Michael Musi
email: michael.musi@unileoben.ac.at

Benjamin Galy

Jean-Philippe Monchoux

Alain Couret

Helmut Clemens

Svea Mayer

In-situ observation of the phase evolution during an electromagnetic-assisted sintering experiment of an intermetallic γ-TiAl based alloy

Keywords: Titanium aluminides, Sintering, Phase transformation kinetics, Synchrotron radiation

Electromagnetic-assisted sintering offers the possibility for a time-efficient densification of intermetallic γ-TiAl based powders. Since the microstructure of the densified material and, thus, its mechanical properties can be controlled by the imposed temperature profile, the kinetics and transformations of the occurring phases are of particular interest. The present study describes a diffraction setup for the in-situ observation of the phase evolution by high-energy X-ray diffraction during an electromagnetic-assisted sintering process using induction heating. Starting from Ti-46.3Al-2.2W-0.2B powder (in at.%), this experiment grants time-resolved insights into the non-equilibrium and equilibrium phase transformations during this powder consolidation process for the first time. The microstructural accordance of the electromagnetic-assisted sintered specimen with spark plasma sintered material densified at the same dwell temperature highlights the transferability of both techniques and allows an allocation of the determined phase transformation data to the spark plasma sintering technology.

3 Intermetallic γ-TiAl based alloys are considered excellent candidates for applications in the automotive and aeronautic industries due to their outstanding material-specific properties.

These alloys are characterized by a high creep resistance, a low density of around 4 g/cm 3 , depending on the exact alloy composition, and, consequently, excellent specific mechanical properties [1,2]. In the Al range of technical γ-TiAl based alloys, i.e. 42-48 at.%, different phases occur in dependence of the temperature [3]. At low temperatures, the name-giving, ordered tetragonal face-centred γ-TiAl phase and the ordered hexagonal α 2 -Ti 3 Al phase are stable in binary TiAl alloys. The α 2 phase shows a disorder reaction into the disordered hexagonal α phase upon heating at the eutectoid temperature. Additionally, the disordered body-centered cubic (bcc) β phase occurs at high temperatures in the phase diagram. The alloying with β-stabilizing elements, i.e. Nb, Mo and W, results in its stabilization down to lower temperatures and also higher Al contents as well as in the occurrence of the ordered bcc β o phase at service temperature [1,3].

Field-assisted sintering includes a variety of different densification techniques distinguishable by the underlying thermal and electrical phenomena [START_REF] Asai | Electromagnetic processing of materials[END_REF][START_REF] Biesuz | [END_REF]. Of particular interest for the present work are sintering via an electromagnetic field as well as spark plasma sintering (SPS). While in both cases the material is heated via the Joule's effect, the associated current in the metallic powder is inductively generated in the first case and directly applied in the latter case [START_REF] Biesuz | [END_REF]6]. Furthermore, SPS relies on the additional application of an external pressure.

A major advantage of field-assisted sintering techniques based on solid state processes is the possibility of a direct microstructure adjustment [START_REF] Biesuz | [END_REF]7]. By changing the dwell temperature with respect to the alloy's phase diagram, different microstructures and, consequently, tailored mechanical properties can be obtained in γ-TiAl based alloys. Generally, dwell temperatures above the γ-solvus temperature result in a fully lamellar microstructure characterized by excellent creep resistance, but low room temperature ductility. Dwell temperatures situated at lower temperatures within the (α+γ) phase field region result in a socalled near gamma microstructure with a low creep resistance, but superior room temperature ductility [3,8]. Since high heating rates as well as short processing times can be achieved by field-assisted sintering techniques, phase transformation kinetics have a major impact on the occurring phases and, thus, on the final microstructure and the related mechanical properties [3,[START_REF] Biesuz | [END_REF]. Therefore, we report here on the use of high-energy X-ray diffraction (HEXRD), a powerful tool for monitoring the phase transformations in γ-TiAl based alloys [9], to investigate for the first time these transformations during an electromagnetic-assisted sintering. Emphasis is laid on the experimental diffraction setup and the resulting phase evolution, which is discussed regarding the occurring phase transformations. Combined with a microstructural characterization of the in-situ HEXRD specimen and SPS material processed at the same dwell temperature, the present work also highlights the similarities and differences between the described electromagnetic-assisted sintering and the SPS technology.

