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Gd-doped Ceria (GDC) barrier layers are widely used in solid oxide electrolysis cells to prevent reactions between the Y-stabilized Zirconia (YSZ) electrolyte and oxygen electrode. In some cases, electrolysis operation causes fracture near the GDC/YSZ interface. Here, we explain this effect using a numerical calculation, showing that a peak oxygen pressure is observed near the GDC/YSZ interface during electrolysis operation. Moreover, GDC/YSZ interdiffusion and possible zirconate phase formation occurring during electrode firing yield a low oxygen ion conductivity region that introduces a much higher peak oxygen partial pressure at the interdiffusion layer/YSZ interface, thereby exacerbating degradation. The results indicate that the peak pressure can be reduced and, thereby, damage can be mitigated by altering processing in order to minimize interdiffusion, decreasing the GDC layer thickness, and reducing oxygen electrode polarization resistance or altering electrolyte transport properties, e.g., changing the Gd doping level of GDC to increase the oxygen vacancy diffusivity.

This paper investigates effects of surface stress and wetting layers on the morphological instability of a growing epitaxially strained dislocation-free solid film. Linear stability analysis of the planar film shows that the film, unstable due to lattice mismatch, is affected differently by surface stress for a film under compression than for one under tension and depends on whether the relative stiffness of the film to the substrate is less than or greater than (1−2ν)−1; here ν is Poisson’s ratio. The presence of a wetting layer has the capacity to substantially stabilize the planar film. The critical thickness of the film below which the film is stable depends on the bulk elastic properties of film and substrate and increases with increase of the wetting potential.

Holes formed in a solid film during annealing can grow and lead to the formation of many isolated islands. The morphological evolution of holes is thus of primary importance in the production of planar films. This work studies the linear instability of a stationary axisymmetric hole in a film with zero surface mean curvature. At the hole, the film forms a contact angle α with the substrate at a circular contact line of radius a0. The film is bounded by an outer wall at a distance a0L from the center. An infinitesimal disturbance in the form of a normal mode is applied and its stability analyzed for 0⩽α⩽180° and 1⩽L

The linear morphological instability of a line of film on a substrate has been examined for contact angles between 0 and π. The base state of the line is an infinitely long cylinder with cross‐sectional shape a segment of a circle. We assume that mass flows by diffusion along the film surface and that local equilibrium holds. We find that for non‐zero contact angles there is a finite range of perturbation wavenumbers in the axial direction which correspond to instability and will potentially lead to agglomeration of the line of film. All unstable perturbations are of the varicose (sausage) type. The presence of the substrate is stabilizing; the range of unstable wavelengths is always less than that of a freely‐suspended circular cylinder with the same volume and decreases to zero width at zero contact angle. The maximum growth rate of the instability varies strongly with the contact angle and approaches zero as the contact angle approaches zero. Our results agree qualitatively with the experimentally observed wavelength and growth rates of the instability.

Nanocrystal formation on patterned substrates during heteroepitaxy is studied. Deposition on a substrate with a mesa induces a qualitatively new morphological instability that is driven solely by capillarity. If the film possesses a lattice parameter misfit with the substrate, this instability then propagates as a traveling wave along the substrate. This traveling wave yields large regions of highly ordered nanocrystals. Strongly anisotropic surface energy greatly increases the growth rate of the instability of a planar film and, thus, decreases the distance over which the traveling wave propagates. Even in this case, however, deposition on a substrate with a periodic arrangement of mesas can yield highly ordered arrays of nanocrystals.

The morphological instability of a growing epitaxially strained dislocation-free solid film is analyzed. An evolution equation for the film surface is derived in the dilute limit of vacancies based on surface diffusion driven by a stress-dependent chemical potential. From the time-dependent linear stability problem the conditions for which a growing film is unstable are determined. It is found that the instability is driven by the lattice mismatch between the film and the substrate; however, low temperatures as well as elastically stiff substrates are stabilizing influences. The results also reveal that the critical film thickness for instability depends on the growth rate of the film itself. Detailed comparison with experimental observations indicates that the instability described exhibits many of the observed features of the onset of the 'island instability'.

