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In the two parts of the present note we discuss questions concerning the implementation of overdetermined least-squares collocation methods for higher index differential-algebraic equations (DAEs). Since higher index DAEs lead to ill-posed problems in natural settings, the discrete counterparts are expected to be very sensitive, which attaches particular importance to their implementation. We provide in Part 1 a robust selection of basis functions and collocation points to design the discrete problem whereas we analyze the discrete least-squares problem and substantiate a procedure for its numerical solution in Part 2.

In the two parts of the present note we discuss several questions concerning the implementation of overdetermined least-squares collocation methods for higher index differential-algebraic equations (DAEs). Since higher index DAEs lead to ill-posed problems in natural settings, the discrete counterparts are expected to be very sensitive, which attaches particular importance to their implementation. In the present Part 1, we provide a robust selection of basis functions and collocation points to design the discrete problem. We substantiate a procedure for its numerical solution later in Part 2. Additionally, in Part 1, a number of new error estimates are proven that support some of the design decisions.

Combining graphene and the insulating hexagonal boron nitride (h-BN) into two-dimensional heterostructures is promising for novel, atomically thin electronic nanodevices. A heteroepitaxial growth, in which these materials are grown on top of each other, will be crucial for their scalable device integration. However, during this so-called van der Waals epitaxy, not only the atomically thin substrate itself must be considered but also the influences from the supporting substrate below it. Here, we report not only a substantial difference between the formation of h-BN on single- (SLG) and on bi-layer epitaxial graphene (BLG) on SiC, but also vice versa, that the van der Waals epitaxy of h-BN at growth temperatures well below 1000 °C affects the varying number of graphene layers differently. Our results clearly demonstrate that the additional graphene layer in BLG enhances the distance to the corrugated, carbon-rich interface of the supporting SiC substrate and thereby diminishes its influence on the van der Waals epitaxy, leading to a homogeneous formation of a smooth, atomically thin heterostructure, which will be required for a scalable device integration of 2D heterostructures.

Differential-algebraic equations with higher-index give rise to essentially ill-posed problems. The overdetermined least-squares collocation for differential-algebraic equations which has been prop ...

Context. We present a large homogeneous set of stellar parameters and abundances across a broad range of metallicities, involving 13 classical dwarf spheroidal (dSph) and ultra-faint dSph (UFD) galaxies. In total, this study includes 380 stars in Fornax, Sagittarius, Sculptor, Sextans, Carina, Ursa Minor, Draco, Reticulum II, Bootes I, Ursa Major II, Leo I, Segue I, and Triangulum II. This sample represents the largest, homogeneous, high-resolution study of dSph galaxies to date. Aims. With our homogeneously derived catalog, we are able to search for similar and deviating trends across different galaxies. We investigate the mass dependence of the individual systems on the production of α-elements, but also try to shed light on the long-standing puzzle of the dominant production site of r-process elements. Methods. We used data from the Keck observatory archive and the ESO reduced archive to reanalyze stars from these 13 classical dSph and UFD galaxies. We automatized the step of obtaining stellar parameters, but ran a full spectrum synthesis (1D, local thermal equilibrium) to derive all abundances except for iron to which we applied nonlocal thermodynamic equilibrium corrections where possible. Results. The homogenized set of abundances yielded the unique possibility of deriving a relation between the onset of type Ia supernovae and the stellar mass of the galaxy. Furthermore, we derived a formula to estimate the evolution of α-elements. This reveals a universal relation of these systems across a large range in mass. Finally, we show that between stellar masses of 2.1 × 107 M⊙ and 2.9 × 105 M⊙, there is no dependence of the production of heavy r-process elements on the stellar mass of the galaxy. Conclusions. Placing all abundances consistently on the same scale is crucial to answering questions about the chemical history of galaxies. By homogeneously analyzing Ba and Eu in the 13 systems, we have traced the onset of the s-process and found it to increase with metallicity as a function of the galaxy’s stellar mass. Moreover, the r-process material correlates with the α-elements indicating some coproduction of these, which in turn would point toward rare core-collapse supernovae rather than binary neutron star mergers as a host for the r-process at low [Fe/H] in the investigated dSph systems.

We present chemodynamical links between the present-day Milky Way halo field star population and Galactic globular clusters (GCs) using a dataset that combines information from the $\rm{\it Gaia}$ space mission and the Sloan Digital Sky Survey (SDSS-IV, DR14). Moreover, we incorporated a sample of halo giant stars with a distinct chemical signature (strong CN bandheads) that resembles the light-elements anomaly otherwise only seen in the second generation of GC stellar populations. Using three different tagging techniques, we could successfully establish unique associations between 151 extratidal stars in the neighborhood of eight GCs. In addition, we traced the possible origin of about $62\%$ of the sample of CN-strong giants to their potential host clusters. Several of the involved GCs have been brought into connection with the Gaia-Enceladus and Sequoia merger events. By establishing kinematic and chemical connections between 17 CN-strong stars and their surrounding fields, we could identify co-moving groups of stars at the same [Fe/H] with a possible cluster origin. We found strong evidence that four CN-strong stars and their associates are connected to the Sagittarius stream whilst their tightly confined [Fe/H] may hint to a birth site in M 54. Finally, we provide tentative estimates for the fraction of first-generation cluster stars among all stars lost to the halo. In the immediate cluster vicinity, this value amounts to $50.0\pm16.7\%$ while the associations in the halo field rather imply $80.2_{-5.2}^{+4.9}\%$. We speculate that -- if proven real by spectroscopic follow-up -- the disparity between these numbers could indicate a major contribution of low-mass clusters to the overall number of stars escaped to the halo or, alternatively, point toward a strong mass loss from the first generation during early cluster dissolution. [abridged], Comment: 20 pages (+9 pages of appendices), 39 figures, 4 tables, accepted for publication in A&A

