Orientation-dependent Surface Energy Research Articles

Microstructure-dependent etching behavior of a partially recrystallized Invar alloy

Due to their low coefficient of thermal expansion, Invar sheets are used as the material for fine metal masks (FMM). In producing theses masks, the sheets are often chemically etched to produce arrays of micro-holes. Because etching behavior of a material depends not only on the chemical composition of the material, but also on the surface microstructure of the material, an in depth exploration on the role of the surface microstructure of an Invar alloy on the etching behavior of the alloy is fundamental in manufacturing high quality FMMs. In this study, microstructure dependent etching behavior of a partially recrystallized Invar sheet is investigated. The Invar alloy was partially recrystallized at 750℃ to examine how recrystallized and non-crystallized grains differ in their etching behaviors using electron backscatter diffraction (EBSD) and atomic force microscope (AFM) techniques. The results show that the overall etching behavior of the partially recrystallized Invar sheet not only depends on the properties of individual grains such as orientation dependent surface energy and geometrically necessary dislocation (GND) content, but also on the properties of aggregates of grains such as grain boundary density.

Effect of grain orientations on the thermal grain boundary grooving in a three‐dimensional setting

AbstractThe objective of this work is to study the effect of grain orientation on the thermal grooving by surface diffusion. Hackl et al. [1] have presented a finite element model for thermal grooving in three‐dimensions. This variational model involves surface energy, grain boundary energy, external and internal triple line energy. In this study, We use an orientation dependent surface energy. For {1 0 0} grain orientation in the normal direction, we have self‐similar groove profiles for increasing extent of anisotropy of the surface energy. For {1 1 0} and {1 1 1} orientations, there are formation of facets for critical anisotropic cases. These formations are due to so‐called missing orientations concerning the shape of an unconstrained crystal in equilibrium. The rate of grooving varies with change in the extent of surface free energy anisotropy. Flux along the triple line is also important in determining the groove root shape. Triple line energy and its mobility lead to deviate from a typical t1/4 scaling law. For all theses simulations, grain boundary energies are constant, satisfying Herring's relation. Comparisons are made for different values of mobilities for groove shape and its growth rate, using different grain orientations.

Effect of additional solute elements (X= Al, Ca, Y, Ba, Sn, Gd and Zn) on crystallographic anisotropy during the dendritic growth of magnesium alloys

Based on the first-principles calculations and crystallographic anisotropy analysis, the effect of additional solute elements on the dendritic growth behavior of binary Mg-X (X = Al, Ca, Y, Ba, Sn, Gd and Zn) alloys are investigated in terms of the orientation-dependent surface energy. The preferred growth direction of the α-Mg dendrite is found to be dependent on the magnitude of the anisotropic surface energy and the difference of crystallographic anisotropy between the matrix Mg and the additional solute X. The most densely packed crystallographic planes are found to be the energetically favorable planes with the minimum surface energy, as exemplified by the {111} plane of Al with fcc (face-centered cubic) structure, the {110} plane of Ba with bcc (body-centered cubic) structure, and the {0001} plane of Y with hcp (hexagonal-close packed) structure. For all additional solute elements studied, Zn exhibits the maximum anisotropy and the according effect on the growth behavior of the α-Mg dendrite is the most significant, which could also be reflected by the complex growth patterns of the Mg-Zn alloy dendrite observed in experiments. Compared with Zn, the crystallographic anisotropy of the other additional solutes is weaker, and their effect on the α-Mg dendrite growth is not as significant as Zn, which is reflected by their similar eighteen-primary branch dendritic morphology in 3D.

Amphiphile-Induced Phase Transition of Liquid Crystals at Aqueous Interfaces.

Monolayer assemblies of amphiphiles at planar interfaces between thermotropic liquid crystals (LCs) and an aqueous phase can give rise to configurational transitions of the underlying LCs. A common assumption has been that a reconfiguration of the LC phase is caused by an interdigitation of the hydrophobic tails of amphiphiles with the molecules of the LC at the interface. A different mechanism is discovered here, whereby reorientation of the LC systems is shown to occur through lowering of the orientation-dependent surface energy of the LC due to formation of a thin isotropic layer at the aqueous interface. Using a combination of atomistic molecular dynamics simulations and experiments, we demonstrate that a monolayer of specific amphiphiles at an aqueous interface can cause a local nematic-to-isotropic phase transition of the LC by disturbing the antiparallel configuration of the LC molecules. These results provide new insights into the interfacial, molecular-level organization of LCs that can be exploited for rational design of biological sensors and responsive systems.

