Scanning helium microscopy - Knowledge (XXG)

609:, which is appealing since the focussing is independent of the velocity distribution of the incoming atoms. However the material challenges to produce an appropriate surface that is macroscopically curved and defect free on an atomic length-scale has proved too challenging so far. King and Bigas, showed that an image of a surface can be obtained by heating a sample and monitoring the atoms that evaporate from the surface. King and Bigas suggest it could be possible to form an image by scattering atoms from the surface, though it was some time before it was demonstrated. 635:

an atom mirror by using a pinhole, but to still use a conventional helium source to produce a high quality beam. Other differences from the Witham and Sánchez design include using a larger sample to pinhole distance, so that a larger variety of samples can be used and to use a smaller collection solid angle, so that it may be possible to observe more subtle contrast. These changes also reduced the total flux in the detector meaning that higher efficiency detectors are required (which in itself is an active area of research.

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feasibility of the technique. However, the setup used by Koch et al. with a zone plate did not produce a high enough signal to observe the reflected signal from the surface at the time. Nevertheless, the focussing obtained with a zone plate offers the potential for improved resolution due to the small beam spot size in the future. Research into neutral helium microscopes that use a Fresnel zone plate is an active area in Holst’s group at the University of Bergen.

652: 1674: 631:. The first published demonstration of a two-dimensional image formed by helium reflecting from the surface was by Witham and Sánchez, who used a pinhole to form the helium beam. A small pinhole is placed very close to a sample and the helium scattered into a large solid angle is fed to a detector. Images are collected by moving the sample around underneath the beam and monitoring how the scattered helium flux changes. 251:(STXM). By focussing the X-rays to a small point and rastering across a sample, a very high resolution can be obtained with light. The small wavelength of X-rays comes at the expense of a high photon energy, meaning that X-rays can cause radiation damage. Additionally, X-rays are weakly interacting, so they will primarily interact with the bulk of the sample, making investigations of a surface difficult. 28: 504: 667:. The centreline of the gas is selected by a skimmer to form an atom beam with a narrow velocity distribution. The gas is then further collimated by a pinhole to form a narrow beam, which is typically between 1–10 μm. The use of a focusing element (such as a zone plate) allows beam spot sizes below 1 μm to be achieved, but currently still comes with low signal intensity. 1909: 427:

changes the structure, and knock-on damage in metals that creates a vacancy in the lattice, which changes to the surface chemistry. Additionally, the electron beam is charged, which means that the surface of the sample needs to be conducting to avoid artefacts of charge accumulation in images. One method to mitigate the issue when imaging insulating surfaces is to use an

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optical microscopy, it may be appropriate to use atoms as a probe instead. While neutrons can be used as a probe, they are weakly interacting with matter and can only study the bulk structure of a material. Neutron imaging also requires a high flux of neutrons, which usually can only be provided by a nuclear reactor or particle accelerator.

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the zone plate configuration. In the pinhole configuration, a small opening (the pinhole) selects a section of the supersonic expansion far away from its origin, which has previously been collimated by a skimmer (essentially, another small pinhole). This section then becomes the imaging beam. In the zone plate configuration a Fresnel

1665:. The global maximum of intensity can then be obtained numerically by replacing these values in the intensity equation above. In general, smaller skimmer radii coupled with smaller distances between the skimmer and the pinhole are preferred, leading in practice to the design of increasingly smaller pinhole microscopes. 1695: 422:

The high energy of the electrons leads to the electron beam interacting not only with the surface of a material, but forming a tear-drop interaction volume underneath the surface. While the spot size on the surface can be extremely low, the electrons will travel into the bulk and continue interacting

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atoms to image the surface of a sample without any damage to the sample caused by the imaging process. Since helium is inert and neutral, it can be used to study delicate and insulating surfaces. Images are formed by rastering a sample underneath an atom beam and monitoring the flux of atoms that are

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This cubic equation is obtained under a series of geometrical assumptions and has a closed-form analytical solution that can be consulted in the original paper or obtained through any modern-day algebra software. The practical consequence of this equation is that zone plate microscopes are optimally

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in the pinhole case: a bigger zone plate (taken all parameters constant) corresponds to a bigger focal spot size. The third term differs from the pinhole configuration optics as it includes a quadratic relation with the skimmer size (which is imaged through the zone plate) and a linear relation with

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is the distance between the skimmer and the pinhole. There are several other versions of this equation that depend on the intensity model, but they all show a quadratic dependency on the pinhole radius (the bigger the pinhole, the more intensity) and an inverse quadratic dependency with the distance

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In parallel to the work by Witham and Sánchez, a proof of concept machine named the scanning helium microscope (SHeM) was being developed in Cambridge in collaboration with Dastoor's group from the University of Newcastle. The approach that was adopted was to simplify previous attempts that involved

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Metastable atoms are atoms that have been excited out of the ground state, but remain in an excited state for a significant period of time. Microscopy using metastable atoms has been shown to be possible, where the metastable atoms release stored internal energy into the surface, releasing electrons

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Thermal energy helium atom beams are exclusively surface sensitive, giving helium scattering an advantage over other techniques such as electron and x-ray scattering for surface studies. For the beam energies that are used, the helium atoms will have classical turning points 2–3 Å away from the

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Since electrons are charged, they can be manipulated using electromagnetic optics to form extremely small spot sizes on a surface. Due to the wavelength of an electron beam being low, the Abbe diffraction limit can be pushed below atomic resolution and electromagnetic lenses can be used to form very