Context: The effective temperature is a key parameter governing the properties of a star. For stellar chemistry, it has the strongest impact on the accuracy of the abundances derived. Since Cepheids are pulsating stars, determining their effective temperature is more complicated that in the case of non-variable stars. Aims: We want to provide a new temperature scale for classical Cepheids, with a high precision and full control of the systematics. Methods: Using a data-driven machine learning technique employing observed spectra, and taking great care to accurately phase single-epoch observations, we have tied flux ratios to (label) temperatures derived using the infrared surface brightness method. Results: We identified 143 flux ratios that allow us to determine the effective temperature with a precision of a few K and an accuracy better than 150 K, which is in line with the most accurate temperature measures available to date. The method does not require a normalization of the input spectra and provides homogeneous temperatures for low- and high-resolution spectra, even at the lowest signal-to-noise ratios. Due to the lack of a dataset of sufficient sample size for Small Magellanic Cloud Cepheids, the temperature scale does not extend to Cepheids with [Fe/H] < -0.6 dex but nevertheless provides an exquisite, homogeneous means of characterizing Galactic and Large Magellanic Cloud Cepheids. Conclusions: The temperature scale will be extremely useful in the context of spectroscopic surveys for Milky Way archaeology with the WEAVE and 4MOST spectrographs. It paves the way for highly accurate and precise metallicity estimates, which will allow us to assess the possible metallicity dependence of Cepheids' period-luminosity relations and, in turn, to improve our measurement of the Hubble constant H0., 16 pages, 13 figures, accepted in A&A

We present our chemical abundance investigation of the metal-poor ([Fe/H]=-1.60 dex), r-process-enriched ([Eu/Fe]=0.73 dex) halo star HD 20 using novel and archival high-resolution spectra at outstanding signal-to-noise ratios. By combining one of the first asteroseismic gravity measurements in the metal-poor regime from a TESS light curve with non-LTE analyses of iron lines, we derive a set of highly accurate and precise stellar parameters. These allow us to delineate a chemical pattern comprised of solid detections of 48 elements, including 28 neutron-capture elements, which establishes HD 20 among the few benchmark stars that have almost complete patterns with low systematic dependencies on the stellar parameters. Our light-element (Z, Comment: 23 pages (+10 pages appendix), 27 figures, 8 tables, revised version resubmitted to A&A

We develop a simulation algorithm that generates multivariate samples with exact means, covariances, and multivariate skewness. If required for financial applications, absence of arbitrage can be ensured. Potential applications include the simulation of risk factors for the risk management of financial institutions. We use the Kollo measure of multivariate skewness, which is more informative for these applications than the Mardia skewness previously used in this context.

Recently reported experiments and theoretical contributions concerning overdetermined polynomial collocation applied to higher-index differential–algebraic equations give rise to the conjecture tha ...

Differentialalgebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differentialalgebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discretizing the pre-image space. Numerical experiments show that the resulting method has excellent convergence properties and is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations or index-1 differentialalgebraic equations. Convergence is shown for a limited class of linear higher-index differentialalgebraic equations.

International audience; We present a study in which ferroelectric phase transition temperatures in epitaxial KxNa1−xNbO3 films are altered systematically by choosing different (110)-oriented rare-earth scandate substrates and by variation of the potassium to sodium ratio. Our results prove the capability to continuously shift the ferroelectric-to-ferroelectric transition from the monoclinic MC to orthorhombic c-phase by about 400 °C via the application of anisotropic compressive strain. The phase transition was investigated in detail by monitoring the temperature dependence of ferroelectric domain patterns using piezoresponse force microscopy and upon analyzing structural changes by means of high resolution X-ray diffraction including X-ray reciprocal space mapping. Moreover, the temperature evolution of the effective piezoelectric coefficient d33,f was determined using double beam laser interferometry, which exhibits a significant dependence on the particular ferroelectric phase.

We present a chemo-dynamical study of the Orphan stellar stream using a catalog of RR~Lyrae pulsating variable stars for which photometric, astrometric, and spectroscopic data are available. Employing low-resolution spectra from the Sloan Digital Sky Survey (SDSS), we determined line-of-sight velocities for individual exposures and derived the systemic velocities of the RR~Lyrae stars. In combination with the stars' spectroscopic metallicities and \textit{Gaia} EDR3 astrometry, we investigated the northern part of the Orphan stream. In our probabilistic approach, we found 20 single mode RR~Lyrae variables likely associated with the Orphan stream based on their positions, proper motions, and distances. The acquired sample permitted us to expand our search to nonvariable stars in the SDSS dataset, utilizing line-of-sight velocities determined by the SDSS. We found 54 additional nonvariable stars linked to the Orphan stream. The metallicity distribution for the identified red giant branch stars and blue horizontal branch stars is, on average, $-2.13\pm0.05$ dex and $-1.87\pm0.14$ dex, with dispersions of 0.23 and 0.43dex, respectively. The metallicity distribution of the RR~Lyrae variables peaks at $-1.80\pm0.06$ dex and a dispersion of 0.25dex. Using the collected stellar sample, we investigated a possible link between the ultra-faint dwarf galaxy Grus II and the Orphan stream. Based on their kinematics, we found that both the stream RR~Lyrae and Grus II are on a prograde orbit with similar orbital properties, although the large uncertainties on the dynamical properties render an unambiguous claim of connection difficult. At the same time, the chemical analysis strongly weakens the connection between both. We argue that Grus II in combination with the Orphan stream would have to exhibit a strong inverse metallicity gradient, which to date has not been detected in any Local Group system., 22 pages, 12 figures, Accepted for publication in A&A, final version

