Facet Nucleation Research Articles

Lengthscale-dependent, elastically anisotropic, physically-based hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys

A crystal plasticity model for hcp materials is presented which is based on dislocation glide and pinning. Slip is assumed to occur on basal and prismatic systems, and dislocation pinning through the generation of geometrically necessary dislocations (GNDs). Elastic anisotropy and, through the coupling of GNDs with slip rate, physically-based lengthscale effects are included. A model polycrystal representative of the alloy Ti–6Al, which shows creep and strain rate effects at 20 °C, is developed and it is shown that the primary effect of elastic anisotropy during subsequent plastic flow is to increase local, grain-level, accumulated slip. Lengthscale effects, however, are shown to lead to quite considerable increases in grain-boundary stresses, and to the re-distribution of accumulated slip local to grain boundaries. In particular, an initially highly non-uniform slip distribution tends to be made more uniform through the hardening effect of sessile GNDs at grain boundaries. The concept of a rogue grain combination is presented; that is, a ‘primary’ grain with c-axis orientation at or near parallel to macro-level loading, together with adjacent grains with a prismatic plane orientated at about 70° to the normal to the load direction. This particular combination of orientations leads to the highest stresses normal to the primary basal, together with high levels of accumulated slip in adjacent grains. The presence of a rogue grain combination in cycles both with and without cold dwell is examined. The cycle with cold dwell is shown to be the more damaging, and a possible criterion for facet nucleation in Ti-alloys is introduced.

Nanoisland shape relaxation mechanism

The shape relaxation of supported crystallites is studied by means of kinetic Monte Carlo simulations, initialising the system with different configurations. At low temperature, when the facet nucleation limits the relaxation, the simulations show that the equilibration mechanism and the equilibration time scaling laws depend strongly on the initialisation. In this regime, the adhesion strongly increases the stability of intermediate configurations with large contact area. The relationship between the different equilibration pathways and the equilibration scaling laws is discussed considering the dependence of the nucleation barrier energy G ∗ on the particle energetics in the regions with the largest kinks and steps density.

Modeling and visualization of polycrystalline thin film growth

A novel polycrystalline thin film growth simulator, FACET, has been developed. FACET is a multi-scale model with two major components: an atomic level one-dimensional kinetic lattice Monte Carlo (1D KLMC) model and a real time feature scale two-dimensional facet nucleation and growth model. The 1D KLMC model has been developed to calculate inter-facet diffusion rates. By inputting the diffusion activation energies, the model will calculate the inter-facet atomic flux between {1 0 0}, {1 1 0}, and {1 1 1} facets of FCC materials at any temperature. The results of the 1D KLMC model have been verified by comparison with a full three-dimensional kinetic lattice Monte Carlo (3D KLMC) model. The feature scale polycrystalline thin film nucleation and growth model is based on describing grains in terms of two-dimensional faceted surfaces and grain boundaries. The profile of the nuclei are described by crystallographically appropriate facets. The position and orientation of the nuclei can be randomly selected or preferred textures can be created. Growth rates are determined from different deposition fluxes and surface diffusion effects. Quantitative microstructural characterization tools, including roughness analysis, average grain size analysis, and orientation distribution analysis, were incorporated into the model, which allows the users to design, conduct and analyze the virtual experiments within one integrated graphical user interface. Users can also visualize the nucleation and growth process of the film and obtain the final film microstructure. The effects of thickness, temperature, and deposition flux on thin film microstructures have been studied by FACET.

Effects of Facet Growth and Nucleation on Microcrystalline Silicon by Numerical Model

ABSTRACTWe have presented a model of microcrystalline silicon (μc-Si) growth based on the Van der Drift model. The model needs growth velocities of the facets (100) and (111), an amorphous silicon growth velocity and a grain nucleation rate. The growth velocity ratio of the facets, (100) and (111), determines the preferred orientation and the morphology of the μc-Si film, especially oriented to (110). As the grain nucleation rate increases, the ratio of the living grain number to the total grain number decreases and the crystallinity increases, so the grain nucleation rate governs the trade-off relation of the μc-Si cells between decreasing the open circuit voltage and increasing the short circuit current as the crystallinity increases.

