A general expression for the critical terrace width for step flow growth accounting for both the step permeability and the asymmetric incorporation of atoms to ascending and descending steps is derived. It covers both cases of diffusion and attachment-detachment limited regimes of growth at high and low temperatures. It is found that when at least one of the excess step-edge barriers is equal to zero, only diffusion-limited behavior regime is allowed. The step permeability does not affect both limiting cases at high and low temperatures. Comparing the theory with experimental data for the Si͑111͒͑7 ϫ 7͒ surface leads to the conclusion that the nucleation process in the interval 700-850 K takes place in an attachment-detachment limited regime with critical nuclei consisting of one and three atoms below and above 750 K, respectively. Step flow and two-dimensional island nucleation and growth ͑2DNG͒ are two basic mechanisms of crystal growth. 1 A crystal grows exclusively by step flow when the temperature is sufficiently high so that the mean free path of the adatoms is longer than the mean terrace width. Decreasing temperature leads to a drastic decrease of the adatom diffusivity, which gives rise to island nucleation and growth on the terraces. 1,2 The interplay of surface diffusion and step attachment in growth produces an adatom concentration on terraces that generally increases with increasing spacing between step sinks. Consequently, a transition between step flow and 2DNG occurs as a function of terrace width. This transition is characterized by a quantity called the critical terrace width. Since growth involves a number of thermally activated processes, it is not surprising that the critical terrace width also displays an Arrhenius behavior as a function of deposition temperature. [3][4][5] Island nucleation occurs with greatest probability at the points where the adatom concentration is the highest. 6 Therefore, a full understanding of the transition between step flow and 2DNG requires accurate knowledge of the adatom concentration profile on a terrace. The latter is determined during growth by several factors. This includes the relative importance of diffusion and step attachment, i.e., the ratelimiting step, which is characterized in opposite extremes as attachment-detachment limited ͑ADL͒ and diffusion-limited ͑DL͒ regimes. Asymmetry of the kinetic coefficients for step attachment from opposite sides of a step 7 and step permeability 2,8 are also known to affect the adatom concentration profile. Therefore, the critical terrace width should depend on the rate-limiting step, the kinetic coefficient asymmetry, and step permeability, and may be used, in principle, to determine these important microscopic details. Various models of the critical terrace width have been presented that loosely correspond to the different extremes of the ratelimiting step. 4,9,10 However, these models did not take into account the kinetic coefficient asymmetry or step permeability. In this paper, we develop a more general model ...

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We studied the step dynamics during crystal sublimation and growth in the limit of fast surface diffusion and slow kinetics of atom attachmentdetachment at the steps. For this limit we formulate a model free of the quasi-static approximation in the calculation of the adatom concentration on the terraces at the crystal surface. Such a model provides a relatively simple way to study the linear stability of a step train in a presence of step-step repulsion and an absence of destabilizing factors (as Schwoebel effect, surface electromigration etc.). The central result is that a critical velocity of the steps in the train exists which separates the stability and instability regimes. Instability occurs when the step velocity exceeds its critical valuewhere K is the step kinetic coefficient, Ω is the area of one atomic site at the surface, and the energy of step-step repulsion iswhere l is the interstep distance. Integrating numerically the equations for the time evolution of the adatom concentrations on the terraces and the equations of step motion we obtained the step trajectories. When the step velocity exceeds its critical value the plot of these trajectories manifests clear space and time periodicity (step density compression waves propagate on the vicinal surface). This ordered motion of the steps is preceded by a relatively short transition period of disordered step dynamics.

The Saric ßic ßek howardite meteorite shower consisting of 343 documented stones occurred on September 2, 2015 in Turkey and is the first documented howardite fall. Cosmogenic isotopes show that Saric ßic ßek experienced a complex cosmic-ray exposure history, exposed during~12-14 Ma in a regolith near the surface of a parent asteroid, and that añ 1 m sized meteoroid was launched by an impact 22 AE 2 Ma ago to Earth (as did one-third of all HED meteorites). SIMS dating of zircon and baddeleyite yielded 4550.4 AE 2.5 Ma and 4553 AE 8.8 Ma crystallization ages for the basaltic magma clasts. The apatite U-Pb age of 4525 AE 17 Ma, K-Ar age of~3.9 Ga, and the U,Th-He ages of 1.8 AE 0.7 and 2.6 AE 0.3 Ga are interpreted to represent thermal metamorphic and impact-related resetting ages, respectively. Petrographic; geochemical; and O-, Cr-, and Ti-isotopic studies confirm that Saric ßic ßek belongs to the normal clan of HED meteorites. Petrographic observations and analysis of organic material indicate a small portion of carbonaceous chondrite material in the Saric ßic ßek regolith and organic contamination of the meteorite after a few days on soil. Video observations of the fall show an atmospheric entry at 17.3 AE 0.8 km s À1 from NW; fragmentations at 37, 33, 31, and 27 km altitude; and provide a pre-atmospheric orbit that is the first dynamical link between the normal HED meteorite clan and the inner Main Belt. Spectral data indicate the similarity of Saric ßic ßek with the Vesta asteroid family (V-class) spectra, a group of asteroids stretching to delivery resonances, which includes (4) Vesta. Dynamical modeling of meteoroid delivery to Earth shows that the complete disruption of ã 1 km sized Vesta family asteroid or a~10 km sized impact crater on Vesta is required to provide sufficient meteoroids ≤4 m in size to account for the influx of meteorites from this HED clan. The 16.7 km diameter Antionia impact crater on Vesta was formed on terrain of the same age as given by the 4 He retention age of Saric ßic ßek. Lunar scaling for crater production to crater counts of its ejecta blanket show it was formed~22 Ma ago.A field expedition to the area was conducted by the