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raster a small probe across the surface of a sample and monitor the interaction of the probe with the sample. The resolution of scanning probe microscopies is set by the size of the interaction region between the probe and the sample, which can be sufficiently small to allow atomic resolution. Using

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A diagram showing how a scanning helium microscope works. A beam is formed by a gas expansion and collimation through a skimmer and pinhole. The beam is then incident on the sample, where the gas is scattered and collected through a detector aperture. The scattered gas is then detected using a mass

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In order to generate a high-intensity beam, scanning helium microscopes are designed to generate a supersonic expansion of the gas into vacuum, that accelerates neutral helium atoms to high velocities. Scanning helium microscopes exist in two different configurations: the pinhole configuration and

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Given the equation for the de Broglie wavelength above, the same wavelength of a beam can be achieved at lower energies by using a beam of particles that have a higher mass. Thus, if the objective were to study the surface of a material at a resolution that is below that which can be achieved with

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The electron beam can also damage the material, destroying the structure that is to be studied due to the high beam energy. Electron beam damage can occur through a variety of different processes that are specimen-specific. Examples of beam damage include the breaking of bonds in a polymer, which

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Yamamoto, Susumu; Masuda, Shigeru; Yasufuku, Hideyuki; Ueno, Nobuo; Harada, Yoshiya; Ichinokawa, Takeo; Kato, Makoto; Sakai, Yuji (1997-09-15). "Study of solid surfaces by metastable electron emission microscopy: Energy-filtered images and local electron spectra at the outermost surface layer of

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When designing a scanning helium microscope, scientists strive to maximise the intensity of the imaging beam while minimising its width. The reason behind this is that the beam's width gives the resolution of the microscope while its intensity is proportional to its signal to noise ratio. Due to

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by Koch et al. in a transmission setup. Helium will not pass through a solid material, therefore a large change in the measured signal is obtained when a sample is placed between the source and the detector. By maximising the contrast and using transmission mode, it was much easier to verify the

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The observed contrast in helium images has typically been dominated by the variation in topography of the sample. Typically, since the wavelength of the atom beam is small, surfaces appear extremely rough to the incoming atom beam. Therefore, the atoms are diffusely scattered and roughly follow

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The gas then scatters from the surface and is collected into a detector. In order to measure the flux of the neutral helium atoms, they must first be ionised. The inertness of helium that makes it a gentle probe means that it is difficult to ionise and therefore reasonably aggressive electron

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in optics). However, more recently work has begun to see divergence from diffuse scattering due to effects such as diffraction and chemical contrast effects. However, the exact mechanisms for forming contrast in a helium microscope is an active field of research. Most cases have some complex

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The first discussion of obtaining an image of a surface using atoms was by King and Bigas, who showed that an image of a surface can be obtained by heating a sample and monitoring the atoms that evaporate from the surface. King and Bigas suggest that it could be possible to form an image by

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Therefore, in general, electrons are often not particularly suited to studying delicate surfaces due to the high beam energy and lack of exclusive surface sensitivity. Instead, an alternative beam is required for the study of surfaces at low energy without disturbing the structure.

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The idea of imaging with atoms instead of light was subsequently widely discussed in the literature. The initial approach to producing a helium microscope assumed that a focussing element is required to produce a high intensity beam of atoms. An early approach was to develop an

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designed when the distances between the components are small, and the radius of the zone plate is also small. This goes in line with the results obtained for the pinhole configuration, and has as its practical consequence the design of smaller scanning helium microscopes.

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Fladischer, K.; Reingruber, H.; Reisinger, T.; Mayrhofer, V.; Ernst, W. E.; Ross, A. E.; MacLaren, D. A.; Allison, W.; D Litwin; Galas, J.; Sitarek, S.; Nieto, P.; Barredo, D.; Farías, D.; Miranda, R.; Surma, B.; Miros, A.; Piatkowski, B.; E Søndergård; Holst, B. (2010).

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that provide information on the electronic structure. The kinetic energy of the metastable atoms means that only the surface electronic structure is probed, but the large energy exchange when the metastable atom de-excites will still perturb delicate sample surfaces.

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step function used here to indicate that the presence of the diffraction term depends on the value of the Fresnel number. Note that there are variations of this equation depending on what is defined as the "beam width" (for details compare and ). Due to the small

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X-rays have a much smaller wavelength than visible light, and therefore can achieve superior resolutions when compared to optical techniques. Projection X-ray imaging is conventionally used in medical applications, but high resolution imaging is achieved through

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Barredo, D.; Calleja, F.; Weeks, A. E.; Nieto, P.; Hinarejos, J. J.; Laurent, G.; Vazquez de Parga, A. L.; MacLaren, D. A.; Farías, D.; Allison, W.; Miranda, R. (2007-01-01). "Si(111)–H(1×1): A mirror for atoms characterized by AFM, STM, He and H2 diffraction".

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20 meV, which is about the same as the thermal energy. Using particles of a higher mass than that of an electron means that it is possible to obtain a beam with a wavelength suitable to probe length scales down to the atomic level with a much lower energy.

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Once the flux from a specific part of the surface is collected, the sample is moved underneath the beam to generate an image. By obtaining the value of the scattered flux across a grid of positions, then values can then be converted to an image.

2187: 893: 2729: 1904:{\displaystyle \Phi =K{\sqrt {\sigma _{cm}^{2}+\sigma _{A}^{2}+\left({\frac {Mr_{S}}{\sqrt {3}}}\right)^{2}}}\sim K{\sqrt {\left({\frac {r_{ZP}}{S{\sqrt {2}}}}\right)^{2}+0.42\Delta r+\left({\frac {Mr_{S}}{\sqrt {3}}}\right)^{2}}}.} 1240: 423:

with the sample. Transmission electron microscopy avoids the bulk interaction by only using thin samples, however usually the electron beam interacting with the bulk will limit the resolution of a scanning electron microscope.

