Christos Bilitos

David González-Ovejero

Jorge Ruiz García

Dayan Pérez-Quintana

Jorge Ruiz-García

Iñigo Ederra
email: inigo.ederra@unavarra.es

Jorge Teniente-Vallinas

Miguel Beruete
email: miguel.beruete@unavarra.es

Fully Metallic Luneburg Metalens Antenna in Gap Waveguide Technology at V-Band



Abstract-This paper presents the design of a flat Luneburg metalens antenna at V-band using Gap Waveguide (GW) technology. The metalens consists of a parallel plate waveguide loaded with metallic pins whose height is modulated to get an effective refractive index that follows the Luneburg equation. A Groove Gap Waveguide (GGW) H-plane horn is used to illuminate the metalens, such that the rays are collimated and a planar wavefront is generated in the direction of propagation. Since the structure at hand is planar, it can be efficiently integrated on flat surfaces. Moreover, the fully metallic structure is mechanically robust and presents lower losses than lenses including dielectric substrates. A prototype has been fabricated and tested, simulations and experimental results are in very good agreement. The metalens yields an input reflection coefficient (S11) below -10 dB from 45 to 70 GHz, whereas the -3dB gain fractional bandwidth is 26.2% with respect to a center frequency of 60 GHz, with a peak of 22.5 dB at 61 GHz. These features make this design an interesting solution for millimeter-wave applications.

Index Terms-Luneburg lens, gap waveguide technology, millimeter-waves, metalens, metasurface.

I. INTRODUCTION

IRELESS COMMUNICATION systems are in constant evolution, with each new standard defining higher data rates in order to satisfy the demands of a hyperconnected society. The race for data rate along with the saturation of the microwave spectrum are driving the exploration of higher frequency bands, which can provide broader bandwidths able to cope with these requirements. The millimeter-wave (MMW) band (from 30 to 300 GHz) can fulfill this purpose, since it allows for wide channelization bandwidths that fit the specifications of the fifth-generation (5G) and the incoming sixth-generation (6G) mobile communication systems [START_REF] Tataria | 6G Wireless Systems: Vision, Requirements, Challenges, Insights, and Opportunities[END_REF]. Nevertheless, there remain some challenges that must be addressed to fully exploit all the potential of MMW in wireless communication technologies. For instance, highly directive antennas are needed to compensate for the increased free-space Manuscript received XX; revised XX; accepted XX. Date of publication XX; date of current version XX. This work was supported This work was supported by MCIN/AEI/10.13039/ 501100011033/FEDER "Una manera de hacer Europa" via Project No. RTI2018-094475-B-I00. (Corresponding author: Miguel Beruete.) Dayan Pérez-Quintana, Iñigo Ederra, Jorge Teniente and Miguel Beruete are with the Antennas Group, Universidad Pública de Navarra, 31006 Pamplona, Spain, and also with the Institute of Smart Cities (ISC), Universidad Pública de Navarra, 31006 Pamplona, Spain (e-mail: dayan.perez@unavarra.es; propagation loss compared to microwaves (due to the higher carrier frequencies) as well as additional losses due to atmospheric absorption.

Several solutions have been proposed to tackle these issues, including antenna arrays and reflector antennas with high directivity and good scanning performance [START_REF] Dadgarpour | High-Gain 60 GHz Linear Antenna Array Loaded With Electric and Magnetic Metamaterial Resonators[END_REF], [START_REF] Li | A Low-Cost Vertically Integrated Antenna Array at 60 GHz With 85% Efficiency[END_REF]. Despite being a feasible solution, antenna arrays need complex feeding networks, which lead to increased losses jeopardizing its practical applicability at MMW. Regarding reflector antennas, although cost-effective, the designs are bulky and require a mechanical steering of the complete antenna assembly.

Lens antennas have emerged in recent years as an alternative for wireless devices at high frequencies due to the high directivity and scanning resolution they offer with relatively simple structures [START_REF] Yuan | Glide-Symmetric Lens Antenna in Gap Waveguide Technology[END_REF]- [START_REF] Zetterstrom | Experimental Validation of a Metasurface Luneburg Lens Antenna Implemented With Glide-Symmetric Substrate-Integrated Holes[END_REF]. Although lens antennas can be bulky at microwaves, they become more compact when scaled at MMW. One of the most versatile solutions is the Luneburg lens (LL) [START_REF] Luneburg | Mathematical Theory of Optics[END_REF], whose rotationally symmetric graded index (GRIN) profile transforms a spherical wave into a planar wavefront with perfect impedance matching to free space. In turn, flat LLs [START_REF] Bosiljevac | Non-Uniform Metasurface Luneburg Lens Antenna Design[END_REF], [START_REF] Zetterstrom | Experimental Validation of a Metasurface Luneburg Lens Antenna Implemented With Glide-Symmetric Substrate-Integrated Holes[END_REF] collimate cylindrical wavefronts to radiate a fan beam.

The spatially varying refractive index in such lenses can be synthesized using metasurfaces and metamaterials with hybrid metallodielectric [START_REF] Bosiljevac | Non-Uniform Metasurface Luneburg Lens Antenna Design[END_REF], [START_REF] Zetterstrom | Experimental Validation of a Metasurface Luneburg Lens Antenna Implemented With Glide-Symmetric Substrate-Integrated Holes[END_REF], [START_REF] Li | Design of a Broadband Metasurface Luneburg Lens for Full-Angle Operation[END_REF], [START_REF] Marin | Lens Antenna With Planar Focal Surface for Wide-Angle Beam-Steering Application[END_REF] or fully metallic unit cells [START_REF] Lu | Fully Metallic Anisotropic Lens Crossover-in-Antenna Based on Parallel Plate Waveguide Loaded With Uniform Posts[END_REF]- [START_REF] Fan | Wideband Low-Profile Luneburg Lens Based on a Glide-Symmetric Metasurface[END_REF]. For example, metallodielectric Luneburg lenses (LL) were implemented in [START_REF] Bosiljevac | Non-Uniform Metasurface Luneburg Lens Antenna Design[END_REF] and [START_REF] Li | Design of a Broadband Metasurface Luneburg Lens for Full-Angle Operation[END_REF] by modulating the surface impedance inside a parallel-plate structure. However, the use of dielectrics is not recommendable at MMW due to the dielectric losses which, in some cases, can be high [START_REF] Rajo-Iglesias | Gap Waveguide Technology for Millimeter-Wave Antenna Systems[END_REF]. To avoid this limitation, fully metallic LL devices have been proposed. The multibeam LL antennas in [START_REF] Quevedo-Teruel | Glide-Symmetric Fully Metallic Luneburg Lens for 5G Communications at Ka-Band[END_REF] and [START_REF] Liu | Fully Metallic Dual-Polarized Luneburg Lens Antenna Based on Gradient Parallel Plate Waveguide Loaded With Nonuniform Nail[END_REF] yielded good results using a bed of nails (metallic pins) with varying height to modulate the refractive index. To simplify the manufacturing process, a bed of nails with homogenous pin height was proposed in [START_REF] Lu | Fully Metallic Anisotropic Lens Crossover-in-Antenna Based on Parallel Plate Waveguide Loaded With Uniform Posts[END_REF], and the refractive index modulation was implemented by varying the height of the metallic plate opposite to the bed of nails.

