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Equilibrium shape and dislocation nucleation in strained epitaxial nanoislands  [PDF]
J. Jalkanen,O. Trushin,E. Granato,S. C. Ying,T. Ala-Nissila
Physics , 2005, DOI: 10.1103/PhysRevB.72.081403
Abstract: We study numerically the equilibrium shapes, shape transitions and dislocation nucleation of small strained epitaxial islands with a two-dimensional atomistic model, using simple interatomic pair potentials. We first map out the phase diagram for the equilibrium island shapes as a function of island size (up to N = 105 atoms) and lattice misfit with the substrate and show that nanoscopic islands have four generic equilibrium shapes, in contrast with predictions from the continuum theory of elasticity. For increasing substrate-adsorbate attraction, we find islands that form on top of a finite wetting layer as observed in Stranski-Krastanow growth. We also investigate energy barriers and transition paths for transitions between different shapes of the islands and for dislocation nucleation in initially coherent islands. In particular, we find that dislocations nucleate spontaneously at the edges of the adsorbate-substrate interface above a critical size or lattice misfit.
Spiral growth, two-dimensional nucleation, and the Ehrlich-Schwoebel effect  [PDF]
Joachim Krug
Physics , 2007,
Abstract: Frank's prediction of the spiral growth mode in 1949 defined a pivotal moment in the history of crystal growth. In recent decades the topic has received less attention, and instead we have seen a resurrection of two-dimensional nucleation theory in the context of growth experiments on defect-free homoepitaxial thin films. In particular, the key role of interlayer transport controlled by step edge barriers of the Ehrlich-Schwoebel type in shaping the morphology of multilayer films has been increasingly recognized. After a brief review of the classical theory, this paper reports on a recent study of spiral growth in the presence of step edge barriers. Our key observation is that step edge barriers lead to unconventionally shaped spiral hillocks that display the same characteristic ever-steepening height profiles as wedding cakes formed during growth by two-dimensional nucleation. This prediction was verified experimentally by inducing screw dislocations through ion bombardment of the Pt(111) surface, thus creating a homoepitaxial growth system on which spiral hillocks and wedding cakes coexist.
Scaling regimes for second layer nucleation  [PDF]
Joachim Krug
Physics , 2000, DOI: 10.1007/s100510070019
Abstract: Nucleation on top of two-dimensional islands with step edge barriers is investigated using scaling arguments. The nucleation rate is expressed in terms of three basic time scales: The time interval between deposition events, the residence time of atoms on the island, and the encounter time required for $i^\ast + 1$ atoms forming a stable nucleus to meet. Application to the problem of second-layer nucleation on growing first layer islands yields a sequence of scaling regimes with different scaling exponents relating the critical island size, at which nucleation takes place, to the diffusion and deposition rates. Second layer nucleation is fluctuation-dominated, in the sense that the typical number of atoms on the island is small compared to $i^\ast + 1$, when the first layer island density exponent $\chi$ satisfies $\chi (i^\ast + 1) < 2$. The upper critical nucleus size, above which the conventional mean-field theory of second layer nucleation is valid, increases with decreasing dimensionality. In the related case of nucleation on top of multilayer mounds fluctuation-dominated and mean-field like regimes coexist for arbitrary values of the critical nucleus size $i^\ast$.
Spiral Growth and Step Edge Barriers  [PDF]
A. Redinger,O. Ricken,P. Kuhn,A. Raetz,A. Voigt,J. Krug,T. Michely
Physics , 2007, DOI: 10.1103/PhysRevLett.100.035506
Abstract: The growth of spiral mounds containing a screw dislocation is compared to the growth of wedding cakes by two-dimensional nucleation. Using phase field simulations and homoepitaxial growth experiments on the Pt(111) surface we show that both structures attain the same characteristic large scale shape when a significant step edge barrier suppresses interlayer transport. The higher vertical growth rate observed for the spiral mounds on Pt(111) reflects the different incorporation mechanisms for atoms in the top region and can be formally represented by an enhanced apparent step edge barrier.
Shape and area fluctuation effects on nucleation theory  [PDF]
Santi Prestipino,Alessandro Laio,Erio Tosatti
Physics , 2014, DOI: 10.1063/1.4866971
Abstract: In standard nucleation theory, the nucleation process is characterized by computing $\Delta\Omega(V)$, the reversible work required to form a cluster of volume $V$ of the stable phase inside the metastable mother phase. However, other quantities besides the volume could play a role in the free energy of cluster formation, and this will in turn affect the nucleation barrier and the shape of the nucleus. Here we exploit our recently introduced mesoscopic theory of nucleation to compute the free energy cost of a nearly-spherical cluster of volume $V$ and a fluctuating surface area $A$, whereby the maximum of $\Delta\Omega(V)$ is replaced by a saddle point in $\Delta\Omega(V,A)$. Compared to the simpler theory based on volume only, the barrier height of $\Delta\Omega(V,A)$ at the transition state is systematically larger by a few $k_BT$. More importantly, we show that, depending on the physical situation, the most probable shape of the nucleus may be highly non spherical, even when the surface tension and stiffness of the model are isotropic. Interestingly, these shape fluctuations do not influence or modify the standard Classical Nucleation Theory manner of extracting the interface tension from the logarithm of the nucleation rate near coexistence.
