arXiv subjects

Paolo Politi

Publications and source records attributed to Paolo Politi.

At least 73 records · Page 4Linked to original sources

arXiv2006

Fluctuations and scaling in models for particle aggregation

We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to diffuse up to \ell steps. Therefore the second model incorporates more fluctuations than the first, but still less than usual (Full Diffusion) models of deposition and diffusion on a crystal surface. We study the time dependence of the average densities of atoms and islands and the island size distribution. The Sequential Diffusion model displays a nontrivial steady-state regime where the island density increases and the island size distribution obeys scaling, much in the same way as the standard Full Diffusion model for epitaxial growth. Our results also allow to gain insight into the role of different types of fluctuations.

cond-mat.mtrl-sci↗

arXiv2006

Surface currents and slope selection in crystal growth

We face the problem to determine the slope dependent current during the epitaxial growth process of a crystal surface. This current is proportional to delta=(p+) + (p-), where (p+/-) are the probabilities for an atom landing on a terrace to attach to the ascending (p+) or descending (p-) step. If the landing probability is spatially uniform, the current is proved to be proportional to the average (signed) distance traveled by an adatom before incorporation in the growing surface. The phenomenon of slope selection is determined by the vanishing of the asymmetry delta. We apply our results to the case of atoms feeling step edge barriers and downward funnelling, or step edge barriers and steering. In the general case, it is not correct to consider the slope dependent current j as a sum of separate contributions due to different mechanisms.

cond-mat.mtrl-sci↗

arXiv2006

Nonlinear dynamics in one dimension: On a criterion for coarsening and its temporal law

We develop a general criterion about coarsening for a class of nonlinear evolution equations describing one dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process takes place and the one where the wavelength is fixed in the course of time. An intermediate scenario may occur, namely `interrupted coarsening'. The power of the criterion lies in the fact that the statement about the occurrence of coarsening, or selection of a length scale, can be made by only inspecting the behavior of the branch of steady state periodic solutions. The criterion states that coarsening occurs if lambda'(A)>0 while a length scale selection prevails if lambda'(A)<0, where $lambda$ is the wavelength of the pattern and A is the amplitude of the profile. This criterion is established thanks to the analysis of the phase diffusion equation of the pattern. We connect the phase diffusion coefficient D(lambda) (which carries a kinetic information) to lambda'(A), which refers to a pure steady state property. The relationship between kinetics and the behavior of the branch of steady state solutions is established fully analytically for several classes of equations. Another important and new result which emerges here is that the exploitation of the phase diffusion coefficient enables us to determine in a rather straightforward manner the dynamical coarsening exponent. Our calculation, based on the idea that |D(lambda)|=lambda^2/t, is exemplified on several nonlinear equations, showing that the exact exponent is captured. Some speculations about the extension of the present results to higher dimension are outlined.

cond-mat.stat-mech↗

arXiv2005

Dipolar ground state of planar spins on triangular lattices

An infinite triangular lattice of classical dipolar spins is usually considered to have a ferromagnetic ground state. We examine the validity of this statement for finite lattices and in the limit of large lattices. We find that the ground state of rectangular arrays is strongly dependent on size and aspect ratio. Three results emerge that are significant for understanding the ground state properties: i) formation of domain walls is energetically favored for aspect ratios below a critical valu e; ii) the vortex state is always energetically favored in the thermodynamic limit of an infinite number of spins, but nevertheless such a configuration may not be observed even in very large lattices if the aspect ratio is large; iii) finite range approximations to actual dipole sums may not provide the correct ground sta te configuration because the ferromagnetic state is linearly unstable and the domain wall energy is negative for any finite range cutoff.

cond-mat.stat-mech↗

arXiv2005

Breakdown of metastable step-flow growth on vicinal surfaces induced by nucleation

We consider the growth of a vicinal crystal surface in the presence of a step-edge barrier. For any value of the barrier strength, measured by the length l_es, nucleation of islands on terraces is always able to destroy asymptotically step-flow growth. The breakdown of the metastable step-flow occurs through the formation of a mound of critical width proportional to L_c=1/sqrt(l_es), the length associated to the linear instability of a high-symmetry surface. The time required for the destabilization grows exponentially with L_c. Thermal detachment from steps or islands, or a steeper slope increase the instability time but do not modify the above picture, nor change L_c significantly. Standard continuum theories cannot be used to evaluate the activation energy of the critical mound and the instability time. The dynamics of a mound can be described as a one dimensional random walk for its height k: attaining the critical height (i.e. the critical size) means that the probability to grow (k->k+1) becomes larger than the probability for the mound to shrink (k->k-1). Thermal detachment induces correlations in the random walk, otherwise absent.

