A geometric interpretation of the roughening transition in Ising models

Progress in the area of the Ising model roughening transition has previously been limited by the lack of a good definition for the interface separating the pure phases. In the present work, a graphical definition is introduced and it is shown that roughening occurs precisely when this interface fluctuates to infinity.     

Morphology transition and slow dynamics in the collapse of amphiphilic monolayers at the air-water interface

The morphology on collapsed monolayers at the air-water interface has been studied using phase contrast microscopy. It is found that the transition from randomly distributed to quasi-one dimensional crack pattern takes place, depending on the pH value of the subphase and the presence of specific divalent metal ions. In these macroscopic patterns, the former exhibits a surface roughening due to a monolayer buckling while the latter becomes more smooth and uniform. The occurrence of the former is instantaneous and the latter follows a slow dynamics, i.e., the crack propagation in monolayers occurs with a delay for crack nucleation. Thus the change of pattern indicates the existence of a dynamic transition. The transition is discussed with the scenario of a crack instability in brittle materials. The changes of viscous nature and of ion binding, and the compression direction probably operate for the observed behavior effectively. Received 11 January 1999     

Effect of the amorphous thin layer on the surface growth of amorphous/crystalline binary multilayer films

The effect of the amorphous thin layer on the surface growth of amorphous/crystalline binary multilayer films has been studied by using a continuum model. It is shown that both the surface roughness and the growth exponent of amorphous/crystalline binary multilayer films decrease with increasing thickness ratio between amorphous and crystalline layers. Our simulations have also revealed, in contrast to the monotonous rise in surface roughness observed in single-layer films grown on flat substrates, the surface growth of a multilayer film consists of two processes: interface smoothing and roughening, namely the film roughness decreases during the growth of amorphous thin layers but increases monotonously during the growth of crystalline thin layers. The observed interface smoothing and roughening can be obviously influenced by the change in the thickness ratio between amorphous and crystalline layers. The rise in thickness ratio between amorphous and crystalline layers enhances the interface smoothing effect but lowers the interface roughening effect and consequently shows a marked smoothing effect on the surface roughness.     

The roughening transition of the three-dimensional Ising interface: A Monte Carlo study

We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite-size scaling method. The particular method has recently been proposed and successfully tested for various solid-on-solid models. The basic idea is the matching of the renormalization-groupflow of the interface with that of the exactly solvable body-centered cubic solid-on-solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperatureK _r=0.40754(5) is almost two orders of magnitude more accurate than the estimate of Mon, Landau, and Stauffer.     

晶体取向对定向凝固枝晶生长的影响

采用类金属透明模型合金丁二腈-1.0 wt%乙醇(SCN-1.0 wt% Eth)合金, 考察了晶体取向对定向凝固过程中晶粒的平界面失稳孕育时间、枝晶形态演化以及枝晶一次间距的影响. 结果表明, 随着枝晶择优生长方向与温度梯度方向夹角的增大, 晶粒的平界面失稳孕育时间增加, 界面的稳定性增强; 对于不同晶体取向的枝晶形态演化, 枝晶择优生长方向与温度梯度方向夹角越大, 枝晶二次臂不对称生长越严重, 同时, 具有生长优势的枝晶二次臂对相邻枝晶的生长的抑制越强烈; 至于不同晶体取向的枝晶一次间距, 随着枝晶择优生长方向与温度梯度方向夹角的增大, 枝晶一次间距增大. 关键词： 定向凝固 平界面失稳 枝晶间距 晶体取向     

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.     

Scaling,propagation, and kinetic roughening of flame fronts in random media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with meanfield theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time-dependent width and equal-time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.     

Generalized roughening transition and its effect on the string tension

The well-understood roughening transition of an interface in the d = 3 Ising model implies an essential singularity in the string tension of the dual Z₂ gauge model. The roughening transition corresponds to the delocalization of the string due to strong long-wavelength fluctuations, and this reformulation can be generalized to other gauge groups and to d = 4 also. It is not a deconfining transition - it is expected to occur deep in the confining region - but its presence would raise serious questions about the continuation of strong coupling expansions of the tension beyond this point. In this paper predictions on the roughening transition are confronted with the available information on the string tension for different gauge groups in three dimensions.     

Nanoscale periodic morphologies on the fracture surface of brittle metallic glasses

Out-of-plane, nanoscale periodic corrugations are observed in the dynamic fracture surface of brittle bulk metallic glasses with fracture toughness approaching that of silica glasses. A model based on the meniscus instability and plastic zone theory is used to explain such dynamic crack instability. The results indicate that the local softening mechanism in the fracture is an essential ingredient for controlling the formation of the unique corrugations, and might provide a new insight into the origin of fracture surface roughening in brittle materials.     

Anomalous roughening of Hele-Shaw flows with quenched disorder

The kinetic roughening of a stable oil-air interface moving in a Hele-Shaw cell that contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough interface, which exhibits anomalous scaling. The three independent exponents needed to characterize the anomalous scaling are determined experimentally. The anomalous scaling is explained in terms of the initial acceleration and subsequent deceleration of the interface tips in the tracks coupled by mass conservation. A phenomenological model that reproduces the measured global and local exponents is introduced.     

