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Type II and IV twins with irrational twin boundaries are studied by high-resolution transmission electron microscopy in two plagioclase crystals. The twin boundaries in these and in NiTi are found to relax to form rational facets separated by disconnections. The topological model (TM), amending the classical model, is required for a precise theoretical prediction of the orientation of the Type II/IV twin plane. Theoretical predictions also are presented for types I, III, V, and VI twins. The relaxation process that forms a faceted structure entails a separate prediction from the TM. Hence, faceting provides a difficult test for the TM. Analysis of the faceting by the TM is in excellent agreement with the observations. 

Abstract The mechanical behavior and microstructural evolution of a BCC‐phase NbTaTiV refractory multi‐principal element alloy (RMPEA) is studied over a wide range of strain rates (10⁻³to 10³s⁻¹) and temperatures (room temperature to 850 °C). The mechanical property of present RMPEA shows less strain‐rate dependence and strong resistance to softening at high temperatures. Under high strain‐rate loading, the formation of thin type‐I twins is observed, which could lead to an increase in strain‐hardening rates. However, this hardening mechanism competes with adiabatic heating effects, resulting in the deterrence of strain‐hardening behaviors. In contrast, substantial strain‐hardening occurs at cryogenic temperatures due to the formation of twins, which act as stronger barriers to dislocation motion and interact with each other. To further understand the different strain‐hardening behaviors, density functional theory (DFT) calculations predict relatively low stacking fault energies and high twinning stress for the NbTaTiV RMPEA.