Erratum: Bending Rigidity of 2D Silica [Phys. Rev. Lett. 120, 226101 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.120.226101.

Temperature-Dependent Bending Rigidity of AB-Stacked Bilayer Graphene.

The change in bending rigidity with temperature κ(T) for 2D materials is highly debated: theoretical works predict both increase and decrease. Here we present measurements of κ(T), for a 2D material: AB-stacked bilayer graphene. We obtain κ(T) from phonon dispersion curves measured with helium atom scattering in the temperature range 320-400 K. We find that the bending rigidity increases with temperature. Assuming a linear dependence over the measured temperature region we obtain κ(T)=[(1.3±0.1)+(0.006±0.001)T/K] eV by fitting the data. We discuss this result in the context of existing predictions and room temperature measurements.

Velocity distributions in microskimmer supersonic expansion helium beams: High precision measurements and modeling.

Supersonic molecular beams are used in many applications ranging from spectroscopy and matter wave optics to surface science. The experimental setup typically includes a conically shaped, collimating aperture, the skimmer. It has been reported that microskimmers with diameters below 10 µm produce beams with significantly broader velocity distributions (smaller speed ratios) than larger skimmers. Various explanations for this phenomenon have been proposed, but up till now, only a limited amount of data has been available. Here we present a systematic study of the velocity distribution in microskimmer supersonic expansion helium beams. We compare a 4 µm diameter skimmer with a 390 µm diameter skimmer for room temperature and cooled beams in the pressure range 11-181 bars. Our measurements show that for properly aligned skimmers, the only difference is that the most probable velocity for a given pressure and temperature is slightly lower for a microskimmed beam. We ascribed this to the comparatively narrow and long geometry of the microskimmers which can lead to local pressure variations along the skimmer channel. We compare our measurements to a model for the supersonic expansion and obtain good agreement between the experiments and simulations.

Fast resolution change in neutral helium atom microscopy.

In neutral helium atom microscopy, a beam of atoms is scanned across a surface. Though still in its infancy, neutral helium microscopy has seen a rapid development over the last few years. The inertness and low energy of the helium atoms (less than 0.1 eV) combined with a very large depth of field and the fact that the helium atoms do not penetrate any solid material at low energies open the possibility for a non-destructive instrument that can measure topology on the nanoscale even on fragile and insulating surfaces. The resolution is determined by the beam spot size on the sample. Fast resolution change is an attractive property of a microscope because it allows different aspects of a sample to be investigated and makes it easier to identify specific features. However up till now it has not been possible to change the resolution of a helium microscope without breaking the vacuum and changing parts of the atom source. Here we present a modified source design, which allows fast, step wise resolution change. The basic design idea is to insert a moveable holder with a series of collimating apertures in front of the source, thus changing the effective source size of the beam and thereby the spot size on the surface and thus the microscope resolution. We demonstrate a design with 3 resolution steps. The number of resolution steps can easily be extended.

Bending Rigidity of 2D Silica.

A chemically stable bilayers of SiO_{2} (2D silica) is a new, wide band gap 2D material. Up till now graphene has been the only 2D material where the bending rigidity has been measured. Here we present inelastic helium atom scattering data from 2D silica on Ru(0001) and extract the first bending rigidity, κ, measurements for a nonmonoatomic 2D material of definable thickness. We find a value of κ=8.8 eV±0.5 eV which is of the same order of magnitude as theoretical values in the literature for freestanding crystalline 2D silica.

Image formation in the scanning helium microscope.

The scanning helium microscope (SHeM) is a new addition to the array of available microscopies, particularly for delicate materials that may suffer damage under techniques utilising light or charged particles. As with all other microscopies, the specifics of image formation within the instrument are required to gain a full understanding of the produced micrographs. We present work detailing the basics of the subject for the SHeM, including the specific nature of the projection distortions that arise due to the scattering geometry. Extension of these concepts allowed for an iterative ray tracing Monte Carlo model replicating diffuse scattering from a sample surface to be constructed. Comparisons between experimental data and simulations yielded a minimum resolvable step height of (67 ±â€¯5) µm and a minimum resolvable planar angle of (4.3 ±â€¯0.3)° for the instrument in question.

A modified time-of-flight method for precise determination of high speed ratios in molecular beams.