The alloy investigated in the current study has the composition Ti-46.3Al-2.2W-0.2B (in at.%), which was determined by X-ray fluorescence spectroscopy and inductively coupled plasma atomic emission spectroscopy. The amount of O measured by carrier gas hot extraction is 720 m.-ppm. The powder was produced by electrode induction melting inert gas atomization by GfE Metalle und Materialien GmbH, Germany. Powder in the particle size range of 25-50 µm with a homogeneous microstructure was used for the in-situ HEXRD sintering experiment and the SPS densification, which was conducted on a SYNTEX 2080 machine under vacuum (5-10 Pa) with a temperature of 1325 °C, a dwell time of 120 s, and a pressure of 50 MPa as reported in [8,10]. For the in-situ observation of the phase fractions, the electromagnetic-assisted sintering process has to be implemented in a suitable experimental diffraction setup for the in-situ HEXRD experiment. As the temperature applied to the material is the main driving force for the phase evolution, an exact temperature control is crucial for a successful experiment. This is realized during the sintering process with a modified dilatometer 805A/D by TA Instruments, USA, in which the specimen is heated inductively by an induction coil in a high-purity Ar atmosphere and cooled by Ar gas [11]. A self-designed sample holder served the purpose of containing the powder during the in-situ HEXRD sintering experiment and acting as the attachment point for the thermocouple (type S). A schematic drawing of the sample holder is shown in Fig. 1a. It consists of a hollow tube with a length of 10 mm and an inner radius of 5 mm. Its low wall thickness of 500 µm allows a sufficient penetration of the synchrotron radiation into the material. This hollow tube is sealed by two caps to ensure the containment of the powder during the experiment. The sample holder is made of technical pure Mo to withstand the temperatures during the experiment. Additionally, only a minor contamination of the material is expected due to the low diffusivity of Mo in γ-TiAl based alloys and the short dwelling time. The temperature profile experienced by the material during the in-situ HEXRD sintering experiment matches the temperature profile of a real SPS process and is shown in detail in Fig. 1b [10]. A dwell temperature of 1325 °C and a dwell time of 3 min have been chosen. The in-situ HEXRD sintering experiment has been conducted at the beamline P07 at the storage ring PETRA III at the synchrotron facility Deutsches Elektronen Synchrotron (DESY), Hamburg, Germany, using a synchrotron radiation with a mean photon energy of 73.6 keV. During the experiment, whole diffraction rings emitted by the material were captured using a Perkin-Elmer X-ray area detector 1621 placed at a distance of approximately 1500 mm behind the specimen (Fig. 1a).

The experimental setup was calibrated using a LaB 6 sample. The obtained diffraction data were azimuthally integrated with the software fit2D [12]. The evolution of the volume fraction of the individual phases was determined by sequential Rietveld refinement using the batch processing mode of the software MAUD [13]. Since no phase transformation occurs under the applied cooling rate of 100 °C/min at low temperatures, the experiment was terminated at 700 °C.

The room temperature diffraction spectrum of the powder recorded before starting the in-situ HEXRD sintering experiment, depicted in Fig. 2a, shows several distinct peaks. Along with the peaks of the intermetallic Ti-Al related phases, peaks belonging to the Mo sample holder are also observed (orange diamonds in Fig. 2a). However, these additional Mo peaks need to be accounted for in the Rietveld analysis of the diffraction data by introducing an additional phase. In this material condition, i.e. in the powder, the superstructure peaks belonging to the α 2 phase and the β o phase could not be detected at room temperature. Generally, these peaks, e.g. So while the presence of the disordered α phase in the powder, as indicated by the absence of the α 2 superstructure peaks, is in accordance with literature, an ordering into α 2 during powder atomization cannot be completely ruled out [14][15][16]. However, during the in-situ HEXRD sintering experiment, α 2 superstructure peaks were indeed observed. Contrarily, no β o superstructure peaks occurred in the investigated temperature range. Thus, the present bcc phase will be designated as β/β o phase, although ordering of this phase during rapid cooling after atomization has been reported in literature [17]. Consequently, it should be mentioned that in the Rietveld analysis the disordered α and β phase have been used to model the hexagonal and the bcc phase throughout the whole experiment.

The evolution of the volume fractions of the α/α 2 , the β/β o and the γ phase during the in-situ HEXRD sintering experiment determined by Rietveld analysis is shown in Fig. 2b. The distribution of the phase fractions at room temperature, i.e. the high amount of α and the rather low amount of γ, is a consequence of the high cooling rate occurring during powder atomization, i.e. 10 5 -10 6 °C/s [17], resulting in a material condition far from thermodynamic equilibrium. During the first part of the heating segment, the phase fractions stay relatively constant due to lack of thermal activation. However, once a temperature of about 700 °C is exceeded, the amount of α drastically decreases, while the amount of γ increases due to the high driving force. Consequently, this non-equilibrium phase transformation shifts the system towards thermodynamic equilibrium. Additionally, the decrease in the α fraction is accompanied by a decrease in the β/β o fraction. At a temperature of around 920 °C, the metastable α phase undergoes an ordering transformation into the thermodynamically stable α 2 phase as it could be deduced from the occurrence of its superstructure peaks in the diffraction pattern. This α 2 phase disorders again into the α phase upon further heating, i.e. at 65 °C. The γ phase, which is the alloy's main constituent at this temperature, starts to dissolve and the volume fraction of the disordered α phase strongly increases. Before the dwell temperature of 1325 °C is reached during the experiment, the γ phase has completely dissolved. Thus, only the α and the β/β o phase, which can be expected to has disordered at this temperature [18], are present during dwelling. Furthermore, an increase of the β/β o phase fraction is observed after the γ phase dissolution, since the material is moving through the (α+β) phase field region of the alloy system. Consequently, during the cooling segment after dwelling, a lowering of the β/β o phase fraction is observed. Once the temperature falls below the γ-solvus temperature, a significant amount of γ phase is formed. Further cooling yields the ordering of α into α 2 at around 1120 °C followed by only minor adjustments of the phase fractions. After the in-situ HEXRD sintering experiment, the material consists of 90 vol.% γ, 7 vol.% α 2 and 3 vol.% β/β o at room temperature as indicated by the respective symbols in Fig. 2b.

