Low-coverage surface diffusion in complex periodic energy landscapes: Analytical solution for systems with symmetric hops and application to intercalation in topological insulators

This is the first of two papers that introduce a general expression for the tracer diffusivity in complex, periodic energy landscapes with M distinct hop rates in one-, two-, and three-dimensional diluted systems (low-coverage, single-tracer limit). The present report focuses on the analysis of diffusion in systems where the end sites of the hops are located symmetrically with respect to the hop origins (symmetric hops), as encountered in many ideal surfaces and bulk materials. For diffusion in two dimensions, a number of formulas are presented for complex combinations of the different hops in systems with triangular, rectangular, and square symmetry. The formulas provide values in excellent agreement with kinetic Monte Carlo simulations, concluding that the diffusion coefficient can be directly determined from the proposed expressions without performing the simulations. Based on the diffusion barriers obtained from first-principles calculations and a physically meaningful estimate of the attempt frequencies, the proposed formulas are used to analyze the diffusion of Cu, Ag, and Rb adatoms on the surface and within the van der Waals (vdW) gap of a model topological insulator, Bi2Se3. Considering the possibility of adsorbate intercalation from the terraces to the vdW gaps at morphological steps, we infer that, at low coverage and room temperature, (i) a majority of the Rb atoms bounce back at the steps and remain on the terraces, (ii) Cu atoms mostly intercalate into the vdW gap, the remaining fraction staying at the steps, and (iii) Ag atoms essentially accumulate at the steps and gradually intercalate into the vdW gap. These conclusions are in good qualitative agreement with previous experiments. The companion report (M. A. Gosálvez et al., Phys. Rev. B, submitted] extends the present study to the description of systems that contain asymmetric hops.We acknowledge support from the Ramon y Cajal Fellowship Program of the Spanish Ministry of Science and Innovation (M. A. Gosalvez), the JAE-Doc grant from the Junta para la Ampliacion de Estudios program cofunded by FSE (N. Ferrando), the University of the Basque Country (Grant No. GIC07IT36607), the Spanish Ministry of Science and Innovation (Grant Nos. FIS2013-48286-C02-02-P and FIS2013-48286-C02-01-P), the Basque Government through the Nanomaterials project under the nanoGUNE2014 program (Grant No. IE05-151), the Tomsk State University Academic D. I. Mendeleev Fund Program in 2015 (Research Grant No. 8.1.05.2015), and partial support from Saint Petersburg State University (Project No. 15.61.202.2015).Peer reviewe

Seasonal differences in drivers of species richness of waders in inland wetlands of La Mancha Húmeda Biosphere Reserve

1. Temporary inland wetlands are among the most threatened ecosystems worldwide, and recognition of the factors that determine species richness in different seasons is key for developing conservation plans for these systems. La Mancha Húmeda Biosphere Reserve in central Spain has many inland wetlands of this type, but the driving ecological processes of species richness are poorly understood. 2. This study examines the association of landscape and local variables with species richness patterns of inland wetlands of La Mancha Húmeda Biosphere Reserve during winter and the breeding season. The number of lakes in several increasing radii was a proxy of connectivity, and maximum flooded surface and shoreline length were surrogates of the species–area relationship. 3. Other landscape and local habitat variables, such as hydroperiod (length of inundation period), distance from human settlements, shoreline development index, vegetation surface cover, average lake depth, number of islands and surface area of islands were also analysed. Hierarchical partitioning analysis was used to evaluate the contribution of the environmental variables to explain the species richness of waders. 4. Species richness (26 species, four threatened in Europe) had different associations with the variables during the wintering and breeding seasons. The richness of breeding and wintering species was positively associated with hydroperiod and maximum flooded surface area respectively. No variable measured was negatively associated with species richness in any season. 5. Hydroperiod and flooded surface area are altered directly by human activities. Water extraction for irrigation reduces hydroperiod in some wetlands, whereas wastewater input extends hydroperiod in others, promoting wader concentrations in lakes flooded in summer and potentially favouring botulism outbreaks. In addition, the lack of protection and management on most of the lakes in La Mancha Húmeda Biosphere Reserve also favours encroachment of agriculture, destroying and degrading habitat for wintering and breeding waders.This study forms part of the doctoral thesis of M. S. S. G., supported by a grant from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil. This study was jointly supported by the Ministry of Economy and Competitiveness of the Government of Spain (MINECO) and Competitiveness and the European Regional Development Fund (FEDER) ‘One way to make Europe’, through the projects: ‘CLIMAWET’ – Climate change mitigation and adaptation in the main types of Iberian Mediterranean wetlands: carbon budget and response models of species and habitats (CGL2015‐69557‐R); and ‘ECOLAKE’ – Ecological patterns in endorheic lakes: keys to their conservation (CGL2012‐38909)