We analyze the development of compositional and surface nonuniformities during the growth of strained alloy films, for the case of different surface mobilities of the alloy components. We find that a difference in surface mobilities can completely suppress the stress-driven morphological instability. The stabilization occurs under compressive misfit when one atomic species is both large and fast relative to the other, and similarly under tensile misfit when one species is small and fast.

The Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation is widely used to describe phase transformation kinetics. This description, however, is not valid in finite size domains, in particular, thin films. A new computational model incorporating the level-set method is employed to study phase evolution in thin film systems. For both homogeneous (bulk) and heterogeneous (surface) nucleation, nucleation density and film thickness were systematically adjusted to study finite-thickness effects on the Avrami exponent during the transformation process. Only site-saturated nucleation with isotropic interface-kinetics controlled growth is considered in this paper. We show that the observed Avrami exponent is not constant throughout the phase transformation process in thin films with a value that is not consistent with the dimensionality of the transformation. Finite-thickness effects are shown to result in reduced time-dependent Avrami exponents when bulk nucleation is present, but not necessarily when surface nucleation is present.

It is well known that the morphology of nanowire grown using the Vapor-Liquid-Solid mechanism depends substantially on the stability and configuration of the catalyst droplet. Whereas many of the earlier studies have focused on the conditions under which the liquid droplet remains stable, in the present article, we enquire as to what happens if and when the liquid droplet unpins from the corner. We employ a perturbation approach and arrive at the fact that there is a much larger tendency for the liquid droplet to unpin in an asymmetric manner than in a symmetric manner even in the absence of any underlying geometric asymmetry or anisotropy. The implications of this to a number of experimental observations are discussed.

The Vapor-Liquid-Solid method is one of the most popular techniques for growing semiconducting nanowires, and the stability of the liquid droplet is an important factor controlling wire morphology and, ultimately, functionality. Earlier theoretical work on axisymmetric systems indicates that the lowest-energy liquid configuration varies with surface energies, wire radius, and fluid volume. We test these predictions with a fully dynamic phase-field model that incorporates viscous fluid flow. Under conditions predicted by this earlier theoretical work, we observe the pinning of the liquid to the top face of a nanowire, a condition necessary for wire growth. To study the stability of the droplet, we apply perturbations to the liquid shape and find that the system can transition to a metastable configuration, a local minimum in the energy landscape. Furthermore, the transition pathway to this local minimum depends on the magnitude of the perturbations. Under conditions that favor a liquid on the sidewalls of ...

We report real-time high temperature scanning electron microscopy observations of the growth of bismuth nanowires via the on-film formation of nanowires (OFF-ON) method. These observations provide experimental evidence that thermally induced-stress on a Bi film is the driving force for the growth of Bi nanowires with high aspect ratios, uniform diameter, and high-quality crystallinity. Our results show that immobile grain boundaries in the Bi film are required for the growth of nanowires so that grain broadening resulting in hillock formation can be prevented. This study not only provides an understanding of the underlying mechanism, but also affords a strategy for facilitating nanowire growth by OFF-ON.

The requirements for steady nanowire growth under near-equilibrium conditions in the vapor-liquid-solid (VLS) method is examined with particular emphasis on the configuration of the liquid droplet. It is found that the final radius of a cylindrical wire is selected by the fixed volume of liquid VL and the surface-energy ratio γsl/γlv but is independent of the solid-vapor energy γsv. Existing models for growth, based on a balance of configurational forces at the triple junction, are shown to be consistent with the principle of maximal release of free energy. Gibbs’s results on allowable contact angles at a sharp corner predict conditions on γsl/γlv and γsv/γlv for the existence of straight-wire growth. For parameter values that violate these conditions the droplet atop the wire is expected to unpin. A range of alternative configurations for the liquid exist and their relative energies are compared. In particular, it is found that for a certain region in parameter space—not extraordinary in VLS growth—a sph...

