The mechanical properties of two-dimensional materials are important for a wide range of applications including composite and van der Waals-materials, flexible electronics and superconductivity. Several aspects are highly debated in the literature: For example, the theoretically predicted bending rigidity x at 0 K for quasi free-standing graphene varies from 0.8 to 1.6 eV, and there are predictions that it could either increase or decrease with temperature. Here we present an experimental study of the temperature-dependent bending rigidity x(T) of graphene. From the phonon dispersion relation measured with helium atom scattering for the out-of-plane acoustic (ZA) mode, we find x(T) to increase with sample temperature. We compare our experimental results with novel molecular dynamics (MD) simulations performed as part of this study as well as available literature data. The calculations reproduce the temperature trend of our experiments, but with a slightly weaker slope. A probable cause for the observed differences is the slight strain associated with experimental substrate supported graphene that is not present in the calculations.

The boson peak was recently detected experimentally for the first time in a 2D material (bilayer silica). The experiment was performed using helium atom scattering. Here we apply helium atom scattering in further experimental investigations of the presence of the boson peak in 2D materials. We investigate two crystalline 2D materials (graphene and AB-bilayer graphene) as well as one amorphous 2D material: a 2D silica sample containing nanoscale holes, thus displaying a different mass density from the 2D silica investigated in the previously published experiment. The crystalline materials graphene and bilayer graphene show no indication of the presence of a boson peak. The boson peak in the bilayer silica containing a random distribution of holes is identified at 7 +/- 1 meV, which is within the error bars of the value for the first bilayer silica sample previously investigated.

Supersonic molecular beams are used in several scientific fields ranging from surface science to the spectroscopy of molecules, nanoparticles, and even viruses. It is therefore of interest to understand the fundamental properties of the expansion and resulting beam. Here, we present a study of the change in the most probable velocity with reservoir pressure, using a so-called Even-Lavie pulsed source with a 200-mu m-diam nozzle. Experiments were carried out in the throughput range p0d = 400-2000 mbar cm, where p0 is the reservoir stagnation pressure and d is the nozzle diameter. Experiments were done on both neutral and metastable helium beams. A two-detector measurement setup was used to account for the valve opening delay. The measurements are modeled with theory which has hitherto only been applied to a p0d regime up to 190 mbar cm, showing good agreement.

Neutral helium atom microscopy is a novel microscopy technique which offers strictly surface-sensitive, non-destructive imaging. Several experiments have been published in recent years where images are obtained by scanning a helium beam spot across a surface and recording the variation in scattered intensity at a fixed total scattering angle θSD and fixed incident angle θi relative to the overall surface normal. These experiments used a spot obtained by collimating the beam (referred to as helium pinhole microscopy). Alternatively, a beam spot can be created by focusing the beam with an atom optical element. However up till now imaging with a focused helium beam has only been demonstrated in transmission (using a zone plate). Here we present the first reflection images obtained with a focused helium beam (also using a zone plate). Images are obtained with a spot size (FWHM) down to 4.7μm ±0.5μm, and we demonstrate focusing down to a spot size of about 1μm. Furthermore, we present experiments measuring the scattering distribution from a focused helium beam spot. The experiments are done by varying the incoming beam angle θi while keeping the beam-detector angle θSD and the point where the beam spot hits the surface fixed - in essence, a microscopy scale realization of a standard helium atom scattering experiment. Our experiments are done using an electron bombardment detector with adjustable signal accumulation, developed particularly for helium microscopy.