In addition to the evolution of the phase fractions, Rietveld analysis of the diffraction data provides insight into the lattice parameters of the occurring phases. Exemplarily, the c/a ratio of the α/α 2 phase is shown in Fig. 2c. Prior to the transition towards thermodynamic equilibrium, only a slight decrease of the c/a ratio is observable. However, during aforementioned non-equilibrium phase transformation, it increases drastically due to the change in the chemical composition of α. Generally, the c/a ratio of the α/α 2 phase is found to increase with increasing Ti content and decreasing Al content [19]. Thus, the Al redistribution between α and γ during this transition towards thermodynamic equilibrium results in the observed c/a ratio increase. Furthermore, a discontinuity in the c/a ratio occurs during the heating segment (grey area in Fig. 2c). This arises from the momentary presence of two hexagonal phases with different lattice parameters as indicated by the insert in Fig. 2c. This shows the evolution of the hexagonal (200) peak, which, generally, should shift towards lower Bragg angles due to thermal expansion during the heating segment. However, a double peak rather than an individual peak is observed at 557 s (see arrows). The peak at the higher Bragg angle corresponds to α phase with a composition far from its ideal stoichiometry, while the peak at the lower Bragg angle belongs to a newly formed α 2 phase with an adjusted composition in order to bring the material closer towards thermodynamic equilibrium. Further heating manifests in a decreasing c/a ratio due to an Al enrichment, attributed to the fact that the phase boundary separating the (α+β) and the (α+β+γ) phase field region is generally shifted towards higher temperatures with an increasing Al content [17]. Once the γ-solvus temperature is exceeded and the material is within the (α+β) phase field region, the c/a ratio remains constant. Its increase during cooling can be attributed to the Al exchange between α and γ in the (α+β+γ) phase field region as well as to the ordering into α 2 .

The microstructure of the specimen was investigated by scanning electron microscopy (SEM) to verify the observations of the in-situ HEXRD sintering experiment. For this, the in-situ HEXRD specimen and the as-SPSed material were metallographically prepared as described in [20]. Micrographs of the individual microstructures were taken with a Tescan CLARA SEM, Czech Republic, using backscattered electron (BSE) mode. An overview of the crosssection of the specimen is shown in Fig. 3a. Although no pressure was applied, sintering occurred to some extend during the in-situ HEXRD sintering experiment. However, a high porosity is still present within the material. At the surface of the specimen, a bright layer can be detected in BSE mode indicating a Mo contamination layer. A micrograph of this layer at a higher magnification is depicted in the insert in Fig. 3a. Although, this suggests diffusion of Mo from the sample holder into the material, the thickness of this layer is rather small, i.e. 50 µm, and, thus, is expected to be not significant. The microstructure of the in-situ HEXRD sintering specimen, shown in Fig. 3b, consists of lamellar α 2 /γ colonies, which are surrounded by β o and γ phase. This microstructure is in accordance with the phases observed during the in-situ HEXRD sintering experiment. As described above, α and β phase are present at the dwell temperature, where the β phase limits the α grain growth and, thus, improves the alloy's ductility by reducing the lamellar colony size [7]. During the cooling segment, the α phase transforms into lamellar α 2 /γ colonies by the formation of γ lamellae and a subsequent ordering of the remaining α phase into α 2 . Additionally, γ phase is formed in the β o phase, resulting in the formation of a β o /γ seam around the colony boundaries [7].

Finally, to compare the electromagnetic-assisted sintering experiment with a real SPS process, the microstructure of as-SPSed material of the same alloy, processed at 1325 °C, is shown in Fig. 3c. A comparison with the in-situ HEXRD specimen (Fig. 3b) reveals the same microstructural features, e.g. the size and shape of α 2 /γ colonies as well as the presence of β o and γ grains at the colony boundaries. The only difference is the absence of pores due to the applied pressure in the case of SPS. This shows that the same microstructure with respect to the phase distribution could be achieved during the described electromagnetic-assisted sintering experiment. As this experiment and the conducted SPS densification share the same temperature profile characteristics as well as essentially the same heating mechanism, i.e. the Joule's effect [6], this ultimately proves that the observed phase evolution can be applied to the SPS cycle. Thus, the insights into the non-equilibrium and equilibrium phase kinetics and transformations generated in this work are transferable to the SPS technology.

α 2 -

 2 (10 ) and β o -(100), possess a very low intensity when compared to the main peaks of the respective phases in the HEXRD signal, which is further reduced by the Mo sample holder.

  This research was funded in part by the Austrian Science Fund (FWF) [Project Number I 3932-N36]. For the purpose of open access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. The support of the DESY management and photon science user office is gratefully acknowledged. We appreciate the commitment of the Helmholtz-Zentrum Hereon beamline staff, who contributed greatly to the success of the experiments performed.

Figure 1 .

 1 Figure 1. a) Schematic drawing of the experimental diffraction setup. Note that the front side of the Mo sample holder tube is not shown for a better visibility of the material and the sample holder caps; b) temperature profile used for the electromagnetic-assisted sintering during in-situ HEXRD experiment as experienced by the material indicating the heating, dwelling and cooling segment. The sample holder, containing the pre-alloyed powder, is heated inductively via an induction coil in a high-purity Ar atmosphere.

Figure 2 .