Another obstacle that must be circumvented to fully develop MMW technology resides in effectively guiding waves in closed structures. Typical solutions that perform well at microwaves, such as standard metallic waveguides, become more and more challenging as the frequency approaches the MMW band. At these frequencies, strict tolerances are required to get a good electrical contact and, hence, avoid additional losses. Respecting such tolerances by typical fabrication technologies might be difficult or have an excessive cost. A promising alternative at MMW is the Gap Waveguide (GW) technology, developed during the last decade to give a satisfactory technological response to this question [START_REF] Kildal | Local Metamaterial-Based Waveguides in Gaps Between Parallel Metal Plates[END_REF]. GW has three main variants: groove-gap waveguide (GGW) [START_REF] Berenguer | Propagation Characteristics of Groove Gap Waveguide Below and Above Cutoff[END_REF], ridge-gap waveguide (RGW) [START_REF] Perez-Quintana | Compact Groove Diamond Antenna in Gap Waveguide Technology With Broadband Circular Polarization at Millimeter Waves[END_REF] and microstrip-gap waveguide (MGW) [START_REF] Liu | Design and Fabrication of a High-Gain 60-GHz Cavity-Backed Slot Antenna Array Fed by Inverted Microstrip Gap Waveguide[END_REF]. In its most general configuration, GW technology uses a couple of bed of nails instead of lateral metallic walls. The pins' dimensions are selected to create a propagation bandgap, which confines the wave propagation within the volume delimited by the bed of nails and a couple of conducting plates on the top and bottom. A relevant feature of this technology is that electric contact between the top plate and the bed of nails is not required, so tolerances can be coarser alleviating the manufacturing constraints and, hence, its cost. In addition, losses at MMW are lower compared with standard rectangular waveguides and it is easily adaptable to flat surfaces [START_REF] Park | A photonic bandgap (PBG) structure for guiding and suppressing surface waves in millimeter-wave antennas[END_REF].

In this article, we exploit the benefits of GGW technology to design and experimentally demonstrate a fully metallic flat LL antenna at 60 GHz, which is above the operation frequency of most LL-based antennas found in the literature. The LL is synthesized using metallic pins with variable height to implement the target refractive index profile. The LL is excited by a GGW horn antenna, whose phase center is placed at the focus of the metasurface LL. The proposed structure can be easily integrated with more ports to provide scanning capabilities with a fan beam radiation pattern. The experimental results show an excellent impedance matching and directivity in the entire operating bandwidth with a good agreement with the numerical simulations. The overall good performance of the device demonstrates that standard fabrication techniques are still valid at high frequencies where tolerances are stringent and the manufacturing of small details is challenging. This article builds upon our prior work in [START_REF] Perez-Quintana | Fully Metallic Luneburg Lens Antenna in Gap Waveguide Technology at 60 GHz[END_REF], [START_REF] Perez-Quintana | Flat Lens Antenna using Gap Waveguide Technology at Millimeter Waves[END_REF], by presenting a more detailed design, comprehensive manufacturing and experimental demonstration of a metalens based on metallic pins with variable height.

II. LUNEBURG LENS ANTENNA DESIGN

As mentioned in the introduction, a fully metallic design is implemented to avoid the loss of typical dielectric substrates in the MMW range, as well as to let the antenna withstand harsh environmental conditions. As explained in [START_REF] Bosiljevac | Non-Uniform Metasurface Luneburg Lens Antenna Design[END_REF], it is possible to modulate the effective refractive index for a transverse magnetic (TM) surface wave by loading a parallel plate waveguide with a bed of nails consisting of metallic posts of different heights. The refractive index profile of a LL obeys the following equation:

𝑛(𝑟) = √ 2 -( 𝑟 𝑅 ) 2 ( 1
)
where r is the radial distance between a point inside the lens and its center, and R is the external radius of the lens. In our design we consider a planar LL which radiates a fan beam. The design of both the GRIN LL lens and the GGW horn antenna was carried out using the commercial simulator CST Microwave Studio® [START_REF] Cst | [END_REF]. Aluminum was considered for all of the constituent pieces and was modeled as a lossy metal with a conductivity of 1.72×10 7 S/m [START_REF] Strober | Shaped Parallel-Plate Lens for Mechanical Wide-Angle Beam Steering[END_REF].

Since the height variation between neighboring pins inside the lens is smooth, each pin can be considered as immersed in a locally periodic environment. Such local periodicity entitles one to treat each pin as a unit-cell in a periodic problem. Therefore, the dispersion characteristics for each unit-cell can be obtained in a straightforward manner by employing CST's eigenmode solver. For instance, Fig. 1(a) shows the dispersion curves obtained for 3 different pin heights, hlens. Using these curves, one can construct maps that link, for a specific frequency, the pin height to the wavenumber kx of the fundamental TM mode inside the loaded PPW. The effective refractive index neff can, thus, be retrieved using kx=neffk0, as shown in Fig. 1(b) and inset.

The GRIN LL is synthesized by dividing the circular area according to a Cartesian lattice that matches the selected periodicity, plens, of the unit-cell. Then, (1) is applied to compute the ideal refractive index in each square of the lattice. Such values can be mapped to a pin height (hlens) using the curve depicted in the inset of Fig. 1(b). Fig. 1(c) shows the structure resulting of this synthesis process. The lens has an external diameter of 50 mm (10λ0, where λ0 is the free space wavelength at the design frequency f0 = 60 GHz) and the metallic pin height varies between 0.3 and 0.8 mm. A flare section is implemented to improve the radiation pattern and the matching to free space, as shown in Fig. 1(d) and its inset. The PPW opens gradually with an angle of 21°, and its length is 20.8 mm. The height and width are 14.5×62.6 mm 2 and, hence, the physical aperture area is 907 mm 2 .

The next step is to design the GGW horn antenna feeding the LL. It must be ensured that the wave is confined within the groove of width 4.2 mm and height 1.75 mm by the metallic pins and the top and bottom metallic plates. Again, the eigenmode solver of CST Studio Suite ® was employed to obtain the pin dimensions that fix a bandgap around the operation frequency. As shown in Fig. 2(a), with a width of ahorn = 0.5 mm, a height of hhorn = 1.5 mm, periodicity phorn = 1 mm and distance to the upper metallic layer of 0.25 mm, a bandgap arises centered at 60 GHz and spanning from 40 to 80 GHz.

Using these dimensions for the GGW pins, the H-plane horn was designed by gradually opening the waveguide with a linear variation and an angle of ψ = 35° for operation at 60 GHz. To emulate the experimental setup, the GGW was connected to a standard WR-15 waveguide. As the WR-15 waveguide and the GGW have different widths, a step transition was designed to avoid impedance mismatch. To optimize the performance of the lens-antenna system, the focus of the lens (which in an ideal LL should be exactly at the circumference) must be carefully aligned with the phase center of the GGW horn antenna. The phase center is determined from the simulation results of the H-plane at 60 GHz. First, we determine the angular aperture where the directivity decreases around 12 dB from its maximum value and find that it is 42, see Fig. 2(c). This value ensures a correct illumination of the lens without excessive spillover. Next, the phase center is found by searching a phase curve between these angles as flat as possible, Fig 2(d). After this process, it is concluded that the phase center is inside the GGW horn at 3 mm from the aperture, as depicted in the inset of Fig. 2 The GGW horn antenna is therefore slightly inserted into the LL, as shown in Fig 1(c), to match the LL focal circumference with the horn's phase center. This is corroborated by a parametric analysis using an auxiliary parameter mx, which represents how much the antenna is inserted inside the lens (mx = 0 means that the antenna aperture coincides with the LL focal circumference and a positive mx means that the horn goes into the lens). Fig. 3(b) shows the reflection coefficient and directivity for several mx varying from 0 to 4 mm. When the GGW horn aperture is exactly at the rim of the lens (mx = 0 mm), the directivity drops at the upper frequency limit. The maximum directivity over the bandwidth is achieved when mx = 3 mm, in good agreement with the phase center position previously calculated.

