The new small-angle X-ray scattering beamline for materials research at PETRA†III: SAXSMAT beamline P62.

The SAXSMAT beamline P62 (Small-Angle X-ray Scattering beamline for Materials Research) is a new beamline at the high-energy storage ring PETRA III at DESY. This beamline is dedicated to combined small- and wide-angle X-ray scattering (SAXS/WAXS) techniques for both soft and hard condensed matter systems. It works mainly in transmission geometry. The beamline covers an energy range from 3.5 keV to 35.0 keV, which fulfills the requirements of the user community to perform anomalous scattering experiments. Mirrors are used to reduce the intensity of higher harmonics. Furthermore, the mirrors and 2D compound refracting lenses can focus the beam down to a few micrometres at the sample position. This option with the high photon flux enables also SAXS/WAXS tensor tomography experiments to be performed at this new beamline in a relatively short time. The first SAXS/WAXS pattern was collected in August 2021, while the first user experiment was carried out two months later. Since January 2022 the beamline has been in regular user operation mode. In this paper the beamline optics and the SAXS/WAXS instrument are described and two examples are briefly shown.

Crystal growth of bcc titanium from the melt and interfacial properties: A molecular dynamics simulation study.

The crystal growth kinetics and interfacial properties of titanium (Ti) are studied using molecular dynamics computer simulation. The interactions between the Ti atoms are modeled via an embedded atom method potential. First, the free solidification method (FSM) is used to determine the melting temperature Tm at zero pressure where the transition from liquid to body-centered cubic crystal occurs. From the simulations with the FSM, the kinetic growth coefficients are also determined for different orientations of the crystal, analyzing how the coupling to the thermostat affects the estimates of the growth coefficients. At Tm, anisotropic interfacial stiffnesses and free energies as well as kinetic growth coefficients are determined from capillary wave fluctuations. The so-obtained growth coefficients from equilibrium fluctuations and without the coupling of the system to a thermostat agree well with those extracted from the FSM calculations.

Nonmonotonic Classical Magnetoconductivity of a Two-Dimensional Electron Gas in a Disordered Array of Obstacles.

Magnetotransport measurements in combination with molecular dynamics simulations on two-dimensional disordered Lorentz gases in the classical regime are reported. In quantitative agreement between experiment and simulation, the magnetoconductivity displays a pronounced peak as a function of the perpendicular magnetic field B which cannot be explained by existing kinetic theories. This peak is linked to the onset of a directed motion of the electrons along the contour of the disordered obstacle matrix when the cyclotron radius becomes smaller than the size of the obstacles. This directed motion leads to transient superdiffusive motion and strong scaling corrections in the vicinity of the insulator-to-conductor transitions of the Lorentz gas.

Angular vibrations of cryogenically cooled double-crystal monochromators.

The effect of angular vibrations of the crystals in cryogenically cooled monochromators on the beam performance has been studied theoretically and experimentally. A simple relation between amplitude of the vibrations and size of the focused beam is developed. It is shown that the double-crystal monochromator vibrations affect not only the image size but also the image position along the optical axis. Several methods to measure vibrations with the X-ray beam are explained and analyzed. The methods have been applied to systematically study angular crystal vibrations at monochromators installed at the PETRA III light source. Characteristic values of the amplitudes of angular vibrations for different monochromators are presented.

Complex banded structures in directional solidification processes.

A combination of theory and numerical simulation is used to investigate impurity superstructures that form in rapid directional solidification (RDS) processes in the presence of a temperature gradient and a pulling velocity with an oscillatory component. Based on a capillary wave model, we show that the RDS processes are associated with a rich morphology of banded structures, including frequency locking and the transition to chaos.

Creep and flow of glasses: strain response linked to the spatial distribution of dynamical heterogeneities.