On the effects of elastic stress on the motion of fully faceted interfaces

In this paper we develop conditions that govern the evolution of a fully faceted interface separating elastic phases. To focus attention on the effects of elastic stress, we restrict attention to interface-controlled kinetics, neglecting bulk transport; and to avoid geometric complications, we limit our discussion to two space-dimensions. We consider a theory in which the orientations present on the evolving particle are not necessarily those given by the Wulff shape: we allow for metastable crystallographic orientations as well as stable orientations. We find that elastic stress affects the velocity of a facet through the average value of the normal component of the jump in configurational stress (Eshelby stress) over the facet. Within our theory singularities in stress induced by the presence of corners do not influence the velocity of the facet. We discuss the nucleation of facets from corners; the resulting nucleation condition is shown to be independent of elastic stress. We also develop equations governing the equilibrium shape of a faceted particle in the presence of elastic stress.

Mechanisms of surface faceting and coarsening

The progression of surface faceting on ceramic substrates is explored using the {101̄0} and (0001) surfaces of Al 2O 3 (α-Al 2O 3, corundum structure) as model systems. Atomic-force microscopy and electron microscopy techniques are used to monitor the progression of faceting as a function of annealing time. Whether the surface facets into a hill-and-valley structure, such as the {101̄0} surface, or into a terrace-and-step structure, such as the (0001) surface, faceting starts with the nucleation and growth of individual facets. The growth of individual facets is found to promote the nucleation of adjacent facets, and thus leads to the formation of facet domains. As domains that are out of phase with each other coalesce regions with a high density of facet junctions are formed. Facet junctions, points where two facets merge to form one, are found to have an important role in facet coarsening. The mechanism for the coarsening of the completely faceted surface involves the motion and elimination of facet junctions. Both the facet wavelength and density of facet junctions are monitored as a function of annealing time for the {101̄0} and (0001) Al 2O 3 surfaces.

Self-Organized Growth of II-VI Wide Bandgap Quantum Dot Structures

We present our recent investigations on the self-organized growth and optical properties of quantum structures including CdSe quantum dots (QDs) embedded in ZnSe, ZnSe QDs in ZnS, and ZnO quantum pyramids. The self-organized mechanism is shown to play an important role in the formation of CdSe QDs on ZnSe(111). The ZnSe QDs are found to form on a 1 ML thick ZnSe wetting layer embedded in ZnS(100). The self-organized ZnO quantum pyramids form on ZnO(0001) buffer layers through preferred facet nucleation rather than strain-induced islanding.

Two-dimensional facet nucleation and growth on Si(111)

The lateral growth of an isolated nucleated facet is studied using a simple two-dimensional step model. An effective Hamiltonian that causes a planar surface to phase separate into facets and step bunches is proposed. The motions of the steps are determined by the relaxational dynamics of the effective Hamiltonian with and without a local conservation requirement. An even simpler mean-field-like model is used to illustrate the mechanism of the experimentally observed constant-velocity facet tip propagation. Numerical calculations using thermodynamic and transport coefficients previously measured give good agreement with experiments under the local conservation requirement.

On the faceting of ceramic surfaces

A model is proposed by which ceramic surfaces change from flat vicinal surfaces into those of a faceted hill-and-valley structure. This model is based on scanning electron microscopy, transmission electron microscopy and atomic-force microscopy observations of facet formation on annealed ( 10 10 ) α-alumina surfaces. The progression of surface faceting starts with the nucleation and growth of an individual facet. The growth of this facet creates local surface disturbances that promote the nucleation of adjacent facets; thus, domains of faceted surface form on the otherwise smooth surface. Through time, these domains coalesce and the facets coarsen into the final hill-and-valley morphology.

Real-space observation of (111) facet formation on vicinal Si(111) surfaces.

We report real-space observations of nucleation of (111) facets with 7\ifmmode\times\else\texttimes\fi{}7 structures on a vicinal Si(111) surface using ultrahigh-vacuum scanning electron microscopy. As reported previously by Phaneuf et al., who used low-energy electron microscopy [Phys. Rev. Lett. 67, 2986 (1991)], (111) facets grow in very anisotropic shapes and are much longer along steps than normal to steps. In addition, we show that (1) the facet width is dependent on the heating current direction and (2) the facets tend to nucleate adjacent to one another. The second result is explained by the fact that stepped regions near the facets are not uniformly inclined but undulated. The local inclination is directly observed using ex situ atomic force microscopy and is in good agreement with calculated results accounting for step-motion kinetics. Additionally, we link the disappearance of the (111) facets to As adsorption.

