Decay of one dimensional surface modulations

The relaxation process of one dimensional surface modulations is re-examined. Surface evolution is described in terms of a standard step flow model. Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz D(x,t)=alpha(t)F(x) is provided. We use the scaling ansatz to transform the discrete step model into a continuum model for surface dynamics. The model consists of differential equations for the functions alpha(t) and F(x). The solutions of these equations agree with simulation results of the discrete step model. We identify two types of possible scaling solutions. Solutions of the first type have facets at the extremum points, while in solutions of the second type the facets are replaced by cusps. Interactions between steps of opposite signs determine whether a system is of the first or second type. Finally, we relate our model to an actual experiment and find good agreement between a measured AFM snapshot and a solution of our continuum model.Comment: 18 pages, 6 figures in 9 eps file

The profile of a decaying crystalline cone

The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both cases, we describe the decay kinetics in terms of step flow models. Numerical simulations of the models indicate that in the attachment-detachment limited case the system undergoes a step bunching instability if the repulsive interactions between steps are weak. Such an instability does not occur in the diffusion limited case. In stable cases the height profile, h(r,t), is flat at radii r<R(t)\sim t^{1/4}. Outside this flat region the height profile obeys the scaling scenario \partial h/\partial r = {\cal F}(r t^{-1/4}). A scaling ansatz for the time-dependent profile of the cone yields analytical values for the scaling exponents and a differential equation for the scaling function. In the long time limit this equation provides an exact description of the discrete step dynamics. It admits a family of solutions and the mechanism responsible for the selection of a unique scaling function is discussed in detail. Finally we generalize the model and consider permeable steps by allowing direct adatom hops between neighboring terraces. We argue that step permeability does not change the scaling behavior of the system, and its only effect is a renormalization of some of the parameters.Comment: 25 pages, 18 postscript figure

Structure determination of the (1×2) and (1×3) reconstructions of Pt(110) by low-energy electron diffraction

The atomic geometry of the (1×2) and (1×3) structures of the Pt(100) surface has been determined from a low-energy electron-diffraction intensity analysis. Both structures are found to be of the missing-row type, consisting of (111) microfacets, and with similar relaxations in the subsurface layers. In both reconstructions the top-layer spacing is contracted by approximately 20% together with a buckling of about 0.17 Å in the third layer and a small lateral shift of about 0.04 Å in the second layer. Further relaxations down to the fourth layer were detectable. The surface relaxations correspond to a variation of interatomic distances, ranging from -7% to +4%, where in general a contraction of approximately 3% for the distances parallel to the surface occurs. The Pendry and Zanazzi-Jona R factors were used in the analysis, resulting in a minimum value of RP=0.36 and RZJ=0.26 for 12 beams at normal incidence for the (1×2) structure, and similar agreement for 19 beams of the (1×3) structure. The (1×3) structure has been reproducibly obtained after heating the crystal in an oxygen atmosphere of 5×10-6 mbar at 1200 K for about 30 min and could be removed by annealing at 1800 K for 45 min after which the (1×2) structure appeared again. Both reconstructed surfaces are clean within the detection limits of the Auger spectrometer. CO adsorption lifts the reconstruction in both structures. After desorption at 500 K the initial structures appear again, indicating that at least one of the reconstructions does not represent the equilibrium structure of the clean surface and may be stabilized by impurities

Wetting layer thickness and early evolution of epitaxially strained thin films

We propose a physical model which explains the existence of finite thickness wetting layers in epitaxially strained films. The finite wetting layer is shown to be stable due to the variation of the non-linear elastic free energy with film thickness. We show that anisotropic surface tension gives rise to a metastable enlarged wetting layer. The perturbation amplitude needed to destabilize this wetting layer decreases with increasing lattice mismatch. We observe the development of faceted islands in unstable films.Comment: 4 pages, 3 eps figure

Effect of surrounding environment on atomic structure and equilibrium shape of growing nanocrystals: gold in/on SiO2