Mechanical properties are of central importance to materials sciences, in particular if they depend on external stimuli. Here we investigate the rheological response of amorphous solids, namely colloidal glasses, to external forces. Using confocal microscopy and computer simulations, we establish a quantitative link between the macroscopic creep response and the microscopic single-particle dynamics. We observe dynamical heterogeneities, namely regions of enhanced mobility, which remain localized in the creep regime, but grow for applied stresses leading to steady flow. These different behaviors are also reflected in the average particle dynamics, quantified by the mean squared displacement of the individual particles, and the fraction of active regions. Both microscopic quantities are found to be proportional to the macroscopic strain, despite the non-equilibrium and non-linear conditions during creep and the transient regime prior to steady flow.

Residual stresses in glasses.

The history dependence of glasses formed from flow-melted steady states by a sudden cessation of the shear rate γ[over ˙] is studied in colloidal suspensions, by molecular dynamics simulations and by mode-coupling theory. In an ideal glass, stresses relax only partially, leaving behind a finite persistent residual stress. For intermediate times, relaxation curves scale as a function of γ[over ˙]t, even though no flow is present. The macroscopic stress evolution is connected to a length scale of residual liquefaction displayed by microscopic mean-squared displacements. The theory describes this history dependence of glasses sharing the same thermodynamic state variables but differing static properties.

Nonlinear active micro-rheology in a glass-forming soft-sphere mixture.

We present extensive molecular dynamics computer simulations of a glass-forming Yukawa mixture, investigating the nonlinear response of a single particle that is pulled through the system by a constant force. Structural changes around the pulled particle are analyzed by pair correlation functions, measured in the deeply supercooled state of the system. A regime of intermediate force strengths is found where the structural changes around the pulled particle are small, although its steady-state velocity shows a strong nonlinear response. This nonlinear response regime is characterized by a force-temperature superposition principle of a Peclet number and anisotropic diffusive behavior. In the direction parallel to the force, mean-square displacements show anomalous superdiffusion in the long time limit. We analyze this superdiffusive behavior by means of the van Hove correlation function of the pulled particle. Perpendicular to the force, the driven particle shows diffusive behavior for all considered force strengths and temperatures. We discuss the dynamics perpendicular and parallel to the force in terms of effective temperatures.

Bcc crystal-fluid interfacial free energy in Yukawa systems.

We determine the orientation-resolved interfacial free energy between a body-centered-cubic (bcc) crystal and the coexisting fluid for a many-particle system interacting via a Yukawa pair potential. For two different screening strengths, we compare results from molecular dynamics computer simulations, density functional theory, and a phase-field-crystal approach. Simulations predict an almost orientationally isotropic interfacial free energy of 0.12k(B)T/a(2) (with k(B)T denoting the thermal energy and a the mean interparticle spacing), which is independent of the screening strength. This value is in reasonable agreement with our Ramakrishnan-Yussouff density functional calculations, while a high-order fitted phase-field-crystal approach gives about 2-3 times higher interfacial free energies for the Yukawa system. Both field theory approaches also give a considerable anisotropy of the interfacial free energy. Our result implies that, in the Yukawa system, bcc crystal-fluid free energies are a factor of about 3 smaller than face-centered-cubic crystal-fluid free energies.

Transient dynamics in dense colloidal suspensions under shear: shear rate dependence.

A combination of confocal microscopy and rheology experiments, Brownian dynamics (BD) and molecular dynamics (MD) simulations and mode coupling theory (MCT) have been applied in order to investigate the effect of shear rate on the transient dynamics and stress-strain relations in supercooled and glassy systems under shear. Immediately after shear is switched on, the microscopic dynamics display super-diffusion and the macroscopic rheology a stress overshoot, which become more pronounced with increasing shear rate. MCT relates both to negative sections of the generalized shear modulus, which grow with increasing shear rate. When the inverse shear rate becomes much smaller than the structural relaxation time of the quiescent system, relaxation through Brownian motion becomes less important. In this regime, larger stresses are accumulated before the system yields and the transition from localization to flow occurs earlier and more abruptly.

Force-induced diffusion in microrheology.