Finally, Fig. 3(c) and (d) show the top view of the normalized vertical component of the simulated electric field at 60 GHz with and without the lens. It is clear that the lens shapes the cylindrical wavefront radiated by the GGW horn into a planar wavefront. After all the design steps, the system has a total volume of 88.5×62.6×19.05 mm 3 , see Fig. 1(e) and (f).

III. PROTOTYPE FABRICATION AND RESULT ANALYSIS

The previously discussed LL GGW antenna was manufactured and measured. A standard computer numerical control (CNC) milling machining with a tolerance of ± 20 m was selected to manufacture the two blocks in Fig. 1. As mentioned above, the material employed was aluminum due to its good conductivity and mechanical properties. Photographs of the manufactured prototype are shown in Fig. 1

(e) and (f).

The far-field measurements were performed using two different setups. Radiation pattern planes, peak directivity and aperture efficiency (eff) were obtained using the planar near field setup shown in Fig. 4(a). In this setup, the lens antenna (Antenna Under Test, AUT) was aligned with its H-plane parallel to the z-axis and the E-plane parallel to the y-axis, see Fig. 4(a). An open-ended waveguide probe with sharp edges (surrounded with TK-RAM absorbing material to reduce undesired reflections [START_REF]TK-RAM absorbing material to reduce scattered fields[END_REF]) was used to scan the electric field at a distance dm = 70 mm from the AUT, far enough to prevent reactive coupling between the AUT and the probe and close enough to avoid measuring a very large plane. The measurements were taken by moving the probe position along the yz-plane in a rectangle of 560×240 mm 2 with a step of 2 mm (less than λ0/2) and sweeping the frequency at each point. A precise alignment process was done to ensure that the AUT and the probe were parallel prior to recording the co-polar and cross-polar planar near fields. A PNA network analyzer E8361C (Agilent Technologies) was used to measure the antenna in the frequency range from 45 to 70 GHz, with the frequency span discretized in steps of 50 MHz. A single-port calibration was performed to measure the reflection coefficient of the lens antenna system. The far field radiation patterns and, from them, the directivity and aperture efficiency were finally obtained by applying a near to far field transformation and probe correction.

In addition, a far field setup was implemented to measure the gain by applying the gain comparison (or gain transfer) method [START_REF] Hurd | IEEE Standard Test Procedures for Antennas[END_REF], see Fig. 4(b). Two identical calibrated standard horn antennas (source and detector) of known gain and linear polarization were carefully aligned and placed at a distance of 2000 mm, farther than the minimum far field distance determined by the AUT dimensions, which is around 1930 mm at the maximum frequency of the band (70 GHz). To avoid undesired reflections on the ground between the antennas, the floor was covered with RAM. Nevertheless, the setup does not use an anechoic chamber and hence is prone to reflections with the objects in the laboratory, introducing some ripple and uncertainty in the measurements, at it will be shown below. The measurements were performed using an AB Millimetre Vector Network Analyzer MVNA-8-350 operating from 45 to 70 GHz with a frequency step of 0.5 GHz Fig. 5(a) shows the simulated (dashed) and experimental (solid) results corresponding to the magnitude of the input reflection coefficient (red) and the realized gain (blue) of the lens antenna. The antenna has a good impedance matching in all the considered band (from 45 to 70 GHz), with a reflection coefficient below -10 dB and an excellent agreement between simulation and experimental results. The experimental realized gain reaches a maximum value of 22.5 dB at 61 GHz and is above 20 dB in almost all the band, with a fair agreement with the simulation results. Furthermore, the realized gain bandwidth (defined as the frequency range where the gain is above 3 dB with respect to the maximum) is close to 15.7 GHz (from 50.7 GHz to 66.4 GHz). Hence, the fractional bandwidth is around 26.2%. Fig. 5(b) shows the measured directivity (blue curve) and aperture efficiency (eff, green curve). Notice that the realized gain and directivity have similar values thanks to the fully metallic design that has low ohmic loss. Indeed, the numerically simulated radiation efficiency reaches a high value of 96.8%. Nevertheless, experimental values of the gain must be taken with some caution since there are some regions where the it is above the experimental directivity, a result that is obviously unphysical. These happen due to the mentioned measurement uncertainties of the far field setup. Hence, it is not possible to retrieve the experimental radiation efficiency from these measurements. The aperture efficiency, extracted from the directivity, is between 0.2 and 0.3 from 50 to 65 GHz and decreases at higher frequencies, see Fig. 5(b). This parameter could be improved with a different flare implementation aimed at reducing the E-plane beamwidth by following a different shape such as an exponential curve for example [START_REF] Fonseca | Equivalent Planar Lens Ray-Tracing Model to Design Modulated Geodesic Lenses Using Non-Euclidean Transformation Optics[END_REF]. Nevertheless, given that antennas with a fan-beam pattern like the one considered here usually have moderate values of aperture efficiency (as a result of the wide beamwidth in one of the radiation planes) a linear flare was chosen in the design to simplify the manufacturing process.

The co-polar and cross-polar radiation patterns are shown in Fig. 5(c)-(f). Radiation patterns are only represented from -60°≤θ≤60°. This limitation comes from the size of the sampled plane along with the AUT size and the distance between the AUT and the probe, which do not allow to obtain larger angles with the applied near-field setup method. To illustrate the antenna performance, several representative frequencies were selected and plotted (from 50 to 65 GHz with steps of 5 GHz). The E-plane (co-polar in red and cross-polar in cyan) and Hplane (co-polar in blue and cross-polar in green) normalized radiation patterns are included in all cases. Again, an excellent agreement between simulation and experimental results is observed. Obviously, the antenna presents a narrower beamwidth in H-plane than in E-plane (at 60 GHz, HHPBW = 6.8° and EHPBW = 21°), since the former one is the plane where the LL collimates the beam. The side lobe level at 60 GHz is around 22 dB and in the worst case is 15 dB at 50 GHz. An excellent cross-polar discrimination, higher than 25 dB, is noticed in all cases.

There are nevertheless some experimental results that need further clarification. First, there is a dip in the measured directivity between 55 and 60 GHz that does not appear in the simulation results [Fig. 5(b)]. Furthermore, this dip is in apparent contradiction with the behavior observed in the radiation patterns, where the beamwidth in the measured Hplane is narrower than in the simulation [Fig. 5(d),(e)]. However, looking closely, it can be observed that the measured E-plane is wider and has higher side lobes, counterweighting the beamwidth reduction in the H-plane and leading to a decrease of the measured directivity in that frequency range. This phenomenon can be attributed to very small errors in the manufactured prototype.

