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

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

Unexpected softness of bilayer graphene and softening of A-A stacked graphene layers

Density functional theory has been used to investigate the behavior of the π electrons in bilayer graphene and graphite under compression along the c axis. We have studied both conventional Bernal (A-B) and A-A stackings of the graphene layers. In bilayer graphene, only about 0.5% of the π-electron density is squeezed through the sp2 network for a compression of 20%, regardless of the stacking order. However, this has a major effect, resulting in bilayer graphene being about six times softer than graphite along the c axis. Under compression along the c axis, the heavily deformed electron orbitals (mainly those of the π electrons) increase the interlayer interaction between the graphene layers as expected, but, surprisingly, to a similar extent for A-A and Bernal stackings. On the other hand, this compression shifts the in-plane phonon frequencies of A-A stacked graphene layers significantly and very differently from the Bernal stacked layers. We attribute these results to some sp2 electrons in A-A stacking escaping the graphene plane and filling lower charge-density regions when under compression, hence, resulting in a nonmonotonic change in the sp2-bond stiffness

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