We investigate the force-induced diffusive motion of a tracer particle inside a glass-forming suspension when a strong external force is applied to the probe (active nonlinear microrheology). A schematic model of mode-coupling theory introduced recently is extended to describe the transient dynamics of the probe particle, and used to analyze recent molecular-dynamics simulation data. The model describes non-trivial transient displacements of the probe before a steady-state velocity is reached. The external force also induces diffusive motion in the direction perpendicular to its axis. We address the relation between the transverse diffusion coefficient D(perpendicular) and the force-dependent nonlinear friction coefficient ζ. Non-diffusive fluctuations in the direction of the force are seen at long times in the MD simulation, while the model describes cross-over to long-time diffusion.

Tension and stiffness of the hard sphere crystal-fluid interface.

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66k(B)T/σ(2) with a small anisotropy of about 0.025k(B)T and stiffnesses with, e.g., 0.53k(B)T/σ(2) for the (001) orientation and 1.03k(B)T/σ(2) for the (111) orientation. Here k(B)T is denoting the thermal energy and σ the hard-sphere diameter. We compare our results with existing experimental findings.

Active nonlinear microrheology in a glass-forming Yukawa fluid.

A molecular dynamics computer simulation of a glass-forming Yukawa mixture is used to study the anisotropic dynamics of a single particle pulled by a constant force. Beyond linear response, a scaling regime is found where a force-temperature superposition principle of a Peclet number holds. In the latter regime, the diffusion dynamics perpendicular to the force can be mapped on the equilibrium dynamics in terms of an effective temperature, whereas parallel to the force a superdiffusive behavior is seen in the long-time limit. This behavior is associated with a hopping motion from cage to cage and can be qualitatively understood by a simple trap model.

The high-resolution diffraction beamline P08 at PETRA III.

The new third-generation synchrotron radiation source PETRA III located at the Deutsches Elektronen-Synchrotron DESY in Hamburg, Germany, has been operational since the second half of 2009. PETRA III is designed to deliver hard X-ray beams with very high brilliance. As one of the first beamlines of PETRA III the high-resolution diffraction beamline P08 is fully operational. P08 is specialized in X-ray scattering and diffraction experiments on solids and liquids where extreme high resolution in reciprocal space is required. The resolving power results in the high-quality PETRA III beam and unique optical elements such as a large-offset monochromator and beryllium lens changers. A high-precision six-circle diffractometer for solid samples and a specially designed liquid diffractometer are installed in the experimental hutch. Regular users have been accepted since summer 2010.

Nucleation barriers for the liquid-to-crystal transition in Ni: experiment and simulation.

Nucleation in undercooled Ni is investigated by a combination of differential scanning calorimetry (DSC) experiments and Monte Carlo (MC) simulation. By systematically varying the sample size in the DSC experiments, nucleation rates J over a range of 8 orders of magnitude are obtained. Evidence is given that these rates correspond to homogeneous nucleation. Free energy barriers ΔG*, as extracted from the measured J, are in very good agreement with those from the MC simulation. The MC simulation indicates a nonspherical geometry of crystalline clusters, fluctuating between prolate and oblate shape at a given size. Nevertheless, the temperature dependence of ΔG* is well described by classical nucleation theory.

Is there a relation between excess volume and miscibility in binary liquid mixtures?

Molecular dynamics computer simulations of various symmetrical Lennard-Jones (LJ) models are used to elucidate how the excess volume in dense binary liquids is related to the microscopic interactions between the particles. Both fully miscible systems and systems with a liquid-liquid phase separation are considered by varying systematically the parameters of the LJ potentials. The phase diagrams with the critical points of the demixing systems are determined by means of Monte Carlo simulations in the semigrandcanonical ensemble. The different LJ models are investigated by computing Bhatia-Thornton structure factors, enthalpy of mixing, and excess volume. For the demixing systems, the LJ models show a positive enthalpy of mixing while it is negative for the systems without miscibility gap. In contrast to that, the excess volume can be negative and positive for both demixing and fully miscible systems. This behavior is explained in terms of the interplay between the repulsive and attractive terms in the LJ potential. Whereas repulsions dominate the packing of particles as reflected by the number-density structure factor, the chemical ordering and thus the concentration structure factor are strongly affected by attractive interactions, leading to the "anomalies" of the excess volume.