On the Roughening of Ceramic Surfaces

ABSTRACTThe faceting of single-crystal ceramic surfaces has been investigated by atomic force microscopy, scanning electron microscopy and transmission electron microscopy. Single-crystals of α-Al2O3 (alumina) with different nominal surface orientations were annealed and used as a model system to investigate the faceting of a polished ceramic surfaces. The {1010} orientation of α-alumina, which facets into a hill-and-valley morphology, provides a dramatic representation of the different stages by which a surface facets. This surface starts faceting with the growth of an individual facet. The growth of this facet creates local surface disturbances that promote the nucleation of adjacent facets; thus, domains of faceted surface form on the otherwise smooth surface. Through time, these domains coalesce and the facets coarsen into a hill-and-valley morphology. Surfaces which facet into a terrace-and-step structure, such as (0001) and {1120} surfaces of alumina, are characterized for their progression of surface faceting and are compared with the stages of faceting observed for the {1010} surface.

Crossover from metastable to unstable facet growth on Si(111).

Vicinal Si(111) surfaces misoriented towards the [2\ifmmode\bar\else\textasciimacron\fi{}11] direction facet reversibly upon cooling through the (1\ifmmode\times\else\texttimes\fi{}1) to (7\ifmmode\times\else\texttimes\fi{}7) reconstructive phase transition. We have used low-energy electron microscopy to examine the kinetics of this phase separation. Nucleation and growth of facets occur when the surfaces are quenched just below the phase boundary. However, at lower temperatures we find evidence for the existence of a spinodal which divides the faceting kinetics into unstable and metastable regions. The location of the spinodal is consistent with previous measurements of Si(111) step energetics.

Kinetics of faceting of crystals in growth, etching, and equilibrium.

The faceting of crystals in equilibrium with the gas phase and also during crystal growth and etching conditions is studied using the Monte Carlo method. The dynamics of the transformation of unstable crystallographic orientations into hill and valley structures and the spatial patterns that develop are examined as functions of surface temperature, crystallographic orientation, and strength of interatomic potential for two transport processes: adsorption-desorption and surface diffusion. The results are compared with the continuum theory for facet formation. Thermodynamically unstable orientations break into hill and valley structures, and faceting exhibits three time regimes: disordering, facet nucleation, and coarsening of small facets to large facets. Faceting is accelerated as temperature increases, but thermal roughening can occur at high temperatures. Surface diffusion is the dominant mechanism at short times and small facets but adsorption-desorption becomes important at long times and large facets. Growth and etching promote faceting for conditions close to equilibrium but induce kinetic roughening for conditions far from equilibrium. Simultaneous irreversible growth and etching conditions with fast surface diffusion result in enhanced faceting.

On Microfaceting Instability of Pt(110) Under Catalytic Oxidation of Adsorbed Co

ABSTRACTAs demonstrated by recent STM [1] and LEED [2] experiments the platinum (110) surface undergoes, at carbon monoxide submonolayer coverages, a phase transition from the 1 x 2 “missing-row” (reconstructed) state to the 1 x 1(bulk-like) state under specific temperature and partial-pressure conditions. The catalytic oxidation reaction CO + 1/2 → CO2 drives a microfaceting instability [3] [4] of the Pt(110) surface which ends up in a regular sawtooth profile with a period ≈ 200 Å, along the [110] direction.We introduce the idea that the rather extensive Pt mass transport, as involved in the process, could be energetically assisted by the reaction itself. Energy and momentum-balance considerations lead us to expect an energy ≲ 0.5 eV to be transferrable to thesubstrate. This should efficiently contribute to initiating the “scraping”process that leads to the microfaceted pattern.A simple model for nucleation and growth of facets is presented (see ref. 5), yielding characteristic times of order minutes (at T = 500 K), in fair agreement with experiment.Independently of the structural/catalytic problem, adsorption of CO at submonolayer coverages on, e.g., Pt(110) might be of interest from a surfactantphysics point of view (see ref. 6 for a very recent study on layer-by-layer homoepitaxial metal growth).

