Using Ion Imaging to Measure Velocity Distributions in Surface

Article pubs.acs.org/JPCA

Using Ion Imaging to Measure Velocity Distributions in Surface Scattering Experiments Dan J. Harding,*,†,‡ J. Neugebohren,†,‡ Daniel J. Auerbach,†,‡ T. N. Kitsopoulos,*,†,‡,§,∥ and Alec M. Wodtke*,†,‡ †

Institute for Physical Chemistry, Georg-August University of Göttingen, 37077 Göttingen, Germany Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany § Department of Chemistry, University of Crete, 71003 Heraklion, Greece ∥ Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, 71003 Heraklion, Greece ‡

ABSTRACT: We present a new implementation of ion imaging for the study of surface scattering processes. The technique uses a combination of spatial ion imaging with laser slicing and delayed pulsed extraction. The scattering velocities of interest are parallel to the imaging plane, allowing speed and angular distributions to be extracted from a single image. The first results of direct scattering of N2 from a clean, single-crystal Au(111) surface are reported, and the speed resolution is shown to be competitive with current state-of-the-art time-of-flight methods for velocity measurements while providing simultaneous measurements of in-plane angular distributions.

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INTRODUCTION Ion imaging1 and its offspring (velocity map imaging (VMI),2 slicing,3−6 and 3D-imaging7) have revolutionized the fields of photodissociation dynamics, crossed-beam scattering,8−11 and photoelectron spectroscopy.12−16 Efficient detection of the scattering or photoproducts allows full quantum-state-resolved speed and angular distributions to be measured in a single image with high resolution.17,18 The details of these scattering distributions are determined by the potential energy surfaces governing the scattering event and therefore provide a stringent test for the theoretical treatment of scattering and calculated potential energy surfaces. We can safely assert that product imaging detection has come to dominate these fields, but prior to the development of imaging techniques, these dynamical fingerprints were obtained using other methods. Speed distributions can be measured by the time of flight (TOF) of the particles of interest, be it photoelectrons, photofragments, or molecules scattered from a surface, from their creation to a detector some distance away, provided the process that generates the particles is short compared to the flight time. For beam-surface scattering experiments, this typically means either using short (few microseconds) chopped molecular beams19−22 or infrared−ultraviolet (IR-UV) double-resonance “tagging” experiments,23,24 where the molecules are first excited to a known rovibrational state and their arrival time is measured at a second resonant UV ionization laser a known distance away. Tagging experiments can provide high-resolution TOF data but are limited in their applicability by the need for suitable IR-active transitions to long-lived states and the © XXXX American Chemical Society

corresponding knowledge and understanding of their spectroscopy. Angular distributions can be obtained by rotating a detector19,25,26 or moving the ionization laser,23,27,28 but typically these methods are extremely time-consuming, requiring mechanical adjustments to the setup between each measured angle, and often have relatively low angular resolution. The advantages offered by imaging detection have been recognized in the surface scattering community, and there were several relatively early implementations of imaging for surface scattering experiments, particularly looking at photodesorption or ion beam scattering. The earliest examples of techniques using position sensitive detectors for surface experiments actually predate those in the gas phase.29,30 However, imaging-based surface experiments remain rare. Most of the experiments that have been performed using imaging have used geometries where the surface and imaging detector were parallel, i.e., the imaging plane was perpendicular to the scattering plane. Experimentally, this is convenient because it maintains the symmetry of the surface sample and ion optics but means that a significant fraction of the scattering velocity is in the direction toward the detector, and that the arrival time of each particle must also be measured in order to extract Special Issue: Dynamics of Molecular Collisions XXV: Fifty Years of Chemical Reaction Dynamics Received: June 30, 2015 Revised: September 8, 2015