Correlation between crystallographic anisotropy and dendritic orientation selection of binary magnesium alloys

Both synchrotron X-ray tomography and EBSD characterization revealed that the preferred growth directions of magnesium alloy dendrite change as the type and amount of solute elements. Such growth behavior was further investigated by evaluating the orientation-dependent surface energy and the subsequent crystallographic anisotropy via ab-initio calculations based on density functional theory and hcp lattice structure. It was found that for most binary magnesium alloys, the preferred growth direction of the α-Mg dendrite in the basal plane is always langle 11bar{2}0rangle , and independent on either the type or concentration of the additional elements. In non-basal planes, however, the preferred growth direction is highly dependent on the solute concentration. In particular, for Mg-Al alloys, this direction changes from langle 11bar{2}3rangle to langle 22bar{4}5rangle as the Al-concentration increased, and for Mg-Zn alloys, this direction changes from langle 11bar{2}3rangle to langle 22bar{4}5rangle or langle 11bar{2}2rangle as the Zn-content varied. Our results provide a better understanding on the dendritic orientation selection and morphology transition of magnesium alloys at the atomic level.

Effects of surface energy anisotropy on void evolution during irradiation: A phase-field model

A phase-field model is employed to investigate the effects of surface energy anisotropy on void evolution during irradiation. By incorporating a simple orientation dependent surface energy with sharp cusps on given crystallographic orientations, experimentally observed void shape with facets and rounded corners is captured. When applied to polycrystalline materials, grain dependent void morphologies are predicted, and the simulation results are qualitatively similar to reported void morphologies in irradiated copper. In addition, the formation of void denuded zones and vacancy depleted zones adjacent to the grain boundaries (GBs) in bicrystalline and polycrystalline structures are studied.

Equilibrium Crystal Shape of Ni from First Principles

We have determined the equilibrium crystal shape of Ni at 0 K using Wulff construction based on 36 orientation-dependent surface energies, which are calculated from first principles. The (111), (100), (110), (210), (221), (311), and (322) surfaces are found in the predicted equilibrium shape based on DFT data, whereas the commonly used broken-bond model predicts that only (111) and (100) surfaces are present. This significant difference of equilibrium shape can be ascribed to the fact that the calculated surface energies show an orientation-dependent deviation from that predicted by the broken-bond model. Moreover, the (111), (100), (110), and (210) surfaces observed in available experiments have also been identified in the present calculations. This indicates that the broken-bond model is insufficient for obtaining the accurate surface energies and their anisotropy of real systems, and the high Miller index surfaces have to be considered to predict the reliable equilibrium shape of the metal.

A Phase Field Model for grain Growth and Thermal Grooving in Thin Films with Orientation Dependent Surface Energy

A phase field model for simulating grain growth and thermal grooving in thin films is presented. Orientation dependence of the surface free energy and misorientation dependence of the grain boundary free energy are included in the model. Moreover, the model can treat different mechanisms for groove formation, namely through volume diffusion, surface diffusion, evaporation-condensation, or a combination of these mechanisms. The evolution of a groove between two grains has been simulated for different surface and grain boundary energies and different groove formation mechanisms.

The three-dimensional equilibrium crystal shape of Pb: Recent results of theory and experiment

The three-dimensional equilibrium crystal shape (ECS) is constructed from a set of 35 orientation-dependent surface energies of fcc Pb which are calculated by density functional theory in the local-density approximation and distributed over the [110] and [001] zones of the stereographic triangle. Surface relaxation has a pronounced influence on the equilibrium shape. The (111), (100), (110), (211), (221), (411), (665), (15,1,1), (410) and (320) facets are present after relaxation of all considered surfaces, while only the low-index facets (111), (100) and (110) exist for the unrelaxed ECS. The result for the relaxed Pb crystal state is in support of the experimental ECS of Pb at 320–350 K. On the other hand, approximating the surface energies of vicinal surfaces by assuming a linear relationship between the Pb(111) first-principles surface energy and the number of broken bonds of surface atoms leads to a trivial ECS that shows only (111) and (100) facets, with a sixfold symmetric (111) facet instead of the correct threefold symmetry. It is concluded that the broken bond rule in this simple linear form is not a suitable approximation for obtaining the proper three-dimensional ECS and correct step formation energies.

Orientation-dependent surface and step energies of Pb from first principles

The orientation-dependent surface energies of 35 low-index and vicinal Pb surface orientations, located in the [001], $[\overline{1}10]$, and $[01\overline{1}]$ zones, have been calculated by density-functional theory within the local-density approximation. The highest surface energy anisotropies in these zones are at the (210), (110), and (311) directions. Surface relaxation decreases the surface energy anisotropy significantly. For misorientations smaller than 12\ifmmode^\circ\else\textdegree\fi{} the (projected) surface energy in a given zone increases linearly with step density, while curvature is found at higher misorientations, indicative of repulsive step-step interactions. These results are fully consistent with the orientation-dependent surface energy predicted by the statistical mechanics of the terrace-step-kink model of vicinal surfaces. The step formation energies and surface and step relaxation energies are derived and analyzed. There is good agreement with available experimental data. The calculated surface energies in eV/atom correlate linearly with the number of broken surface bonds. Deviations from perfect linearity are found to be essential for a proper description of the equilibrium crystal shape of Pb.