 2 Figure 2. a) Integrated diffraction spectrum of the powder recorded at room temperature before the in-situ HEXRD sintering experiment was started. The peaks belonging to the different phases are marked by individual symbols; b) phase fraction evolution of the α/α 2 , the β/β o and the γ phase in the course of the in-situ HEXRD sintering experiment. The symbols on the right side correspond to the room temperature volume fraction of the α 2 (square), the β/β o (circle) and the γ phase (triangle); c) evolution of the c/a ratio of the α/α 2 phase during the in-situ HEXRD sintering experiment. Note that the presented c/a ratio values were extracted from the disordered hexagonal phase model used for the Rietveld analysis. The grey area marks a region, which is characterized by the presence of both hexagonal phases. For a better illustration, the insert presents the diffraction spectra for different times showing the presence of two hexagonal (200) peaks (arrows) at 557 s (for more details see text).

Figure 3 .

 3 Figure 3. a) Overview of the cross-section of the in-situ HEXRD specimen showing densified areas as well as areas with a high porosity. The insert shows the Mo contamination layer at a higher magnification (see text). In b) and c) SEM-BSE micrographs of the microstructure of the in-situ HEXRD specimen and the as-SPSed material densified at the same dwell temperature are presented. The γ phase exhibits a dark grey contrast, while the α 2 phase appears in a grey contrast and the β/β o phase shows a bright contrast. No oxides were observed neither in the in-situ HEXRD specimen nor in the as-SPSed material.


C Garcion

N Fabre

H Bricha

F Perales

S Scheel

M Ducloy

G Dutier

Intermediate-range Casimir-Polder interaction probed by high-order slow atom diffraction

At nanometer separation, the dominant interaction between an atom and a material surface is the fluctuation-induced Casimir-Polder potential. We demonstrate that slow atoms crossing a silicon nitride transmission nanograting are a remarkably sensitive probe for that potential. A 15% difference between nonretarded (van der Waals) and retarded Casimir-Polder potentials is discernible at distances smaller than 51 nm. We discuss the relative influence of various theoretical and experimental parameters on the potential in detail. Our work paves the way to high-precision measurement of the Casimir-Polder potential as a prerequisite for understanding fundamental physics and its relevance to applications in quantum-enhanced sensing.

The Casimir-Polder (CP) interaction between an atom or molecule and polarizable matter [START_REF] Casimir | The influence of retardation on the London-van der Waals forces[END_REF] has been intensively studied theoretically as a fundamental electromagnetic dispersion force [START_REF] Scheel | Macroscopic quantum electrodynamics -concepts and applications[END_REF][START_REF] Buhmann | Dispersion Forces I -Macroscopic Quantum Electrodynamics and ground-state Casimir, Casimir-Polder and van der Waals forces[END_REF]. It originates from quantum fluctuations of the electromagnetic field that spontaneously polarizes otherwise neutral objects. Interaction strength and spatial dependence are the result of a unique combination of atom species, internal atomic state and material properties and geometry. The Casimir-Polder interaction is part of a larger family of fluctuationinduced electromagnetic forces that also include the wellknown Casimir force [START_REF] Casimir | On the Attraction between Two Perfectly Conducting Plates[END_REF] that has been studied, e.g., between a metallic sphere and a nanostructured surface [START_REF] Mohideen | Precision Measurement of the Casimir Force from 0.1 to 0.9 µm[END_REF][START_REF] Intravaia | Strong Casimir force reduction through metallic surface nanostructuring[END_REF]. Historically, and rather confusingly, the nonretarded regime with U vdw (z) = -C 3 /z 3 is sometimes called the van der Waals (vdW) potential in order to distinguish it from the retarded (or Casimir-Polder) regime, which asymptotically converges to U ret (z) = -C 4 /z 4 at a large distance from the surface z. In the current usage, the Casimir-Polder interaction consistently refers to the dispersion interaction between a microscopic (atom or molecule) and a macroscopic object independent of the distance regime.

Pioneering work with Rydberg atoms [START_REF] Sandoghdar | Direct measurement of the van der Waals interaction between an atom and its images in a micron-sized cavity[END_REF] predominantly probed the nonretarded regime even at atomsurface distances as large as 1 µm due to major contributions from atomic transitions in the mid-IR. On the other hand, when the atomic transitions are in visible or near UV regions -such as for atoms in their ground statesthe atom-surface interaction will be in the CP regime. This scenario is relevant for ground-state atomic beams [START_REF] Sukenik | Measurement of the Casimir-Polder force[END_REF], cold atoms near atomic mirrors [START_REF] Landragin | Measurement of the van der Waals Force in an Atomic Mirror[END_REF] and quantum reflection [START_REF] Shimizu | Specular Reflection of Very Slow Metastable Neon Atoms from a Solid Surface[END_REF]. Very few experiments thus far have studied the crossover regime where neither limit holds, typically using an adjustable repulsive dipolar force [START_REF] Bender | Direct Measurement of Intermediate-Range Casimir-Polder Potentials[END_REF]. Studying atom-surface interactions with reasonable accuracy is of major importance as these fundamental fluctuationinduced interactions have not been yet measured with an accuracy better than 5-10% whatever the experimental approach.