Nanoscale thin film coatings and surface treatments are ubiquitous across industry, science, and engineering; imbuing specific functional or mechanical properties (such as corrosion resistance, lubricity, catalytic activity and electronic behaviour). Non-destructive nanoscale imaging of thin film coatings across large (ca. centimetre) lateral length scales, crucial to a wide range of modern industry, remains a significant technical challenge. By harnessing the unique nature of the helium atom-surface interaction, neutral helium microscopy images these surfaces without altering the sample under investigation. Since the helium atom scatters exclusively from the outermost electronic corrugation of the sample, the technique is completely surface sensitive. Furthermore, with a cross-section that is orders of magnitude larger than that of electrons, neutrons and photons, the probe particle routinely interacts with features down to the scale of surface defects and small adsorbates (including hydrogen). Here, we highlight the capacity of neutral helium microscopy for sub-resolution contrast using an advanced facet scattering model based on nanoscale features. By replicating the observed scattered helium intensities, we demonstrate that sub-resolution contrast arises from the unique surface scattering of the incident probe. Consequently, it is now possible to extract quantitative information from the helium atom image, including localised ångström-scale variations in topography.

Neutral helium atom microscopy, also referred to as scanning helium microscopy and commonly abbreviated SHeM or NAM (neutral atom microscopy), is a novel imaging technique that uses a beam of neutral helium atoms as an imaging probe. The technique offers a number of advantages such as the very low energy of the incident probing atoms (less than 0.1 eV), unsurpassed surface sensitivity (no penetration into the sample bulk), a charge neutral, inert probe and a high depth of field. This opens up for a range of interesting applications such as: imaging of fragile and/or non-conducting samples without damage, inspection of 2D materials and nano-coatings, with the possibility to test properties such as grain boundaries or roughness on the Å ngström scale (the wavelength of the incident helium atoms) and imaging of samples with high aspect ratios, with the potential to obtain true to scale height information of 3D surface topography with nanometer resolution: nano stereo microscopy. However, for a full exploitation of the technique, a range of experimental and theoretical issues still needs to be resolved. In this paper we review the research in the field. We do this by following the trajectory of the helium atoms step by step through the microscope: from the initial acceleration in the supersonic expansion used to generate the probing beam over the atom optical elements used to shape the beam (resolution limits), followed by interaction of the helium atoms with the sample (contrast properties) to the final detection and post-processing. We also review recent advances in scanning helium microscope design including a discussion of imaging with other atoms and molecules than helium.

The boson peak is an excess in the phonon vibrational density of states relative to the Debye model. It has been observed in a wide range of amorphous materials, from inorganic glasses to polymers. Two-dimensional random matrix models and molecular dynamics simulations predict that the boson peak should also be present in amorphous two-dimensional materials, a notion that is of practical importance because it leads to an excess of heat capacity and influences transport properties. However, up until now, experimental observations in actual materials have not been possible due to the limited surface sensitivity of the methods usually applied to measure the boson peak. Here we present the experimental evidence of a boson peak in two-dimensional silica, through phonon spectra measured by means of inelastic helium-atom scattering. We identify the boson peak as a wavenumber-independent spectral maximum at a frequency similar to what has been observed in and predicted for bulk vitreous silica. Furthermore, we present a heterogeneous-elastic theory calculation in two dimensions, which shows how the vibrational coupling of the transversal and flexural shear vertical phonon modes produces the boson peak in two-dimensional materials at a frequency similar to that of the bulk, in agreement with our measurements. The boson peak refers to an excess in the phonon density of states seen in three-dimensional amorphous materials. Helium-atom scattering experiments have now revealed a boson peak in a two-dimensional material, too, at a frequency similar to that of the bulk material.

Two dimensional (2D) materials are a young class of materials that is foreseen to play an important role as building blocks in a range of applications, e.g. flexible electronics. For such applications, mechanical properties such as the bending rigidity κ are important. Only a few published measurements of the bending rigidity are available for 2D materials. Nearly unexplored is the question of how the 2D material density influences the bending rigidity. Here, we present helium atom scattering measurements on a "holey" bilayer silica with a density of 1.4 mg m-2, corresponding to 1.7 monolayers coverage. We find a bending rigidity of 6.6 ± 0.3 meV, which is lower than previously published measurements for a complete 2D film, where a value of 8.8 ± 0.5 meV was obtained. The decrease of bending rigidity with lower density is in agreement with theoretical predictions.