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DOI: 10.1021/acs.jpca.5b06272 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A scattering velocities (three-dimensional (3D) imaging7). As the count rate in such an experiment must be kept low, typically of the order of 1 event per laser shot, 3D imaging is only truly practical with high repetition rate lasers. In comparison, conventional phosphor screen detectors allow multiparticle detection but do not, generally, allow timing measurements of the individual events. Chuang et al. used spatial imaging to measure angular and speed distributions of photodesorbed molecules,31 and Burns and co-workers have measured angular distributions of electron-stimulated desorption.32,33 In both cases information about the speed of the molecules could be obtained by varying the delay between the pump (laser or electron) and probe laser pulses. More recently, similar approaches, now using VMI rather than ion imaging, have been developed. Some of us have investigated the photodesorption of Br from a KBr surface,34,35 while Rosciolli et al. have performed molecular beam-scattering experiments with the same imaging geometry.36 Kershis et al. have used a rather similar setup combined with a PImMS camera to measure the angular distributions of photodesorption products with a small velocity spread defined by the pump−probe delay.37 This sophisticated camera allows multiple mass channels to be measured concurrently. Measuring scattering velocities using conventional imaging detectors incorporating phosphor screens, where only the position of each particle is measured and not its arrival time, requires the imaging plane to be parallel to the velocities of interest. For gas-phase experiments, this is readily achieved, but for surface scattering experiments it is more challenging to incorporate the surface while maintaining suitable electric fields for imaging. Such geometries have, however, been implemented. Wanner and co-workers avoided problems with electric fields by directly imaging (Doppler-resolved) laserinduced fluorescence to measure state-selective speed and angular distributions of associatively desorbing CuF from the reaction of F atoms on Cu.38,39 Jacobs and co-workers pioneered measurements of product translational energy distributions for low-energy ions scattered from surfaces using imaging.40−42 In this case, pulsed extraction fields were necessary to avoid perturbations to the incident ion beam velocity. Freund and co-workers used laser desorption combined with a broad “sheet” ionization laser to directly measure desorption speeds and angles for NO from NiO(111)43 and Pt(111)44 allowing angular distributions for different velocity components to be obtained from a single image. Here, we report on a new instrument built to perform molecular beam surface scattering experiments using ion imaging with laser slicing and delayed pulsed extraction to measure the velocity (speed and angular) distributions of scattered molecules. Our detection geometry is similar to that introduced by Jacobs and co-workers. We demonstrate the capabilities of this instrument by investigating a simple system for which data from similar systems is available from conventional techniques: N2 scattered from Au(111) at different incidence energies and surface temperatures. Previous results for N2 scattering from a range of metal surfaces are summarized in refs 45 and 46 and references therein. Statespecific speed distributions of N2 scattered from Ag(111)21 and Cu(110)47 have been reported, measured using short chopped beams and TOF with resonance-enhanced multiphoton ionization (REMPI) detection. In both cases, anticorrelation between final translational and rotational energy was observed.

Lykke and Kay have measured rotational state distributions for N2/Au(111), observing direct scattering and clear rotational rainbows, but they did not measure speed distributions, preventing us from making a direct comparison.48

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EXPERIMENTAL SECTION The imaging setup is part of a new machine being developed to allow a range of surface scattering and reaction experiments. The complete machine will be described elsewhere, but briefly, the machine consists of a source region with two custom-built piezo-valve molecular beam sources producing pulses of full width at half-maximum (fwhm) ca. 30 μs, two stages of differential pumping, and an ultrahigh vacuum main chamber (ca. 3 × 10−10 mbar) housing the imaging ion optics and detector. The sample is cleaned by Ar-ion sputtering and annealed at 1000 K. Auger electron spectroscopy is used to check sample cleanliness. N2 molecules are detected using 2 + 1 REMPI through the a″ 1Σg+ state at around 202.3 nm.49−51 The light is generated by frequency tripling of a pulsed dye laser and focused into the machine with a 200 mm focal length UV fused silica lens. In the spatial imaging configuration used here, shown schematically in Figure 1, the ion optics consist of a repeller

Figure 1. Schematic drawing of the imaging setup. The gap between the electrodes is 8 mm.

(pulsed to high voltage to extract the ions) and a grounded flat grid electrode (Precision Eforming, 670 lines/inch, 49% transmission). The 65 mm × 40 mm rectangular electrodes produce a uniform electric field which directly maps the positions of the ions in the extraction region onto the detector. We have chosen to use ion/spatial imaging with homogeneous fields to reduce potential problems with fringe fields with the open electrode geometries popular in VMI methods. The electrodes are shaped in such a way as to allow close approach of the surface sample and laser access for ionization. The space between them is kept small (currently 8 mm) to minimize distortions due to the presence of the grounded surface. Velocity mapping conditions can be realized by adding an einzel lens to our present setup and will be presented elsewhere. The detector consists of a z-stack of three multichannel plates (MCPs) and a phosphor screen (ProxiVision P43). The MCPs and phosphor screen are pulsed, which has several beneficial effects; short pulses (100 ns) slice the ion packet, improving speed resolution by increasing the selectivity to B