In this Letter, we present our experimental and theoretical investigations of matter-wave diffraction of metastable argon atoms by a transmission nanograting at atom-surface distances below 51 nm. The geometric constraint on the atom-surface distance provided by the two adjacent walls is a major asset that eliminates the quasi-infinite open space over a single surface, similar to an ultrathin vapor cell [START_REF] Fichet | Exploring the van der Waals atom-surface attraction in the nanometric range[END_REF]. Atom-surface interactions have previously been studied using transmission nanogratings with atoms at thermal velocities [START_REF] Grisenti | Determination of Atom-Surface van der Waals Potentials from Transmission-Grating Diffraction Intensities[END_REF][START_REF] Lonij | Magic ratio of window width to grating period for van der Waals potential measurements using material gratings[END_REF]. This Letter shows that lowering the atomic beam velocity below 26 ms -1 opens up new experimental opportunities due to larger interaction times, and produces diffraction spectra dominated by the atom-surface interaction [START_REF] Nimmrichter | Theory of near-field matter-wave interference beyond the eikonal approximation[END_REF]. The precise control of nanograting geometry and experimental parameters related to the atom beam leads us to observe the minute influence of retardation. This paves the way to accurate CP potential measurements that can be compared against detailed theoretical models.

Transmission gratings etched into a 100 nm thick silicon nitride (Si 3 N 4 ) membrane are commonly made using achromatic interferometric lithography [START_REF] Savas | Achromatic interferometric lithography for 100-nm-period gratings and grids[END_REF] using UV light, resulting in gratings with pitch down to 100 nm covering areas of several mm 2 . For its versatility in nanograting design, we chose electron beam lithography to pattern a new generation of resists with high selectivity during etching and low line edge roughness [START_REF] Thoms | Investigation of CSAR 62, a new resist for electron beam lithography[END_REF]. A 200 nm-period transmission nanograting has been fabricated on a 100 nm thick membrane of 1 × 1 mm 2 in size. The combination of 100 keV e-beam lithography and anisotropic reactive ion etching ensures parallel walls with deviations smaller than 0.5 degrees from the vertical [START_REF] Krückel | Optical bandgap engineering in nonlinear silicon nitride waveguides[END_REF][START_REF] Kaspar | Silicon nitride hardmask fabrication using a cyclic CHF3-based reactive ion etching process for vertical profile nanostructures[END_REF][20]. The SEM image of a cleaved nanograting shows smooth and anisotropically etched walls, rounded with a 21 nm radius of curvature along the atom propagation x axis [Fig. 1(a) and inset]. Statistical analysis of SEM images reveals a slotted hole geometry of the slits (with straight section along 90% of the total slit length), with a main width W = 102.7 ± 0.3 nm and a FWHM distribution of 7 nm [Fig. 1(b)].

Hybrid experiments at the interface between atomic physics and nanoscience often use alkali atoms for convenient laser cooling and manipulation. However, nanostructures chemically react with residual vapor that alters the CP potential unpredictably [START_REF] Mcguirk | Alkali-metal adsorbate polarization on conducting and insulating surfaces probed with Bose-Einstein condensates[END_REF]. Using noble gas atoms in a metastable state prevents chemical damage on nanostructures while retaining the ability for laser manipulation. The (3p 5 4s; 3 P 2 ), metastable state of argon is used for an efficient and accurate time-position detection by microchannel plates with 80 mm diameter in front of a delay line detector (DLD80 from RoentDek Handels GmbH). The experiment starts with a supersonic beam of argon followed by a counterpropagating electron gun, which provides a flux of 10 8 Ar * atoms per second. The cycling transition (3p 5 4s; 3 P 2 ) ←→ (3p 5 4p; 3 D 3 ) (with Γ = 2π × 5.8 MHz, λ = 811.531 nm) is used by a Zeeman decelerator to trap atoms in a magneto-optical trap (MOT). The trap consists of anti-Helmholtz coils providing the magnetic field and three retroreflected laser beams, red-detuned by 2Γ, with 7 mW total power and 2.54 cm beam diameter. Approximately 10 7 atoms are trapped at a temperature of ≈ 20 mK.

An initial pulse sequence pushes an atom cloud at a chosen velocity orthogonally to the incoming supersonic beam at 13 Hz repetition rate [START_REF] Taillandier-Loize | A simple velocity-tunable pulsed atomic source of slow metastable argon[END_REF]. During this time, the magnetic field remains constant and the molasses laser beams are switched off. Simultaneously, the circularly polarized pushing laser beam (5 mW, frequency adjustable on the same cycling transition) is turned on for 0.4 ms toward the detector and focused to 20 cm after the MOT position. Atoms remain in the m = +2 state without any influence on the diffraction process. A TOF measurement is then performed, with the time-position detector 86.8 cm away from the MOT. With this pushing technique, the relative spread of the atomic velocity distribution, ∆v/v, is already less than 10%. Moreover, a time selection of 1 ms is applied to obtain an even narrower velocity distribution. Additionally, for an absolute velocity determination, we used a light chopper with two resonant lasers of 1 mm diameter perpendicular to the atomic beam axis, separated by ∆x = 266.5 ± 1.3 mm and time triggered with a time sequence accuracy below 50 µs. We obtained mean velocities and respective uncertainties of 19.1±0.2 ms -1 and 26.2±0.1 ms -1 for both recorded spectra.