We recently introduced a novel model of step flow crystal growth -the so-called "" model [B. Ranguelov et al., CR Acad. Bul. Sci. 60, 389 (2007)]. In this paper we aim to develop a complete picture of the model's behaviour in the framework of the notion of universality classes. The basic assumption of the model is that the reference ("equilibrium") densities used to compute the supersaturation might be different on either side of a step, so R L C C / region where the above scaling exists cannot be assigned to a specific universality class and thus should be considered non-universal. I. IntroductionMonatomic steps on crystal surfaces appear when the crystal is cut along a plane that is not parallel to the atomic planes. These steps are the subject of longstanding interest both from a technological and a fundamental point of view. So-called step flow growth, in which the crystal grows via attachment of atoms to the existing network of steps and not through nucleation of islands on the terraces between the steps -is the growth mode of technological importance. This is also the reason for intensive theoretical work involving playing with steps and their movement. One independent direction is the study of unstable step flow growth leading to two general instabilities -step bunching, when the initial equidistant step spacing is lost and steps group to form bunches, and step meandering, when the initially straight steps bend to form meanders similar to those formed by rivers in nature. The interest in introducing novel models of surface instabilities has recently been stimulated further by experiments on step flow growth of Cu-[1,2] and Si-vicinals [3] in which simultaneous step bunching and step meandering was observed. This phenomenon is quite unexpected and contradicts the contemporary paradigm of surface instabilities. The reason is that according to the present concepts, the normal Schwoebel effect in growth, i.e. adatoms attach to the steps preferentially from the lower terrace, results in step meandering, while the inverse Schwoebel effect, in which adatoms attach to the steps preferentially from the higher terraces, results in step bunching. In principal, besides the destabilization from various sources, all of the models of step bunching instability contain also a stabilizing factor due to the step-step repulsion. Typically the destabilizing factors are the electromigration force acting on adatoms or the Ehrlich-Schwoebel effect. Step-step repulsions of different nature stabilize and promote the equidistant step distribution. In the models, the stepstep repulsion affects the equilibrium concentrations used to compute the supersaturation/undersaturation and thus, the step velocity in growth/sublimation. Here we present a new model in which a difference of the "equilibrium" adatom concentrations on both sides of the step is assumed. In this manner the destabilization and stabilization are "intrinsic" and a consequence of the same source -the step-step repulsion. In the new model the shape of the bunches formed as...

coefficient and F is a force acting on the adatoms ( F is related to the electric current heating the crystal ). In the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps we formulate a model free of the quasi-static approximation in the calculation of the adatom concentration on the terraces. The linear stability analysis of a step train results in an instability condition in the formτ is the dimensionless life-time of an adatom before desorption, f and η are dimensionless electromigration force and the force of step repulsion whereas V and cr V are the velocity of steps in the train and the critical velocity respectively. As seen instability is expected when either the velocity V is larger than cr V ( this instability is related to the "kinetic memory effect" ), or steps. Numerical integration of the equations for the time evolution of the adatom concentrations and the equations of step motion reveals two different step bunching instabilities: 1) step density waves (small bunches which do not manifest any coarsening) induced by the kinetic memory effect and 2) step bunching with coarsening when the dynamics is dominated by the electromigration. The model developed in this paper also provides very instructive illustrations of the Popkov-Krug dynamical phase transition during sublimation and growth of a vicinal crystal surface. IntroductionIn a recent paper [1] we advanced a new model for the step dynamics during sublimation and growth of a vicinal crystal surface. This model contains the same physics as the classical Burton, Cabrera, Frank (BCF) theory [2,3,4] but the mathematical treatment deviates from the BCF procedure. In contrast to their assumption that the adatom concentrations i n on the terraces reach instantly their steady state for a given step configuration we analyzed the non-steady state problem [1]. This is relatively easy in the limiting case of fast surface diffusion and slow kinetics of atom attachment and detachment at the steps, since the fast diffusion provides for a constant value of the adatom concentration all over a given terrace. We derived equations for the time evolution of the adatom concentration on the terraces and, also, equations for the step motion. In this way we were able to treat accurately the case when the time to reach steady state concentration of adatoms on the terraces is compatible with the time for nonnegligible change of the step configuration. In such a situation a new effect becomes important -the adatom concentration on a given terrace depends not only on the terrace size but on the "past of the terrace" as well. We call this a "kinetic memory effect". This effect provides a ground for a new type of instability of the regular step distribution.Step density compression waves appear at the vicinal surface as shown by both linear stability analysis and numerical integration of the equations for step motion [1]. Here our aim is to see how the "kinetic memory effect" competes with another (well known) destabilizing factor -th...

The critical terrace width λ for 2D island nucleation and growth (2DNG) on large-scale atomically flat terraces of a step-bunched Si(111)-(7×7) surface has been studied by in situ ultrahigh vacuum reflection electron microscopy as a function of the substrate temperature T and Si deposition rate R. The dependence of λ(2)(R) is characterized by a power law with scaling exponent χ=1.36-1.46, validating an attachment limited (AL) growth kinetics up to 720 °C. At this temperature, the Arrhenius dependencies lnλ(2)(1/T) change their slope, so that the effective 2DNG activation energy E(2D) drops from 2.4 eV down to 0.5 eV at T>720 °C. We first show that the E(2D) change is caused by a transition between AL and DL (diffusion limited) growth kinetics accompanied by a step shape transformation. The AL growth mode is characterized by kinetic length d(-)~10(5)a and the preferential step-down attachment of atoms to steps limited by an energy barrier E(ES)(-)≈0.9 eV.