cond-mat.stat-mech↗

arXiv2005

Nucleation and step-edge barriers always destabilize step-flow growth of a vicinal surface

We consider the effect of nucleation on a one-dimensional stepped surface, finding that step-flow growth is metastable for any strength of the additional step-edge barrier. The surface is made unstable by the formation of a critical nucleus, whose lateral size is related to the destabilization process on a high-symmetry surface. Arguments based on a critical nucleus of height two, which suggest the existence of a fully stable regime for small barrier, fail to describe this phenomenon.

cond-mat.mtrl-sci↗

arXiv2004

Random Deposition Model with a Constant Capture Length

We introduce a sequential model for the deposition and aggregation of particles in the submonolayer regime. Once a particle has been randomly deposited on the substrate, it sticks to the closest atom or island within a distance \ell, otherwise it sticks to the deposition site. We study this model both numerically and analytically in one dimension. A clear comprehension of its statistical properties is provided, thanks to capture equations and to the analysis of the island-island distance distribution.

cond-mat.stat-mech↗

arXiv2004

When does coarsening occur in the dynamics of one-dimensional fronts ?

Dynamics of a one-dimensional growing front with an unstable straight profile are analyzed. We argue that a coarsening process occurs if and only if the period λof the steady state solution is an increasing function of its amplitude A. This statement is rigorously proved for two important classes of conserved and nonconserved models by investigating the phase diffusion equation of the steady pattern. We further provide clear numerical evidences for the growth equation of a stepped crystal surface.

cond-mat.stat-mech↗

arXiv2002

Irreversible nucleation in molecular beam epitaxy: From theory to experiments

Recently, the nucleation rate on top of a terrace during the irreversible growth of a crystal surface by MBE has been determined exactly. In this paper we go beyond the standard model usually employed to study the nucleation process, and we analyze the qualitative and quantitative consequences of two important additional physical ingredients: the nonuniformity of the Ehrlich-Schwoebel barrier at the step-edge, because of the existence of kinks, and the steering effects, due to the interaction between the atoms of the flux and the substrate. We apply our results to typical experiments of second layer nucleation.

cond-mat.mtrl-sci↗

arXiv2002

Dipolar interaction between two-dimensional magnetic particles

We determine the effective dipolar interaction between single domain two-dimensional ferromagnetic particles (islands or dots), taking into account their finite size. The first correction term decays as 1/D^5, where D is the distance between particles. If the particles are arranged in a regular two-dimensional array and are magnetized in plane, we show that the correction term reinforces the antiferromagnetic character of the ground state in a square lattice, and the ferromagnetic one in a triangular lattice. We also determine the dipolar spin-wave spectrum and evaluate how the Curie temperature of an ensemble of magnetic particles scales with the parameters defining the particle array: height and size of each particle, and interparticle distance. Our results show that dipolar coupling between particles might induce ferromagnetic long range order at experimentally relevant temperatures. However, depending on the size of the particles, such a collective phenomenon may be disguised by superparamagnetism.

cond-mat.mtrl-sci↗

arXiv2002

The process of irreversible nucleation in multilayer growth. I. Failure of the mean-field approach

The formation of stable dimers on top of terraces during epitaxial growth is investigated in detail. In this paper we focus on mean-field theory, the standard approach to study nucleation. Such theory is shown to be unsuitable for the present problem, because it is equivalent to considering adatoms as independent diffusing particles. This leads to an overestimate of the correct nucleation rate by a factor N, which has a direct physical meaning: in average, a visited lattice site is visited N times by a diffusing adatom. The dependence of N on the size of the terrace and on the strength of step-edge barriers is derived from well known results for random walks. The spatial distribution of nucleation events is shown to be different from the mean-field prediction, for the same physical reason. In the following paper we develop an exact treatment of the problem.

cond-mat.stat-mech↗

arXiv2002

The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions

We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random walker in a higher-dimensional space. The spatial distribution of nucleation events is shown to differ markedly from the mean-field estimate except in the limit of very weak step-edge barriers. The nucleation rate is computed exactly, including numerical prefactors.

cond-mat.stat-mech↗

arXiv2002

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time. In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (model B): coarsening is known to be logarithmic in the absence of noise (L(t)=log t) and to follow a power law (L(t)=t^{1/3}) when noise is present. If surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stage of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster: if alpha is the exponent describing the steepening of the maximal slope M of mounds (M^alpha = L) we find that L(t)=t^n: n is equal to 1/4 for 1 2, according to n=alpha/(5*alpha -2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t)=t^{1/4}, irrespectively of alpha. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model alpha=1, both in the absence and in the presence of noise.