The vertical y axis [see Fig. 1(c)] has been chosen for the slit alignment in order to impose a diffraction expansion perpendicular to the Earth's gravitational field. At 56 cm from the MOT, the atomic beam diameter is much larger (≈ 5 cm) than the entire nanograting surface and all slits along the y axis contribute equally to the signal. This is not the case along the z axis (diffraction axis) where the angular beam distribution acts as an incoherent source and smears the signal out, in particular interference orders that are separated by more than 2.6 (1.9) mrad for 19.1 (26.2) ms -1 . A compro-mise between atomic flux through the nanograting and fringe visibility (smearing) is achieved with a free opening of L g = 306 ± 5 µm between the vertical edge of the plate and the nanograting boundary. The atomic beam divergence, ∆ beam θ , through the 306 µm slit at a distance L 1 from the MOT fits a Gaussian profile with 1.4 mrad FWHM. As a consequence, the beam divergence alters perceptibly the measured diffraction spectra, but in a controlled way. The nanograting is fixed on a 6D piezo system (SmarPod 11.45 from SmarAct GmbH) to ensure a 90.0 ± 0.1 degree angle between the atomic beam and the z axis on the nanograting. An angular deviation as small as 0.2 degrees introduces noticeable asymmetry of the intensities of the diffraction orders. Two experimental diffraction spectra are shown in Fig. 2 for contributing velocities between 18.7 -19.5 ms -1 and 25.5 -26.9 ms -1 . Small electronic aberrations in position have been corrected by the use of a 2600hole grid pattern, and no intensity inhomogeneity has been noticed at the experimental accuracy level. The recording times were 40 and 13 hours for 1.006 × 10 5 and 1.512 × 10 5 atoms, respectively. In general, for matter waves propagating through a transmission grating, the diffraction spectrum envelope is determined by the wavelength and the single slit width, while the interference peak visibility stems from the transverse coherence length of the source. In the present situation, the nanograting slit width effectively narrows due to atoms that are close enough to a surface being mechanically attracted and deflected by the Casimir-Polder potential. Metastable atoms colliding with the surface at room temperature are scattered randomly at high velocity, and will return to their ground state [START_REF] Hagstrum | Theory of Auger ejection of electron from metal by ions[END_REF].

For atoms at thermal velocities, the region near the surfaces the atoms needed to avoid was assumed to be a few nanometers [START_REF] Grisenti | Determination of Atom-Surface van der Waals Potentials from Transmission-Grating Diffraction Intensities[END_REF][START_REF] Lonij | Magic ratio of window width to grating period for van der Waals potential measurements using material gratings[END_REF]. Using classical trajectories, we can estimate a lower limit for the distance at which the atoms can pass the nanobars to be d 0 = 16.2 (14.2) nm at a beam velocity of 19.1 (26.2) ms -1 or, equivalently, an effective slit width of W eff = 70.3 (74.3) nm. Such a major reduction cannot be neglected when explaining experimental diffraction spectra (2λ dB /W eff = 14 mrad at 19.1 ms -1 ). The effective slit width and the exerted CP forces elsewhere in the grating explain the overall broadening of the spectra compared with an equivalent optical picture with first zeros at 5 mrad. The fringe visibility depends only on the transverse coherence length of the atomic beam, L c = λ dB L 1 /a, with a the diameter of the incoherent source, as given by the van Cittert-Zernike theorem [START_REF] Born | Principles of optics[END_REF]. However, the quadratic dispersion relation for matter waves suppresses the dephasing compared with light [START_REF] Taylor | The van Cittert-Zernike theorem in atom optics[END_REF], and hence enlarges L c . From the cloud size in the MOT, a = 330 ± 40 µm, followed by thermal expansion, one finds L c = 560 ± 45 (380 ± 30) nm at 19.1 (26.2) ms -1 beam velocity.

The Huygens-Kirchhoff principle can be utilized for atoms propagating in a potential that is small compared with their kinetic energy [START_REF] Feynman | Space-Time Approach to Non-Relativistic Quantum Mechanics[END_REF][START_REF] Kholodenko | Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics[END_REF]. This can be justified with the help of the effective slit approximation, which removes atoms with potential energies that are too large. Additionally, the detection in the far field validates the Fraunhofer approximation (x W 2 eff /λ dB ), in which the diffraction pattern results from the sum of wave path differences at the nanograting output. The CP potential is included in the wave propagation as an additional phase Φ CP (z) that depends on the atom-surface distance inside the nanograting slit z. In short, the total phase can be written as F (z, θ) = kz sin θ + Φ CP (z) for a detection angle θ and a wave number k. The incoming Gaussian wave packets have a standard deviation σ coh = L c /2 [START_REF] Zecca | Double Slit Diffraction Pattern of Gaussian Wave Packet Interacting with the Wall[END_REF][START_REF] Thompson | Two-Beam Interference with Partially Coherent Light[END_REF]. The experimental value for L c covers up to seven slits coherently and hence, the beam cannot be considered as a plane wave. The diffraction intensity then reads as

I(θ) = slits W eff exp [iF (z , θ)] exp - z 2 2σ 2 coh dz 2 . (1)
In eikonal approximation, the phase shift imprinted by a potential U CP (z) is the integral of the potential along the particle trajectory [START_REF] Landau | Quantum Mechanics: Non-Relativistic Theory[END_REF]. Neglecting the surface potential outside the grating, one finds

Φ CP (z) = - 1 v L 0 U CP (x, z)dx (2)
where L = 100 nm is the nanograting depth and v the beam velocity. However, it is necessary to account for the exact shape of the grating along the x axis, because the slit widths increase near the output. We incorporate this effect by using a smaller slit thickness of L eff = 95 nm.