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Recent efforts have avoided focussing elements and instead are directly collimating a beam with a pinhole. The lack of atom optics means that the beam width will be significantly larger than in an

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intense spots on the surface of a material. The optics in a scanning electron microscope usually require the beam energy to be in excess of 1 keV to produce the best-quality electron beam.

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Doak, R.; Grisenti, R.; Rehbein, S.; Schmahl, G.; Toennies, J.; W ll, C. (1999). "Towards Realization of an Atomic de Broglie Microscope: Helium Atom Focusing Using Fresnel Zone Plates".

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can be obtained analytically. The derivative of the intensity with respect to the zone plate radius can be reduced the following cubic equation (once it has been set equal to zero):

1659: 73:) does have some disadvantages though including a reasonably small imaging area and difficulty in observing structures with a large height variation over a small lateral distance. 2239:, which should be made equal to the smallest achievable value, the maxima of the intensity equation with respect to the zone plate radius and the skimmer-zone plate distance 1437: 1989: 101: 2634: 967: 2070: 624:

Since using a zone plate proved difficult due to the low focussing efficiency, alternative methods for forming a helium beam to produce images with atoms were explored.

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Harada, Y.; Yamamoto, S.; Aoki, M.; Masuda, S.; Ichinokawa, T.; Kato, M.; Sakai, Y. (1994). "Surface spectroscopy with high spatial resolution using metastable atoms".

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To overcome the diffraction limit, a probe that has a smaller wavelength is needed, which can be achieved using either light with a higher energy, or through using a

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is a constant that stems from the definition of the beam width. Note that both equations are given with respect to the distance between the skimmer and the pinhole,

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Geometry of a scanning helium microscope in its zone plate configuration showing the variables used in this article. Image taken from (uploaded by the author).

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Geometry of a scanning helium microscope in its pinhole configuration showing the variables used in this article. Image taken from (uploaded by the author).

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is the radius of the supersonic expansion quitting surface (the point in the expansion from which atoms can be considered to travel in a straight line),

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The optimal configurations of scanning helium microscopes are geometrical configurations that maximise the intensity of the imaging beam within a given

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surface atom cores. The turning point is well above the surface atom cores, meaning that the beam will only interact with the outermost electrons.

1991:). The approximation sign indicates the regime in which the distance between the zone plate and the skimmer is much bigger than its focal length. 1689:) instead of a pinhole to focus the atom beam into a small focal spot. This means that the beam width equation changes significantly (see below). 258:

opened up a variety of new materials that could be studied due to the enormous improvement in the resolution when compared to optical microscopy.

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Microscopes can be divided into two general classes: those that illuminate the sample with a beam, and those that use a physical scanning probe.

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Matter waves have a much shorter wavelength than visible light and therefore can be used to study features below about 1 μm. The advent of

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is a constant that gives the relative size of the smallest aperture of the zone plate compared with the average wavelength of the beam and

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to produce partial three dimensional images, especially valuable for biological samples subject to degradation in electron microscopes.

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bombardment is typically used to create the ions. A mass spectrometer setup is then used to select only the helium ions for detection.

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The intensity of the beam (which we aim to maximise) is given by the following equation (according to the Sikora and Andersen model):

587: 525: 518: 547: 746:. The size of the beam at the sample plane is given by the lines connecting the skimmer edges with the pinhole edges. When the 49: 2636:

is the modified beam width, which is used through the derivation to avoid explicitly operating with the constant airy term:

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is the refractive index of the medium the wave is travelling in and the wave is converging to a spot with a half-angle of

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is the total intensity stemming from the supersonic expansion nozzle (taken as a constant in the optimisation problem),

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Barr, M.; Fahy, A.; Martens, J.; Jardine, A. P.; Ward, D. J.; Ellis, J.; Allison, W.; Dastoor, P. C. (April 2016).

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Hence, for an electron beam to resolve atomic structure, the wavelength of the matter wave would need be at least

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Barr, M.; Fahy, A.; Jardine, A.; Ellis, J.; Ward, D.; MacLaren, D. A.; Allison, W.; Dastoor, P. C. (2014-12-01).

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Barr, M.; Fahy, A.; Jardine, A.; Ellis, J.; Ward, D.; MacLaren, D. A.; Allison, W.; Dastoor, P. C. (2014-12-01).

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Myles, Thomas A.; Eder, Sabrina D.; Barr, Matthew G.; Fahy, Adam; Martens, Joel; Dastoor, Paul C. (2019-02-14).

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Each of these configurations have different optimal designs, as they are defined by different optics equations.

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Analysis of Asymptotic Behavior of Free Jets: Prediction of Molecular Beam Intensity and Velocity Distributions

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combination of several contrast mechanisms making it difficult to disentangle the different contributions.

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Alderwick, A. R.; Jardine, A. P.; Hedgeland, H.; MacLaren, D. A.; Allison, W.; Ellis, J. (December 2008).

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Transmission electron microscopy: a textbook for materials science / David B. Williams and C. Barry Carter

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Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms

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Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms

1574:{\displaystyle r_{S}^{max}={\frac {\Phi a}{2W_{D}K}},\qquad r_{ph}^{max}={\frac {\Phi a}{2K(a+W_{D})}}.} 561: 262: 4088: 4046: 3969: 3922: 3910: 3857: 3814: 3684: 3619: 3530: 3480: 3406: 3336:

Koch, M.; Rehbein, S.; Schmahl, G.; Reisinger, T.; Bracco, G.; Ernst, W. E.; Holst, B. (2008-01-01).