In addition to this, there is an important directivity drop at 65 GHz that appears both in the simulation and experimental results. This is a consequence of the dispersion of the metallic pin array used to modulate the refractive index by varying the pin height as presented in Fig. 1(a). From that figure and also from Fig. 1(b), it is clear that the refractive index is dispersive and has an abrupt variation from 65 GHz onwards, especially for pin heights between 0.7 and 0.8 mm. To fully understand the underlying physics, the discretization applied to modulate the LL must also be considered. A contour plot of the ideal refractive index distribution applying (1) is presented in Fig. 6(a), where a small discretization step of 0.1 mm has been employed. However, the implemented lens has a coarser period (plens = 1.1 mm) leading to the discretized index profile shown in Fig. 6(b). Gray circles superimposed in that figure delimit the boundaries of regions of pins with the same height (up to 22 different pin heights were used in the lens). Looking closely, it is found that most of the lens area (up to 48.1%) contains pins with heights above 0.7 mm, which have strong dispersion above 65 GHz. Therefore, it can be concluded that the drop in directivity beyond this frequency is a consequence of the pin dispersion, which leads to refractive index values far from the Luneburg equation. This is corroborated in Figs. 6(c) and(d) that show the electric field distribution at 65 and 70 GHz. It is appreciated that the field inside the lens greatly differs from the electric field when the refractive index matches the Luneburg equation [Fig. 3(d)]. Hence, the output wavefront is no longer planar and this effect leads to the observed directivity drop.

There are excellent works in the literature that propose metamaterial unit cells with low dispersion [START_REF] Zetterstrom | Experimental Validation of a Metasurface Luneburg Lens Antenna Implemented With Glide-Symmetric Substrate-Integrated Holes[END_REF], [START_REF] Quevedo-Teruel | Glide-Symmetric Fully Metallic Luneburg Lens for 5G Communications at Ka-Band[END_REF], [START_REF] Arayeshnia | High-Efficiency Metallic Elliptical Lens Antenna Based on Glide-Symmetric Nails Bed[END_REF]. For instance, some implementations such as glide symmetric unit cell designs are less dispersive, giving rise to wide bandwidth and good directivity performances. However, this technology is difficult to implement as frequency increases due to the small gap between lower and upper pins needed to obtain wide bandwidth. All the antenna results, both numerical and experimental, are summarized in Table I.

IV. CONCLUSION

To conclude, we have demonstrated a fully metallic LL antenna system excited by a GGW horn operating at V-band. The LL has been synthesized using metallic pins to obtain the desired refractive index profile, which provides a planar wavefront in the direction of propagation. A GGW horn antenna has been also designed and combined with the LL to get a fully metallic design compatible with the requirements of wireless communication systems at MMW. Owing to the fully metallic design, this system is more robust and presents lower losses than solutions involving typical dielectric substrates. Moreover, the final design is flat, making it easy to adapt to planar surfaces. The simulated and experimental results are in good agreement, demonstrating that CNC micromachining is a viable manufacturing alternative even at high frequencies where tolerances are critical and designs based on small constituents such as metallic pins are challenging. A peak realized gain of 22.5 dB is achieved at 61 GHz, with a gain bandwidth of around 26.2%. A cross-polarization discrimination higher than 25 dB is observed in the measured bandwidth. The physical behavior of the antenna has been analyzed in detail to understand the performance worsening beyond 65 GHz. It has been concluded that it is a consequence of the bed of nails dispersion, which is especially critical for pin heights from 0.7 to 0.8 mm that form a 48.1% of the total area of the lens. This antenna based on GGW technology is able to generate excellent radiation characteristics and could be used in applications at MMW.

Fig. 1 .

 1 Fig. 1. (a) Dispersion diagram of a periodic metal pin structure for LL [shown in the inset of panel (c)] with the following dimensions: plens = 1.1 mm, alens= 0.5 mm and hlens varying from 0.3 to 0.8 mm. (b) Equivalent refractive index as function of pin height at f0 = 60 GHz. (Inset) Equivalent refractive index as a function of frequency for different pin heights (from 0.3 to 0.8 mm). (c) Schematic showing the LL and the GGW horn antenna; (top inset) zoom into the pins of the metalens in the central region; (bottom inset) sketch showing the metalens side view and pin schematic with main dimensions. (d) Perspective view of the bottom plate (top panel) and a zoom into the flared section (bottom panel). (e) Picture of the fabricated antenna showing a top view of the upper block (left) and bottom block (right) with the metalens horn antenna. (f) Photograph of the bottom piece in perspective view (top) and profile view (bottom) to show clearly both the lens and GGW antenna pins.

  Fig 2(b) shows that the input reflection coefficient is below 10 dB from 54 GHz up to the upper limit of V band (70 GHz). The inset in Fig. 2(b) shows a top cross section view of the antenna highlighting the designed step s = 4.2 mm.

  (b). As shown in Fig 2(d), a small variation lower than 10° is achieved between ±42°.

Fig. 2 .

 2 Fig. 2. (a) Dispersion diagram of a periodic metallic pin structure (shown in the inset) for GGW horn with dimensions: phorn = 1 mm, ahorn = 0.5 mm and hhorn = 1.5 mm. (b) Simulated input reflection coefficient of the GGW horn antenna in dB; (inset) top view showing the width of the step (s=4.2 mm) the horn flare angle (Ψ=35°) and an estimation of the phase center. (c) Normalized magnitude of the H-plane radiation pattern at 60 GHz (simulation result); the shaded region is the angular aperture where the directivity is above 12 dB from the maximum (d) Phase of the H-plane radiation pattern at 60 GHz (simulation result); (inset) detail showing the phase variation in the 50 range with the region where the phase variation is below 10° highlighted.

Fig. 3 .

 3 Fig. 3. (a) Schematic of LL, GGW horn antenna and flare (top view) highlighting the parameter mx that controls the relative position of the lens and the horn antenna. (b) Parametric simulation results of reflection coefficient and directivity varying mx from 0 to 4 mm. (c) Normalized |Ez| without metalens at 60 GHz in decibel scale. (d) Normalized |Ez| at 60 GHz with metalens in logarithmic scale.

Fig. 4 .

 4 Fig. 4. Experimental setups used to characterize the AUT. (a) Near field setup highlighting the distance between the AUT and the probe (dm = 70 mm); red circles mark the LL antenna (AUT) and the probe positions. (b) Far field setup (top view) highlighting the distance between the AUT and the source horn antenna of 2000 mm.

Fig. 5 .

 5 Fig. 5. Simulated (dashed lines) and measured (solid lines) results of several antenna parameters. (a) Reflection coefficient (red) and realized gain (blue) versus frequency in dB. (b) Directivity (blue curve) versus frequency response in dB and aperture efficiency (eff) from 45 to 70 GHz (green curve). Normalized far field radiation patterns at: (c) 50 GHz, (d) 55 GHz, (e) 60 GHz and (f) 65 GHz.

Fig. 6 .

 6 Fig. 6. (a) Planar LL and its radially symmetric refractive index n(r) with a discretization of 0.1 mm. (b) Mapping representation of the LL refractive index implemented with discretization of plens = 1.1 mm, where the gray dashed circles delimit the regions with pins of the same height (black dashed circles are some selected labels). (c) Top view of the normalized |Ez| metalens in decibel scale at 65 GHz. (d) Idem at 70 GHz.

TABLE I COMPARISON

 I BETWEEN SIMULATED AND MEASURED RESULTS Defined as the bandwidth where S11 < -10 dB. Total BW is in GHz. + Defined as the bandwidth where the directivity is reduced by 3 dB with respect to the maximum, divided by the frequency of maximum directivity. article has been accepted for publication in IEEE Transactions on Antennas and Propagation. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TAP.2023.3243277Ph.D. Prize from UPNA for the Best Doctoral Thesis(2006 - 2007), the Research Prize UPNA for the best scientific contribution (2017 -0218), three CST University Publication awards(2005, 2012, 2016), the XII Talgo Award of Technological Innovation in 2011, and several awards of international conferences. He is a reviewer for more than 50 international journals.