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The Journal of Physical Chemistry A molecules moving in the plane parallel to the detector. The pulse timing also provides mass selection, and the low duty cycle reduces background due to light and ions. A LaVision Imager E-lite CCD camera and Davis software is used to record the images of the phosphor screen. The experimental scheme uses a combination of laser slicing and delayed pulsed extraction. Laser ionization is performed in the extraction region, between 20 mm and 30 mm from the surface. Ionizing at this distance from the surface ensures effective laser slicing, as only molecules moving in a plane parallel to the detector will be ionized, and avoids fringe fields near the edge of the electrodes that can cause distortion in the images. Because the images we obtain are sliced, we do not need an inverse-Abel type transformation. This is a particular advantage if the surface breaks the cylindrical symmetry parallel to the imaging plane, analogous to gas-phase experiments with polarized product states, which cannot be reconstructed by Abel-inversion. For the 2 + 1 REMPI scheme used here, the Rayleigh length of the laser beam is sufficiently large that molecules across the full extraction region are ionized, allowing us to detect the full in-plane scattering distribution and to correct for the different ionization probabilities. The delay between molecular beam pulse and laser ionization is scanned to collect the full speed distribution of scattered molecules integrated over the energy spread in the incident molecular beam. To obtain velocity information using spatial imaging we need to determine the change in the ion positions with time. As in the original ion imaging experiments, velocity extraction from a single image requires spatial calibration of our images, i.e., pixels per millimeter determined from the number of pixels covered by the phosphor screen (⌀ 51 mm) in the image, and the TOF of the ions from the laser ionization position to the detector. Adding an extra delay (the extraction delay, Δt) between the laser ionization and the pulsed extraction of the ions, during which the ions fly under field-free conditions, has several advantages: (i) It allows us to perform slice imaging to improve our velocity and angular resolution by rejecting ions with velocity components out of the imaging plane. (ii) Increasing the extraction delay effectively increases the TOF and thus the size of the image, further improving the resolution. (iii) Using multiple images with different extraction delays allows us to test and calibrate the imaging fields. Figure 2 shows typical images for 1000 laser shots taken with 0 μs, 1 μs, and 2 μs extraction delay. At 0 μs delay, three features are clearly visible: the small, intense incoming molecular beam; a broad line due to direct scattered molecules; and a diffuse feature in between due to the buildup of molecules which have undergone collisions with the ion optics after scattering from the Au(111) surface. After 2 μs both the incoming and scattered molecules have moved, in opposite directions, and both features are broader because of their velocity spread. The build-up disperses quickly because these molecules have larger out-of-plane velocity components and are therefore effectively rejected by the delayed extraction and pulsed detection scheme.

Figure 2. Ion images for N2 scattering from Au(111). The nominal extraction delays are shown. The labeled features in the top image are the incident (i) and scattered (s) beam and build-up (b). The position of the surface is shown by the yellow rectangle, and the incident beam by the green arrow. The offset in the y-direction between the incident and scattered beams is due to a slight misalignment of the surface caused by the tungsten wires supporting the crystal which can move when heated.

normal to the surface are used to extract the position distributions of the molecules from the images. We have used slices rather than segments to determine the position distributions because they are not dependent on the precise position of the surface. We are currently performing simulations of the scattering and detection processes to determine the most reliable analysis methods, and these results will be reported elsewhere. Figure 3 shows position distributions extracted from images with different delay times. Fitting these distributions with appropriate functions, here Gaussian functions (two Gaussians are used to account for the build-up signal), allows the most probable position at each delay time to be determined. Plotting the most probable positions as a function of delay time should produce a straight

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RESULTS AND DISCUSSION Testing and Calibrating the Imaging Fields. To test the imaging fields, we first take multiple slice images with different time delays between ionization laser and extraction pulse (extraction delay, Δt). Background corrections are performed using images taken without the molecular beam. Narrow slices C


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Figure 4. Speed distributions for different rotational states of N2 scattered from Au(111) at 0.25 eV incidence energy (Ts = 300 K). The nominal extraction delay was 2.0 μs. The blue lines show fits with a flowing Maxwell−Boltzmann distribution used to determine the mean energy and energy spread.