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For the pinhole configuration the width of the beam (which we aim to minimise) is largely given by

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Farias, Daniel; Rieder, Karl-Heinz (1998-12-01). "Atomic beam diffraction from solid surfaces".

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The equation to maximise, the intensity, is the same as the pinhole case with the substitution

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Microscopes that use a beam have a fundamental limit on the minimum resolvable feature size,

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The first two-dimensional neutral helium images were obtained using a conventional Fresnel

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scattering atoms from the surface, though it was some time before this was demonstrated.

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for the geometrical optics regime the following values correspond to intensity maxima:

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By combining the two equations shown above, one can obtain that for a given beam width

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Berkhout, J.; Luiten, O.; Setija, I.; Hijmans, T.; Mizusaki, T.; Walraven, J. (1989).

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4082: 3999: 3895: 3780: 3741:"A method for constrained optimisation of the design of a scanning helium microscope" 3354: 3337: 2997: 2886: 1935: 1408:

between the skimmer and the pinhole (the more the atoms spread, the less intensity).

606: 3450: 3227: 1235:{\displaystyle I=I_{0}{\frac {r_{ph}^{2}}{(R_{F}+a)^{2}}}\left(1-\exp \left\right).} 3756: 3379: 3278: 3084: 2932: 40:(SHeM) is a novel form of microscopy that uses low-energy (5–100 meV) neutral 232:. While it is possible to overcome the diffraction limit on resolution by using a 4014: 3394: 32:

spectrometer. By then rastering the sample, an image of the sample can be formed.

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the zone plate magnification, which will at the same time depend on its radius.

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is the width of the smallest zone. Note the presence of chromatic aberrations (

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of the helium beam, the Fraunhofer diffraction term can usually be omitted.

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The first term in this equation is similar to the geometric contribution

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Eder, S D; Reisinger, T; Greve, M M; Bracco, G; Holst, B (2012-07-06).

3586: 3183:"An ellipsoidal mirror for focusing neutral atomic and molecular beams" 4033:

Salvador Palau, Adrià; Bracco, Gianangelo; Holst, Bodil (2017-01-12).

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Palau, Adrià Salvador; Bracco, Gianangelo; Holst, Bodil (2016-12-20).

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Instrumentation and contrast mechanisms in scanning helium microscopy

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Bergin, M.; Ward, D. J.; Ellis, J.; Jardine, A. P. (December 2019).

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King, John G.; Bigas, William R. (1969-04-19). "Molecular Scanner".

395:= 1 Å, and therefore the beam energy would need to be given by 3075: 3050: 650: 642: 162:{\displaystyle d_{\text{A}}={\frac {\lambda }{2n\sin {\theta }}},} 26: 723:

focuses the atoms coming from a skimmer into a small focal spot.

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Scattering of Thermal Energy Atoms from Disordered Surfaces

3338:"Imaging with neutral atoms—a new matter-wave microscope" 687:

Combinations of images from multiple perspectives allows

3673:"Taxonomy through the lens of neutral helium microscopy" 3608:"Unlocking new contrast in a scanning helium microscope" 4035:"Theoretical model of the helium zone plate microscope" 1387:

is the distance between the nozzle and the skimmer and

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represents the working distance of the microscope and

