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

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

Profile scaling in decay of nanostructures

The flattening of a crystal cone below its roughening transition is studied by means of a step flow model. Numerical and analytical analyses show that the height profile, h(r,t), obeys the scaling scenario dh/dr = F(r t^{-1/4}). The scaling function is flat at radii r<R(t) \sim t^{1/4}. We find a one parameter family of solutions for the scaling function, and propose a selection criterion for the unique solution the system reaches.Comment: 4 pages, RevTex, 3 eps figure

Novel continuum modeling of crystal surface evolution

We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual approach where the continuum limit is achieved when typical surface features consist of many steps, our continuum limit is approached when the number of step configurations of the ensemble is very large. The model can handle singular surface structures such as corners and facets. It has a clear computational advantage over discrete models.Comment: 4 pages, 3 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

How metal films de-wet substrates - identifying the kinetic pathways and energetic driving forces

We study how single-crystal chromium films of uniform thickness on W(110) substrates are converted to arrays of three-dimensional (3D) Cr islands during annealing. We use low-energy electron microscopy (LEEM) to directly observe a kinetic pathway that produces trenches that expose the wetting layer. Adjacent film steps move simultaneously uphill and downhill relative to the staircase of atomic steps on the substrate. This step motion thickens the film regions where steps advance. Where film steps retract, the film thins, eventually exposing the stable wetting layer. Since our analysis shows that thick Cr films have a lattice constant close to bulk Cr, we propose that surface and interface stress provide a possible driving force for the observed morphological instability. Atomistic simulations and analytic elastic models show that surface and interface stress can cause a dependence of film energy on thickness that leads to an instability to simultaneous thinning and thickening. We observe that de-wetting is also initiated at bunches of substrate steps in two other systems, Ag/W(110) and Ag/Ru(0001). We additionally describe how Cr films are converted into patterns of unidirectional stripes as the trenches that expose the wetting layer lengthen along the W[001] direction. Finally, we observe how 3D Cr islands form directly during film growth at elevated temperature. The Cr mesas (wedges) form as Cr film steps advance down the staircase of substrate steps, another example of the critical role that substrate steps play in 3D island formation

A contiuum model for low temperature relaxation of crystal steps

High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step free energy. Results are in agreement with experiments and Monte Carlo simulations of step fluctuations and monolayer cluster diffusion and relaxation. In an extended model where mass exchange with neighboring terraces is allowed, step transparency and a low temperature regime for unstable step meandering are found.Comment: Submitted to Phys.Rev.Let

Long-term kidney function recovery and mortality after COVID-19-associated acute kidney injury: An international multi-centre observational cohort study

Background: While acute kidney injury (AKI) is a common complication in COVID-19, data on post-AKI kidney function recovery and the clinical factors associated with poor kidney function recovery is lacking. Methods: A retrospective multi-centre observational cohort study comprising 12,891 hospitalized patients aged 18 years or older with a diagnosis of SARS-CoV-2 infection confirmed by polymerase chain reaction from 1 January 2020 to 10 September 2020, and with at least one serum creatinine value 1–365 days prior to admission. Mortality and serum creatinine values were obtained up to 10 September 2021. Findings: Advanced age (HR 2.77, 95%CI 2.53–3.04, p < 0.0001), severe COVID-19 (HR 2.91, 95%CI 2.03–4.17, p < 0.0001), severe AKI (KDIGO stage 3: HR 4.22, 95%CI 3.55–5.00, p < 0.0001), and ischemic heart disease (HR 1.26, 95%CI 1.14–1.39, p < 0.0001) were associated with worse mortality outcomes. AKI severity (KDIGO stage 3: HR 0.41, 95%CI 0.37–0.46, p < 0.0001) was associated with worse kidney function recovery, whereas remdesivir use (HR 1.34, 95%CI 1.17–1.54, p < 0.0001) was associated with better kidney function recovery. In a subset of patients without chronic kidney disease, advanced age (HR 1.38, 95%CI 1.20–1.58, p < 0.0001), male sex (HR 1.67, 95%CI 1.45–1.93, p < 0.0001), severe AKI (KDIGO stage 3: HR 11.68, 95%CI 9.80–13.91, p < 0.0001), and hypertension (HR 1.22, 95%CI 1.10–1.36, p = 0.0002) were associated with post-AKI kidney function impairment. Furthermore, patients with COVID-19-associated AKI had significant and persistent elevations of baseline serum creatinine 125% or more at 180 days (RR 1.49, 95%CI 1.32–1.67) and 365 days (RR 1.54, 95%CI 1.21–1.96) compared to COVID-19 patients with no AKI. Interpretation: COVID-19-associated AKI was associated with higher mortality, and severe COVID-19-associated AKI was associated with worse long-term post-AKI kidney function recovery. Funding: Authors are supported by various funders, with full details stated in the acknowledgement section

International comparisons of laboratory values from the 4CE collaborative to predict COVID-19 mortality

Given the growing number of prediction algorithms developed to predict COVID-19 mortality, we evaluated the transportability of a mortality prediction algorithm using a multi-national network of healthcare systems. We predicted COVID-19 mortality using baseline commonly measured laboratory values and standard demographic and clinical covariates across healthcare systems, countries, and continents. Specifically, we trained a Cox regression model with nine measured laboratory test values, standard demographics at admission, and comorbidity burden pre-admission. These models were compared at site, country, and continent level. Of the 39,969 hospitalized patients with COVID-19 (68.6% male), 5717 (14.3%) died. In the Cox model, age, albumin, AST, creatine, CRP, and white blood cell count are most predictive of mortality. The baseline covariates are more predictive of mortality during the early days of COVID-19 hospitalization. Models trained at healthcare systems with larger cohort size largely retain good transportability performance when porting to different sites. The combination of routine laboratory test values at admission along with basic demographic features can predict mortality in patients hospitalized with COVID-19. Importantly, this potentially deployable model differs from prior work by demonstrating not only consistent performance but also reliable transportability across healthcare systems in the US and Europe, highlighting the generalizability of this model and the overall approach