Kinetic roughening and pinning of two coupled interfaces in disordered media

We studied the kinetic roughening dynamic of two coupled interfaces formed in paper wetting experiments at low evaporation rate. We observed three different regimes of impregnation in which kinetic roughening dynamics of coupled precursor and main fronts belong to different universality classes; nevertheless both interfaces are pinned in the same configuration. Reported experimental observations provide a novel insight into the nature of kinetic roughening phenomena occurring in the vast variety of systems far from equilibrium.     

Scaling of the interface roughness in Fe-Cr superlattices: self-affine versus non-self-affine

We have analyzed kinetic roughening in Fe-Cr superlattices by energy-filtered transmission electron microscopy. The direct access to individual interfaces provides both static and dynamic roughness exponents. We find an anomalous non-self-affine scaling of the interface roughness with a time dependent local roughness at short length scales. While the deposition conditions affect strongly the long-range dynamics, the anomalous short-range exponent remains unchanged. The different short- and long-range dynamics outline the importance of long-range interactions in kinetic roughening.     

Growth of rough surfaces

The growth of objects with rough surfaces is a common phenomenon. We describe several models used in the study of the temporal evolution of fluctuating interfaces and then we explain the dynamical scaling in this class of growth models with self-affine surfaces. The recent progress in this field is reviewed. Much emphasis is put on roughness properties and in particular on a possible kinetic roughening transition — a nonequilibrium analog of the thermal roughening transition. Both analytical and numerical results for scaling exponents are summarized and indications of a phase transition in some models are discussed.     

序参量守恒系统中空间相关的界面生长

用重整化群方法分析了序参量守恒系统在空间关联下的界面生长行为。得到了标度指数x和z作为空间维数d和相关指数ρ的函数。结果表明,序参量守恒条件使生长弛豫时间增长,空间相关使生长表面粗化。并与E.Medina等人和T.Sun等人的结果作了比较。 关键词：     

Interplay between phase ordering and roughening on growing films

We study the interplay between surface roughening and phase separation during the growth of binary films. Renormalization group calculations are performed on a pair of equations coupling the interface height and order parameter fluctuations. We find a larger roughness exponent at the critical point of the order parameter compared to the disordered phase, and an increase in the upper critical dimension for the surface roughening transition from two to four. Numerical simulations performed on a solid-on-solid model with two types of deposited particles corroborate some of these findings. However, for a range of parameters not accessible to perturbative analysis, we find non-universal behavior with a continuously varying dynamic exponent.Received: 23 July 2003, Published online: 23 December 2003PACS: 68.35.Rh Phase transitions and critical phenomena - 05.70.Jk Critical point phenomena - 05.70.Ln Nonequilibrium and irreversible thermodynamics - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems     

Atomic force microscopy study of growth kinetics: Scaling in TiN-TiB2 nanocomposite films on Si(1 0 0)

We used the reactive unbalanced close-field dc-magnetron sputtering growth of TiN-TiB₂ on Si(1 0 0) at room temperature to determine if scaling theory provides insight into the kinetic mechanisms of two-phase nanocomposite thin films. Scaling analyses along with height-difference correlation functions of measured atomic force microscopy (AFM) images have shown that the TiN-TiB₂ nanocomposite films with thickness ranging from 70 to 950 nm exhibit a kinetic surface roughening with the roughness increasing with thickness exponentially. The roughness exponent α and growth exponent β are determined to be ∼0.93 and ∼0.25, respectively. The value of dynamic exponent z, calculated by measurement of the lateral correlation length ξ, is ∼3.70, agreeing well with the ratio of α to β. These results indicate that the surface growth behavior of sputter-deposited TiN-TiB₂ thin films follows the classical Family-Vicseck scaling and can be reasonably described by the noisy Mullins diffusion model, at which surface diffusion serves as the smoothing effect and shot noise as the roughening mechanism.     