3856:. Springer Series in Surface Sciences. Vol. 51. 2642: 2617: 2597: 2268: 2245: 2222: 2198: 2073: 2024: 2000: 1967: 1944: 1920: 1698: 1617: 1590: 1440: 1417: 1393: 1366: 1339: 1312: 1278: 1251: 1014: 979: 948: 928: 904: 789: 756: 468: 448: 401: 381: 334: 311: 291: 271: 218: 198: 178: 116: 82: 3958:"Focusing of a neutral helium beam below one micron" 3803:"Theoretical model of the helium pinhole microscope" 3683:(1). Springer Science and Business Media LLC: 2148. 3911:"A design for a pinhole scanning helium microscope" 3516:"Simulation and analysis of solenoidal ion sources" 3466:"A design for a pinhole scanning helium microscope" 285:, of a matter wave in terms of its kinetic energy, 2780: 2723: 2628: 2603: 2580: 2251: 2231: 2204: 2181: 2056: 2006: 1983: 1953: 1926: 1903: 1653: 1603: 1573: 1423: 1399: 1379: 1352: 1325: 1294: 1264: 1234: 985: 961: 934: 910: 887: 768: 477: 454: 407: 387: 365:{\displaystyle \lambda ={\frac {h}{\sqrt {2mE}}}.} 364: 317: 297: 277: 224: 204: 184: 161: 95: 2064:. By substitution of the magnification equation: 3570: 3568: 3850:Bracco, Gianangelo; Holst, Bodil, eds. (2013). 3395:"A simple approach to neutral atom microscopy" 942:is the geometrical projection of the beam and 8: 3393:Witham, Philip; Sánchez, Erik (2011-10-01). 2057:{\displaystyle r_{ph}\leftrightarrow r_{ZP}} 429:environmental scanning electron microscope 4066: 3981: 3834: 3712: 3647: 3353: 3209: 3074: 2825: 2715: 2697: 2687: 2673: 2665: 2651: 2641: 2616: 2596: 2562: 2554: 2537: 2523: 2496: 2488: 2474: 2460: 2450: 2440: 2435: 2418: 2409: 2389: 2380: 2364: 2351: 2327: 2313: 2304: 2289: 2273: 2267: 2244: 2221: 2197: 2162: 2147: 2111: 2101: 2080: 2072: 2045: 2029: 2023: 1999: 1972: 1966: 1943: 1919: 1890: 1872: 1862: 1836: 1822: 1809: 1803: 1796: 1782: 1764: 1754: 1740: 1735: 1722: 1714: 1708: 1697: 1641: 1627: 1616: 1595: 1589: 1556: 1526: 1511: 1503: 1483: 1465: 1450: 1445: 1439: 1416: 1392: 1371: 1365: 1344: 1338: 1317: 1311: 1283: 1277: 1256: 1250: 1213: 1191: 1178: 1165: 1144: 1131: 1124: 1113: 1075: 1059: 1045: 1037: 1031: 1025: 1013: 978: 953: 947: 927: 903: 850: 845: 829: 823: 813: 799: 788: 755: 588:Learn how and when to remove this message 467: 447: 442:A beam of helium atoms with a wavelength 400: 380: 341: 333: 310: 290: 270: 217: 197: 177: 148: 130: 121: 115: 87: 81: 45:scattered into a detector at each point. 1672: 733: 663:, which is a standard technique used in 3044: 3042: 2771: 2648: 2534: 2471: 1685:(that acts roughly like as a classical 679:Knudsen's Law (the atom equivalent of 192:is the wavelength of the probing wave, 4099:Atomic, molecular, and optical physics 3734: 3732: 3096: 3094: 2810:"Neutron imaging in materials science" 2787:. New York, New York; London: Plenum. 776:), the beam width is also affected by 524:Please improve this section by adding 249:scanning transmission X-ray microscopy 4028: 4026: 3796: 3794: 3792: 3790: 1654:{\displaystyle K=2{\sqrt {2\ln 2/3}}} 7: 3523:The Review of Scientific Instruments 2973:Helium Atom Scattering from Surfaces 2898: 2896: 659:The atomic beam is formed through a 3581:(Thesis). University of Cambridge. 2644: 2619: 2598: 2530: 2505: 2467: 2423: 2394: 2318: 2223: 2156: 2120: 1945: 1848: 1699: 1529: 1468: 1418: 905: 790: 647:A helium atom image of a fly's eye 48:The technique is different from a 25: 1681:The zone plate microscope uses a 3399:Review of Scientific Instruments 3355:10.1111/j.1365-2818.2007.01874.x 1306:is the speed ratio of the beam, 703:and under certain technological 502: 3049:Holst, B.; Allison, W. (1997). 2216:of the beam. Taking a constant 1498: 3757:10.1016/j.ultramic.2019.112833 3575:Bergin, Matthew (2019-04-27). 2851:Reports on Progress in Physics 2591:Here some groupings are used: 2514: 2502: 2428: 2399: 2357: 2170: 2131: 2038: 1562: 1543: 1333:is the radius of the skimmer, 1302:is the radius of the pinhole, 1203: 1171: 1156: 1137: 1072: 1052: 877: 874: 868: 856: 50:scanning helium ion microscope 1: 3983:10.1088/1367-2630/14/7/073014 3211:10.1088/1367-2630/12/3/033018 2827:10.1016/S1369-7021(11)70139-0 526:secondary or tertiary sources 1984:{\displaystyle \sigma _{cm}} 655:SHeM Contrast Mechanism Tree 537:"Scanning helium microscopy" 462:= 1 Å has an energy of 96:{\displaystyle d_{\text{A}}} 3293:silicon oxide on Si(100)". 