	This
	Parameter	Simulated	Measured
	S11 (dB) BW*	50-65 GHz	50-65 GHz
	Peak Gain	23.2 dB at 61 GHz	22.5 dB at 61 GHz
	Fractional Gain BW +	24.8%	26.2%
	SLL (at 60 GHz)	20 dB	22.4 dB
	HPBW (at 60 GHz)	E-plane = 21° H-plane = 7°	E-plane = 21° H-plane = 6.8°

*

This article has been accepted for publication in IEEE Transactions on Antennas and Propagation. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TAP.2023.3243277

ACKNOWLEDGEMENT

The authors are grateful to Laurent Cronier and Xavier Morvan (Université de Rennes 1 and IETR's M 2 ARS platform) for the fabrication of the prototype.


Tso-Wei Chen

Pei-Te Wang

Yung-Chang Kang

Po-Cheng Wu

Nien-Ti Tsou

Uwe Glatzel

Stéphane Gorsse

An-Chou Yeh

Grain boundary serration tuning and its effect on hot workability of a wrought superalloy

Keywords: superalloys, heat treatment, serrated grain boundary, isothermal compression

This study aims to elucidate the underlying mechanism of grain boundary serration and investigate its effects on hot workability of U720Li superalloy. Industrial scale as-cast ingots were subjected to heat treatments with varying cooling rates (15°C/s, 0.1°C/s, 0.02°C/s and 0.003°C/s) prior hot deformation. With 15°C/s cooling process, samples possessed straight boundaries and fine L1 2 structured γ' particles dispersion. When the cooling rate was decreased to 0.1°C/s and below, coarsened γ' particles could pin grain boundaries and lead to undulation in morphology. Continuous and discontinuous precipitation of γ' phase were both associated with the formation of grain boundary serration. And, two types of grain boundary serrations were identified, the first type (Type-I) was associated with an average interparticle spacing of 1.31 m, and the second type (Type-II) was related to an average interparticle spacing of 5.98 m. Discontinuous formation of long strip γ' behind the mobile grain boundary was observed for Type-II boundary, and it exhibited larger degree of undulation than that of Type-I boundary. With increasing fractions of Type-II boundary, the hot formability of U720Li was significantly improved during compression tests at 1000 °C. With grain boundary serration, the sample could be compressed up to 70% reduction ratio (1.2 strain) without crack formation. Analysis indicates that straight grain boundaries were prone to formation of cavitation and intergranular crack. On the other hand, serrated grain boundaries could distribute the strain evenly and inhibit crack propagation. This work presents a simple approach to improve the hot deformability of U720Li fabricated by industrial facility.

Introduction

Udimet-720Li is an advanced nickel-based superalloy with excellent creep, fatigue, oxidation and corrosion resistances [START_REF] Evans | The interac ons between fa gue, creep and environmental damage in Ti 6246 and Udimet 720Li[END_REF][START_REF] Marchionni | High temperature low cycle fa gue behaviour of UDIMET 720 Li superalloy[END_REF][START_REF] Sczerzenie | Development of Udimet 720 for High Strength Disk Applica ons[END_REF][START_REF] Chen | Oxida on behavior of several chromia-forming commercial nickel-base superalloys[END_REF], it is utilized mainly for the turbine disk application in aerospace engines [START_REF] Sczerzenie | Development of Udimet 720 for High Strength Disk Applica ons[END_REF]. The industrial production of U720Li disk is primarily based on powder metallurgy process, since the alloy contains high fraction of strengthening precipitates (L1 2 structured γ' phase) to resist high temperature deformation, thermos-mechanical production process can be very challenging [5][START_REF] Furrer | Ni-based superalloys for turbine discs[END_REF][START_REF] Couturier | Process Development and Mechanical Proper es of Alloy U720LI for High Temperature Turbine Disks[END_REF]. Nevertheless, plastic deformation of U720Li has remained a subject of interest to-date due to continuing industrial demands to lower down the processing cost. A relatively narrow hot working window between 1100°C and 1150°C has been proposed by previous studies [START_REF] Sczerzenie | Development of Udimet 720 for High Strength Disk Applica ons[END_REF][START_REF] Qu | Hot Deforma on Behavior of Nickel-Based Superalloy GH4720Li[END_REF][START_REF] Wan | Hot deforma on behavior and processing workability of a Nibased alloy[END_REF], at temperatures just below 1100°C, large amount of γ' precipitation could increase the flow stress and result strain localization, typically the reduction ratios couldn't reach over 50% without severe crack formation [START_REF] Zhao | Role of carbides on hot deforma on behavior and dynamic recrystalliza on of hard-deformed superalloy U720Li[END_REF][START_REF] Li | Microstructure Evolu on and Processing Map of Superalloy GH720Li during Isothermal Compression[END_REF]. On the other hand, intergranular fracture could occur at high temperatures above the γ' solvus temperature (about 1150 °C) and cause a limited reduction ratio of 30% [START_REF] Fan | An op miza on method of upse ng process for homogenized, nickel-based superalloy Udimet 720Li ingot considering both cracking and recrystalliza on[END_REF][START_REF] Monaja | Deforma on characteris cs of isothermally forged UDIMET 720 nickel-base superalloy[END_REF]. Fahrmann et al. [START_REF] Fahrmann | COOLING RATE ON GLEEBLE HOT DUCTILITY OF UDIMET ALLOY 720 BILLET[END_REF] reported that the cross sectional reduction ratio of U720Li could reach 60% by controlling the cooling rate from an annealing temperature of 1110°C to a testing temperature of 1010 °C with 3 °C/s in order to prevent the formation of secondary γ'. In another study, an increase in carbon content from 0.014 to 0.071 wt% could promote dynamic recrystallization, which could result softening mechanism and delay crack formation during hot deformation [START_REF] Zhao | Role of carbides on hot deforma on behavior and dynamic recrystalliza on of hard-deformed superalloy U720Li[END_REF]; a reduction ratio of 45% was achieved at 1060 °C.

