Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation

We consider the coarsening dynamics of multiscale solutions to a dissipative singularly perturbed partial differential equation which models the evolution of a thermodynamically unstable crystalline surface. The late-time leading-order behavior of solutions is identified, through the asymptotic expansion of a maximal-dissipation principle, with a completely faceted surface governed by an intrinsic dynamical system. The properties of the resulting piecewise-affine dynamic surface predict the scaling law L(Mu) approximately t(1/3), for the growth in time of a characteristic morphological length scale L(Mu). A novel computational geometry tool which directly simulates a million-facet piecewise-affine dynamic surface is also introduced. Our computed data are consistent with the dynamic scaling hypothesis, and we report a variety of associated morphometric scaling functions.     

Dynamics and stability of nanostructures on metal surfaces

Ultrathin metal films consisting of two-dimensional clusters are typically unstable: the cluster ensemble has the tendency to reduce its total free energy via Ostwald ripening or dynamic coalescence of mobile clusters. In this paper we give an overview of recent model experiments addressing these coarsening mechanisms. The experiments have been performed using STM on ensembles consisting of adatom or vacancy clusters with typical diameters in the nanometer range on fcc(111)-metal surfaces. Agreement with and deviations from conventional theories are discussed. Received: 29 March 1999 / Accepted: 17 August 1999 / Published online: 30 September 1999     

Coulomb sink effect on coarsening of metal nanostructures on surfaces

We discuss Coulomb effects on the coarsening of metal nanostructures on surfaces. We have proposed a new concept of a “Coulomb sink” [Phys. Rev. Lett., 2004, 93: 106102] to elucidate the effect of Coulomb charging on the coarsening of metal mesas grown on semiconductor surfaces. A charged mesa, due to its reduced chemical potential, acts as a Coulomb sink and grows at the expense of neighboring neutral mesas. The Coulomb sink provides a potentially useful method for the controlled fabrication of metal nanostructures. In this article, we will describe in detail the proposed physical models, which can explain qualitatively the most salient features of coarsening of charged Pb mesas on the Si(111) surface, as observed by scanning tunneling microscopy (STM). We will also describe a method of precisely fabricating large-scale nanocrystals with well-defined shape and size. By using the Coulomb sink effect, the artificial center-full-hollowed or half-hollowed nanowells can be created.     

An extended hydrodynamic theory for particle coarsening—II: Understanding the inhibited coarsening of faceted particles

A particle coarsening mechanism is derived for the case where the rate controlling step is the nucleation of atomic pillboxes on the external surfaces of the growing particles. The kinetics of such coarsening is derived, based on an extension of the Lifshitz-Slyozov-Wagner asymptotic hydrodynamic theory described in Part I of this paper. The derived coarsening kinetics are discussed with respect to the recent Wynblatt-Gjostein data on the inhibited coarsening of faceted platinum particles on flat alumina substrates.     

Instability of thin liquid films by density variations: a new mechanism that mimics spinodal dewetting

Based on the linear stability analysis and nonlinear simulations, conditions are established under which instability and dewetting of a thin liquid film can be engendered solely by the density variations (for example, due to confinement, layering, defects, and restructuring) related to changes in the local film thickness. An increase in the density with the increasing film thickness can stabilize a thermodynamically unstable film, and, equally interesting, a decrease in the density with increasing film thickness can render a thermodynamically stable film unstable. Morphological characteristics of this novel density variation induced instability closely resemble the well-known spinodal dewetting.     

Coulomb sink effect on coarsening of metal nanostructures on surfaces

We discuss Coulomb effects on the coarsening of metal nanostructures on surfaces. We have proposed a new concept of a “Coulomb sink” [Phys. Rev. Lett., 2004, 93: 106102] to elucidate the effect of Coulomb charging on the coarsening of metal mesas grown on semiconductor surfaces. A charged mesa, due to its reduced chemical potential, acts as a Coulomb sink and grows at the expense of neighboring neutral mesas. The Coulomb sink provides a potentially useful method for the controlled fabrication of metal nanostructures. In this article, we will describe in detail the proposed physical models, which can explain qualitatively the most salient features of coarsening of charged Pb mesas on the Si(111) surface, as observed by scanning tunneling microscopy (STM). We will also describe a method of precisely fabricating large-scale nanocrystals with well-defined shape and size. By using the Coulomb sink effect, the artificial center-full-hollowed or half-hollowed nanowells can be created.      