3123:10.1103/PhysRevLett.83.4229 3025:10.1103/PhysRevLett.63.1689 2975:. Berlin: Springer-Verlag. 2950:. Berlin: Springer-Verlag. 2871:10.1088/0034-4885/61/12/001 2779:Williams, David B. (1996). 962:{\displaystyle \sigma _{A}} 62:Scanning probe microscopies 4115: 4059:10.1103/PhysRevA.95.013611 3935:10.1016/j.nimb.2014.06.028 3853:Surface Science Techniques 3827:10.1103/PhysRevA.94.063624 3697:10.1038/s41598-018-36373-5 3493:10.1016/j.nimb.2014.06.028 3295:Journal of Applied Physics 3159:10.1016/j.susc.2006.08.048 920:Full Width at Half Maximum 711:their neutrality and high 38:scanning helium microscope 3870:10.1007/978-3-642-34243-1 3051:"An atom-focusing mirror" 478:{\displaystyle E\approx } 4013:Sikora, Gary S. (1973). 2232:{\displaystyle \Delta r} 2205:{\displaystyle \lambda } 1954:{\displaystyle \Delta r} 1669:Zone plate configuration 455:{\displaystyle \lambda } 388:{\displaystyle \lambda } 278:{\displaystyle \lambda } 185:{\displaystyle \lambda } 103:, which is given by the 4019:. Princeton University. 3529:(12): 123301–123301–9. 3405:(10): 103705–103705–9. 3103:Physical Review Letters 3005:Physical Review Letters 2946:Poelsema, Bene (1989). 2604:{\displaystyle \Gamma } 2007:{\displaystyle \delta } 986:{\displaystyle \theta } 935:{\displaystyle \delta } 639:Image formation process 225:{\displaystyle \theta } 3962:New Journal of Physics 3190:New Journal of Physics 2971:Hulpke, Erika (1992). 2745:Helium atom scattering 2725: 2630: 2629:{\displaystyle \Phi '} 2605: 2582: 2253: 2233: 2206: 2183: 2058: 2008: 1985: 1955: 1928: 1905: 1678: 1655: 1605: 1575: 1425: 1401: 1381: 1354: 1327: 1296: 1295:{\displaystyle r_{ph}} 1266: 1236: 987: 963: 936: 912: 889: 780:(see equation below). 778:Fraunhofer diffraction 770: 769:{\displaystyle F\ll 1} 739: 695:Optimal configurations 665:helium atom scattering 656: 648: 513:relies excessively on 479: 456: 409: 389: 366: 319: 299: 279: 226: 206: 186: 163: 105:Abbe diffraction limit 97: 33: 3612:Nature Communications 3342:Journal of Microscopy 2726: 2631: 2606: 2583: 2254: 2234: 2214:de-Broglie wavelength 2207: 2184: 2059: 2009: 1986: 1956: 1929: 1906: 1676: 1656: 1606: 1604:{\displaystyle W_{D}} 1576: 1426: 1424:{\displaystyle \Phi } 1402: 1382: 1380:{\displaystyle x_{S}} 1355: 1353:{\displaystyle R_{F}} 1328: 1326:{\displaystyle r_{S}} 1297: 1267: 1265:{\displaystyle I_{0}} 1237: 988: 964: 937: 913: 911:{\displaystyle \Phi } 890: 771: 737: 730:Pinhole configuration 654: 646: 480: 457: 410: 390: 367: 320: 305:, and particle mass, 300: 280: 263:de Broglie wavelength 227: 207: 187: 164: 98: 65:a physical tip (e.g. 30: 2640: 2615: 2595: 2266: 2243: 2220: 2196: 2071: 2022: 1998: 1965: 1942: 1918: 1696: 1615: 1588: 1438: 1415: 1391: 1364: 1337: 1310: 1276: 1249: 1012: 977: 946: 926: 902: 787: 754: 689:stereophotogrammetry 681:Lambert's cosine law 661:supersonic expansion 466: 446: 399: 379: 332: 309: 289: 269: 234:near-field technique 216: 196: 176: 114: 80: 4051:2017PhRvA..95a3611S 3974:2012NJPh...14g3014E 3927:2014NIMPB.340...76B 3862:2013sst..book.....B 3819:2016PhRvA..94f3624P 3689:2019NatSR...9.2148M 3632:10.1038/ncomms10189 3624:2016NatCo...710189B 3535:2008RScI...79l3301A 3485:2014NIMPB.340...76B 3411:2011RScI...82j3705W 3307:1997JAP....82.2954Y 3255:1994Natur.372..657H 3202:2010NJPh...12c3018F 3151:2007SurSc.601...24B 3115:1999PhRvL..83.4229D 3067:1997Natur.390..244H 3017:1989PhRvL..63.1689B 2917:1969Natur.222..261K 2863:1998RPPh...61.1575F 2678: 2567: 2501: 2445: 1745: 1727: 1522: 1461: 1050: 855: 629:electron microscope 256:electron microscopy 3677:Scientific Reports 3587:10.17863/CAM.37853 2721: 2661: 2626: 2601: 2578: 2550: 2484: 2431: 2249: 2229: 2202: 2179: 2054: 2004: 1981: 1951: 1934:is the zone plate 1924: 1901: 1731: 1710: 1679: 1651: 1601: 1571: 1499: 1441: 1421: 1397: 1377: 1350: 1323: 1292: 1262: 1232: 1033: 983: 959: 932: 908: 885: 841: 766: 744:geometrical optics 740: 701:lateral resolution 657: 649: 475: 452: 415:> 100 eV. 405: 385: 362: 315: 295: 275: 222: 202: 182: 159: 93: 34: 4039:Physical Review A 3879:978-3-642-34242-4 3807:Physical Review A 3543:10.1063/1.3030858 3419:10.1063/1.3650719 3249:(6507): 657–659. 