Van der Waals heterostructures have captured scientific attention due to their unique properties obtained through the stacking of 2D crystals. Large-area synthesis of such structures is crucial to implement them in future applications. In this work, we investigated the effect of the substrate on the structural properties of MoS2 grown by chemical vapor deposition on epitaxial graphene (EG)/SiC(0 0 0 1) and SiO2/Si(1 0 0). We also investigated the effect of each substrate on the thermal stability of the resulting MoS2 in face of hexagonal boron nitride (h-BN) growth by MBE on its surface. Structural characterization of samples was performed by atomic force microscopy and Raman spectroscopy. MoS2 islands grown on EG offered improved morphology in comparison to those formed on amorphous SiO2. Synchrotron-based grazing-incidence X-ray diffraction has confirmed epitaxial growth of MoS2 on EG at a relatively low temperature (of 600 °C). X-ray photoelectron spectroscopy data have revealed that MoS2/EG remains stable during h-BN growth, while the use of SiO2 as substrate led to its complete degradation. These results elucidate the effect of different substrates on the growth behavior and thermal stability of MoS2 and illustrate the great potential of EG as a template for scalable fabrication of high-quality van der Waals heterostructures.

Scalable fabrication of magnetic 2D materials and heterostructures constitutes a crucial step for scaling down current spintronic devices and the development of novel spintronic applications. Here, we report on van der Waals (vdW) epitaxy of the layered magnetic metal Fe3GeTe2 (FGT) - a 2D crystal with highly tunable properties and a high prospect for room temperature ferromagnetism (FM) - directly on graphene by employing molecular beam epitaxy. Morphological and structural characterization confirmed the realization of large-area, continuous FGT/graphene heterostructure films with stable interfaces and good crystalline quality. Furthermore, magneto-transport and x-ray magnetic circular dichroism investigations confirmed a robust out-of-plane FM in the layers, comparable to state-of-the-art exfoliated flakes from bulk crystals. These results are highly relevant for further research on wafer-scale growth of vdW heterostructures combining FGT with other layered crystals such as transition metal dichalcogenides for the realization of multifunctional, atomically thin devices., They also acknowledge the provision of beamtime under the project HC-4068 at the European Synchrotron Radiation Facility (ESRF), located in Grenoble (France). ICN2 researchers acknowledge support from the European Union Horizon 2020 research and innovation programme under Grant Agreement No. 881603 (Graphene Flagship).

Journal of applied physics 128(18), 184101 (2020). doi:10.1063/5.0029167 special issue: "Domains and Domain Walls in Ferroic Materials", The three-dimensional arrangement and orientation of domain walls in ferroelectric K$_{0.9}$Na$_{0.1}$NbO$_{3}$/(110)NdScO$_{3}$ epitaxial thin films wereinvestigated at different temperatures both experimentally by means of piezoresponse force microscopy and three-dimensional x-ray diffractionand theoretically by three-dimensional phase-field simulations. At room temperature, a well-ordered herringbone-like domain patternappears in which there is a periodic arrangement of a$_1$a$_2$/M$_C$ monoclinic phases. Four different types of domain walls are observed, whichcan be characterized by out-of-plane tilt angles of ±45° and in-plane twist angles of ±21°. For the orthorhombic high-temperature phase, aperiodic $_1$a$_2$ stripe domain pattern with exclusive in-plane polarization is formed. Here, two different types of domain walls are observed,both of them having a fixed out-of-plane domain wall angle of 90° but distinguished by different in-plane twist angles of ±45°. The experimentalresults are fully consistent with three-dimensional phase-field simulations using anisotropic misfit strains. The qualitative agreementbetween the experiment and the theory applies, in particular, to the wide phase transition range between about 180 °C and 260 °C. In thistemperature range, a complex interplay of coexisting monoclinic $_1$a$_2$/M$_C$ and orthorhombic $_1$a$_2$ phases takes place., Published by American Inst. of Physics, Melville, NY

A highly regular one-dimensional domain pattern is formed in ferroelectric K0.75Na0.25NbO3 thin films grown on (110) TbScO3 substrates using metal–organic chemical vapour deposition (MOCVD). The domain pattern exhibits a lateral periodicity of about 50 nm and extends over several micrometres. The monoclinic symmetry of the domains is controlled by the elastic anisotropy of K0.75Na0.25NbO3 and the anisotropic lattice strain, which is highly compressive in one in-plane direction and weakly tensile in the corresponding orthogonal direction. Using piezoresponse force microscopy and X-ray diffraction, the monoclinic MA phase is identified, which is associated with both a strong vertical and a lateral electric polarization component. The lateral component of the polarization vector is collinear with the ±[{\overline 1}10]pc shear direction of the pseudocubic unit cell of the film and changes periodically by 180° in adjacent domains. A structural variant of a 90° rotated MA domain pattern, where the monoclinic distortion of the pseudocubic unit cells occurs along ±[110]pc, is also observed. However, this variant appears with significantly lower probability, in agreement with energy considerations based on linear elasticity theory. Thus, the incorporation of highly anisotropic lattice strain provides the opportunity to grow one-dimensional nanostructures with high ferroelectric properties.