We report on the equilibrium shape and atomic structure of thermally-processed Au nanocrystals (NCs) as determined by high resolution transmission electron microscopy (TEM). The NCs were either deposited on SiO2surface or embedded in SiO2layer. Quantitative data on the NCs surface free energy were obtained via the inverse Wulff construction. Nanocrystals inside the SiO2layer are defect-free and maintain a symmetrical equilibrium shape during the growth. Nanocrystals on SiO2surface exhibit asymmetrical equilibrium shape that is characterized by the introduction of twins and more complex atomic defects above a critical size. The observed differences in the equilibrium shape and atomic structure evolution of growing NCs in and on SiO2is explained in terms of evolution in isotropic/anisotropic environment making the surface free energy function angular and/or radial symmetric/asymmetric affecting the rotational/translational invariance of the surface stress tensor

Mutation analysis of 18 nephronophthisis associated ciliopathy disease genes using a DNA pooling and next generation sequencing strategy

Background Nephronophthisis associated ciliopathies (NPHP-AC) comprise a group of autosomal recessive cystic kidney diseases that includes nephronophthisis (NPHP), Senior-Loken syndrome (SLS), Joubert syndrome (JBTS), and Meckel-Gruber syndrome (MKS). To date, causative mutations in NPHP-AC have been described for 18 different genes, rendering mutation analysis tedious and expensive. To overcome the broad genetic locus heterogeneity, a strategy of DNA pooling with consecutive massively parallel resequencing (MPR) was devised.Methods In 120 patients with severe NPHP-AC phenotypes, five pools of genomic DNA with 24 patients each were prepared which were used as templates in order to PCR amplify all 376 exons of 18 NPHP-AC genes (NPHP1, INVS, NPHP3, NPHP4, IQCB1, CEP290, GLIS2, RPGRIP1L, NEK8, TMEM67, INPP5E, TMEM216, AHI1, ARL13B, CC2D2A, TTC21B, MKS1, and XPNPEP3). PCR products were then subjected to MPR on an Illumina Genome-Analyser and mutations were subsequently assigned to their respective mutation carrier via CEL I endonuclease based heteroduplex screening and confirmed by Sanger sequencing.Results For proof of principle, DNA from patients with known mutations was used and detection of 22 out of 24 different alleles (92% sensitivity) was demonstrated. MPR led to the molecular diagnosis in 30/120 patients (25%) and 54 pathogenic mutations (27 novel) were identified in seven different NPHP-AC genes. Additionally, in 24 patients only single heterozygous variants of unknown significance were found.Conclusions The combined approach of DNA pooling followed by MPR strongly facilitates mutation analysis in broadly heterogeneous single gene disorders. The lack of mutations in 75% of patients in this cohort indicates further extensive heterogeneity in NPHP-AC

Absolute values of surface and step free energies from equilibrium crystal shapes

It is shown that exact images of the three-dimensional equilibrium shape of crystallites (ECS), recorded at several temperatures between 0.3 and 0.8 of the melting temperature of a solid, can be evaluated to yield absolute values of the surface and step free energies versus temperature, in addition to the formation energy of kinks. The essential input for this novel approach is the temperature variation of the size of a facet on the ECS and of the separation between the Wulff point and that particular facet. This approach promises access to surface free energies over a large temperature range and for well-defined low-index surface orientations

Orientation-dependent surface and step energies of Pb from first principles

The orientation-dependent surface energies of 35 low-index and vicinal Pb surface orientations, located in the [001], [(1) over bar 10], and [01 (1) over bar] zones, have been calculated by density-functional theory within the local-density approximation. The highest surface energy anisotropies in these zones are at the (210), (110), and (311) directions. Surface relaxation decreases the surface energy anisotropy significantly. For misorientations smaller than 12 degrees the (projected) surface energy in a given zone increases linearly with step density, while curvature is found at higher misorientations, indicative of repulsive step-step interactions. These results are fully consistent with the orientation-dependent surface energy predicted by the statistical mechanics of the terrace-step-kink model of vicinal surfaces. The step formation energies and surface and step relaxation energies are derived and analyzed. There is good agreement with available experimental data. The calculated surface energies in eV/atom correlate linearly with the number of broken surface bonds. Deviations from perfect linearity are found to be essential for a proper description of the equilibrium crystal shape of Pb