[1] The effects of grain grooves on grain boundary migration in nanofilms

A Novick-Cohen et al

Using numerical computations and asymptotic analysis, we study the effects of grain grooves on grain boundary migration in nanofilms, focusing for simplicity on axisymmetric bicrystals containing an embedded cylindrical grain located at the origin. We find there is a critical initial grain radius, R*, such that if RR*, groove growth during grain shrinkage leads to film break-up. The central cross-section of the grain boundary profile is seen to be parabolic, and an ordinary differential equation which depends on the tilt angle and the groove depth is seen to govern the location of the groove root. Near the annihilation–pinch-off transition, temporary stagnation occurs; thereafter, the shrinking grain accelerates rapidly, then disappears.

[2] Misfit strain–film thickness phase diagrams and related electromechanical properties of epitaxial ultra-thin lead zirconate titanate films

Q Y Qiu et al

The phase stability of ultra-thin (0 0 1) oriented ferroelectric PbZr1–xTixO3 (PZT) epitaxial thin films as a function of the film composition, film thickness, and the misfit strain is analyzed using a non-linear Landau–Ginzburg–Devonshire thermodynamic model taking into account the electrical and mechanical boundary conditions. The theoretical formalism incorporates the role of the depolarization field as well as the possibility of the relaxation of in-plane strains via the formation of microstructural features such as misfit dislocations at the growth temperature and ferroelastic polydomain patterns below the paraelectric–ferroelectric phase transformation temperature. Film thickness–misfit strain phase diagrams are developed for PZT films with four different compositions (x = 1, 0.9, 0.8 and 0.7) as a function of the film thickness. The results show that the so-called rotational r-phase appears in a very narrow range of misfit strain and thickness of the film. Furthermore, the in-plane and out-of-plane dielectric permittivities ε11 and ε33, as well as the out-of-plane piezoelectric coefficients d33 for the PZT thin films, are computed as a function of misfit strain, taking into account substrate-induced clamping. The model reveals that previously predicted ultrahigh piezoelectric coefficients due to misfit-strain-induced phase transitions are practically achievable only in an extremely narrow range of film thickness, composition and misfit strain parameter space. We also show that the dielectric and piezoelectric properties of epitaxial ferroelectric films can be tailored through strain engineering and microstructural optimization.

[3] A more accurate two-dimensional grain growth algorithm

E A Lazar et al

We describe a method for evolving two-dimensional polycrystalline microstructures via mean curvature flow that satisfies the von Neumann–Mullins relation with an absolute error O(Δt2). This is a significant improvement over a different method currently used that has an absolute error O(Δt). We describe the implementation of this method and show that while both approaches lead to indistinguishable evolution when the spatial discretization is very fine, the differences can be substantial when the discretization is left unrefined. We demonstrate that this new front-tracking approach can be pushed to the limit in which the only mesh nodes are those coincident with triple junctions. This reduces the method to a vertex model that is consistent with the exact kinetic law for grain growth. We briefly discuss an extension of the method to higher spatial dimensions.

[4] Point defects in multicomponent ordered alloys: Methodological issues and working equations

R Besson

The aim of this work is to give the independent-point-defect thermodynamics of ordered compounds a sufficiently general flavour, adapted to and working for multicomponent alloys. Generalizing previous approaches, we first show that an appropriate description for a crystal with point defects allows treatment of the practically important pressure and defect volume parameters in the grand canonical framework, the equivalence of which is explicited with the closer to experiments isothermal–isobaric conditions. Since industrial applications often involve multialloyed compounds, we then derive an operational tool for atomic-scale investigations of long-range order alloys with complex crystallographies and multiple additions.

[5] Misorientation texture development during grain growth. Part II: Theory

J Gruber et al

A critical event model for the evolution of number- and area-weighted misorientation distribution functions (MDFs) during grain growth is proposed. Predictions from the model are compared to number- and area-weighted MDFs measured in Monte Carlo simulations with anisotropic interfacial properties and several initial orientation distributions, as well as a dense polycrystalline magnesia sample. The steady-state equation of our model appears to be a good fit to all data. The relation between the grain boundary energy and the normalized average boundary area is discussed in the context of triple junction dynamics.

[6] Spatial correlations in symmetric and asymmetric bicontinuous structures

A L Genau and P W Voorhees

Spatial correlations of interfacial curvature are compared for symmetric and asymmetric two-phase mixtures produced following spinodal decomposition as given by a numerical solution to the Cahn–Hilliard equation in three dimensions. By calculating radial distribution functions of the density of interfacial area as a function of the mean interfacial curvature of these bicontinuous microstructures, it is found that long-range diffusive interactions, in combination with the morphology of the system, yield a variety of correlations and anticorrelations over a range of length scales. The asymmetric mixtures show some similarities to the symmetric mixtures, as well as other unique features.