We use deep multi-epoch near-IR images of the VISTA Variables in the Via Lactea (VVV) Survey to measure proper motions (PMs) of stars in the Milky Way globular cluster FSR1716 = VVV-GC05. The color-magnitude diagram of this object, made using PM selected members, shows an extended horizontal branch, nine confirmed RR Lyrae members in the instability strip, and possibly several hotter stars extending to the blue. Based on the fundamental-mode (ab-type) RR Lyrae stars that move coherently with the cluster, we confirmed that FSR1716 is an Oosterhoff I globular cluster with a mean period Pab = 0.574 days. Intriguingly, we detect tidal extensions to both sides of this cluster in the spatial distribution of PM selected member stars. Also, one of the confirmed RRabs is located 11 arcmin in projection from the cluster center, suggesting that FSR1716 may be losing stars due to the gravitational interaction with the Galaxy. We also measure radial velocities (RVs) for five cluster red giants selected using the PMs. The combination of RVs and PMs allow us to compute for the first time the orbit of this globular cluster, using an updated Galactic potential. The orbit results to be confined within |Zmax | < 2.0 kpc, and has eccentricity 0.4 < e < 0.6, with perigalactic distance 1.5 < Rperi (kpc) < 2.3, and apogalactic distance 5.3 < Rapo (kpc) < 6.4. We conclude that, in agreement with its relatively low metallicity ([Fe/H]= -1.4 dex), this is an inner halo globular cluster plunging into the disk of the Galaxy. As such, this is a unique object to test the dynamical processes that contribute to the disruption of Galactic globular clusters., 6 figures, 4 tables, accepted in APJ

${\mathrm{Fe}}_{3}\mathrm{Si}/\mathrm{Ge}(\mathrm{Fe},\mathrm{Si})/{\mathrm{Fe}}_{3}\mathrm{Si}$ thin-film stacks were grown by a combination of molecular beam epitaxy and solid-phase epitaxy (Ge on ${\mathrm{Fe}}_{3}\mathrm{Si}$). The stacks were analyzed using electron microscopy, electron diffraction, and synchrotron x-ray diffraction. The Ge(Fe,Si) films crystallize in the well-oriented, layered tetragonal structure ${\mathrm{FeGe}}_{2}$ with space group $P4mm$. This kind of structure does not exist as a bulk material and is stabilized by the solid-phase epitaxy of Ge on ${\mathrm{Fe}}_{3}\mathrm{Si}$. We interpret this as an ordering phenomenon induced by minimization of the elastic energy of the epitaxial film.

Globular clusters (GCs) and their dynamic interactions with the Galactic components provide an important insight into the structure and formation of the early Milky Way. Here, we present a kinematic study of two outer halo GCs based on a combination of VLT/FORS2, VLT/FLAMES, and Magellan/MIKE low- and high-resolution spectroscopy of 32 and 27 member stars, respectively. Although both clusters are located at Galactocentric distances of 15 kpc, they have otherwise very different properties. M 75 is a luminous and metal-rich system at [Fe/H] = $-1.2$ dex, a value that we confirm from the calcium triplet region. This GC shows mild evidence for rotation with an amplitude of A$_{\rm rot}\sim$5 km s$^{-1}$. One of the most metal-poor GCs in the Milky Way (at [FeII/H] = $-2.3$ dex), NGC 6426 exhibits marginal evidence of internal rotation at the 2 km s$^{-1}$ level. Both objects have velocity dispersions that are consistent with their luminosity. Although limited by small-number statistics, the resulting limits on their $A_{\rm rot}/\sigma_0$ ratios suggest that M 75 is a slow rotator driven by internal dynamics rather than being effected by the weak Galactic tides at its large distances. Here, M 75 ($A_{\rm rot}/\sigma=0.31$) is fully consistent with the properties of other, younger halo clusters. At $A_{\rm rot}/\sigma_0=0.8\pm0.4$, NGC 6426 appears to have a remarkably ordered internal motion for its low metallicity, but the large uncertainty does not allow for an unambiguous categorization as a fast rotator. An accretion origin of M 75 cannot be excluded, based on the eccentric orbit, which we derived from the recent data release 2 of Gaia, and considering its younger age., Comment: 9 pages, 9 figures, accepted for publication in Astronomy & Astrophysics

A route to realize strain engineering in weakly bonded heterostructures is presented. Such heterostructures, consisting of layered materials with a pronounced bond hierarchy of strong and weak bonds within and across their building blocks respectively, are anticipated to grow decoupled from each other. Hence, they are expected to be unsuitable for strain engineering as utilized for conventional materials which are strongly bonded isotropically. Here, it is shown for the first time that superlattices of layered chalcogenides (Sb2Te3/GeTe) behave neither as fully decoupled two-dimensional (2D) materials nor as covalently bonded three-dimensional (3D) materials. Instead, they form a novel class of 3D solids with an unparalleled atomic arrangement, featuring a distribution of lattice constants, which is tunable. A map to identify further material combinations with similar characteristic is given. It opens the way for the design of a novel class of artificial solids with unexplored properties.

Frontiers in Materials 4, 26 (2017). doi:10.3389/fmats.2017.00026, The application of lattice strain through epitaxial growth of oxide films on lattice mismatched perovskite-like substrates strongly influences the structural properties of ferroelectric domains and their corresponding piezoelectric behavior. The formation of different ferroelectric phases can be understood by a strain-phase diagram, which is calculated within the framework of the Landau–Ginzburg–Devonshire theory. In this paper, we illustrate the opportunity of ferroelectric domain engineering in the KxNa1−xNbO3 lead-free material system. In particular, the following examples are discussed in detail: (i) Different substrates (NdGaO3, SrTiO3, DyScO3, TbScO3, and GdScO3) are used to systematically tune the incorporated epitaxial strain from compressive to tensile. This can be exploited to adjust the NaNbO3 thin film surface orientation and, concomitantly, the vector of electrical polarization, which rotates from mainly vertical to exclusive in-plane orientation. (ii) In ferroelectric NaNbO3, thin films grown on rare-earth scandate substrates, highly regular stripe domain patterns are observed. By using different film thicknesses, these can be tailored with regard to domain periodicity and vertical polarization component. (iii) A featured potassium concentration of x = 0.9 of KxNa1−xNbO3 thin films grown on (110) NdScO3 substrates favors the coexistence of two equivalent, monoclinic, but differently oriented ferroelectric phases. A complicated herringbone domain pattern is experimentally observed which consists of alternating MC and a1a2 domains. The coexistence of different types of ferroelectric domains leads to polarization discontinuities at the domain walls, potentially enabling high piezoelectric responses. In each of these examples, the experimental results are in excellent agreement with predictions based on the linear elasticity theory., Published by Frontiers Media, Lausanne