Figure 3. (a) Ion position distributions for different extraction delay times. The movement of the ion peak can be clearly seen. The red points show experimental data, and the blue lines are the fits used to determine the center positions. Panel b shows the peak center positions as a function of extraction delay time. The most probable speed of the ions is obtained from the slope of a straight line fit (shown in blue) to these positions. The error bars show an estimate of the uncertainty in the fit to the center of the scattered ion peak.

directly converted into a speed distribution. We use single images with a relatively long delay (Δt = 2 μs) for the best resolution. In the examples shown here we used narrow slices taken along the center of the image normal to the surface. Angle-resolved speed distributions could also be determined by taking a suitable part of the radial distribution, while integration over the whole image will provide the complete speed distribution. The experimental speed distribution can then be fit with a flowing Maxwell−Boltzmann distribution:20

line whose slope is the most probable speed of the molecules (shown in Figure 3b). This calibration method has the advantage that it does not rely on knowing either the position of the laser or the ion flight time. Extrapolating such fits back to the point where the incident and scattered beams cross provides an independent means to determine the ionization position and the ion TOF. In addition, the linearity of the plot is a quick and stringent test of the quality of the ion optics, the homogeneity of the extraction fields, and the absence of any stray fields in the extraction region. Speed Distributions. As in the original ion imaging experiments,1 if the time between ionization and detection (note that this is not the same as the extraction delay) and the pixel position where ionization occurred (here determined from the position of the background buildup in the image) are known, then the spatial field-free flight distribution can be

f (v) ∝ v 3 exp{− [(v − v0)2 /α 2]}

where f(v) is the flux as a function of velocity v, v0 is the flow velocity and α2 = (2kBTpara)/m, where Tpara is the characteristic temperature in the frame of reference moving with v0, to obtain the mean energy and width of the energy distribution. Figure 4 shows the final speed distributions, corrected with a density-to-flux transformation, and fits for a range of different rotational states of N2 scattered from Au(111) at 0.25 eV mean incidence energy, the full width at half-maximum energy spread in the beam is around 20% of the mean energy over the full temporal duration of the pulse. The different final speeds of the different J-states are clearly visible in the speed distributions. As D


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Figure 6. Mean final translational energy as a function of incidence energy for different Ts. The solid lines show the hard cube Baule limit for N2/Au(111) plus a Ts-dependent component equivalent to a quarter of the average energy for a molecule thermalized at Ts.

Boltzmann fits as a function of the final rotational state for three incidence energies and two surface temperatures. We clearly see the expected anticorrelation between final rotational, R, and translational, T, energy22 for low to intermediate J-states. At higher J-states, this anticorrelation disappears and the molecules with higher rotational energy also have higher translational energy. The point at which this occurs depends upon the incidence energy. Siders and Sitz observed the T-to-R curve for N2/Cu(110) to flatten out at high-J and concluded that this was evidence for multibounce collisions.47 Molecules that convert a large proportion of their energy into rotation will be moving more slowly after the collision and are therefore more likely to undergo further collisions before scattering back into the gas phase. The highest rotational energies are above the incidence energy for the slow (0.11 eV) beam, which demonstrates that the molecules are gaining energy from the surface. To quantify the energy transfer between the molecule and the surface during scattering we have determined the final translational energy for rotationally inelastic scattering (obtained by extrapolating ⟨Ef⟩ to J = 0) as a function of incidence energy and surface temperature, shown in Figure 6. For Ts = 300 K, the final translational energy lies close to that expected for the hard cube limit,52 also known as the Baule limit,53 from conservation of energy and momentum. At each incidence energy, the molecules scattered from a hot surface (Ts = 1000 K) have gained a constant amount of energy compared to those scattered from the cold surface, a factor of approximately 1/2kBΔTs, where ΔTs is the difference in the surface temperatures, equivalent to a quarter of the mean energy (2kBTs) for a molecule thermalized at the surface. The energy gain from the surface is similar to that observed for the N2/Pt(111) system.54 This constant energy gain during scattering from a hot surface can also be seen for each of the individual rotational states in Figure 5. Angular Distributions. The angular spread of the scattered molecules can be clearly seen in the images. However, because we use 2 + 1 REMPI with a focused laser, the ionization probability is not uniform across the detection region. Therefore, we have measured an image for background N2