Serrated grain boundary is known to inhibit grain boundary sliding and retard crack propagation [START_REF] Zhao | Heat treatment method for realizing grain boundary sawtooth of ironnickel-based alloy[END_REF][START_REF] Koul | On the mechanism of serrated grain boundary forma on in Ni-based superalloys[END_REF][START_REF] Koul | Serrated grain boundary forma on poten al of Ni-based superalloys and its implica ons[END_REF][START_REF] Mitchell | On the forma on of serrated grain boundaries and fan type structures in an advanced polycrystalline nickel-base superalloy[END_REF][START_REF] Qiu | On the forma on of irregular-shaped gamma prime and serrated grain boundaries in a nickel-based superalloy during con nuous cooling[END_REF][START_REF] Tanaka | Effects of serrated grain boundaries on the crack growth in austeni c heat-resis ng steels during high-temperature creep[END_REF][START_REF] Mcqueen | Forma on and applica on of grain boundary serra ons[END_REF][START_REF] Hong | The effect of grain boundary serra on on creep resistance in a wrought nickel-based superalloy[END_REF][START_REF] Yeh | Effect of serrated grain boundaries on the creep property of Inconel 718 superalloy[END_REF][START_REF] Kim | Effect of serrated grain boundary on stress corrosion cracking of Alloy 600[END_REF][START_REF] Danflou | EFFECT ON THE MECHANICAL PROPERTIES IN A P/M NICKEL BASE SUPERALLOY[END_REF][START_REF] Tang | Grain Boundary Serra on in Nickel-Based Superalloy Inconel 600: Genera on and Effects on Mechanical Behavior[END_REF][27]. It can also provide resistance against hydrogen-induced intergranular crack formation and propagation in nickel-based alloys [START_REF] Zhao | Heat treatment method for realizing grain boundary sawtooth of ironnickel-based alloy[END_REF]. Several studies have reported that serrated grain boundary can be induced by heat treatment with slow cooling process to promote interaction between grain boundaries and second phases, such as γ' [START_REF] Koul | On the mechanism of serrated grain boundary forma on in Ni-based superalloys[END_REF][START_REF] Koul | Serrated grain boundary forma on poten al of Ni-based superalloys and its implica ons[END_REF][START_REF] Mitchell | On the forma on of serrated grain boundaries and fan type structures in an advanced polycrystalline nickel-base superalloy[END_REF][START_REF] Qiu | On the forma on of irregular-shaped gamma prime and serrated grain boundaries in a nickel-based superalloy during con nuous cooling[END_REF][START_REF] Danflou | EFFECT ON THE MECHANICAL PROPERTIES IN A P/M NICKEL BASE SUPERALLOY[END_REF], δ [START_REF] Yeh | Effect of serrated grain boundaries on the creep property of Inconel 718 superalloy[END_REF], M 23 C 6 -carbide [START_REF] Hong | The effect of grain boundary serra on on creep resistance in a wrought nickel-based superalloy[END_REF]…etc. For Inconel718, precipitation and growth of δ phase could result zigzag grain boundary morphology, and it was found to increase creep resistance under 650 °C/625 MPa condition and prolong the creep life by 400 h [START_REF] Yeh | Effect of serrated grain boundaries on the creep property of Inconel 718 superalloy[END_REF]. Serrated grain boundary induced by the precipitation of MC-carbide in IN600 could improve creep life and creep strain under 815 °C/70 MPa [START_REF] Tang | Grain Boundary Serra on in Nickel-Based Superalloy Inconel 600: Genera on and Effects on Mechanical Behavior[END_REF].

For Astrology, crack propagation rate during fatigue test at 750 °C was notably decreased by a factor of about 3 to 5 due to grain boundary serration [START_REF] Danflou | EFFECT ON THE MECHANICAL PROPERTIES IN A P/M NICKEL BASE SUPERALLOY[END_REF]. The formation of serrated grain boundary in U720Li alloy has also been reported in previous study [27], it was found to increase the Charpy impact energy by 25 J and prolong creep life by 250 h under 704 °C/690 MPa. Koul et al. [START_REF] Koul | On the mechanism of serrated grain boundary forma on in Ni-based superalloys[END_REF] proposed that the net strain energy difference between the coherent matrix and incoherent side of γ' precipitate along grain boundary could cause grain boundary serration. Mitchell et al. [START_REF] Mitchell | On the forma on of serrated grain boundaries and fan type structures in an advanced polycrystalline nickel-base superalloy[END_REF] observed the preferential growth of γ' precipitates to induce protrusions along the grain boundaries in RR1000 alloy. Qiu et al. [START_REF] Qiu | On the forma on of irregular-shaped gamma prime and serrated grain boundaries in a nickel-based superalloy during con nuous cooling[END_REF] studied the microstructures of RR1000 alloy and proposed that grain boundary migration could be pinned by the coarsened γ' precipitates during slow cooling to result periodic wavy grain boundary structures. Based on existing literatures of grain boundary serration in Ni-based alloys, continuous precipitation and coarsening of the γ' phase were the main attributing factors to grain boundary serration, although discontinuous precipitation of γ' precipitates in stripe form was also reported, this feature has not yet analyzed and discussed in details [START_REF] Mitchell | On the forma on of serrated grain boundaries and fan type structures in an advanced polycrystalline nickel-base superalloy[END_REF]. This study aims to investigate the underlying mechanism for the formation of serrated grain boundary of U720Li alloy with respect to both continuous and discontinuous precipitations of γ', and most importantly this work is the first to investigate the effect of grain boundary serration on hot formability at 1000 o C, which is below the lower boundary of the proposed hot working temperatures in between 1100 o C~1150 o C; findings in this work can provide a guideline to design wrought processing route for high strength superalloys such as U720Li.

Materials and methods

In this work, U720Li was supplied by Gloria Material Technology Corporation, Taiwan (R.O.C.), an ingot was fabricated by the industrial scale vacuum induction melting (VIM furnace, Consarc corp.) followed by vacuum arc remelting process (V700, Consarc corp.); the size of ingot was 580 mm in diameter and 1200 mm in length. Chemical compositions were measured in different parts of the ingot by X-Ray fluorescence (XRF, Axios FAST PW4600, Malvern Panalytical Ltd), spark optical emission spectrometer (Spark-OES, ARL3460, Thermo Fisher Scientific Inc.) and carbon and sulfur determinator (CS844ES, LECO corp.). The chemical composition in weight percentage is shown in table. 1. In order to design heat treatment, samples of U720Li ingot were subjected to differential scanning calorimeter analysis (DSC, STA PT 1750C, Linseis Inc.). Measurements were conducted at a heating rate of 10 °C/s, the DSC curve is shown in Figure 1; the solidus temperature and γ' solvus are 1280 °C and 1155 °C, respectively. Cylindrical specimens, 8mm in diameter and 12mm in height, were machined by electro-discharge machining. In order to ensure the consistency of microstructure and chemical composition, all of the specimens were machined from a half radius of the ingot. Figure 2 shows the heat treatment profiles in the present study. Homogenization treatment was conducted to minimize elemental segregation, and the temperature was chosen at 1180 °C for 16 h to fully dissolve the γ' phase. Different cooling rates (15 °C/s, 0.1 °C/s, 0.02 °C/s and 0.003 °C/s in average) were conducted to an intermediate temperature at 950 °C followed by air cooling. The 15 °C/s cooling process was achieved by air cooling and the cooling rate was measured by recording the temperature change using K-type thermocouple. The other three cooling processes (0.1 °C/s, 0.02 °C/s and 0.003 °C/s) were achieved by setting the time course of temperature changes of the heating furnace. HT-1, HT-2, HT-3, and HT-4 are designated for samples subjected to 4 different heat treatment profiles, Figure 2.