Shape transition and dislocation nucleation in strained epitaxial islands
Jalkanen, J.;Trushin, O.;Granato, E.;Ying, S.C.;Ala-Nissila, T.;
Brazilian Journal of Physics , 2006, DOI: 10.1590/S0103-97332006000300025
Abstract: we study numerically the equilibrium shape, shape transition and dislocation nucleation in strained epitaxial islands with a two-dimensional atomistic model, using interatomic potentials of lennard-jones type. the phase diagram for the equilibrium island shapes as a function of island size and lattice misfit with the substrate is obtained by an energy minimization procedure which does not require predefined faceted shapes. we determine the energy barrier and transition path for transition between different shapes of the islands and for dislocation nucleation in initially coherent islands using a method introduced recently, based on a systematic search of the transition paths for activated events.
A study of the porosity of gas filtration cakes
Ito, L. X.;Aguiar, M. L.;
Brazilian Journal of Chemical Engineering , 2009, DOI: 10.1590/S0104-66322009000200008
Abstract: the purpose of this work was to determine the porosity of gas filtration cakes composed of powdery organic and inorganic materials, employing a technique whereby an optical microscope generates images of the powdery layer deposited on the surface of the filtering medium. to this end, experimental cake filtration porosity data were obtained as a function of the surface filtration velocity. the images generated by the optical microscope were analyzed by using an image analyzing program that supplied the cake porosity values. the results revealed that porosity decreases as surface filtration velocity increases. the average porosity of corn starch was higher than that of tapioca powder and phosphate concentrate, possibly due to the shape of the particles, differences in the physicochemical characteristics of the materials, and grain distribution. based on the relation of the experimental average porosity data and the filtration velocity, an empirical correlation was found that better fit these parameters.
Influence of adatom interactions on second layer nucleation  [PDF]
S. Heinrichs,P. Maass
Physics , 2002, DOI: 10.1103/PhysRevB.66.073402
Abstract: We develop a theory for the inclusion of adatom interactions in second layer nucleation occurring in epitaxial growth. The interactions considered are due to ring barriers between pairs of adatoms and binding energies of unstable clusters. The theory is based on a master equation, which describes the time development of microscopic states that are specified by cluster configurations on top of an island. The transition rates are derived by scaling arguments and tested against kinetic Monte-Carlo simulations. As an application we reanalyze experiments to determine the step edge barrier for Ag/Pt(111).
Aerosol nucleation spikes in the planetary boundary layer
J.-P. Chen, T.-S. Tsai,S.-C. Liu
Atmospheric Chemistry and Physics (ACP) & Discussions (ACPD) , 2011,
Abstract: Photochemically driven nucleation bursts, which typically occur within a few hours after sunrise, often produce strong aerosol number concentration (ANC) fluctuations. The causes of such ANC spikes were investigated using a detailed aerosol model running in the parcel mode. Two potential mechanisms for the ANC spikes were proposed and simulated. The blocking of actinic flux by scattered clouds can significantly influence new particle production, but this does not cause strong fluctuations in the number of aerosols within sizes greater than the detection limit of our measurements. A more plausible mechanism is the turbulence eddy effect. Strong aerosol nucleation may occur in both updrafts and downdrafts, while the cloud formation at the boundary layer top strongly reduces the number of aerosols. As the number of aerosols is sensitive to turbulence eddy and cloud formation properties, a changing turbulence condition would result in large fluctuations in the evolution of ANC similar to that observed at the surface.
Second-layer nucleation in coherent Stranski-Krastanov growth of quantum dots  [PDF]
J. E. Prieto,I. Markov
Physics , 2011, DOI: 10.1103/PhysRevB.84.195417
Abstract: We have studied the monolayer-bilayer transformation in the case of the coherent Stranski-Krastanov growth. We have found that the energy of formation of a second layer nucleus is largest at the center of the first-layer island and smallest on its corners. Thus nucleation is expected to take place at the corners (or the edges) rather than at the center of the islands as in the case of homoepitaxy. The critical nuclei have one atom in addition to a compact shape, which is either a square of i*i or a rectangle of i*(i-1) atoms, with i>1 an integer. When the edge of the initial monolayer island is much larger than the critical nucleus size, the latter is always a rectangle plus an additional atom, adsorbed at the longer edge, which gives rise to a new atomic row in order to transform the rectangle into the equilibrium square shape.
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