The fabrication of nanowires with axial multiquantum wells or disks presenting a homogeneous size and shape distribution along the whole stack is still an unresolved challenge, despite being essential for narrowing their light emission bandwidth. In this work we demonstrate that the commonly observed change in the shape of the disks along the stacking direction proceeds in a systematic, predictable way. High- resolution transmission electron microscopy of stacked (In,Ga)N quantum discs embedded in GaN nanowires with diameters of ∼40 nm and lengths of ∼700 nm and finite element method calculations show that, contrary to what is normally assumed, this change is not related to the radial growth of the nanowires, which is shown to be negligible, but to the strain relaxation of the whole active region. A simple model is proposed to account for the experimental observations. The model assumes that each disk reaches an equilibrium shape that minimizes the overall energy of the system, given by the sum of the surface and strain energies of the disk itself and the barrier below. The strain state of the barrier is affected by the presence of the disk buried directly below in a way that depends on its shape. This gives rise to a cumulative process, which makes the aspect ratio of each quantum disk to be smaller compared to the disk grown just before, in qualitative agreement with the experimental observations. The obtained results imply that strain relaxation is an important factor to bear in mind for the design of multiquantum disks with controlled shape along the stacking direction in any lattice mismatched nanowire system.

Nanofocus x-ray diffraction is used to investigate the structure and local strain field of an isolated ðIn; GaÞN=GaN core-shell microrod. Because the high spatial resolution of the x-ray beam is only 80 × 90 nm2, we are able to investigate several distinct volumes on one individual side facet. Here, we find a drastic increase in thickness of the outer GaN shell along the rod height. Additionally, we performed highangle annular dark-field scanning-transmission-electron-microscopy measurements on several rods from the same sample showing that (In,Ga)N double-quantum-well and GaN barrier thicknesses also increase strongly along the height. Moreover, plastic relaxation is observed in the top part of the rod. Based on the experimentally obtained structural parameters, we simulate the strain-induced deformation using the finiteelement method, which serves as the input for subsequent kinematic scattering simulations. The simulations reveal a significant increase of elastic in-plane relaxation along the rod height. However, at a certain height, the occurrence of plastic relaxation yields a decrease of the elastic strain. Because of the experimentally obtained structural input for the finite-element simulations, we can exclude unknown structural influences on the strain distribution, and we are able to translate the elastic relaxation into an indium concentration which increases by a factor of 4 from the bottom to the height where plastic relaxation occurs.

Van der Waals heterostructures combining hexagonal boron nitride (h-BN) and graphene offer many potential advantages, but remain difficult to produce as continuous films over large areas. In particular, the growth of h-BN on graphene has proven to be challenging due to the inertness of the graphene surface. Here we exploit a scalable molecular beam epitaxy based method to allow both the h-BN and graphene to form in a stacked heterostructure in the favorable growth environment provided by a Ni(111) substrate. This involves first saturating a Ni film on MgO(111) with C, growing h-BN on the exposed metal surface, and precipitating the C back to the h-BN/Ni interface to form graphene. The resulting laterally continuous heterostructure is composed of a top layer of few-layer thick h-BN on an intermediate few-layer thick graphene, lying on top of Ni/MgO(111). Examinations by synchrotronbased grazing incidence diffraction, X-ray photoemission spectroscopy, and UV-Raman spectroscopy reveal that while the h-BN is relaxed, the lattice constant of graphene is significantly reduced, likely due to nitrogen doping. These results illustrate a different pathway for the production of h-BN/graphene heterostructures, and open a new perspective for the large-area preparation of heterosystems combining graphene and other 2D or 3D materials. Funding Agencies|Leibniz Association; Alexander von Humboldt Foundation

Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations. Electronic Supplementary Material The online version of this article (doi:10.1007/s10827-017-0639-7) contains supplementary material, which is available to authorized users.

Scanning X-ray nanodiffraction on a highly periodic ferroelectric domain pattern of a strained K0.75Na0.25NbO3 epitaxial layer has been performed by using a focused X-ray beam of about 100 nm probe size. A 90°-rotated domain variant which is aligned along [1{\overline 1}2]TSO has been found in addition to the predominant domain variant where the domains are aligned along the [{\overline 1}12]TSO direction of the underlying (110) TbScO3 (TSO) orthorhombic substrate. Owing to the larger elastic strain energy density, the 90°-rotated domains appear with significantly reduced probability. Furthermore, the 90°-rotated variant shows a larger vertical lattice spacing than the 0°-rotated domain variant. Calculations based on linear elasticity theory substantiate that this difference is caused by the elastic anisotropy of the K0.75Na0.25NbO3 epitaxial layer.

Scalable fabrication of atomically thin hexagonal boron nitride (h-BN) films is highly important for the future implementation of this two-dimensional dielectric in various applications. In this contribution, we report on systematical growth experiments of few-layer thick h-BN, synthesized by molecular beam epitaxy (MBE), on crystalline Ni films deposited on MgO(111). The samples are studied using scanning electron microscopy, atomic force microscopy, Raman spectroscopy, and synchrotron-based grazing incidence diffraction. Growth parameters for the realization of continuous h-BN films with high structural quality are presented and discussed. Additionally, our study also aims at gaining insight into the nucleation and growth behavior of h-BN on the Ni surface, which is crucial for achieving further improvement in terms of crystal quality and thickness homogeneity of h-BN layers grown not only by MBE but also by other methods.