Figure. 2. Heat treatment profiles in present work

Isothermal compression tests were conducted on specimens using Gleeble-3500 thermal-mechanical machine (Dynamic Systems Incorporation) at the Industrial Technology Research Institute, Taiwan. Prior to deformation, the samples were heated up to working temperature at a heating rate of 10 °C/s and then held for 5 min to ensure temperature uniformity. The specimens were then compressed at 1000 °C with a strain rate of 0.1 s -1 . Specimens were also subjected to compression to 15% reduction ratio (0.16 strain) in order to analyze the early stage of deformation. Molecular dynamic (MD) simulation was conducted to simulate different strain distributions along triple junctions of straight and serrated grain boundaries. The polycrystalline model of pure nickel was established by Atomsk [29]. The model includes 43256710 atoms in total with a size of 80 x 80 x 80 nm 3 . It is worth noting that the 3-dimensional surface profile of serrated grain boundaries was built by scanning the EBSD figures with Dream.3D [START_REF] Groeber | 3D: A Digital Representa on Environment for the Analysis of Microstructure in 3D[END_REF]. Then, periodic boundary conditions along the x, y, and z directions of the model were applied to reduce the amount of computation. The interatomic interactions in this model were described by 2NN MEAM potentials [START_REF] Lee | Second nearest-neighbor modified embedded-atom-method poten al[END_REF][START_REF] Etesami | Molecular dynamics for near mel ng temperatures simula ons of metals using modified embedded-atom method[END_REF]. The temperature of the models was equilibrated at 1000 o C for 120 ps with the timestep of 2fs to achieve a thermodynamic equilibrium. The model was then compressed along the y direction at a constant strain rate of 10 -3 s -1 . The isothermal-isobaric NPT ensemble was used in both the above-mentioned processes. The molecular dynamics simulations were calculated by LAMMPS [START_REF] Plimpton | Fast Parallel Algorithms for Short-Range Molecular Dynamics[END_REF] and the corresponding results were post-processed by OVITO [START_REF] Stukowski | Visualiza on and analysis of atomis c simula on data with OVITO-the Open Visualiza on Tool[END_REF]. The Voronoi analysis modifier [START_REF] Stukowski | Extrac ng disloca ons and non-disloca on crystal defects from atomis c simula on data[END_REF] and the common neighbor analysis (CNA) [START_REF] Tsuzuki | Structural characteriza on of deformed crystals by analysis of common atomic neighborhood[END_REF] were used here to reveal volumetric strain and crystal structures in the models, respectively.

Results

Heat treated microstructures prior hot deformation

The microstructure of the as-melted U720Li is shown in Fig. 4(a), it contained coarse grains with dendritic structure; the average grain size was 772 μm. After the homogenization heat treatment, the dendrites were all eliminated. In HT-1 sample, fast cooling after homogenization treatment produced straight grain boundaries (Fig. 4 particles could pin grain boundaries and lead to a small degree of undulation, this is termed as the Type-I boundary. On the other hand, further reduction in cooling rate could further coarsen the particles and widen the interspacing in-between the γ' particles to an extent that enabled segments of mobile grain boundary to bend through the supersaturated matrix in-between the particles, and resulted the formation of cellular structure, which is known as the discontinuous precipitation [START_REF] Manna | Discon nuous reac ons in solids[END_REF]; this type of grain boundary migration process resulted a larger degree of grain boundary undulation than that of Type-I, and this is termed as the Type-II boundary in this work. The effect of cooling rates on γ' particle size and interparticle spacing is shown in Fig. 7(a). 3.2 Hot deformation behaviors and microstructure analysis Fig. 8 shows the true stress-strain curves of four different specimens compressed at 1000 °C with a strain rate of 0.1 s -1 ; photographs of the deformed specimens are also shown. The stress-strain data presented are prior the formation of crack, which could lead to a sharp drop in flow stress. HT-1 sample possessed higher flow stress comparing with the others due to fine dispersion of small γ' particles; the yield strength of HT-1 sample was about 333.61MPa. With further decrease in cooling rate, coarsened γ' particles resulted a decrease in yield strength of HT-2, HT-3 and HT-4 samples to be about 283.41, 270.54 and 249.49 MPa, respectively.

Most importantly, the hot formability of U720Li was improved with decreasing cooling rate. Cracks occurred in HT-1 sample after a reduction ratio around 20% (0.22 strain), several cracks could be observed on sample surface (Fig. 8(b)). For HT-2 sample, the hot ductility was improved moderately with Type-I serrated grain boundary, and cracks were observed at 31% reduction ratio (0.37 strain) (Fig. 8(c)). HT-3 sample with 76.20% of Type-II boundary could endure more deformation up to 45% reduction ratio (0.6 strain). HT-4 sample with 100 % Type-II serrated grain boundary could be compressed to 70% reduction ratio (1.2 strain) without crack formation (Fig. 6(e)). The result suggests that hot formability was significantly improved by inducing Type-II grain boundary serration. Microstructures of deformed samples were examined, and intergranular cracks were identified in HT-1, HT-2 and HT-3 samples (Fig. 9). The microstructure of the HT-1 sample shows large intergranular cracks sample. In HT-3 sample, intergranular cracks could only be observed on the Type-I boundary and no cracks were seen along Type-II boundary (Fig. 9(d) and 9(e)). The HT-4 sample, which consisted of 100% Type-II boundary, could be deformed to 70% reduction ratio without crack formation (Fig. 9(f)). 10(a)). The recrystallized grain fraction was increased in HT-2 sample (see Fig. 10(b)), and this was due to a higher amount of strain. Recrystallized grains were found to develop from grain boundary surroundings toward the grain interior in HT-3 sample (see Fig. 10(c)). A fully recrystallized grain structure was identified in HT-4 sample compressed to 70% reduction ratio (see Fig. 10(d)), the recrystallized grain size was about 2μm in average. The formation of Type-II boundary is associated with the formation of cellular structure. Microstructural analysis shows that cellular structure could be deformed without crack formation under 1000 o C (Fig. 11 (a)). EBSD analysis showed dynamic recrystallization occurred in the γ matrix between the coarse γ', and regions around the cellular structure showed finer recrystallized grains with size about 800 nm in average (as shown in the red circle in Fig. 11 In order to examine internal strain under the same reduction ratio for different types of grain boundary, specimens of HT-1, HT-2, HT-3 and HT-4 were compressed to 15% reduction ratio at 1000 o C, and microstructures were analyzed by EBSD. Fig. 12 shows the IPF maps and the kernel average misorientation (KAM) maps. In HT-1 sample, high local misorientation was found to concentrate at grain boundary triple junction (Fig. 12(b)), this could lead grain boundary cavitation and crack propagation with further deformation. In HT-2 sample, local misorientation was found to distribute more uniformly along the Type-I serrated grain boundary instead of concentrating at the triple junction (Fig. 12(d)). Type-II boundaries could exhibit higher degree of undulation than that of Type-I boundaries and resulted a more uniform stress distribution throughout the microstructure (Fig. 12(f) and 12(h)), so samples with higher fractions of Type-II boundaries could withstand higher degree of deformation since sample could be uniformly deformed. 1000°C with a strain rate of 0.1 s -1 to 15% reduction ratio (0.16 strain).

Discussions

In this study, formation of serrated grain boundary and its effect on hot deformation behavior in U720Li alloy has been investigated. Grain boundary serration can be induced in U720Li during solution heat treatment with cooling rate of 0.2 °C/s and below, continuous and discontinuous precipitation of γ' phase could both affect grain boundary serration, causing the Type-I and Type-II serration, respectively. The schematic illustrations of two different mechanisms are shown in Fig. 13. Type-I boundary would occur due to grain boundary pinning by coarse γ' particles (Fig. 13(a)). Type-II boundary would form due to the discontinuous precipitation behind the moving grain boundary, in order to relax the metastable state of supersaturated matrix, boundary migration accompanied by cellular precipitation can lead to large boundary undulation (as shown in Fig. 13(b)). As a lower cooling rate reduces the nucleation rate of γ', coarse precipitates with low number density and high particle interspacing are produced. This provides more space for grain boundaries to migrate freely and allows grain boundaries to pass through more supersaturated matrix. Therefore, discontinuous reaction is enhanced with reducing cooling rate, resulting in a higher fraction of cellular structure and more distorted grain boundary structure; the average amplitude of serrated grain boundary increased dramatically from 1.37 μm (HT-2 sample) to 135.27 μm (HT-4 sample) due to a 93% increment of the fraction of Type-II boundary. According to the results of compression test (Figure 8), HT-1 sample exhibited highest yield strength at 1000 °C, and the strength decreased with reducing cooling rate. The precipitation strengthening of γ' particles is mainly contributed by dislocation shearing based on the weak-pair and strong-pair coupling mechanism [START_REF] Galindo-Nava | On the predic on of the yield stress of unimodal and mul modal γʹ Nickel-base superalloys[END_REF].