The stability of vicinal surfaces and the equilibrium crystal shape of Pb by first principles theory

The orientation-dependent surface energies of fcc Pb for more than 30 vicinal orientations, distributed over the [110] and [001] zones of the stereographic triangle, have been studied by density-functional theory. For bulk-truncated structures almost all vicinal surfaces are found to be unstable and would facet into (111) and (100) orientations. However, after surface relaxation, all vicinal surfaces are stable relative to faceting into (111) and (100) orientations. There are also regions of relaxed vicinal surfaces which will facet into nearby stable vicinal surfaces. Overall, surface relaxation significantly affects the equilibrium crystal shape (ECS) of Pb. In both the [110] and [001] crystallographic zones the (110), (112), (221), and (023) facets are found on the ECS only after relaxation, in addition to (111) and (100). This result is in agreement with the experimental ECS of Pb at 353 K. Step formation energies for various vicinal orientations are estimated from facet diameters of the theoretical ECS and compared with experimental data.

A variational approach to nonlinear dynamics of nanoscale surface modulations

In this paper, we propose a variational formulation to study the singular evolution equations that govern the dynamics of surface modulations on crystals below the roughening temperature. The basic idea of the formulation is to expand the surface shape in terms of a complete set of basis functions and to use a variational principle equivalent to the continuum evolution equations to obtain coupled nonlinear ordinary differential equations for the expansion coefficients. Unlike several earlier approaches that rely on ad hoc regularization procedures to handle the singularities in the evolution equations, the only inputs required in the present approach are the orientation dependent surface energies and the diffusion constants. The method is applied to study the morphological equilibration of patterned unidirectional and bidirectional sinusoidal modulations through surface diffusion. In the case of bidirectional modulations, particular attention is given to the analysis of the profile decay as a function of ratio of the modulating wavelengths in the coordinate directions. A key question that we resolve is whether the one-dimensional decay behavior is recovered as one of the modulating wavelengths of the two-dimensional profiles diverges, or whether one-dimensional decay has qualitatively distinct features that cannot be described as a limiting case of the two-dimensional behavior. In contrast to some earlier suggestions, our analytical and numerical studies clearly show that the former situation is true; we find that the one-dimensional profiles, like the highly elongated two-dimensional profiles, decay with formation of facets. While our results for the morphological equilibration of symmetric one-dimensional profiles are in agreement with the free-boundary formulation of Spohn, the present approach can also be used to study the evolution of asymmetric profile shapes where the free-boundary approach is difficult to apply. The variational method is also used to analyze the decay of unidirectional modulations in the presence of steps that arise in most experimental studies due to a small misorientation from the singular surface.

A model for thin film texture evolution driven by surface energy effects

AbstractA model was developed in order to calculate the texture evolution of a growing film with large atomic diffusion on the surface. The tendency for lowest surface energy was taken as the driving force for the evolution. The orientation dependent surface energy y was approximated by a function with a sharp minimum in two crystallographic directions. The texture evolution was calculated, starting from various initial situations. With realistic assumptions it was found that a texture without preferential orientations evolved to a bimodal texture, and finally to a situation with only lowest y planes parallel to the substrate. For some initial situations a texture turn over from one crystallographic direction to another one can be expected. In all cases a sharpening of the angular distribution of the texture is found near the directions of a local minimum for y. For sufficiently large times the mean top diameter of the columns always increases with layer thickness. The calculated effects describe well a number of experimentally observed phenomena.

The dynamical behavior of periodic surface profiles on metals under the influence of anisotropic surface energy

The kinetics of shaping of periodic surface profiles under the action of surface selfdiffusion were calculated for the special case of anisotropic surface energy. The orientation-dependent surface energy was allowed to contain a local minimum of very high curvature (cusp). The orientation of this cusp was equal to the macroscopic orientation of the crystal surface. The periodic surface profiles exhibited in all cases extended, nearly flat regions centered at the cusp orientation. This type of faceting which causes the profile to be trapezoidal in shape agrees well with experimentally observed profiles on (111) and (100) Ni single crystal surfaces. A procedure is outlined by which the orientation-dependent surface energy along a certain azimuth and the surface self-diffusion coefficient can be extracted from the decay kinetics of faceted periodic surface profiles. This procedure demands the accurate experimental assessment of profile shapes and amplitudes.

Periodic surface profiles under the influence of anisotropic surface energy: A steady-state solution

The steady-state shape of surface profiles under the influence of anisotropic surface energy was calculated. All shape changes were assumed to occur by surface self-diffusion at elevated temperature. The orientation-dependent surface energy γ(θ) was allowed to contain a local minimum of very high curvature (cusp). The orientation of this cusp was equal to the macroscopic-orientation of a single crystal surface. No assumptions were made about the shape of the original profile. Only boundary conditions concerning the amplitude of the profile and several derivatives entered the calculation for the integration of the differential equations. The resulting profiles showed nearly flat regions centered at the cusp orientation. These results agree well with experiments and with previously published profile shapes which had been calculated dynamically. A big advantage of the steady-state calculation were short computing times, even in the case of very high curvature in γ(θ). Hence it could be shown that the profile shape converged towards a limit with increasing curvature of γ(θ). The anisotropy of γ(θ) can be evaluated from experimental shape data of faceted profiles.