Thermodynamics of Third Order Lovelock Anti-de Sitter Black Holes Revisited

We compute the mass and temperature of third order Lovelock black holes with negative Gauss-Bonnet coefficient α₂<0 in anti-de Sitter space and perform the stability analysis of topological black holes. When k=-1, the third order Lovelock black holes are thermodynamically stable for the whole range r₊. When k=1, we found that the black hole has an intermediate unstable phase for D=7. In eight dimensional spacetimes, however, a new phase of thermodynamically unstable small black holes appears if the coefficient \tilde{\alpha} is under a critical value.For D≧ 9, black holes have similar the distributions of thermodynamically stable regions to the case where the coefficient \tilde{\alpha} is under a critical value for D=8. It is worth to mention that all the thermodynamic and conserved quantities of the black holes with flat horizon do not depend on the Lovelock coefficients and are the same as those of black holes in general gravity.     

Unstable step meandering with elastic interactions.

We report on theoretical investigations of the influence of step interactions due to elasticity on unstable step meandering during molecular beam homoepitaxy. It is shown that elasticity causes coarsening of the cellular structure of the meander found in a previous work. The time dependence of step roughness is found to be robust, behaving as t(1/2). The lateral length scale coarsening is shown to be sensitive to the underlying physical mechanisms. In particular, the typical length follows the law t(alpha), with alpha = 1/6 or 1/4 depending on whether line diffusion is negligibly small or not.     

Phase separation in supersolids

We study quantum phase transitions in the ground state of the two dimensional hard-core boson Hubbard Hamiltonian. Recent work on this and related models has suggested "supersolid" phases with simultaneous diagonal and off-diagonal long range order. We show numerically that, contrary to the generally held belief, the most commonly discussed "checkerboard" supersolid is thermodynamically unstable. Furthermore, this supersolid cannot be stabilized by next-near-neighbor interaction. We obtain the correct phase diagram using the Maxwell construction. We demonstrate that the "striped" supersolid is thermodynamically stable and is separated from the superfluid phase by a continuous phase transition.     

Structural stability and electronic properties of Co2N, Rh2N and Ir2N

The structural stability and electronic properties of Co₂N, Rh₂N and Ir₂N were studied by using the first principles based on the density functional theory. Two structures were considered for each nitride, orthorhombic Pnnm phase and cubic Pa3¯ phase. The results show that they are all mechanically stable. Co₂N in both phases are thermodynamically stable due to the negative formation energy, while the remaining two compounds are thermodynamically unstable. The calculated properties show that they are all metallic and non-magnetic. Ir₂N at Pnnm phase is a potentially hard material. The bonding behavior is analyzed.     

Ripening of surface phases coupled with oscillatory dynamics and self-induced spatial chaos through surface roughening

Some pattern formation processes on single-crystal catalytic surfaces involve transitions between alternative surface phases coupled with oscillatory reaction dynamics. We describe a two-tier symmetry-breaking model of this process, based on nanoscale boundary dynamics interacting with oscillations of adsorbate coverage on microscale. The surface phase distribution oscillates together with adsorbate coverage, and, in addition, undergoes a slow coarsening process due to the curvature dependence of the drift velocity of interphase boundaries. The coarsening is studied both statistically, assuming a circular shape of islands of the minority phase, and through detailed Lagrangian modeling of boundary dynamics. Direct simulation of boundary dynamics allows us to take into account processes of surface reconstruction, leading to self-induced surface roughening. As a result, the surface becomes inhomogeneous, and the coarsening process is arrested way before the thermodynamic limit is reached, leaving a chaotic distribution of surface phases. (c) 1999 American Institute of Physics.     

Fast coarsening in unstable epitaxy with desorption

Homoepitaxial growth is unstable towards the formation of pyramidal mounds when interlayer transport is reduced due to activation barriers to hopping at step edges. Simulations of a lattice model and a continuum equation show that a small amount of desorption dramatically speeds up the coarsening of the mound array, leading to coarsening exponents between 1/3 and 1/2. The underlying mechanism is the faster growth of larger mounds due to their lower evaporation rate.     

The cahn—hilliard equation with “frozen-in” fluctuations of mobility

Early time kinetics of a system with conserved order parameter quenched into an unstable two-phase region of the phase diagram is considered. We study the process of phase separation under the influence of random “frozen-in” inhomogencities of mobility. The combined effect of this “frozen-in” randomness and persistent thermal fluctuations on the structure factor is discussed. The maximum instability of the Cahn—Hilliard type shifts to larger wavelengths, which may be interpreted as “coarsening” even for small times.     

Instabilities and coarsening of stressed crystal surfaces in aqueous solution

Strong pattern formation occurs on polished miscut surfaces of sodium chlorate (NaClO3) single crystals that are uniaxially stressed perpendicular to the step edge direction and placed in a saturated aqueous solution. The wavelength lambda of the stress-induced surface instability increased continuously in experiments up to 9 days after placed in the solution. There were three successive regimes of coarsening: (i) one-dimensional step bunching with lambda approximately t(1/4) until an undulation transition was reached, (ii) a two-dimensional coarsening mechanism with lambda approximately t(1/2), and a gradual transition to (iii) Ostwald ripening-like coarsening with lambda approximately t(1/3). The coarsening of the surface patterns towards a stable, flat surface implies the spontaneous formation of a stress-free skin on the surface of the stressed solid.     