Time-of-flight (TOF) is a standard experimental technique for determining, among others, the speed ratio S (velocity spread) of a molecular beam. The speed ratio is a measure for the monochromaticity of the beam and an accurate determination of S is crucial for various applications, for example, for characterising chromatic aberrations in focussing experiments related to helium microscopy or for precise measurements of surface phonons and surface structures in molecular beam scattering experiments. For both of these applications, it is desirable to have as high a speed ratio as possible. Molecular beam TOF measurements are typically performed by chopping the beam using a rotating chopper with one or more slit openings. The TOF spectra are evaluated using a standard deconvolution method. However, for higher speed ratios, this method is very sensitive to errors related to the determination of the slit width and the beam diameter. The exact sensitivity depends on the beam diameter, the number of slits, the chopper radius, and the chopper rotation frequency. We present a modified method suitable for the evaluation of TOF measurements of high speed ratio beams. The modified method is based on a systematic variation of the chopper convolution parameters so that a set of independent measurements that can be fitted with an appropriate function are obtained. We show that with this modified method, it is possible to reduce the error by typically one order of magnitude compared to the standard method.

A Giant Reconstruction of α-quartz (0001) Interpreted as Three Domains of Nano Dauphine Twins.

Silica (SiO2) is one of the most common materials on Earth. The crystalline form α-quartz is the stable silica polymorph at ambient conditions although metastable forms exist. α-quartz is a piezoelectric material, it can be produced artificially and is widely used for example in electronics and the biosciences. Despite the many application areas, the atomic surface structures of silica polymorphs are neither well understood nor well characterized. Here we present measurements of α-quartz (0001). Helium Atom Scattering combined with Atomic Force Microscopy reveals a giant reconstruction consisting of 5.55 ± 0.07 nm wide ribbons, oriented 10.4° ± 0.8° relative to the bulk unit cell. The ribbons, with the aid of atomistic modelling, can be explained as a self-organised pattern of nano Dauphine twins (nano electrical twins).

Two dimensional imaging of the virtual source of a supersonic beam: helium at 125 K.

Here we present the first two-dimensional images of the virtual source of a supersonic helium expansion. The images were obtained using a free-standing Fresnel zone plate with an outermost zone width of 50 nm as imaging lens and a beam cooled to around 125 K. The nozzle diameter was 10 µm. The virtual source diameter was found to increase with stagnation pressure from 140 ± 30 µm at po = 21 bar up to 270 ± 25 µm at po = 101 bar. The experimental results are compared to a theoretical model based on the solution of the Boltzmann equation by the method of moments. The quantum mechanical cross sections used in the model have been calculated for the Lennard-Jones (LJ) and the Hurly-Moldover (HM) potentials. By using a scaling of the perpendicular temperature that parametrizes the perpendicular velocity distribution based on a continuum expansion approach, the LJ potential shows a good overall agreement with the experiment. However, at higher pressures the data points lie in between the two theoretical curves and the slope of the trend is more similar to the HM curve. Real gas corrections to enthalpy are considered but they affect the results less than the experimental errors.

A free jet (supersonic), molecular beam source with automatized, 50 nm precision nozzle-skimmer positioning.

Low energy (thermal) free jet (supersonic) molecular beams are used in a range of applications from surface science and surface deposition to quantum coherence and gas kinetics experiments. A free jet molecular beam is created by a gas expansion from a high pressure reservoir through a small aperture (nozzle). The nozzle typically has a diameter of 2-20 µm. The central part of the beam is selected using a skimmer, typically up to 500 µm in diameter. Recent years have seen the introduction of highly spatially confined beam sources based on micrometer skimmers and micrometer or even sub-micrometer nozzles. Such sources have been applied, for example, in the investigation of superfluidity and in neutral helium microscopy. However, up till now no source design allowing the precise positioning of the micro-skimmer relative to the nozzle has been available. This is an important issue because the relative position of skimmer and nozzle can influence the beam properties considerably. Here we present the design and implementation of a new molecular beam source, which allows an automatized, 50 nm precision positioning of the skimmer relative to the nozzle. The source is liquid nitrogen cooled and the temperature can be controlled between 110 K and 350 K with a temperature fluctuation of less than ±0.1 K over several hours. Beam intensity measurements using a 5 µm nozzle and a skimmer 5 µm in diameter are presented for stagnation pressures po in the range 3-180 bars. A 2D beam profile scan, using a 9.5 µm skimmer and a 5 µm nozzle is presented as a further documentation of the versatility of the new design and as an illustration of the influence of the relative skimmer-nozzle position on the beam properties.