Dynamical scaling and kinetic roughening of single valued fronts propagating in fractal media

We consider the dynamical scaling and kinetic roughening of single-valued interfaces propagating in 2D fractal media. Assuming that the nearest-neighbor height difference distribution function of the fronts obeys Lévy statistics with a well-defined algebraic decay exponent, we consider the generalized scaling forms and derive analytic expressions for the local scaling exponents. We show that the kinetic roughening of the interfaces displays intrinsic anomalous scaling and multiscaling in the relevant correlation functions. We test the predictions of the scaling theory with a variety of well-known models which produce fractal growth structures. Results are in excellent agreement with theory. For some models, we find interesting crossover behavior related to large-scale structural instabilities of the growing aggregates. Received 22 May 2002 Published online 19 November 2002     

Characterisation of Interfaces Between Liquid Tin and Alumina in the Presence of Titanium Alloy Additions

Neutron reflection spectroscopy has been used to characterise the composition of interfaces between liquid Sn-Ti alloys and Al₂O₃. The reflectivity profiles for both 1% and 3% Ti alloys are consistent with the presence of a layer approximately 2 nm thick at the liquid/solid interface, showing extensive segregation of Ti. The composition of this layer is not pure Ti but shows a greater Ti content than any known Ti oxide composition. In all interfaces exposed to liquid metals at elevated temperature (including pure Sn) there is a layer of thickness 20–100 nm on the alumina surface with slightly lower neutron scattering length density than pure alumina. This is interpreted as evidence for surface roughening of the Al₂O₃ surface during exposure to the liquid metal.     

The effects of random fields on the critical and bicritical behavior of Mn x Zn1−x F2

We have carried out a comprehensive study of the static and dynamic spin-spin correlations of Mn _x Zn_1–x F₂ in a magnetic field. Samples withx=0.75 andx=0.5 have been studied. This system exhibits behavior closely related, if not identical, to that of the Random Field Ising Model (RFIM). An additional feature of Mn _x Zn_1–x F₂ is that it exhibits an easily accessible bicritical point; thus one can study the changeover from the RFIM to the uniformXY model with a transverse random field. Quite generally, the instantaneous spin-spin correlations in a field are described by a combination of Lorentzian, Lorentzian-squared and delta function terms the latter corresponds to the long range order (LRO) component. In the Ising phase one finds history dependent behavior as discussed previously. In theXY phase, except very near the spin-flop boundary, one finds ergodic behavior withXY LRO and Lorentzian squared Ising fluctuations. Rather complicated instability effects are found all along the spin-flop boundary. Further, when one establishes LRO in theXY phase and lowers the field through the spin-flop value, one obtains a LRO Ising state in thex=0.75 sample whereas one obtains the field-cooled domain state in thex=0.50 sample. This dramatic difference in behavior is not understood. Our results on the RFIM aspects of the problem are consistent with our previous studies. The transition is dominated by the metastability effects with an underlying equilibrium transition which is either first order or weakly second order (0). The underlying transition manifests itself directly in measurements of the dynamic response nearT _N (H). From the data above the metastability boundary we deduce for the static correlation length exponentv=1.4±0.3 in good agreement with theory. We find for the RFIM crossover exponent _RF=1.5±0.2 where the errors represent the spread in values obtained from different techniques. Finally, we have determined in detail the field-temperature phase diagram of thex=0.5 sample including the critical behavior along the spin-flop line; the latter transition appears to be second order for an extended region.     

The Influence of Boundary Conditions on Solid-on-Solid Models

We investigate various 1D solid-on-solid (SOS) models using the transfer matrix method. The main results of the paper concern SOS interfaces near an attracting wall (line) when the end points of the interface are fixed away from the wall (line). We obtain typical interface shapes in the macroscopic scale. If attraction of the wall is strong enough, then a part of the interface is pinned to the wall (line) and the remaining parts of the interface form angles with the wall (line)—the contact angles. Explicit expressions for the contact angles are derived. We show also that for a certain range of parameters the models exhibit reentrant wetting and drying. As a result the free energy of the SOS model as a function of temperature can have up to three points of nonanalyticity. The fluctuations of the SOS interface are investigated in detail. Quite unusual fluctuations are observed at the contact points—the points where unpinned and pinned parts of the interface meet.     