3011:(16): 1689–1692. 2982:978-3-540-54605-4 2957:978-0-387-50358-5 2911:(5190): 261–263. 2794:978-0-306-45324-3 2709: 2708: 2569: 2426: 2397: 2321: 2252:{\displaystyle a} 2174: 2096: 1927:{\displaystyle M} 1896: 1884: 1883: 1830: 1827: 1788: 1776: 1775: 1649: 1566: 1493: 1400:{\displaystyle a} 1207: 1082: 898:In this equation 880: 821: 713:ionisation energy 598: 597: 590: 572: 408:{\displaystyle E} 357: 356: 318:{\displaystyle m} 298:{\displaystyle E} 205:{\displaystyle n} 154: 124: 90: 16:(Redirected from 4106: 4073: 4072: 4070: 4030: 4021: 4020: 4010: 4004: 4003: 3985: 3953: 3947: 3946: 3906: 3900: 3899: 3847: 3841: 3840: 3838: 3798: 3785: 3784: 3736: 3727: 3726: 3716: 3668: 3662: 3661: 3651: 3603: 3597: 3596: 3594: 3593: 3572: 3563: 3562: 3520: 3511: 3505: 3504: 3470: 3461: 3455: 3454: 3390: 3384: 3383: 3357: 3333: 3327: 3326: 3315:10.1063/1.366130 3301:(6): 2954–2960. 3289: 3283: 3282: 3263:10.1038/372657a0 3238: 3232: 3231: 3213: 3187: 3177: 3171: 3170: 3133: 3127: 3126: 3098: 3089: 3088: 3078: 3046: 3037: 3036: 3002: 2993: 2987: 2986: 2968: 2962: 2961: 2943: 2937: 2936: 2925:10.1038/222261a0 2900: 2891: 2890: 2846: 2840: 2839: 2829: 2805: 2799: 2798: 2786: 2776: 2730: 2728: 2727: 2722: 2720: 2719: 2714: 2710: 2704: 2703: 2702: 2701: 2688: 2677: 2672: 2657: 2656: 2655: 2635: 2633: 2632: 2627: 2625: 2610: 2608: 2607: 2602: 2587: 2585: 2584: 2579: 2574: 2570: 2568: 2566: 2561: 2543: 2542: 2541: 2528: 2527: 2517: 2500: 2495: 2480: 2479: 2478: 2465: 2464: 2451: 2444: 2439: 2427: 2419: 2417: 2416: 2398: 2390: 2388: 2387: 2369: 2368: 2356: 2355: 2340: 2336: 2335: 2334: 2322: 2314: 2309: 2308: 2294: 2293: 2278: 2277: 2258: 2256: 2255: 2250: 2238: 2236: 2235: 2230: 2211: 2209: 2208: 2203: 2188: 2186: 2185: 2180: 2175: 2173: 2166: 2155: 2154: 2126: 2119: 2118: 2102: 2097: 2095: 2081: 2063: 2061: 2060: 2055: 2053: 2052: 2037: 2036: 2013: 2011: 2010: 2005: 1990: 1988: 1987: 1982: 1980: 1979: 1960: 1958: 1957: 1952: 1933: 1931: 1930: 1925: 1910: 1908: 1907: 1902: 1897: 1895: 1894: 1889: 1885: 1879: 1878: 1877: 1876: 1863: 1841: 1840: 1835: 1831: 1829: 1828: 1823: 1817: 1816: 1804: 1797: 1789: 1787: 1786: 1781: 1777: 1771: 1770: 1769: 1768: 1755: 1744: 1739: 1726: 1721: 1709: 1660: 1658: 1657: 1652: 1650: 1645: 1628: 1610: 1608: 1607: 1602: 1600: 1599: 1580: 1578: 1577: 1572: 1567: 1565: 1561: 1560: 1535: 1527: 1521: 1510: 1494: 1492: 1488: 1487: 1474: 1466: 1460: 1449: 1430: 1428: 1427: 1422: 1406: 1404: 1403: 1398: 1386: 1384: 1383: 1378: 1376: 1375: 1359: 1357: 1356: 1351: 1349: 1348: 1332: 1330: 1329: 1324: 1322: 1321: 1301: 1299: 1298: 1293: 1291: 1290: 1271: 1269: 1268: 1263: 1261: 1260: 1241: 1239: 1238: 1233: 1228: 1224: 1223: 1219: 1218: 1217: 1212: 1208: 1206: 1196: 1195: 1183: 1182: 1170: 1169: 1159: 1149: 1148: 1136: 1135: 1125: 1118: 1117: 1083: 1081: 1080: 1079: 1064: 1063: 1049: 1044: 1032: 1030: 1029: 992: 990: 989: 984: 971:Airy diffraction 968: 966: 965: 960: 958: 957: 941: 939: 938: 933: 917: 915: 914: 909: 894: 892: 891: 886: 881: 854: 849: 834: 833: 824: 822: 817: 800: 775: 773: 772: 767: 593: 586: 582: 579: 573: 571: 530: 506: 498: 484: 482: 481: 476: 461: 459: 458: 453: 414: 412: 411: 406: 394: 392: 391: 386: 371: 369: 368: 363: 358: 346: 342: 324: 322: 321: 316: 304: 302: 301: 296: 284: 282: 281: 276: 231: 229: 228: 223: 211: 209: 208: 203: 191: 189: 188: 183: 168: 166: 165: 160: 155: 153: 152: 131: 126: 125: 122: 102: 100: 99: 94: 92: 91: 88: 21: 18:Atomic nanoscope 4114: 4113: 4109: 4108: 4107: 4105: 4104: 4103: 4079: 4078: 4077: 4076: 4032: 4031: 4024: 4012: 4011: 4007: 3955: 3954: 3950: 3908: 3907: 3903: 3880: 3849: 3848: 3844: 3800: 3799: 3788: 3745:Ultramicroscopy 3738: 3737: 3730: 3670: 3669: 3665: 3605: 3604: 3600: 3591: 3589: 3574: 3573: 3566: 3518: 3513: 3512: 3508: 3468: 3463: 3462: 3458: 3392: 3391: 3387: 3335: 3334: 3330: 3291: 3290: 3286: 3240: 