cond-mat.stat-mech↗

arXiv2001

Irreversible nucleation in multilayer growth

The epitaxial growth process of a high symmetry surface occurs because adatoms meet and nucleate new islands, that eventually coalesce and complete atomic layers. During multilayer growth, nucleation usually takes place on top of terraces where the geometry of the diffusion process is well defined: We have studied in detail the spatiotemporal distribution of nucleation events and the resulting nucleation rate, a quantity of primary importance to model experimental results and evaluate diffusion barriers at step-edges. We provide rigorous results for irreversible nucleation and we assess the limits of mean-field theory (MFT): we show that MFT overestimates the correct result by a factor proportional to the number of times an adatom diffusing on the terrace visits an already visited lattice site. In this report we aim at giving a simple physical account of our results.

cond-mat.stat-mech↗

arXiv2001

Spatio-temporal distribution of nucleation events during crystal growth

We consider irreversible second-layer nucleation that occurs when two adatoms on a terrace meet. We solve the problem analytically in one dimension for zero and infinite step-edge barriers, and numerically for any value of the barriers in one and two dimensions. For large barriers, the spatial distribution of nucleation events strongly differs from $ρ^2$, where $ρ$ is the stationary adatom density in the presence of a constant flux. The probability $Q(t)$ that nucleation occurs at time $t$ after the deposition of the second adatom, decays for short time as a power law [$Q(t)\sim t^{-1/2}$] in $d=1$ and logarithmically [$Q(t)\sim 1/\ln(t/t_0)$] in $d=2$; for long time it decays exponentially. Theories of the nucleation rate $ω$ based on the assumption that it is proportional to $ρ^2$ are shown to overestimate $ω$ by a factor proportional to the number of times an adatom diffusing on the terrace visits an already visited lattice site.

cond-mat.stat-mech↗

arXiv2000

Coarsening in surface growth models without slope selection

We study conserved models of crystal growth in one dimension [$\partial_t z(x,t) =-\partial_x j(x,t)$] which are linearly unstable and develop a mound structure whose typical size L increases in time ($L = t^n$). If the local slope ($m =\partial_x z$) increases indefinitely, $n$ depends on the exponent $γ$ characterizing the large $m$ behaviour of the surface current $j$ ($j = 1/|m|^γ$): $n=1/4$ for $1< γ<3$ and $n=(1+γ)/(1+5γ)$ for $γ>3$.

cond-mat.stat-mech↗

arXiv1999

Island nucleation in the presence of step edge barriers: Theory and applications

We develop a theory of nucleation on top of two-dimensional islands bordered by steps with an additional energy barrier $ΔE_S$ for descending atoms. The theory is based on the concept of the residence time of an adatom on the island,and yields an expression for the nucleation rate which becomes exact in the limit of strong step edge barriers. This expression differs qualitatively and quantitatively from that obtained using the conventional rate equation approach to nucleation [J. Tersoff et al., Phys. Rev. Lett.72, 266 (1994)]. We argue that rate equation theory fails because nucleation is dominated by the rare instances when two atoms are present on the island simultaneously. The theory is applied to two distinct problems: The onset of second layer nucleation in submonolayer growth, and the distribution of the sizes of top terraces of multilayer mounds under conditions of strong step edge barriers. Application to homoepitaxial growth on Pt(111) yields the estimate $ΔE_S \geq 0.33$ eV for the additional energy barrier at CO-decorated steps.

cond-mat.mtrl-sci↗

arXiv1999

Crystal symmetry, step-edge diffusion and unstable growth

We study the effect of crystal symmetry and step-edge diffusion on the surface current governing the evolution of a growing crystal surface. We find there are two possible contributions to anisotropic currents, which both lead to the destabilization of the flat surface: terrace current (j_t), which is parallel to the surface slope, and step current (j_s), which has components parallel (j_pa) and perpendicular (j_pe) to the slope. On a high-symmetry surface, terrace and step currents are generically singular at zero slope, and this does not allow to perform the standard linear stability analysis. As far as a one-dimensional profile is considered, (j_pe) is irrelevant and (j_pa) suggests that mound sides align along [110] and [1-10] axes. On a vicinal surface, (j_s) destabilizes against step bunching; its effect against step meandering depends on the step orientation, in agreement with the recent findings by O.Pierre-Louis et al. [Phys. Rev. Lett. 82, 3661 (1999)].

cond-mat.mtrl-sci↗