We give an overview of the influence of the diffusive instability in forming various growth morphologies. We review dendritic growth of crystals, and discuss the DLA model as an approach to the disordered, fractal case. We consider various systems which are reasonably well described by DLA including island shapes in surface growth.

Dendritic growth is the most ubiquitous form of crystal growth encountered when metals and alloys solidify under low thermal gradients. The growth of thermal dendrites in pure melts is generally acknowledged to be controlled by the diffusive transport of latent heat from the moving crystal-melt interface into its supercooled melt. However, this formulation is incomplete, and the physics of an additional selection rule, coupled to the transport solution, is necessary to predict uniquely the dendrite tip velocity and radius of curvature as a function of the supercooling. Unfortunately, experimental confirmation or evidence is ambiguous, because dendritic growth can be severely complicated by buoyancy induced convection. Recent experiments performed in the microgravity environment of the space shuttle Columbia (STS-62) quantitatively show that convection alters tip velocities and radii of curvature of succinonitrile (SCN) dendrites. In addition, these data can be used to evaluate how well the Ivantsov diffusion solution, coupled to a scaling constant, matches the dendritic growth data under microgravity conditions.

I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys. Rev. A 46, 7793 (1992)]. This leads to a result for the cluster dimensionality, D ≍ 1.66, which is close to numerically obtained values. Quenched and annealed multifractal dimensions can also be computed in this theory; the multifractal dimension τ(3) = D, in agreement with a proposed “electro- static” scaling law.

The equations of motion for the interfacial dynamics in the dielectric breakdown model are derived. They form a set of coupled hydrodynamic equations for the interfacial curvature and growth probability in which the conserved densities are transported by a nonlocal velocity. From these equations the dynamical manner in which singularities in these conserved densities evolve can be studied both analytically and numerically. Shock-like behaviour associated with velocity attractor and repellor points on the evolving interface lead to bifurcations in the velocity field and finally to fractal structures in the curvature and growth probability in the absence of surface tension. In the presence of surface tension spatiotemporal chaos is observed.

We discuss the actual relevance of thin gap geometry electrodeposition to generate fractal patterns that mimic the morphology of Witten and Sander's diffusion-limited aggregates (DLA). Eliminating migration and convection, as well as electrochemical side reactions, we show that electroless deposition is a good candidate to meet the requirements for diffusion to be the rate limiting step of the growth process. We use the wavelet transform microscope to achieve a comparative structural characterization of both experimental electroless deposits and numerical DLA clusters. The fact that five-fold symmetry and Fibonacci hierarchical ordering are found as common predominant statistical features is, to our knowledge, the first demonstration, relying on an appropriate structural fractal analysis, of the existence of DLA morphologies in an experimental context.

I formulate a theory for the growth of an interface in a Laplacian field. The problem is mapped to a many-body system and the process is shown to be Hamiltonian. The corresponding set of dynamical equations is analysed and surface effects are introduced as a term in the Hamiltonian that gives rise to a repulsion between the quasi-particles and the interface. The theory accommodates anisotropic surface effects. The underlying Hamiltonian allows a statistical-mechanical analysis of the limit distribution of the quasi-particles. Noise can be naturally incorporated in this formalism. Finally the distribution of the particles is translated into the statistics of the interface, which leads to predictions on the morphology. The main thrust of this approach is in finding a statistical mechanical approach to this nonequilibrium process.

We have experimentally studied the growth morphologies of carbon tetrabromide CBr4 and fullerene C60crystals in their orientationally disordered solid phases. Very rich growth morphologies have been observed from these crystals, ranging from facets to dendrites and to fractals. In the vapor growth of CBr4crystals, we found that the growth morphologies depend not only on temperature and supersaturation, but also sensitively on the total pressure of the inert gas in the growth chamber. With increasing total pressure, under otherwise the same growth conditions, crystals with initially smooth surfaces evolve into dendritic structures. For fullerene C60, the growth morphologies from solution are mainly fractals with strong anisotropy in the individual crystals. The growth morphologies from vapor are normally faceted and the growth proceeds via a layer-by-layer mode.