In this work, we report on the spontaneous formation of ordered arrays of nanometer-sized Bi-rich structures due to lateral composition modulations in Ga(As,Bi)/GaAs quantum wells grown by molecular beam epitaxy. The overall microstructure and chemical distribution is investigated using transmission electron microscopy. The information is complemented by synchrotron x-ray grazing incidence diffraction, which provides insight into the in-plane arrangement. Due to the vertical inheritance of the lateral modulation, the Bi-rich nanostructures eventually shape into a three-dimensional assembly. Whereas the Bi-rich nanostructures are created via two-dimensional phase separation at the growing surface, our results suggest that the process is assisted by Bi segregation which is demonstrated to be strong and more complex than expected, implying both lateral and vertical (surface segregation) mass transport. As demonstrated here, the inherent thermodynamic miscibility gap of Ga(As,Bi) alloys can be exploited to create highly uniform Bi-rich units embedded in a quantum confinement structure.

The anisotropic coefficient of thermal expansion for single-crystalline monoclinic β-Ga2O3 has been precisely measured by synchrotron-based high resolution x-ray diffraction in the temperature range from 298 to 1200 K. We derived values along the three main crystallographic directions, based on spacings for (600), (020), and ( 2 ¯ 04 ) lattice planes. αa changes non-linearly between 0.10 × 10–6 K–1 and 2.78 × 10–6 K–1 in the temperature range of 298 to 1200 K, while the values of αb and αc along the further two directions are nearly double. Within the Einstein model, we have numerically modeled the functional dependencies applying a single phonon mode.

We present a detailed analysis of the ferroelectric domain structure of K0.70Na0.30NbO3 thin films on (110) TbScO3 grown by metal-organic chemical vapor deposition. Upon piezoresponse force microscopy and nanofocus x-ray diffraction measurements we derive a domain model revealing monoclinic MC domains. The complex domain pattern is formed out of four co-existing in-plane orientations of the shearing direction of the monoclinic unit cell resulting in four types of superdomains each being composed of well-ordered stripe domains. Finally, we present surface acoustic wave (SAW) experiments that exhibit extraordinary signal intensities given the low thickness of the tested film. Moreover, the SAW propagation is found to occur selectively along the identified shearing directions.

This work focuses on homoepitaxial growth of β-Ga2O3 on (100)-oriented substrates during molecular beam epitaxy. It provides a comprehensive study on the growth mode by combining in situ with ex situ tools. In situ reflection high-energy electron diffraction (RHEED) indicates 2D layer-by-layer mode accompanied by (1 × 1) surface reconstruction. The homoepitaxial layers are grown pseudomorphic with the substrate without in-plane strain as probed by in-plane azimuthal RHEED and out-of-plane synchrotron-based high resolution x-ray diffraction. In contrast to the substrate, stacking faults and twin domains are present in the layer.

The formation process of a ferroelectric multi-rank domain pattern in the thickness range of 7-52 nm is investigated for monoclinic K0.9Na0.1NbO3 strained epitaxial films on (110) NdScO3 substrates. Although the elastic strain energy density is degenerated for two pseudocubic orientations, a distinctive hierarchy of domain evolution is observed with exclusive in-plane a1a2 domains for very thin films and the retarded onset of a ferroelectric MC phase at larger film thickness. This is accompanied by a thickness dependent transformation from stripe domains to a herringbone pattern and, eventually, for the thickest film, to a checkerboard-like structure. These transformations in the domain arrangement and width are correlated to energetic aspects as depolarization field and anisotropic strain relaxation in the film. While for the MC domains plastic strain relaxation is throughout observed, the a1a2 domains show a two-step strain relaxation mechanism starting with an in-plane elastic shearing, which is followed by plastic lattice relaxation. Our results highlight a pathway for engineering and patterning of periodic ferroelectric domain structures.

Heteroepitaxial Ga2O3 was deposited on c-plane and a-plane oriented sapphire by plasma-assisted molecular beam epitaxy and probed by ex-situ and in-situ synchrotron-based x-ray diffraction. The investigation on c-plane sapphire determined a critical thickness of around 33 A, at which the monoclinic β-phase forms on top of the hexagonal α-phase. A 143 A thick single phase α-Ga2O3 was observed on a-plane sapphire, much thicker than the α-Ga2O3 on c-plane sapphire. The α-Ga2O3 relaxed very fast in the first 30 A in both out-of-plane and in-plane directions as measured by the in-situ study.

Epitaxial growth of ferroelectric KxNa1−xNbO3 thin films on (110) NdScO3 substrates results in the formation of domain walls which significantly differ in their arrangement from commonly observed 45° or 90° inclinations. The deviation is attributed to the monoclinic symmetry of the evolving a1a2/MC herringbone pattern and can be controlled by the epitaxial strain. In this work, tuning of the in-plane domain angle is systematically performed by the variation of the potassium content in KxNa1−xNbO3. The experimental data are in full agreement with a theoretical model. The observed behavior yields a promising pathway for domain engineering and patterning of periodic structures.

A novel concept to obtain a ferroelectric material with enhanced piezoelectric properties is proposed. This approach is based on the combination of two pathways: (i) the evolution of a ferroelectric monoclinic phase and, (ii) the coexistence of different types of ferroelectric domains leading to polarization discontinuities at the domain walls. Each of these pathways enables polarization rotation in the material which is responsible for giant piezoelectricity. Targeted incorporation of anisotropic epitaxial lattice strain is used to implement this approach. The feasibility of our concept is demonstrated for K0.9Na0.1NbO3 epitaxial layers grown on NdScO3 substrates where the coexistence of (100)pc and (001)pc pseudocubic oriented monoclinic domains is experimentally verified. This coexistence results in a complex periodic domain pattern with alternating emergence of ferroelectric in-plane a 1 a 2 and inclined M C monoclinic phases, which differ in the direction of the electrical polarization vector. Our approach opens the possibility to exploit ferroelectric properties in both vertical and lateral directions and to achieve enhanced piezoelectric properties in lead-free material caused by singularities at the domains walls.