Critical phenomena in ferromagnetic superlattices

Within the framework of the high-temperature series expansions technique, we examine the phase transition and the critical phenomena of a two-component superlattice with simple cubic structure, through three models: Ising, XY and Heisenberg. The reduced critical temperature of the system is studied as a function of the thickness of the constituents and the exchange interactions in each material, and within the interface. We show the existence of a critical thickness of the unit cell at which the reduced critical temperature of the binary superlattice remains insensitive to the exchange coupling within the interfaces. The values of the effective critical exponent γ _eff associated with the magnetic susceptibility agreed with the universal classes in the limit cases where the superlattice is still comparable to an infinite simple cubic lattice. We attribute the breakdown in the universality hypothesis to the crossover effects.     

Direct experimental confirmation of the critical behaviour of antiphase domain boundaries at the second order phase transition of Al-Fe binary alloys

The present work reports, for the first time, a direct experimental observation of the critical phenomenon associated with the B2-A2 order-disorder transition of Al-Fe binary alloys. Transmission electron microscopy and energy dispersion spectroscopy are employed to span the morphological changes through the transition line from the ordered B2 phase to the disordered A2 phase. Dark field images of the microstructure around the transition line for samples aged at 973 and 1073 K for various times show an interface roughening for the {100} antiphase domain boundaries in body-centered cubic binary alloys having the B2 structure. This observation confirms theory about the instability of the second-order transition in such alloys. This behaviour occurs for compositions with Al-content slightly higher (by ∼4 at.% Al) than that of the critical point of the equilibrium order-disorder transition. In addition, roughness-induced wetting transition is also observed for alloys having compositions ranging from 1.3 to 1.5 at.% Al above the transition line. The interface roughening transition is thought to be unstable second-order while the wetting transition is suggested to be a stable first-order one.     

In-Situ Intrinsic Interface Strength Measurement at Elevated Temperatures and its Relationship to Interfacial Structure

A previously developed laser spallation technique has been modified to measure the tensile strength of thin film interfaces in-situ at temperatures up to 1100°C. Tensile strengths of Nb/A-plane sapphire, FeCrAl/A-plane sapphire and FeCrAlY/A-plane sapphire were measured up to 950°C. The measured strengths at high temperatures were substantially lower compared with their corresponding strengths at ambient temperature. For example, at 850°C, the interface tensile strength for the Nb/sapphire (151 ± 17 MPa), FeCrAl/sapphire (62 ± 8 MPa) and FeCrAlY/sapphire (82 ± 11 MPa) interface systems were lower by factors of approximately, 3, 5, and 8, respectively, over their corresponding ambient values. These results underscore the importance of using such in-situ measured values under operating conditions as the failure criterion in any life prediction or reliability models of such coated systems where local interface temperature excursions are expected. The results on alloy film interfaces also demonstrate that the presence of Y increases the strength of FeCrAl/Al₂O₃ interfaces.     

Anomalous roughening of viscous fluid fronts in spontaneous imbibition

We report experiments on spontaneous imbibition of a viscous fluid by a model porous medium in the absence of gravity. The average position of the interface satisfies Washburn's law. Scaling of the interface fluctuations suggests a dynamic exponent z approximately 3, indicative of global dynamics driven by capillary forces. The complete set of exponents clearly shows that interfaces are not self-affine, exhibiting distinct local and global scaling, both for time (beta = 0.64 +/- 0.02, beta(*) = 0.33 +/- 0.03) and space (alpha = 1.94 +/- 0.20, alpha(loc) = 0.94 +/- 0.10). These values are compatible with an intrinsic anomalous scaling scenario.     

Analytic Approximations for the Velocity of Field-Driven Ising Interfaces

We present analytic approximations for the field, temperature, and orientation dependences of the interface velocity in a two-dimensional kinetic Ising model in a nonzero field. The model, which has nonconserved order parameter, is useful for ferromagnets, ferroelectrics, and other systems undergoing order–disorder phase transformations driven by a bulk free-energy difference. The solid-on-solid (SOS) approximation for the microscopic surface structure is used to estimate mean spin-class populations, from which the mean interface velocity can be obtained for any specific single-spin-flip dynamic. This linear-response approximation remains accurate for higher temperatures than the single-step and polynuclear growth models, while it reduces to these in the appropriate low-temperature limits. The equilibrium SOS approximation is generalized by mean-field arguments to obtain field-dependent spin-class populations for moving interfaces, and thereby a nonlinear-response approximation for the velocity. The analytic results for the interface velocity and the spin-class populations are compared with Monte Carlo simulations. Excellent agreement is found in a wide range of field, temperature, and interface orientation.     