We have introduced a new renormalization group approach that allows us to describe the critical stationary state of sandpile models (Phys. Rev. Lett. 72, 1690 (1994)). We define a characterization of the phase space in order to study the evolution of the dynamics under a change of scale. We obtain a non trivial actractive fixed point for the parameters of the model that clarifys the self organized critical nature of these models. We are able to compute the values of the critical exponents and the results are in good agreement with computer simulations. The method can be naturally extended to several other problems with non equilibrium stationary state.

In order to understand better the morphology and the asymptotic behavior in Diffusion Limited Aggregation (DLA), we studied a large numbers of very large off-lattice circular clusters. We inspected both dynamical and geometric asymptotic properties, namely the moments of the particle's sticking distances and the scaling behavior of the transverse growth crosscuts, i.e., the one dimensional cuts by circles. The emerging picture for radial DLA departs from simple self-similarity for any finite size. It corresponds qualitatively to the scenario of infinite drift starting from the familiar five armed shape for small sizes and proceeding to an increasingly tight multi-armed shape. We show quantitatively how the lacunarity of circular clusters becomes increasingly “compact” with size. Finally, we find agreement among transverse cuts dimensions for clusters grown in different geometries, suggesting that the question of universality is best addressed on the crosscut.

Experiments aiming at the measurement of the roughness index ζ of “rapid” fracture surfaces are briefly reviewed. For rapid crack propagation, measured values of ζ are close to 0.8, which seems to be a universal exponent. However, it is argued, by re-writing the Griffith criterion for a self-affine crack, that the self-affine correlation length ξ might depend upon the microstructure, and hence on the fracture toughness. More recent experiments are also described, which reveal at smaller lengthscales the existence of a quasi-static fracture regime separated from the previously studied rapid fracture regime by a crossover length which decreases with increasing crack velocity.

During the peel of a ductile material from a rigid substrate, a number of instabilities can arise in the shape and motion of the peel front. For instance, void formation, viscous fingering, and fibril formation and bifurcation can modulate the local rate of detachment between the two materials. These fluctuations affect the rate of energy dissipation and depend directly on the micromechanics of the detachment zone. Exploiting the consequences of contact charging between dissimilar materials, we have developed sensitive methods for detecting fluctuations during interfacial failure. We have also developed a sensitive probe of ductile deformation in reactive metals and use these measurements to probe energy dissipation during interfacial failure. We present examples of chaotic behavior and discuss the relation between these results with our current understanding of energy dissipation during interfacial crack growth.

Environmentally assisted fracture is in practice one of the most important fracture modes. It is especially dramatic in polycrystalline super-alloys, which are believed to be embrittled by oxygen diffusing along their grain boundaries. We used a large scale atomistic Monte-Carlo simulation to study phenomena of the environmentally assisted fracture nucleation in solids with grain boundaries exposed to an oxygen atmosphere. We find nucleation of inter-granular microcavities in a region which is well in front of the oxidized zone of the sample, apparently due to inhomogeneous stresses induced by the presence of oxide particles. This effect increases with decreasing oxidation rate since then the oxidation front becomes fuzzier and inhomogeneous stresses stronger. These findings compare well with the experimental data on super-alloys which indicate that the environmental embrittlement effects are strong for slower oxidation rates, whereas at higher oxidation rates the embrittlement may be suppressed.

This paper investigates the use of fractal metrics for discrimination of copper surface textures. Measurements of copper surfaces, using contacting profilometry, provided the raw data for the fractal analysis. The samples tested included copper foil samples and a copper lead frame, typical of those in use in plastic electronic packages. The fractal Hausdorf dimension and upper/lower ranges of fractal scale are analyzed by the coastline method and compared using Bonferroni multiple confidence limits. Metrics show significant differences between sample couplets, indicating significant precision in the fractal approach to adequately quantify surface texture qualities.

A small single crystal of copper with a notch has been bent by use of the molecular dynamics method. The bend axis was [110]. Dislocations were created near the tip of the notch and moved on (111) slip plane. Pulling a copper single crystal, half dislocations were created in such a way that the bending was compensated.