Nanoporous gold has numerous potential applications 1 in optical-active materials, catalysts, sensors, mechanical actuators, fuel cell and microbalance electrodes, and as a coating for medical devices. Nanoporous gold is fabricated by dealloying silver-gold solid solutions. This results in fully openporosity bicontinuous nanoporous structures, following the rearrangement of the gold atoms into interconnected ligaments as the silver atoms are selectively removed. 2 Optimization of the optical, chemical, and mechanical properties of nanoporous gold depends on its pore size, which is tunable by structural coarsening during annealing. 3 Various electronbased techniques have been employed to determine the morphology of nanoporous gold films after dealloying, but none are suited to three-dimensional 3D study of thick specimens of coarsened nanoporous gold. Tomographic transmission electron microscopy provides very high spatial resolution but is limited to examining thin films, and cannot image coarsened structures once the gold ligament size is close to the electron penetration depth. 4,5 Focused ion beam FIB-scanning electron microscopy serial sectioning 6 combines high resolution with depth penetration, however, being a destructive method, it cannot be used to observe dynamic processes and structural evolution in 3D. X-ray microcomputed tomography is a powerful nondestructive tomographic tool whose resolution is however typically limited to the micron scale. 7 Transmission x-ray microscopy TXM using synchrotron x-ray sources offers 30 nm resolution, fast image acquisition, and the ability to nondestructively image samples tens of microns thick. Combining TXM with tomographic methods allows complex nanostructures to be imaged in 3D. 8 Here, we perform x-ray nanotomography on a dealloyed and coarsened nanoporous gold wire. We quantitatively analyze the morphological and topological properties of nanoporous gold from the reconstructed images using methods developed in earlier work. 9

Step bunching at a growing crystal surface is usually attributed to the presence of the Ehrlich–Schwoebel (ES) effect caused by the asymmetry of the attachment kinetics at a step. Here, we show that, contrary to the case of rectilinear motion, step bunches at the solid-liquid interface of a nanowire grown by the vapor-liquid-solid process can form even in the absence of the ES effect. It is found that two circular steps propagating from the edge of the nanowire inward form a bunch if the initial distance between the steps is less than a critical value. This effect is caused by the interaction of steps with each other via the diffusion field in the bulk of the liquid catalytic particle. The normal ES effect promotes the bunching, while the anomalous ES effect delays it.

We investigate the morphological instability of ferromagnetic planar thin films using linear perturbation theory. We find that, for a uniformly magnetized ferromagnetic planar film with a nonzero component of the magnetization along the normal to the planar film, the planar surface is unstable with respect to perturbations having a wave number smaller than a critical value. In addition, the critical wave number changes with the direction of the surface perturbations, with the perturbations perpendicular to the in-plane component of the magnetization having the largest critical wave number. Such anisotropy could be important in controlling the evolution of the morphology of the film and nanoscale-island formation.

The ability to dope semiconductor nanowires during growth is an important step toward making functional devices. We develop a model for steady state vapor-liquid-solid growth of a ternary semiconductor-catalyst-dopant nanowire. Our analysis shows that the relative flux of dopant atoms through the liquid controls the mole fraction of dopant in the solid wire, and that local equilibrium constrains the catalyst composition in the solid and the compositions of the dopant and catalyst in the liquid. We find that the phase diagram can be used to determine an upper limit on the dopant composition in the solid.

