Exchange of angular momentum in EMCD experiments

In energy loss magnetic chiral dichroism (EMCD) experiments a chiral electronic transition is induced that obeys the dipole selection rule for the magnetic quantum number Δm=±1$\mathrm{\Delta }m=\pm 1$ or Δ_Lz=±?$\mathrm{\Delta }{L}_z=\pm ?$. The incident plane electron wave is inelastically scattered and is detected in the diffraction plane, i.e. again in a plane wave state. Naïve reasoning suggests that the angular momentum _Lz$L_z$ of the probe electron has not changed in the interaction since plane waves have 〈_Lz〉=0$〈L_z〉=0$. This leads to the seeming contradiction that angular momentum is not conserved in the interaction. A closer inspection shows that the density matrix of the probe has indeed 〈_Lz〉=±?$〈L_z〉=\pm ?$ after a chiral interaction. However, 〈_Lz〉$〈L_z〉$ is not conserved when the probe electron propagates further to the exit surface of the specimen because the rigid lattice breaks rotational symmetry. Thus, the angular momentum of the photo electron that is created in a chiral electronic transition stems from both the probing electron and the crystal lattice.     

A three-point electrical potential difference method for in situ monitoring of propagating mixed-mode cracks at high temperature

In this paper an electrical potential difference method for the real-time assessment of both the length and the direction of Mode II cracks is presented. Three measuring electrodes are placed in selected positions over the gauge area of a specially designed shear specimen and their readings are associated with the actual position of the crack tip using Finite Element Analysis (FEA). This information can be processed in real-time to provide continuous monitoring of the crack as it propagates either in pure Mode II (in-plane shear) or mixed Mode I (tension) and Mode II if the inclination of the crack exceeds 20°. In fatigue testing it is possible to produce dα/dN-Δ_KII$d\alpha /\mathit{dN}-\mathrm{\Delta }{K}_{\text{II}}$ (in pure-shear) and dα/dN-Δ_KI$d\alpha /\mathit{dN}-\mathrm{\Delta }{K}_{\text{I}}$ (in mixed-mode) plots on-line as the test is in execution. The method has been calibrated with optical measurements using a long-distance observation microscope on the nickel-based superalloy CMSX4 at high temperature. The main finding was that the central two sensing electrodes were sensitive to the length of the crack and insensitive to the crack angle, whereas the readings from the third electrode were sensitive to the crack angle and thus the exact position of the crack tip could be traced in real-time. Special techniques were implemented to rule-out thermoelectric effects and thermal stresses on the specimen.