Fractal dimension of the microstructure of AISI 316L steel (17 Cr, 12.7 Ni, 2.1 Mo, 1. 5 Mn, 0.01 C) with different degrees of strain were obtained from Richardson plots of grain boundary perimeter against magnification. Grain boundaries were revealed using conventional metallographic techniques and measurements were taken with the aid of an automatic image analizer (Quantimet 520) attached to an optical microscope. The magnifications used were 50, 100, 200, 400, and 1000X. The samples were obtained from a 4” diameter tubing, machined according to ASTM A370 standard test method and deformed to 5, 10, 15, and 20 % tensile strain. The results show that the fractal dimension of the grain boundaries changes as deformation is imparted to the material.

These results suggest that fractal dimension may be used to describe microstructural evolution of metals during deformation processes.

We study the rupture process of Random Fuse Networks (RFN's) with quenched disorder in the microscopic threshold voltages. If lattices are driven to breakdown in one blow by an externally applied voltage the RFN's are shown to be equivalent to the toughest percolation backbone. Critical path analysis holds exactly in this case for all disorder distributions. For gradual rupture, it is shown that the existence of a lower cutoff in the disorder distributions entails a crossover from ductile to brittle behavior. The crossover length is a function of microscopic disorder and diverges in the limit of infinite disorder.

A study of fatigue cracking in iron-copper compacts was carried out to compare and analyse the performance of four different types of commercially used iron powders. The compacts were all sintered at above the iron copper peritectic temperature to facilitate liquid phase sintering. Results showed that the powder with a high specific surface had inferior fatigue properties, especially at high stress levels. The other powders, however, had very similar fatigue properties, except that at low stresses the grade with the large average particle diameter resulted in significantly longer fatigue lives. The differences in performance were discussed in terms of the microstructure of the compacts and the powder characteristics.

For fracture studies on oriented W monocrystalline specimens it is necessary to produce very sharp, stopped precracks, which presents difficulties in the case of W. The experimental procedure and technique to produce precracks is described. The fracture experiments gave strong indications for a preference of the {100} plane as cleavage plane. It was found that the {110} planes successfully resist crack propagation, although they are the planes with the lowest surface energy. The appearance of the {121} plane as a cleavage plane in our experiments makes further studies with oriented W monocrystalline samples necessary.

The island-size distribution scaling function fi (u) corresponding to submonolayer epitaxial growth with critical island size i is studied via kinetic Monte Carlo simulations for i = 0, 1, 2, and 3. An analytic form for fi (u) based on a conjecture for the small-u behavior is also presented. For i = 1, the scaled island-size distribution is found to depend on island morphology. In particular, for fractal islands with i = 1 there is excellent agreement with our analytical form as well as with experiments on low temperature Fe/Fe(100) deposition. However, for compact islands with i = 1, the scaled distribution is found to deviate slightly at small u. We also find excellent agreement between our analytical form, simulations, and experiment for i =- 2 and i = 3. Good agreement between our simulation results for i = 0 and recent experiments on Fe/Cu(100) deposition is also found. Results for the scaling of the island-density as well as crossover scaling forms for the transition from i = 1 to i = 2 and from i = 1 to i = 3 are also presented and used to determine the one-bond activation energy and critical island size transition temperature for Fe/Fe(100). The morphology of fractal islands for i = 2 is also studied and compared with experiments on Au/Ru(0001).

Static and dynamic scaling behavior in copper electrochemical deposition in the stable growth condition (non-bulk fractal growth) was studied by atomic force microscopy and numerical simulation. We found two distinct scaling regimes with roughness exponent α of 0.6 and 0.87α0.05 corresponding to the concentrations of the “brightener” organic additive higher and lower than 1 mℓ/ℓ, respectively. The rms surface width of the whole measured area of the surfaces in the former regime was smaller than that in the latter regime. For the latter rougher surface, we observed dynamic scaling behavior for longer length scales as well as the stationary scaling behavior for shorter length scales: surface width did not further increase with linear size of the area for longer length scales than a characteristic correlation length and increased as a power of deposition time with the dynamic exponent β of 0.45. The sum of α + (α/β) was larger than the value expected for KPZ local growth, 2. This was understood that in electrochemical deposition there is enhancement of growth at protrusions owing to non-local Laplacian field effect. The smoother (α =0.6) and the rougher (0.87) surfaces were reproduced by numerical solutions of KPZ + (the growth term proportional to height) for the shorter and the longer growth times, respectively. Bifurcation of the surface morphology is understood as a result of decrease of weight of the additional term owing to increase of the additive.