Consider the growth of a nanowire by a step-flow mechanism in the course of vapor-liquid-solid and vapor-solid-solid processes. The growth is initiated by the nucleation of a circular step at the nanowire-catalyst interface near the edge of the nanowire (the triple junction) and proceeds by the propagation toward the center by the Burton–Cabrera–Frank mechanism. Two cases are considered: (i) bulk transport, where the interfacial diffusion of adatoms and the step motion are coupled to the diffusion flux of atoms from the bulk of the catalyst particle, and (ii) surface transport, where atoms from the vapor phase are adsorbed at the surface of the catalyst particle and diffuse along the surface toward the triple line, whence they diffuse to the nanowire-catalyst interface. The attachment kinetics of adatoms at the step, the adsorption kinetics of atoms from the bulk phase, the exchange kinetics at the triple contact line, and the capillarity of the step are taken into account. In case (i) the problem is redu...

Understanding the dynamics of the growth of nanowires by the vapor-liquid-solid (VLS) process is essential in order to relate the properties of the wire to their processing conditions. A theory for VLS growth is developed that incorporates the surface energy of the solid-liquid, liquid-vapor, and solid-vapor interfaces, allows for supersaturation of growth material in the droplet, and employs contact-line conditions. We predict the profile of catalyst concentration in the droplet, the degree of supersaturation, and the modification to the shape of the solid-liquid interface due to growth, as functions of the material properties and process parameters. Under typical experimental conditions the interface deflection due to growth is predicted to be practically zero. We also find that the growth rate of the wire inherits the same dependence on diameter as the flux of growth material at the liquid-vapor interface; thus, if we assume that the flux is independent of radius, we obtain a growth rate that is also independent of radius. To make a prediction about the actual variation with diameter requires a detailed knowledge of the decomposition kinetics at the liquid-vapor interface.

We model the effect of substrate strain patterning on the self-assembly of quantum dots (QDs). When the surface energy is isotropic, we demonstrate that strain patterning via embedded substrate inclusions may result in ordered, self-organized QD arrays. However, for systems with strong cubic surface energy anisotropy, the same patterning does not readily lead to an ordered array of pyramids at long times. We conclude that the form of the surface energy anisotropy strongly influences the manner in which QDs self-assemble into regular arrays.

The elastic interaction energy between several rectangular parallelepipeds and the elastic self‐energy of a cuboid are calculated to first order in the difference in elastic constants between the precipitate and matrix. The system is assumed to be elastically isotropic, the precipitates are coherent with the matrix and possess a dilatational misfit. The functionality and magnitude of the interaction energy per precipitate are extremely sensitive to the precipitate morphology and number of precipitates considered. The interaction energy between three or more precipitates cannot be accurately estimated by summing the pairwise interactions. The influence of the interaction energy on the stability of precipitate arrays is discussed.

A continuum thermodynamic treatment of the local equilibrium concentration at a two‐phase interface during a first‐order diffusional phase transition in crystalline solids is presented. It is assumed that the second‐phase domain has a spherical morphology, is coherent with the matrix, and possesses different elastic constants than the matrix. It is shown that the equilibrium concentration at the solid–solid interface is strongly coupled to the stress states of the matrix, precipitate, and interface as well as the interfacial curvature. This coupling gives rise to many new phenomena, such as the dependence of the equilibrium interfacial concentrations on the magnitude of the supersaturation in the parent phase, the misfit between the precipitate and matrix and the difference in the partial molar volumes of the diffusing species. Capillarity is also strongly influenced by the crystallinity through the surface stress and deformation, supersaturation of the parent phase, and the degree of elastic inhomogeneit...

A Gibbsian thermodynamic description of a simple coherent interface in a nonhydrostatically stressed, N component, crystalline solid is developed. Interfacial excess properties are defined in a manner consistent with the thermodynamics of nonhydrostatically stressed crystalline solids. This formalism is then used to describe the relationship between the independent thermodynamic variables and the interfacial energy. A result of the crystalline nature of the solid is that the interfacial energy and the interfacial stress are distinct quantities. This difference, along with the presence of a nonhydrostatic stress, results in fundamentally different forms for the standard interfacial thermodynamic relationships. In particular, we show that the Gibbs adsorption isotherm for a coherent spherical misfitting particle in a matrix contains terms which are related to both interfacial and bulk stresses and that these terms can be dominant in certain cases.