recently. Various schemes of multi-path interferometers based on optical systems have been put forward. Here, we study a multi-state interferometer with multi-level atoms by projective measurements. Specifically, we investigate its ultimate sensitivity described by quantum Fisher information theory and find that the Cramer–Rao bound can be achieved. In particular, we investigate a specific scheme to improve the sensitivityof magnetometery with a three-state interferometry delivered by a single nitrogen-vacancy (NV) center of diamond with tailor pulses. The impacts of imperfections of the atomic beam-splitter, described by the three-level quantum Fourier transform, on the sensitivity of phase estimation is also discussed.