The boson peak is an excess in the phonon density of states relative to the Debye Model, which occurs at frequencies below the Debye limit. It is present in most amorphous materials and, as was recently shown, can sometimes be found also in crystals. Here we present first experimental evidence of the boson peak in a 2D material, namely 2D silica (SiO$_2$). The measurements were obtained by helium atom scattering. A dispersionless boson peak is seen at $6 \pm 0.5$ meV (1.5$ \pm$ 0.15 THz) and $-6 \pm 1.5$ meV ($-1.5 \pm 0.4$ THz), with reasonable evidence for a double excitation at $\pm 12 \pm 2.5$ meV ($2.9 \pm 0.6$ THz).

Developing the next generation of scanning helium microscopes requires the fabrication of optical elements with complex internal geometries. We show that resin stereolithography (SLA) 3D printing produces low-cost components with the requisite convoluted structures whilst achieving the required vacuum properties, even without in situ baking. As a case study, a redesigned pinhole plate optical element of an existing scanning helium microscope was fabricated using SLA 3D printing. In comparison to the original machined component, the new optical element minimised the key sources of background signal, in particular multiple scattering and the secondary effusive beam.

Neutral helium atom microscopy, also referred to as scanning helium microscopy and commonly abbreviated SHeM or NAM (neutral atom microscopy), is a novel imaging technique that uses a beam of neutral helium atoms as an imaging probe. The technique offers a number of advantages such as the very low energy of the incident probing atoms (less than 0.1 eV), unsurpassed surface sensitivity (no penetration into the sample bulk), a charge neutral, inert probe and a high depth of field. This opens up for a range of interesting applications such as: imaging of fragile and/or non-conducting samples without damage, inspection of 2D materials and nano-coatings, with the possibility to test properties such as grain boundaries or roughness on the Angstr\"om scale (the wavelength of the incident helium atoms) and imaging of samples with high aspect ratios, with the potential to obtain true to scale height information of 3D surface topography with nanometer resolution: nano stereo microscopy. However, for a full exploitation of the technique, a range of experimental and theoretical issues still needs to be resolved. In this paper we review the research in the field. We do this by following the trajectory of the helium atoms step by step through the microscope: from the initial acceleration in the supersonic expansion used to generate the probing beam over the atom optical elements used to shape the beam, followed by interaction of the helium atoms with the sample (contrast properties) to the final detection and post-processing. We also review recent advances in scanning helium microscope design including a discussion of imaging with other atoms and molecules than helium.

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.

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

The field of taxonomy is critically important for the identification, conservation, and ecology of biological species. Modern taxonomists increasingly need to employ advanced imaging techniques to classify organisms according to their observed morphological features. Moreover, the generation of three-dimensional datasets is of growing interest; moving beyond qualitative analysis to true quantitative classification. Unfortunately, biological samples are highly vulnerable to degradation under the energetic probes often used to generate these datasets. Neutral atom beam microscopes avoid such damage due to the gentle nature of their low energy probe, but to date have not been capable of producing three-dimensional data. Here we demonstrate a means to recover the height information for samples imaged in the scanning helium microscope (SHeM) via the process of stereophotogrammetry. The extended capabilities, namely sparse three-dimensional reconstructions of features, were showcased via taxonomic studies of both flora (Arabidopsis thaliana) and fauna (Heterodontus portusjacksoni). In concert with the delicate nature of neutral helium atom beam microscopy, the stereophotogrammetry technique provides the means to derive comprehensive taxonomical data without the risk of sample degradation due to the imaging process.

B. Holst, C. Büchner, S. D. Eder, T. Nesse, D. Kuhness, P. Schlexer, G. Pacchioni, J. R. Manson, M. Heyde, H.-J.Freund Department of Physics and Technology, University of Bergen, Allégaten 55, 5007 Bergen Norway Fritz-Haber-Institut der Max-Planck-gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany Department of Physics, NTNU, NO-7491, Trondheim, Norway Department of Material Science, Università de Milano-Biocca, Via R. Cozzi 55, Milan, Italy Department of Physics and Astronomy, Clemson University, South Carolina 29634, USA bodil.holst@uib.no

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.

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.

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.