In pioneering experiments with nanogratings and supersonic beams [START_REF] Grisenti | Determination of Atom-Surface van der Waals Potentials from Transmission-Grating Diffraction Intensities[END_REF][START_REF] Perreault | Observation of Atom Wave Phase Shifts Induced by Van Der Waals Atom-Surface Interactions[END_REF], the CP potential is modeled in the nonretarded regime as U vdw (z) = -C nr 3 /z 3 for the two adjacent surfaces. Semi-infinite surfaces are implicitly considered everywhere inside the grating even if this is not correct near the edges. Further, the effect of multiple reflection from the bar opposite has been neglected [START_REF] Dutier | Revisiting optical spectroscopy in a thin vapor cell: mixing of reflection and transmission as a Fabry?Perot microcavity effect[END_REF]. These approximations are justified for fast atoms or molecules as the overall phase shift remains small on average [START_REF] Brand | A Green's function approach to modeling molecular diffraction in the limit of ultra-thin gratings[END_REF]. In the nonretarded regime, the coefficient C nr 3 is given by the Lifshitz formula [START_REF] Lifshitz | The theory of molecular attractive forces between solids[END_REF][START_REF] Mavroyannis | The interaction of neutral molecules with dielectric surfaces[END_REF]]

C nr 3 = 16π 2 0 ∞ 0 α(iξ) (iξ) -1 (iξ) + 1 dξ (3)
where α(iξ) denotes the atomic dynamic polarizability, and (iξ) is the surface permittivity taken at imaginary frequencies iξ. For metastable argon in the 3 P 2 state, we obtain C nr 3 = 1.25 a.u., or 5.04 meV nm 3 in front of a Si 3 N 4 surface with spectral responses in the UV and IR [START_REF] Philipp | Optical Properties of SiliconNitride[END_REF]. An estimate of the uncertainty of this value is rather difficult to obtain. First, the material may show imperfections with regard to its fabrication and size [START_REF] Zollner | Optical Constants for Metrology of Hydrogenated Amorphous Silicon-Nitrogen Alloys on Si[END_REF] that alter the index of refraction. Second, the electronic structure of argon in the 3 P 2 metastable state, due to its 11.5 eV internal energy, makes the potential more sensitive to the material optical response in the visible and near-UV regions, where accurate optical response data are difficult to obtain. Third, the electronic core contribution has been estimated to be in the range of 0.03 a.u. using the first ionic state. Such a small core contribution is a clear theoretical advantage of metastable argon compared with heavier (alkali) atoms [START_REF] Derevianko | High-Precision Calculations of Dispersion Coefficients, Static Dipole Polarizabilities, and Atom-Wall Interaction Constants for Alkali-Metal Atoms[END_REF]. The temperature dependence of C nr 3 can be safely neglected here, in contrast to situations in which dominant transitions appear in the mid-IR region [START_REF] Laliotis | Casimir-Polder interactions in the presence of thermally excited surface modes[END_REF]. Altogether, we conservatively estimate a 10% uncertainty that is similar to other CP calculations.

The improvement in experimental accuracy allows us to discern the nonretarded regime and the onset of retardation effects, that arise due to the finite field propagation time between atom and surface. This effect becomes relevant at distances larger than λ opt /(2π). Without resorting to a full calculation of the exact shape of the potential, one can resort to sophisticated interpolations. Here, we use a model derived in Ref. [START_REF] Wylie | Quantum electrodynamics near an interface[END_REF] that is built on a single atomic transition (here, λ opt = 811.5 nm for Ar 3 P 2 ), for which the coefficient C eff 3 (z) reads as

C eff 3 (z) = C nr 3 ζ + (2 -ζ 2 )f 1 (z) + 2ζf 2 (z) /π (4)
with ζ(z) = 2z(2π)/λ opt and f i (z) given in [START_REF]2(z) = -Ci(ζ) cos(ζ) -(Si(ζ) -π/2) sin(ζ) where Ci(z) and Si(z) are the integral cosine and sine functions[END_REF]. This expression provides an interpolation between U vdw ∝ z -3 at short distances and U ret ∝ z -4 for z λ opt . Inside the grating, C eff 3 (z) goes from C nr 3 at z = 0 to C eff 3 (51 nm) = 0.78 C nr 3 [Fig. 3(a)]. On average, the detected atoms will have experienced C eff are the experimental noise standard deviation, and the experimental and theoretical intensities at the angle θ, respectively. Indeed, we find a linear relation between C nr 3 and slit width as well as nanograting thickness L ng to within 10% of their nominal values: ∆W = ±1 nm → ∆C nr 3 = ± 0.07 a.u. and ∆L ng = ±10 nm → ∆C nr 3 = 0.16 a.u. On the other hand, σ coh and ∆ beam θ are not linked to any other parameters.