Coulomb sink: a novel coulomb effect on coarsening of metal nanoclusters on semiconductor surfaces

We propose the concept of a "Coulomb sink" to elucidate the effect of Coulomb charging on coarsening of metal mesas grown on semiconductor surfaces. We show that a charged mesa, due to its reduced chemical potential, acts as a Coulomb sink and grows at the expense of neighboring neutral mesas. The theory explains qualitatively the most salient features of coarsening of charged Pb mesas on the Si(111) surface, as observed by a scanning tunneling microscope. It provides a potentially useful method for controlled fabrication of metal nanostructures.     

Stability of two-dimensional nanostructures

We investigate atomic and molecular nanostructures on metal surfaces by variable low-temperature scanning tunnelling microscopy. In combination with molecular dynamics calculations we achieve a detailed understanding of the stability of these structures.?Atomic nanostructures in homoepitaxial metallic systems are thermodynamically only metastable. Two-dimensional islands on Ag(110) decay above a threshold temperature of T _l=175 K. Caused by the anisotropy of the surface, distinct decay behaviours exist above and below a critical temperature of T _c=220 K. Calculations based on effective medium potentials of the underlying rate limiting atomic processes allow us to identify the one-dimensional decay below T _c as well as the two-dimensional decay above T _c.?In contrast to atoms, the intermolecular electrostatic interaction of polar molecules leads to thermodynamically stable structures. On the reconstructed Au(111) surface, the pseudo-chiral 1-nitronaphthalin forms two-dimensional supermolecular clusters consisting predominantly of ten molecules. Comparison of images with submolecular resolution to local density calculations elucidates the thermodynamical stability as well as the internal structure of the decamers. Received: 25 March 1999 / Accepted: 17 August 1999 / Published online: 6 October 1999     

Entropy corrections for Schwarzschild black holes

Recently it is shown that the Bekenstein–Hawking entropy for black holes receives logarithmic corrections due to thermodynamic fluctuations. Schwarzschild black hole which possesses a negative specific heat is thermodynamically unstable, so the entropy corrections cannot be obtained directly. In this Letter, Schwarzschild black hole will be put in the center of a spherical cavity of finite radius to achieve equilibrium with surroundings, so that a thermodynamically stable solution is obtained based on a uniformly spaced area spectrum approach. Our conclusion show that there are two correction terms for Schwarzschild black holes. The sign of the second correction term depends on the size of the cavity.     

The Stability of Several Triply Periodic Surfaces

The stability of six triply periodic surfaces of constant mean curvature (CMC) is investigated. The relative energy and curvature values of the surfaces comprising the P (Pm3¯m), I-WP (Im3¯m), and G (I4₁32) families are numerically calculated with K. Brakke's Surface Evolver. Regions where the I-WP surface can exist metastable to a complementary I-WP surface are found. This type of metastability is also found in the F-RD surface. Bifurcation points marking the stability limits of the P, I-WP, and G families are also calculated with Evolver. Modes of instability which may occur in the six CMC families are classified. Bifurcations in the P, G, I-WP, C(P), D, and F-RD families are attributed to fundamental instabilities. Lattices of spheres (LOS) are possible extremal surfaces at the bifurcations. It is determined that both the CMC surfaces and the LOS configurations are unstable to coarsening. Because the variation in curvature is lowest for the G family, it is the most robust of the six families to coarsening when the surfaces are otherwise equivalent.     

Defect ensembles on the surface of loaded metals as a result of their reversible aggregation

The structures of nanodefect ensembles formed on the surfaces of copper, gold, and molybdenum under a load have been investigated. The properties of the defect ensembles are described in the framework of the reversible aggregation model. The size distribution of nanodefects is thermodynamically determined by the maximum “entropy of their mixing” with atoms of the crystal lattice. The entropy of mixing reaches a maximum value at a small concentration of defects due to a considerable difference in the sizes of defects and atoms. This concentration agrees closely with the experimental data. The reduced size distribution of defects is universal.     

Kinetic evolution and equilibrium morphology of strained islands

Self-assembled SiGe islands grown on Si(001) leave behind characteristic "footprints" that reveal that small islands shrink, losing material to nearby larger islands. The critical size, dividing shrinking from growing islands, corresponds to the pyramid-to-dome shape transition, consistent with "anomalous coarsening" While shrinking, {105}-faceted pyramids transform into truncated pyramids and ultimately into unfaceted mounds. The similarity to behavior during island growth indicates that island shape and facet formation are thermodynamically determined.