The Role of Surface Stress in the Faceting of Stepped Si(111) Surfaces

ABSTRACTThe nucleation and growth of facets on stepped Si(111) have been observed in real time using the newly developed technique of low-energy electron microscopy (LEEM). The results show that the growth of an isolated facet spontaneously stops at a well-defined size. This is a surprise as classical theories of the growth of linear facets predict a continuous growth, which would only be limited by collisions with neighboring facets. We review predictions that elastic interactions between surface regions of different structure can stabilize finite size domains and facets. We show that a model in which elastic relaxations caused by the facet boundaries stabilize a finite facet width is entirely consistent with the experimental observations.

Crystallographic Etching Phenomenon during Plasma Etching of SiC (100) Thin Films in SF 6

Crystallographic faceting of unmasked monocrystalline (100) thin film surfaces during plasma etching in has been observed using scanning electron microscopy. Although the faceting produced a rough surface, Auger electron spectroscopy showed it to be very chemically clean, having less native oxide than unetched . The facets were determined to be {210} planes using a combination of selected area channeling and small angle tilt measurements. The facet nucleation appears to be surface sensitive and is caused by either crystal defects or compounds formed by reaction of with adsorbed gases on the sample and chamber wall. It is proposed that the subsequent facet growth is due to a surface reconstruction that causes the {210} planes to etch slower.

The growth of helium bubbles in niobium and Nb-1% Zr

Helium bubbles have been precipitated in niobium and Nb-1% Zr by room-temperature irradiation with α-particles followed by isothermal annealing at 1050°C. It has been established that the bubbles grow by a migration and coalescence mechanism. After long annealing times all the bubbles are strongly faceted but many are extremely elongated. From the growth rates of the bubble populations it is possible to establish that the rate-controlling mechanism is surface diffusion for small bubbles and facet nucleation for larger bubbles. A model for the growth of elongated bubbles by facet nucleation is developed and from it the energy of an edge on a {100} facet can be estimated as 1.2 × 10 −11 J/m for niobium. In the Nb-1% Zr alloy the edge energy is at least four times greater.

Effect of S-35 tracer, particle size and imperfection on the solubility of barium sulphate

Solubilities of barium sulphate were enhanced 5–10% with 35S at 5–50 mCi/g-S. These effects of radioisotopic tracer confirm Ramette and Anderson (1963) and Bovington (1965) but are not so large as Spitsyn et al. (1960). They are attributed to structural irregularities arising from nucleation of surface facets by continuous internal irradiation during crystal growth. Kinetic solubilities and saturation solubilities/μmol dm -3 of non-radioactive specimens, were as follows: I (rhombs, 5–15 μm) 10.4, 12.5; II (irreg. stars, <5 μm) 11.0, 10.9; III (agg. colloid, <0.2 μm) 13.5, 13.0; IV (rhombs from anhydrous flux, ~1 mm, crushed) 10.2, -. The sequence of kinetic solubilities IV ≈ I < II < III confirms the enhancemeny of solubility by smaller and less perfect crystal surfaces. The elevated saturation solubility of I is attributed to disintegration of crystal kernels after unravelling of perfected outer layers. With crushed and mounted specimens the effects of irregularities of particle sizes and surface facets were evident.

Faceting of copper surfaces at 1000°C

Polished copper surfaces were observed to facet on annealing at 1000°C in wet hydrogen atmospheres. It was found that the quantity hi p H 2O p H 2 must be greater than zero for extensive faceting to occur, though some faceting, particularly at the sample edges, can occur for In p H 2O p H 2 as small as −3.5. The criteria for faceting to occur by the reduction of surface free energy are discussed and it is shown that facets near the (111) orientation are thermodynamically stable. The effect of anisotropy of surface free energy on facet nucleation is discussed. The outlines of lens-shaped facets were measured. The shapes and sizes of the lens-shaped facets are consistent with a volume diffusion mechanism of facet formation. The observed profiles of the curved surfaces near separated linear facets are compared to theoretically calculated profiles. The calculations by Mullins of facet profiles are extended slightly to facilitate the comparison. The observed profiles are in reasonable agreement with the calculated profiles for facet formation by surface diffusion with the surface diffusion coefficient the same on both the low index and the complex surfaces.