3239: 3235: 3185: 3179: 3178: 3174: 3139:Surface Science 3135: 3134: 3130: 3100: 3099: 3092: 3048: 3047: 3040: 3000: 2995: 2994: 2990: 2983: 2970: 2969: 2965: 2958: 2945: 2944: 2940: 2902: 2901: 2894: 2848: 2847: 2843: 2814:Materials Today 2807: 2806: 2802: 2795: 2778: 2777: 2773: 2768: 2741: 2693: 2689: 2683: 2682: 2647: 2643: 2638: 2637: 2618: 2613: 2612: 2593: 2592: 2533: 2529: 2519: 2518: 2470: 2466: 2456: 2452: 2446: 2405: 2376: 2360: 2347: 2323: 2300: 2299: 2295: 2285: 2269: 2264: 2263: 2241: 2240: 2218: 2217: 2212:is the average 2194: 2193: 2143: 2127: 2107: 2103: 2085: 2069: 2068: 2041: 2025: 2020: 2019: 1996: 1995: 1968: 1963: 1962: 1940: 1939: 1916: 1915: 1868: 1864: 1858: 1857: 1818: 1805: 1799: 1798: 1760: 1756: 1750: 1749: 1694: 1693: 1671: 1613: 1612: 1591: 1586: 1585: 1552: 1536: 1528: 1479: 1475: 1467: 1436: 1435: 1413: 1412: 1389: 1388: 1367: 1362: 1361: 1340: 1335: 1334: 1313: 1308: 1307: 1279: 1274: 1273: 1252: 1247: 1246: 1187: 1174: 1161: 1160: 1140: 1127: 1126: 1120: 1119: 1109: 1105: 1101: 1088: 1084: 1071: 1055: 1051: 1021: 1010: 1009: 975: 974: 949: 944: 943: 924: 923: 900: 899: 825: 785: 784: 752: 751: 750:is very small ( 732: 697: 641: 594: 583: 577: 574: 531: 529: 523: 519:primary sources 507: 496: 464: 463: 444: 443: 397: 396: 377: 376: 330: 329: 325:, is given by 307: 306: 287: 286: 267: 266: 214: 213: 194: 193: 174: 173: 135: 117: 112: 111: 83: 78: 77: 58: 23: 22: 15: 12: 11: 5: 4112: 4110: 4102: 4101: 4096: 4094:Nanotechnology 4091: 4081: 4080: 4075: 4074: 4022: 4005: 3948: 3901: 3878: 3842: 3786: 3728: 3663: 3598: 3564: 3506: 3456: 3385: 3328: 3284: 3233: 3172: 3128: 3090: 3038: 2988: 2981: 2963: 2956: 2938: 2892: 2841: 2820:(6): 248–256. 2800: 2793: 2770: 2769: 2767: 2764: 2763: 2762: 2757: 2752: 2747: 2740: 2737: 2718: 2713: 2707: 2700: 2696: 2692: 2686: 2681: 2676: 2671: 2668: 2664: 2660: 2654: 2650: 2646: 2624: 2621: 2600: 2589: 2588: 2577: 2573: 2565: 2560: 2557: 2553: 2549: 2546: 2540: 2536: 2532: 2526: 2522: 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1559: 1555: 1551: 1548: 1545: 1542: 1539: 1534: 1531: 1525: 1520: 1517: 1514: 1509: 1506: 1502: 1497: 1491: 1486: 1482: 1478: 1473: 1470: 1464: 1459: 1456: 1453: 1448: 1444: 1420: 1396: 1374: 1370: 1347: 1343: 1320: 1316: 1289: 1286: 1282: 1259: 1255: 1243: 1242: 1231: 1227: 1222: 1216: 1211: 1205: 1202: 1199: 1194: 1190: 1186: 1181: 1177: 1173: 1168: 1164: 1158: 1155: 1152: 1147: 1143: 1139: 1134: 1130: 1123: 1116: 1112: 1108: 1104: 1100: 1097: 1094: 1091: 1087: 1078: 1074: 1070: 1067: 1062: 1058: 1054: 1048: 1043: 1040: 1036: 1028: 1024: 1020: 1017: 982: 956: 952: 931: 907: 896: 895: 884: 879: 876: 873: 870: 867: 864: 861: 858: 853: 848: 844: 840: 837: 832: 828: 820: 816: 812: 809: 806: 803: 798: 795: 792: 765: 762: 759: 748:Fresnel number 731: 728: 696: 693: 640: 637: 596: 595: 578:September 2023 510: 508: 501: 495: 492: 474: 471: 451: 404: 384: 373: 372: 361: 355: 352: 349: 345: 340: 337: 314: 294: 274: 221: 201: 181: 170: 169: 158: 151: 147: 144: 141: 138: 134: 129: 120: 86: 57: 54: 24: 14: 13: 10: 9: 6: 4: 3: 2: 4111: 4100: 4097: 4095: 4092: 4090: 4087: 4086: 4084: 4069: 4064: 4060: 4056: 4052: 4048: 4045:(1): 013611. 4044: 4040: 4036: 4029: 4027: 4023: 4018: 4017: 4009: 4006: 4001: 3997: 3993: 3989: 3984: 3979: 3975: 3971: 3968:(7): 073014. 3967: 3963: 3959: 3952: 3949: 3944: 3940: 3936: 3932: 3928: 3924: 3920: 3916: 3912: 3905: 3902: 3897: 3893: 3889: 3885: 3881: 3875: 3871: 3867: 3863: 3859: 3855: 3854: 3846: 3843: 3837: 3832: 3828: 3824: 3820: 3816: 3813:(6): 063624. 3812: 3808: 3804: 3797: 3795: 3793: 3791: 3787: 3782: 3778: 3774: 3770: 3766: 3762: 3758: 3754: 3750: 3746: 3742: 3735: 3733: 3729: 3724: 3720: 3715: 3710: 3706: 3702: 3698: 3694: 3690: 3686: 3682: 3678: 3674: 3667: 3664: 3659: 3655: 3650: 3645: 3641: 3637: 3633: 3629: 3625: 3621: 3617: 3613: 3609: 3602: 3599: 3588: 3584: 3580: 3579: 3571: 3569: 3565: 3560: 3556: 3552: 3548: 3544: 3540: 3536: 3532: 3528: 3524: 3517: 3510: 3507: 3502: 3498: 3494: 3490: 3486: 3482: 3478: 3474: 3467: 3460: 3457: 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