The remaining important parameter, W eff = W -2d 0 in Eq. ( 1), is the maximum additional CP phase shift with Φ max CP = Φ CP (d 0 ). Note that Φ max CP is different for both models as d 0 increases with larger C nr 3 . Also, at larger velocities this parameter was not considered to be critical [START_REF] Bender | Direct Measurement of Intermediate-Range Casimir-Polder Potentials[END_REF].

With this, Figure 3(b) shows (χ 2 min + 40σ) surfaces of C nr 3 and Φ max CP at a beam velocity of 26.2 ms -1 and where σ = 6.2 is the standard deviation for two parameters [START_REF] Press | Numerical Recipes[END_REF]. The chosen magnification of 40σ reveals four local minima for Φ max CP that have previously not been discussed, but which are necessary for a correct analysis using the Kirchhoff approximation. They correspond, respectively, to distances z ≈ 17.5, 13.1, 11.0, 10.1 nm from the surface. We chose the global minimum for further discussion given by Φ max CP = 10.5 rad. The dashed line is the calculated expected C nr 3 . Figure 3(c) is an enlargement of Fig. 3(b) for 1 standard deviation that rejects the van der Waals approximation (blue) by more than 30σ with regard to the calculated C nr 3 . In addition, χ 2 minima for both velocities are found to be smaller with the full CP model. For further clarity, the insets in Fig. 2 emphasize the influence of both models on the spectra calculated at Φ max CP = 10.5 rad with the theoretically expected C nr 3 . Our extracted value of C nr 3 = 1.24±0.15 a.u. is strongly dominated by grating geometry uncertainties (±0.13 a.u.), where statistical error bars -assuming a known grating -represent only ±2% (±0.025 a.u.) at one σ. Such an unprecedented value is clearly connected to the ultra large diffraction spectra broadening. Note that it corrects the rather crude approximation given in Ref. [START_REF] Karam | Atom diffraction with a 'natural' metastable atom nozzle beam[END_REF]. The advantage of using a slow atomic beam with a well-defined velocity rather than a thermal beam derives from the fact that the atom-surface interaction poten-tial can be probed to a much higher accuracy. However, this presents another difficulty: the Kirchhoff approximation stipulates that the (change of the) transverse wave number has to be small compared with the longitudinal wave number, k perp /k 1 [START_REF] Arsenović | Equivalence of two forms of the solution to the Schrödinger equation for a particle passing through a grating[END_REF]. The slower the atoms become, the more (relative) transverse momentum they accumulate whilst traversing the grating. At the cutoff that determines the effective slit width, we can estimate the relative change in transverse wave number to be roughly 5% for a beam velocity of 26.2 ms -1 , but already 10% for a velocity of 19.1 ms -1 . This implies that the Kirchhoff approximation can no longer be relied upon at slower beam velocities, at which a more detailed theoretical description is required.

In conclusion, we have demonstrated the importance of the retarded Casimir-Polder potential for the diffraction of metastable Ar in a range of atom-surface distances as small as ≈ 15 -51 nm with a Si 3 N 4 transmission nanograting. Because of atomic velocities as slow as 19.1 ms -1 as well as an accurate geometrical characterization of the nanograting, we were able to discriminate a difference in the CP potential as small as 15%. For lower velocities or smaller slit widths, the semiclassical model utilized for the simulations should be replaced by a quantum mechanical model. Such a theoretical refinement will introduce quantum reflexion at the slit walls and may produce, in some geometry, gravity Q-bounces as found for neutrons [START_REF] Jenke | Realization of a gravity-resonance-spectroscopy technique[END_REF]. This Letter opens the opportunity for unprecedented and accurate CP potential measurements by controlling the tilt of the nanograting, which, combined with tomography methods, would lead to a thorough understanding of atom-surface interactions with implications for theoretical physics as well as nanometrology. For example, the hypothetical non-Newtonian fifth force [START_REF] Antoniadis | Short-range fundamental forces[END_REF] could be constrained by an atomic physics experiment. Atomic quantum random walks [START_REF] Karski | Quantum Walk in Position Space with Single Optically Trapped Atoms[END_REF] based on multipath beam splitters can be simply realized with two or more nanogratings, and closed-loop interferometers can be made extraordinary compact.

The authors from Laboratoire de Physique des Lasers acknowledge the "Institut Francilien de Recherche sur les Atomes Froids" (IFRAF) for supports. This work has been supported by Region Ile-de-France in the framework of DIM SIRTEQ. The work was partly supported by the French Renatech network. The authors acknowledge B. Darquié for fruitful data analysis discussions.

FIG. 1 .

 1 FIG. 1. SEM images of (a) a cleaved nanograting on a substrate and (b) a free standing membrane. (c) Experimental setup. An atomic cloud is periodically pushed by a laser (red arrow) from a MOT at a chosen velocity through a nanograting L1 = 56 cm away. A time-position detector is located L2 = 308 mm behind the nanograting. A light chopper (blue arrows) is available for accurate velocity measurement. A 6D piezo system controls the grating position.

FIG. 3 .

 3 FIG. 3. (a): C eff 3 /C nr 3 as function of atom-surface distance. The two dashed lines represent the recorded atom-surface distance range. (b),(c): χ 2 min +nσ [n=40 (b), n =1, 3, 6, 9 (c)] as functions of C nr 3 and Φ max CP at 26.2 ms -1 for vdW (blue) and CP (red) potentials. The dashed line shows the theoretical value for C nr 3 .