Figure 5. Final mean translational ⟨Ef⟩ and total ⟨Etot⟩ energies of scattered N2 as a function of final rotational energy at surface temperatures of 300 and 1000 K. The dashed black line shows the incidence energy. The red and blue lines show the fits used to extrapolate ⟨Ef⟩ to J = 0; the fits are constrained to the first few Jstates.

would be expected for a flowing Maxwell−Boltzmann distribution, the mean scattered energies determined using this method are systematically higher than the most probable energies determined using multiple images. We estimate the uncertainties in the absolute energies to be of the order of 10%, primarily due to the uncertainty in the laser position, which determines the zero-velocity position in the image, and the finite size (ca. 2 mm) of the molecular beam. Other factors, including the details of the data analysis procedures and the ion TOF, are expected to be less important for the relatively narrow speed and angular distributions of directly scattered molecules but will be much more significant for systems where trapping− desorption dominates. The first system we have investigated using the new machine is the scattering of N2 from Au(111). We have measured final scattering energies as a function of final rotational state for three incidence energies and two surface temperatures, as this provides a sensitive test of the resolution of the setup. Figure 5 shows the final mean translational energy, ⟨Ef⟩, and mean total energy, ⟨Etot⟩, obtained from the flowing Maxwell− E


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Figure 8. Angular distribution parameter, n, of scattered N2 as a function of final rotational state measured for different incidence energies and surface temperatures (Ts = 300 K blue solid circles, Ts = 1000 K red open circles).

different J-states (⟨Ei⟩ = 0.56 eV, Ts = 300 K) and the fits used to determine the value of n. The n parameters obtained from the fits for the different Jstates, ⟨Ei⟩, and Ts that we have investigated are shown in Figure 8. All of the J-states investigated are characterized by values of n that are consistent with direct scattering, as expected for this system. The angular distributions for the fast beams and cold surface are extremely narrow but become broader with decreasing Ei and increasing surface temperature. The angular distributions also become broader with increasing final-J. Such detailed measurements of rotational state specific angular distributions do not appear to have been reported in the literature for any molecular system. However, the behavior we observe is consistent with published data for other (atomic and molecular) systems undergoing direct scattering25,27,55,56 which have been explained using hard cube scattering models. The broader angular distribution at higher temperature is due to increased corrugation of the surface caused by the motion of the surface atoms while the broader distributions at low incidence energy or high final rotational energy are presumably due to the increasing relative contribution of the parallel component of the velocity to the final translational energy for slow-moving molecules. A quantitative explanation of the changes in the angular distributions requires detailed calculations,57,58 which are beyond the scope of the current study.

Figure 7. Experimental angular distributions and fits to the data (blue lines).

leaked into the chamber via a leak-valve to calibrate the ionization efficiency across the detection region. The ionization efficiency was fit with a form I(θ) ∝ 1/(1 + θ2), where θ is the scattering angle in degrees. The experimental angular distributions, S(θ), extracted by taking slices parallel to the laser propagation direction centered on the scattered peak, were then fit with a convolution of the ionization efficiency function and a cosn(θ) function, i.e., S(θ) ∝ I(θ) cosn(θ). The parameter n is characteristic of the scattering process; trapping desorption is characterized by a distribution with n ≤ 1, while direct scattering has larger values of n. Figure 7 shows the slices through the image along the laser propagation direction for

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CONCLUSIONS AND OUTLOOK We have shown results for a new instrument capable of directly imaging the scattering of molecules from a clean surface. The imaging geometry makes it possible to extract speed and angular distributions from a single image. The speed resolution is competitive with the current state-of-the-art IR-tagging-TOF, but because it does not rely on the population of a long-lived F


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intermediate state, it can also be applied to molecules without allowed IR transitions and could be extended to nonresonant universal ionization schemes such as femtosecond- or vacuum ultraviolet-ionization. The molecular beam-scattering processes studied so far using this novel method involve direct scattering. As we have demonstrated, our velocity analysis can be performed independent of the interaction time of the molecules with the surface, while angular distributions require a single image. The features make the method extremely promising for the study of trapping−desorption scattering. Further developments of the machine are planned, including the addition of a large-aperture einzel lens after the extractor electrode to allow velocity mapping of scattered molecules, which should improve the speed resolution by collapsing the spatial spread parallel to the laser beam to a single narrow line.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the support of the Alexander-von-Humboldt Foundation, the Volkswagen Foundation, and the Deutsche Forschungsgemeinschaft (DFG).

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Using Ion Imaging to Measure Velocity Distributions in Surface

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