Washboard road: the dynamics of granular ripples formed by rolling wheels

We report laboratory experiments on rippled granular surfaces formed under rolling wheels. Ripples appear above a critical speed and drift slowly in the driving direction. Ripples coarsen as they saturate and exhibit ripple creation and destruction events. All of these effects are captured qualitatively by 2D soft-particle simulations in which a disk rolls over smaller disks in a periodic box. The simulations show that compaction and segregation are inessential to the ripple phenomenon. We describe a simplified scaling model which gives some insight into the mechanism of the instability.     

Pinning of a rough interface by an external potential

An analysis is given of the behavior of an interface between two phases in the presence of an external pinning potential in the solid-on-solid limit of the two-dimensional Ising model. It is found that the potential turns a rough interface into a smooth one, except in the case of a boundary potential, where a minimum potential strength is required. The connection with the roughening transition found by Abraham is discussed. The interface width is calculated as a function of the potential parameters in the limit of a weak pining potential.     

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     

Conserved dynamics and interface roughening in spontaneous imbibition: A phase field model

The propagation and roughening of a fluid-gas interface through a disordered medium in the case of capillary driven spontaneous imbibition is considered. The system is described by a conserved (model B) phase-field model, with the structure of the disordered medium appearing as a quenched random field . The flow of liquid into the medium is obtained by imposing a non-equilibrium boundary condition on the chemical potential, which reproduces Washburn's equation for the slowing down motion of the average interface position H. The interface is found to be superrough, with global roughness exponent , indicating anomalous scaling. The spatial extent of the roughness is determined by a length scale arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualitatively reproduces the experimental results of Horv'ath and Stanley (Phys. Rev. E 52, 5166 (1995)) on the temporal scaling of the interface. Received 24 November 1999     

Interface instability in shear-banding flow

We report on the spatiotemporal dynamics of the interface in shear-banding flow of a wormlike micellar system (cetyltrimethylammonium bromide and sodium nitrate in water) during a start-up experiment. Using the scattering properties of the induced structures, we demonstrate the existence of an instability of the interface between bands along the vorticity direction. Different regimes of spatiotemporal dynamics of the interface are identified along the stress plateau. We build a model based on the flow symmetry which qualitatively describes the observed patterns.     

The instability of streaming fluids with fine dust in porous medium

The instability of the plane interface between two uniform, superposed, and streaming fluids permeated with suspended particles through porous medium is considered. The effect of a uniform horizontal magnetic field on the problem is also studied. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored, whereas for perturbations in all other directions there exists instability for a certain wavenumber range. The instability of the system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference in streaming velocities and the Alfvén velocity. The suspended particles do not affect the above results.     

Electromigration-Induced Instability of the Interface between Solid Conductors

A model has been developed to describe the influence of vacancy electromigration in the bulk of joined conducting materials under applied electric current on the shape stability of a flat interface between them. A system of equations is formulated and solved to describe the relationship between changes in the interface profile and mechanical stresses arising in it due to ion and vacancy fluxes, induced by a small spatially periodic perturbation of the interface. Criteria of the perturbation amplitude growth with time, i.e., the shape instability conditions for the interface, are determined. A more detailed analysis and estimation are performed for two special cases: in the first case the interface is between two similar materials, and in the other the mobility of ions and vacancies in one of the materials can be neglected. Perturbation wavelength ranges are determined and studied analytically for these cases; within the intervals the bulk vacancy electromigration is the main factor that leads to the growth of perturbation amplitude and mechanical stresses along the interface with time. Conditions for the existence of such ranges and dependences of their boundaries on the current direction and current density are determined. Particular wavelength and current density ranges of the interface instability are estimated. The estimates show that the interface instability due to bulk electromigration is possible under reasonable (experimentally and practically) conditions in terms of temperature (～100°C), current density (～10¹⁰ ? 10¹² A/m²), and perturbation wavelength (～10¹ ? 10³ μm). The obtained results may be useful, e.g., for improving the reliability and lifetime of micro- and nanoelectronic components.     

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.     

Interfacial Roughening in Field Theory

In the rough phase, the width of interfaces separating different phases of statistical systems increases logarithmically with the system size. This phenomenon is commonly described in terms of the capillary wave model, which deals with fluctuating, infinitely thin membranes, requiring ad hoc cut-offs in momentum space. We investigate the interface roughening in a unified approach, which does not rely on joining different models, namely in the framework of the Landau-Ginzburg model, that is renormalized field theory, in the one-loop approximation. The interface profile and width are calculated analytically, resulting in finite expressions with definite coefficients. They are valid in the scaling region and depend on the known renormalized coupling constant.     

瑞利-泰勒不稳定性中尺度效应的数值模拟研究

 瑞利-泰勒不稳定性是一种由于密度梯度引起的界面不稳定性，在惯性约束聚变中具有重要的意义。利用被动标量输运模型对包含不同尺度初始扰动的界面演化过程进行数值模拟。计算结果表明界面的初始形状对不稳定性的发展具有很大的影响，狭长型扰动比正方型扰动发展慢。另外，不同尺度扰动的相互作用一般会减小沿界面发展方向运动的动能，使能量更多地用于平行于界面方向的运动。