We present a systematic theoretical study of the influence of elastic strain relaxation on the built-in electrostatic potentials and the electronic properties of axial [Formula: see text] nanowire (NW) heterostructures. Our simulations reveal that for a sufficiently large ratio between the thickness of the [Formula: see text] disk and the diameter of the NW, the elastic relaxation leads to a significant reduction of the built-in electrostatic potential in comparison to a planar system of similar layer thickness and In content. In this case, the ground state transition energies approach constant values with increasing thickness of the disk and only depend on the In content, a behavior usually associated to that of a quantum well free of built-in electrostatic potentials. We show that the structures under consideration are by no means field-free, and the built-in potentials continue to play an important role even for ultrathin NWs. In particular, strain and the resulting polarization potentials induce complex confinement features of electrons and holes, which depend on the In content, shape, and dimensions of the heterostructure.

Hardness of epitaxial GaAs1−xNx films on GaAs(001) with different film thicknesses, varying from 80 to 700 nm, and nitrogen compositions x between zero (pure GaAs) and 0.031, were studied by means of nano-indentation. As a result, a disproportionate and monotonic increase by 17% in hardness was proved in the dilute range from GaAs to GaAs0.969N0.031. We are tracing this observation to solid solution strengthening, an extrinsic effect based on dislocation pinning due to interstitial nitrogen. On the other hand, intrinsic effects related to different electronegativities of As and N (i.e., altered bonding conditions) could be ruled out. Furthermore, in tensilely strained GaAs1−xNx layers, the appearance of cracks acts as the main strain relieving mechanism. A correlation between cracking and hardness reduction is investigated and discussed as a further relaxation pathway.

We present our detailed spectroscopic analysis of the chemical composition of four red giant stars in the halo globular cluster NGC 6426. We obtained high-resolution spectra using the Magellan2/MIKE spectrograph, from which we derived equivalent widths and subsequently computed abundances of 24 species of 22 chemical elements. For the purpose of measuring equivalent widths, we developed a new semi-automated tool, called EWCODE. We report a mean Fe content of [Fe/H] = -2.34$\pm$0.05 dex (stat.) in accordance with previous studies. At a mean $\alpha$-abundance of [(Mg,Si,Ca)/3 Fe] = 0.39$\pm$0.03 dex, NGC 6426 falls on the trend drawn by the Milky Way halo and other globular clusters at comparably low metallicities. The distribution of the lighter $\alpha$-elements as well as the enhanced ratio [Zn/Fe] = 0.39 dex could originate from hypernova enrichment of the pre-cluster medium. We find tentative evidence for a spread in the elements Mg, Si, and Zn, indicating an enrichment scenario, where ejecta of evolved massive stars of a slightly older population polluted a newly born younger one. The heavy element abundances in this cluster fit well into the picture of metal-poor globular clusters, which in that respect appear to be remarkably homogeneous. The pattern of the neutron-capture elements heavier than Zn point towards an enrichment history governed by the r-process with only little -if any- sign of s-process contributions. This finding is supported by the striking similarity of our program stars to the metal-poor field star HD 108317., Comment: 14 pages, 12 figures, accepted for publication in Astronomy & Astrophysics

Co$_{2}$TiSi films were grown by molecular beam epitaxy on GaAs(001) and analyzed using reflection high-energy electron diffraction, and electron microscopy. In addition, X-ray diffraction was combined with lattice parameter calculations by density functional theory comparing the \textit{L$2_1$} and \textit{B}2 structures and considering the influence of non--stoichiometry. Columnar growth is found and attributed to inhomogeneous epitaxial strain from non-random alloying. In films with thicknesses up to 13~nm these columns may be the origin of perpendicular magnetization with the easy axis perpendicular to the sample surface. We found \textit{L$2_1$} and \textit{B}2 ordered regions, however the [Co]/[Ti]--ratio is changing in dependence of the position in the film. The resulting columnar structure is leading to anisotropic \textit{B}2--ordering with the best order parallel to the axes of the columns.

Employing nanofocus x-ray diffraction, we investigate the local strain field induced by a five-fold (In,Ga)N multi-quantum well embedded into a GaN micro-rod in core-shell geometry. Due to an x-ray beam width of only 150 nm in diameter, we are able to distinguish between individual m-facets and to detect a significant in-plane strain gradient along the rod height. This gradient translates to a red-shift in the emitted wavelength revealed by spatially resolved cathodoluminescence measurements. We interpret the result in terms of numerically derived in-plane strain using the finite element method and subsequent kinematic scattering simulations which show that the driving parameter for this effect is an increasing indium content towards the rod tip.

The dynamics of strain relaxation and intermixing during molecular beam epitaxy of La2O3 and Lu2O3 superlattices and alloys consisting of both binaries on Si(111) have been studied by real-time in situ grazing incidence x-ray diffraction and high resolution transmission electron microscopy. The presence of both hexagonal and cubic polymorphs of La2O3 influences the epitaxial formation within the superlattice. The process of strain relaxation is closely related to the presence of a (La,Lu)2O3 alloy adopting a cubic symmetry. It is formed by interdiffusion of La and Lu atoms reducing internal lattice mismatch within the superlattice. An interface thickness dominated by interdiffusion regions of about 3 monolayers is determined by high-angle annular dark field scanning transmission electron microscopy.

