Macroscopic Elastic Properties of Textured ZrN--AlN Polycrystalline Aggregates: From Ab initio Calculations to Grain-Scale Interactions

Despite the fast development of computational materials modelling, theoretical description of macroscopic elastic properties of textured polycrystalline aggregates starting from basic principles remains a challenging task. In this communication we use a supercell-based approach to obtain the elastic properties of random solid solution cubic ZrAlN system as a function of the metallic sublattice composition and texture descriptors. The employed special quasi-random structures are optimised not only with respect to short range order parameters, but also to make the three cubic directions $[1\,0\,0]$, $[0\,1\,0]$, and $[0\,0\,1]$ as similar as possible. In this way, only a small spread of elastic constants tensor components is achieved and an optimum trade-off between modelling of chemical disorder and computational limits regarding the supercell size is achieved. The single crystal elastic constants are shown to vary smoothly with composition, yielding $x\approx0.4$-0.5 an alloy constitution with an almost isotropic response. Consequently, polycrystals with this composition are suggested to have Young's modulus independent on the actual microstructure. This is indeed confirmed by explicit calculations of polycrystal elastic properties, both within the isotropic aggregate limit, as well as with fibre textures with various orientations and sharpness. It turns out, that for low AlN mole fractions, the spread of the possible Young's moduli data caused by the texture variation can be larger than 100 GPa. Consequently, our discussion of Young's modulus data of cubic ZrAlN contains also the evaluation of the texture typical for thin films.Comment: 10 pages, 6 figures, 3 table

Mesh Refinement for Anisotropic Diffusion in Magnetized Plasmas

Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers that are expensive to resolve. This work investigates how mesh refinement strategies might reduce that expense to allow for more efficient simulation. It is first verified that higher order discretization only realizes the proper rate of convergence once the mesh resolves the thin boundary layer, motivating the focusing of refinement on the boundary layer. Three mesh refinement strategies are investigated: one that focuses the refinement across the layer by using rectangular elements with a ratio equal to the boundary layer width, one that allows for exponential growth in mesh spacing away from the layer, and one adaptive strategy utilizing the established Zienkiewicz and Zhu error estimator. Across 4 two-dimensional test cases with high anisotropy, the adaptive mesh refinement strategy consistently achieves the same accuracy as uniform refinement using orders of magnitude less degrees of freedom. In the test case where the magnetic field is aligned with the mesh, the other refinement strategies also show substantial improvement in efficiency. This work also includes a discussion generalizing the results to larger magnetic anisotropy ratios and to three-dimensional problems. It is shown that isotropic mesh refinement requires degrees of freedom on the order of either the layer width (2D) or the square of the layer width (3D), whereas anisotropic refinement requires a number on the order of the log of layer width for all dimensions. It is also shown that the number of conjugate gradient iterations scales as a power of layer width when preconditioned with algebraic multigrid, whereas the number is independent of layer width when preconditioned with ILU

Towards predictive modelling of near-edge structures in electron energy loss spectra of AlN based ternary alloys

Although electron energy loss near edge structure analysis provides a tool for experimentally probing unoccupied density of states, a detailed comparison with simulations is necessary in order to understand the origin of individual peaks. This paper presents a density functional theory based technique for predicting the N K-edge for ternary (quasi-binary) nitrogen alloys by adopting a core hole approach, a methodology that has been successful for binary nitride compounds. It is demonstrated that using the spectra of binary compounds for optimising the core hole charge ($0.35\,\mathrm{e}$ for cubic Ti$_{1-x}$Al$_x$N and $0.45\,\mathrm{e}$ for wurtzite Al$_x$Ga$_{1-x}$N), the predicted spectra evolutions of the ternary alloys agree well with the experiments. The spectral features are subsequently discussed in terms of the electronic structure and bonding of the alloys.Comment: 11 pages, 9 figures, 1 tabl

Graphite under uniaxial compression along the c axis: A parameter to relate out-of-plane strain to in-plane phonon frequency

Stacking graphene sheets forms graphite. Two in-plane vibrational modes of graphite, E1u and E2g(2), are derived from graphene E2g mode, the shifts of which under compression are all considered as results of in-plane bond shortening. Values of Gruneisen parameter have been reported to quantify such relation. However, the reason why the shift rates of these three modes with pressure differ is unclear. In this work, we introduce a new parameter to quantify the contribution of out-of-plane strain to the in-plane vibrational frequencies, suggesting that the compression of \pi-electrons plays a non-negligible part in both graphite and graphene under high pressure.Comment: 8 pages, 5 figures, 1 tabl

Why, what, and how? case study on law, risk, and decision making as necessary themes in built environment teaching

The paper considers (and defends) the necessity of including legal studies as a core part of built environment undergraduate and postgraduate curricula. The writer reflects upon his own experience as a lawyer working alongside and advising built environment professionals in complex land remediation and site safety management situations in the United Kingdom and explains how themes of liability, risk, and decision making can be integrated into a practical simulation in order to underpin more traditional lecture-based law teaching. Through reflection upon the writer's experiments with simulation-based teaching, the paper suggests some innovations that may better orientate law teaching to engage these themes and, thereby, enhance the relevance of law studies to the future needs of built environment professionals in practice.</p