It is well known that hydrogen can have a detrimental effect on the mechanical properties of metals. The aim here is to provide a fully coupled model of the HELP (Hydrogen Enhanced Local Plasticity) mechanism with hydrogen transport. Using the similarities between the heat and mass diffusion equations, a coupled temperature–displacement procedure has been adopted to allow the coupling between hydrogen diffusion and the mechanical behaviour of the material to be simulated. The diffusion equation takes into account the fact that hydrogen atoms reside in interstitial sites and in trapping sites such as dislocations. In the simulations presented here it is assumed that concentration of hydrogen at the dislocations is in equilibrium with the concentration in the matrix interstitial sites. The mechanical behaviour of the material is represented by an isotropic hardening law in which the flow stress decreases with increasing hydrogen content in the matrix which is evaluated by solving the fully coupled mechanical diffusion equations. We use the model to analyse the response of a plane strain component which contains deep and sharp doubled-edged notches. For highly constrained components of this type the hydrostatic component of stress scales with the local yield strength of the material. A high local hydrostatic stress would result in a high hydrogen concentration, but a high hydrogen concentration results in softening, i.e. a low yield strength, and therefore a low hydrostatic stress. These conflicting relationships result in a balance being achieved between hydrostatic stress, hydrogen concentration and yield strength, i.e. the response does not become unstable. Also there is a high degree of kinematic determinacy in the way which the component deforms, i.e. the strain pattern in the presence of hydrogen is very similar to that when there is no hydrogen. A consequence of these two effects is that softening of the constitutive response due to the presence of hydrogen, does not lead to localization of strain and a macroscopic brittle response. Softening must be combined with other degradation process for the material to embrittle

Focussed Ion Beam (FIB) milling is a mainstay of nano-scale machining. By manipulating a tightly focussed beam of energetic ions, often gallium (Ga⁺), FIB can sculpt nanostructures via localised sputtering. This ability to cut solid matter on the nano-scale revolutionised sample preparation across the life, earth and materials sciences. Despite its widespread usage, detailed understanding of the FIB-induced structural damage, intrinsic to the technique, remains elusive. Here we examine the defects caused by FIB in initially pristine objects. Using Bragg Coherent X-ray Diffraction Imaging (BCDI), we are able to spatially-resolve the full lattice strain tensor in FIB-milled gold nano-crystals. We find that every use of FIB causes large lattice distortions. Even very low ion doses, typical of FIB imaging and previously thought negligible, have a dramatic effect. Our results are consistent with a damage microstructure dominated by vacancies, highlighting the importance of free-surfaces in determining which defects are retained. At larger ion fluences, used during FIB-milling, we observe an extended dislocation network that causes stresses far beyond the bulk tensile strength of gold. These observations provide new fundamental insight into the nature of the damage created and the defects that lead to a surprisingly inhomogeneous morphology.

The strain rate dependence of the brittle-to-ductile transition (BDT) temperature was investigated in notched and un-notched miniature bars made of high-purity polycrystalline tungsten and in notched bars of less-pure sintered material. The activation energy, E _BDT, for the process controlling the BDT in pure tungsten was equal to 1.0 eV both in un-notched and notched specimens, though the brittle–ductile transition temperature, T _BDT, was ≈ 40 K lower at each strain rate for the un-notched samples, indicating that the activation energy, E _BDT, is a materials parameter, independent of geometrical factors. The experimental data obtained from pure tungsten are described well by a two-dimensional dislocation-dynamics model of crack-tip plasticity, which is also discussed. For sintered tungsten, E _BDT was found to be 1.45 eV; T _BDT at a given strain rate was higher than in the pure tungsten by ≈ 90 K, suggesting that the BDT in tungsten is very sensitive to impurity levels.

We develop a theoretical treatment of polarization spectroscopy and use it to make predictions about the general form of polarization spectra in the alkali-metal atoms. Using our model, we generate theoretical spectra for the $D2$ transitions in ${}^{87}\mathrm{Rb}$, ${}^{85}\mathrm{Rb}$, and ${}^{133}\mathrm{Cs}$. Experiments demonstrate that the model accurately reproduces spectra of transitions from the upper hyperfine level of the ground state only. Among these, the closed transition $F\to F^{\prime }=F+1$ dominates, with a steep gradient through line center ideally suited for use as a reference in laser locking.