Dynamic scaling of non-euclidean interfaces

The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is thus a one-dimensional phenomenon characterized by a marginal logarithmic amplitude of the fluctuations. Models characterized by a planar dynamical exponent z > 1, which include the most common stochastic growth equations, suffer a loss of correlation along the interface, and their dynamics reduce to that of the radial random deposition model in the long time limit. The consequences in several applications are discussed, and we conclude that it is necessary to reexamine some experimental results in which standard scaling analysis was applied.     

Some aspects of the wetting transition1

The wetting of an attractive planar wall by liquid at liquid-gas coexistence is investigated from a microscopic point of view. A model for interface detachment due to thermal fluctuations is first worked out. An empirical framework for distinguishing between first-order and continuous wetting transitions is then set up, and quantified by the introduction of the van der Waals mean field model. This is solved for strong, short-range and weak, long-range forces. The role of fluctuations is reconsidered, and the nature of the required corrections examined, both for wall-fluid and fluid-fluid interfaces.This paper was presented at the conference on the Statistical Mechanics of Phase Transitions-Mathematical and Physical Aspects, Tebo, Czechoslovakia, September 1–6, 1986.     

Superfluid interfaces in quantum solids

One scenario for the nonclassical moment of inertia of solid 4He discovered by Kim and Chan [Nature (London) 427, 225 (2004)] is the superfluidity of microcrystallite interfaces. On the basis of the most simple model of a quantum crystal--the checkerboard lattice solid--we show that the superfluidity of interfaces between solid domains can exist in a wide range of parameters. At strong enough interparticle interaction, a superfluid interface becomes an insulator via a quantum phase transition. Under the conditions of particle-hole symmetry, the transition is of the standard U(1) universality class in 3D, while in 2D the onset of superfluidity is accompanied by the interface roughening, driven by fractionally charged topological excitations.     

Conserved dynamics and interface roughening in spontaneous imbibition: A critical overview

Imbibition phenomena have been widely used experimentally and theoretically to study the kinetic roughening of interfaces. We critically discuss the existing experiments and some associated theoretical approaches on the scaling properties of the imbibition front, with particular attention to the conservation law associated to the fluid, to problems arising from the actual structure of the embedding medium, and to external influences such as evaporation and gravity. Our main conclusion is that the scaling of moving interfaces includes many crossover phenomena, with competition between the average capillary pressure gradient and its fluctuations setting the maximal lengthscale for roughening. We discuss the physics of both pinned and moving interfaces and the ability of the existing models to account for their properties. Received 17 February 1999 and Received in final form 24 November 1999     

Molecular dynamics simulation comparison of atomic scale intermixing at the amorphous Al2O3/semiconductor interface for a-Al2O3/Ge, a-Al2O3/InGaAs, and a-Al2O3/InAlAs/InGaAs

The structural properties of a-Al₂O₃/Ge, a-Al₂O₃/In_0.5Ga_0.5As and a-Al₂O₃/In_0.5Al_0.5As/InGaAs interfaces were investigated by density-functional theory (DFT) molecular dynamics (MD) simulations. Realistic a-Al₂O₃ samples were generated using a hybrid classical-DFT MD “melt and quench” approach. The interfaces were formed by annealing at 700 K/800 K and 1100 K with subsequent cooling and relaxation. The a-Al₂O₃/Ge interface demonstrates pronounced interface intermixing and interface bonding exclusively through Al–O–Ge bonds generating high interface polarity. In contrast, the a-Al₂O₃/InGaAs interface has no intermixing, Al–As and O–In/Ga bonding, low interface polarity due to nearly compensating interface dipoles, and low substrate deformation. The a-Al₂O₃/InAlAs interface demonstrated mild intermixing with some substrate Al atoms being adsorbed into the oxide, mixed Al–As/O and O–Al/In bonding, medium interface polarity, and medium substrate deformation. The simulated results demonstrate strong correlation to experimental measurements and illustrate the role of weak bonding in generating an unpinned interface for metal oxide/semiconductor interfaces.