We study the elastic properties of dilute Ga(As,N) thin films grown on GaAs(001) by means of nano-indentation and complementary dynamic finite element calculations. The experimental results of indentation modulus are compared with simulations in order to extract the cubic elastic constants cij as a function of nitrogen content of the Ga(As,N) alloys. Both, indentation modulus and elastic constants decrease with increasing nitrogen content, which proves a strong negative bowing effect in this system in contrast to Vegard's law.

We study the three-dimensional deformation field induced by an axial (In,Ga)N segment in a GaN nanowire. Using the finite element method within the framework of linear elasticity theory, we study the dependence of the strain field on the ratio of segment length and nanowire radius. Contrary to intuition, the out-of-plane-component of the elastic strain tensor is found to assume large negative values for a length-to-radius ratio close to one. We show that this unexpected effect is a direct consequence of the deformation of the nanowire at the free sidewalls and the associated large shear strain components. Simulated reciprocal space maps of a single (In,Ga)N/GaN nanowire demonstrate that nanofocus x-ray diffraction is a suitable technique to assess this peculiar strain state experimentally.

GaAs/Fe$_{3}$Si core/shell nanowire structures were fabricated by molecular-beam epitaxy on oxidized Si(111) substrates and investigated by synchrotron x-ray diffraction. The surfaces of the Fe$_3$Si shells exhibit nanofacets. These facets consist of well pronounced Fe$_3$Si{111} planes. Density functional theory reveals that the Si-terminated Fe$_3$Si{111} surface has the lowest energy in agreement with the experimental findings. We can analyze the x-ray diffuse scattering and diffraction of the ensemble of nanowires avoiding the signal of the substrate and poly-crystalline films located between the wires. Fe$_3$Si nanofacets cause streaks in the x-ray reciprocal space map rotated by an azimuthal angle of 30{\deg} compared with those of bare GaAs nanowires. In the corresponding TEM micrograph the facets are revealed only if the incident electron beam is oriented along [1$\overline{1}$0] in accordance with the x-ray results. Additional maxima in the x-ray scans indicate the onset of chemical reactions between Fe$_{3}$Si shells and GaAs cores occurring at increased growth temperatures., Comment: 15 pages, 5 figures

The formation mechanisms of GaN nanowires grown on a Si${}_{x}$N${}_{y}$ amorphous interlayer within a self-induced approach by molecular beam epitaxy have been investigated by combining in situ reflection high-energy electron-diffraction measurements with ex situ high-resolution transmission electron microscopy imaging. It is found that GaN initially nucleates as spherical cap-shaped islands with a wetting angle of $42\ifmmode\pm\else\textpm\fi{}{7}^{\ifmmode^\circ\else\textdegree\fi{}}$. Subsequently, these islands coarsen and undergo a shape transition toward the nanowire morphology at an experimental critical radius of 5 nm. As the epitaxial constraint is very weak on an amorphous interlayer, the equivalent Laplace pressure due to the effects of surface stress has been taken into account. Analytical and finite-element method calculations show that the Laplace pressure results at the nanoscale dimensions in significant volume elastic strain in both spherical caps and nanowires. From thermodynamic considerations, it is revealed that the related strain energy density is slightly in favor of the shape transition toward the nanowire geometry owing to its higher ability to relieve the strain. Nevertheless, the anisotropy of surface energy is an even stronger driving force, since the nanowires are composed of $c$- and $m$-planes with very low surface energies. It is deduced that an energy barrier does exit for the shape transition and may be related to edge effects, resulting in a growth condition-dependent critical radius.

Vertical stacks of (In, Ga)N insertions in GaN nanowires are grown by molecular beam epitaxy. The chemical composition and strain within the structure are probed by a combination of high-resolution x-ray diffraction, transmission electron microscopy, and geometrical phase analysis. The (In, Ga)N insertions are coherently strained. Finite-element simulations strongly support an effective strain relaxation mechanism of the surrounding GaN matrix due to the nanowire geometry, leading to high-quality (In, Ga)N/GaN nanowire heterostructures. An intense green photoluminescence emission is observed and attributed to an inter-well transition between the stacked (In, Ga)N insertions.

Multiscale modeling and simulations in neuroscience is gaining scientific attention due to its growing importance and unexplored capabilities. For instance, it can help to acquire better understanding of biological phenomena that have important features at multiple scales of time and space. This includes synaptic plasticity, memory formation and modulation, homeostasis. There are several ways to organize multiscale simulations depending on the scientific problem and the system to be modeled. One of the possibilities is to simulate different components of a multiscale system simultaneously and exchange data when required. The latter may become a challenging task for several reasons. First, the components of a multiscale system usually span different spatial and temporal scales, such that rigorous analysis of possible coupling solutions is required. Then, the components can be defined by different mathematical formalisms. For certain classes of problems a number of coupling mechanisms have been proposed and successfully used. However, a strict mathematical theory is missing in many cases. Recent work in the field has not so far investigated artifacts that may arise during coupled integration of different approximation methods. Moreover, in neuroscience, the coupling of widely used numerical fixed step size solvers may lead to unexpected inefficiency. In this paper we address the question of possible numerical artifacts that can arise during the integration of a coupled system. We develop an efficient strategy to couple the components comprising a multiscale test problem in neuroscience. We introduce an efficient coupling method based on the second-order backward differentiation formula (BDF2) numerical approximation. The method uses an adaptive step size integration with an error estimation proposed by Skelboe (2000). The method shows a significant advantage over conventional fixed step size solvers used in neuroscience for similar problems. We explore different coupling strategies that define the organization of computations between system components. We study the importance of an appropriate approximation of exchanged variables during the simulation. The analysis shows a substantial impact of these aspects on the solution accuracy in the application to our multiscale neuroscientific test problem. We believe that the ideas presented in the paper may essentially contribute to the development of a robust and efficient framework for multiscale brain modeling and simulations in neuroscience. QC 20161024