Aging to equilibrium dynamics of SiO2.

Molecular dynamics computer simulations are used to study the aging dynamics of SiO2 (modeled by the BKS model). Starting from fully equilibrated configurations at high temperatures Ti∊{5000 K,3760 K}, the system is quenched to lower temperatures Tf∊{2500 K,2750 K,3000 K,3250 K} and observed after a waiting time tw. Since the simulation runs are long enough to reach equilibrium at Tf, we are able to study the transition from out-of-equilibrium to equilibrium dynamics. We present results for the partial structure factors, for the generalized incoherent intermediate scattering function Cq(tw,tw+t), and for the mean-square displacement Δr2(tw,tw+t). We conclude that there are three different tw regions: (I) At very short waiting times, Cq(tw,tw+t) decays very fast without forming a plateau. Similarly Δr2(tw,tw+t) increases without forming a plateau. (II) With increasing tw a plateau develops in Cq(tw,tw+t) and Δr2(tw,tw+t). For intermediate waiting times the plateau height is independent of tw and Ti. Time superposition applies, i.e., Cq=Cq(t/trCq) where trCq=trCq(tw) is a waiting time-dependent decay time. Furthermore Cq=C(q,tw,tw+t) scales as Cq=C(q,z(tw,t)) where z is a function of tw and t only, i.e., independent of q. (III) At large tw the system reaches equilibrium, i.e., Cq(tw,tw+t) and Δr2(tw,tw+t) are independent of tw and Ti. For Cq(tw,tw+t) we find that the time superposition of intermediate waiting times (II) includes the equilibrium curve (III).

Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures.

Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura-Oosawa (AO) model where the polymer's degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO model, the polymer reservoir packing fraction is eta(p) (r)=0.1 and the colloid-polymer size ratio is q[triple bond]sigma(p)/sigma=0.15 (with sigma(p) and sigma as the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquid systems are prepared by placing the solid fcc phase in the middle of a rectangular simulation box, creating two interfaces with the adjoined bulk liquid. By analyzing the growth of the crystalline region at various pressures and for different system sizes, the coexistence pressure p(co) is obtained, yielding p(co)=11.576 k(B)T/sigma(3) for the hard-sphere system and p(co)=8.00 k(B)T/sigma(3) for the AO model (with k(B) as the Boltzmann constant and T as the temperature). Several order parameters are introduced to distinguish between solid and liquid phases and to describe the interfacial properties. From the capillary-wave broadening of the solid-liquid interface, the interfacial stiffness is obtained for the (100) crystalline plane, giving the values gamma approximately 0.49 k(B)T/sigma(2) for the hard-sphere system and gamma approximately 0.95 k(B)T/sigma(2) for the AO model.

Computer simulation studies of finite-size broadening of solid-liquid interfaces: from hard spheres to nickel.

Using molecular dynamics (MD) and Monte Carlo (MC) simulations interfacial properties of crystal-fluid interfaces are investigated for the hard sphere system and the one-component metallic system Ni (the latter modeled by a potential of the embedded atom type). Different local order parameters are considered to obtain order parameter profiles for systems where the crystal phase is in coexistence with the fluid phase, separated by interfaces with (100) orientation of the crystal. From these profiles, the mean-squared interfacial width w(2) is extracted as a function of system size. We rationalize the prediction of capillary wave theory that w(2) diverges logarithmically with the lateral size of the system. We show that one can estimate the interfacial stiffness [Formula: see text] from the interfacial broadening, obtaining [Formula: see text] for hard spheres and [Formula: see text] for Ni.

Double transition scenario for anomalous diffusion in glass-forming mixtures.

We study by molecular dynamics computer simulation a binary soft-sphere mixture that shows a pronounced difference in the species' long-time dynamics. Anomalous, power-law-like diffusion of small particles arises that can be understood as a precursor of a double-transition scenario, combining a glass transition and a separate small-particle localization transition. Switching off small-particle excluded-volume constraints slows down, rather than enhances, small-particle transport.