In the present study, different sizes of γ' particles are generated under four different heat treatments. And based on previous study [START_REF] Jackson | Heat treatment of UDIMET 720Li: the effect of microstructure on proper es[END_REF], dislocation shearing of these four sizes of γ' in Udimet720Li alloy are all dominated by strong-pair coupling mechanism. The following equation describes the critical resolved shear stress:

σ strong-pair coupling = 1 2 1.72 T f 1 2 w bd ( 1.28 d γ APB wT ) 1 2
where γ APB is the anti-phase boundary energy (~0.243 J/m 2 at 1000°C [START_REF] Galindo-Nava | On the predic on of the yield stress of unimodal and mul modal γʹ Nickel-base superalloys[END_REF]), b is Burgers vector(~0.257nm calculated from Thermo-Calc software [START_REF] Andersson | Thermo-Calc & DICTRA, computa onal tools for materials science[END_REF]), f is the volume fraction of the particle(~33% at 1000°C), d is the particle diameter, w is a constant describing the repulsion between the pair dislocations and is approximately equal to 1, T is the line tension of the dislocation equal to Gb 2 /2, and G is the elastic shear modulus(~55.1GPa at 1000°C calculated using simple pair-wise mixture model [START_REF] Guo | Modeling Material Proper es of Lead-Free Solder Alloys[END_REF]). The critical resolved shear stress of the HT-1 specimen was calculated to be 133.71 MPa, which is about 65.28, 73.37, and 90.89MPa higher than HT-2, HT-3, and HT-4 specimens, respectively. This is comparable with the difference in yield strength measured from the compression test results, suggesting that the flow stress difference in four specimens is mainly due to the difference in γ' strengthening effect.

This study shows that grain boundary morphologies strongly influence the hot formability of U720Li alloy; the serrated morphology could help to reduce the occurrence of stress concentration (see Fig. 12(d)).

Type-II grain boundary allows a more uniform deformation, as the EBSD results show that the lattice misorientation distributed more uniformly with reducing cooling rate (Fig. 12). Therefore, HT-4 sample with mostly Type-II boundaries showed a ductility improvement over 50% reduction ratio. To clarify the effect of grain boundary morphology on hot deformation behavior, MD simulations of isothermal compression tests have been conducted; the simulated strain distribution are shown in Fig. 14. During deformation, strains distributed more intensely on the straight boundaries and the triple junctions showed highly localized strain (as shown in the red circle in Fig. 14(a)). The average volumetric strain around the triple junction was about 26.02%. While this phenomenon was not observed in serrated grain boundary structure, in contrast, it showed a much uniform strain distribution along the grain boundary (Fig. 14(b)), and the average volumetric strain at triple junction was only about 12.04%. This result confirms that serrated grain boundaries can effectively reduce stress concentration on grain boundary junctions.

Conclusions

The underlying mechanism of grain boundary serration of an advanced superalloy made by industrial scale furnace has been elucidated in this work, as-cast ingots were subjected to heat treatments with varying cooling rates (15°C/s, 0.1°C/s, 0.02°C/s and 0.003°C/s) prior hot deformation. With 15°C/s cooling process, samples possessed straight boundaries and fine L1 2 structured γ' particles dispersion. When the cooling rate was decreased to 0.1°C/s and below, coarsened γ' particles could pin grain boundaries and lead to undulation in morphology. Continuous and discontinuous precipitation of γ' phase were both associated with the formation of grain boundary serration. And, two types of grain boundary serrations were identified, Type-I was associated with an average interparticle spacing of 1.31 m, and Type-II was related to an average interparticle spacing of 5.98 m. Discontinuous formation of long strip γ' behind the mobile grain boundary was observed for Type-II boundary, and it exhibited larger degree of undulation than that of Type-I boundary.

With increasing fractions of Type-II boundary, the hot formability of the superalloy was significantly improved during compression tests at 1000 °C. With grain boundary serration, the sample could be compressed up to 70% reduction ratio (1.2 strain) without crack formation. Analysis indicates that straight grain boundaries were prone to formation of cavitation and intergranular crack, and serrated grain boundaries could distribute the strain evenly and inhibit crack propagation.

Figure. 1 .

 1 Figure. 1. DSC heating curve of the U720Li ingot.

Figure. 3 .

 3 Figure. 3. Isothermal compression tests.

  (b)), and the average grain size was 1150 μm. With the cooling rate reduced to 0.1 o C/s, the grain boundary turned from straight to serrated morphology in HT-2 sample (Fig. 4(c)), and the average grain size was 1280 μm. Further decrease in cooling rate to 0.02 o C/s resulted more pronounced serrated grain boundaries (Fig. 4(d)), the average grain size of HT-3 sample was 1290 μm. More undulation of grain boundary was observed with cooling rate about 0.003 o C/s (Fig, 4(e)); cellular structures were identified around the serrated grain boundaries, the average grain size of HT-4 sample was 1580 μm.

Figure. 4 .

 4 Figure. 4. OM image showing macroscopic grain structures of (a) as-cast, (b) HT-1 sample, (c)HT-2 sample, (d) HT-3 sample and (e) HT-4 sample.

Fig. 5 .

 5 Fig.5. reveals that both size and distribution of γ' precipitates were affected by the cooling rates after heat treatment. The 15 °C/s cooling process in HT-1 sample resulted fine dispersion of γ' particles (Fig.5(a)), the average γ' diameter was 113 nm and the average interparticle spacing was 0.27 m. Slower cooling rates yielded larger particles with lower number density and larger interparticle spacing (Fig.5(b, c, d)). The average γ' diameter of HT-2, HT-3 and HT-4 samples was 444, 662 and 1208 nm, and the average interparticle spacing was 1.31, 2.19 and 5.98 μm, respectively. Furthermore, cellular precipitates were observed in HT-3 and HT-4 samples (Fig.5(e, f)), this phenomenon was associated with discontinuous

Figure. 5 .

 5 Figure. 5. SEM image showing γ' precipitates of (a) HT-1, (b) HT-2, (c) HT-3, (d) HT-4 specimens and cellular precipitates in (e) HT-3, (f) HT-4 specimens.

Fig. 6 .

 6 Fig. 6. shows that continuous precipitation and discontinuous precipitation of γ' phase were both associated with grain boundary serration during slow cooling process. Continuous precipitation of coarsened γ'

Figure. 6 .

 6 Figure. 6. SEM image showing (a) straight boundary in HT-1 sample, CP-type boundary in (b)HT-2 sample, (c) HT-3, DP-type boundary in (d) HT-3 sample, (e), (f) HT-4 sample. The correlation between fractions of two different types of serrated grain boundaries versus the undulation of grain boundaries is quantified in Fig. 7(b). HT-2 sample consisted of 93.94% of Type-I boundary, the amplitude of its serrated structures was about 1.37 μm. Further decrease in cooling rate could promote higher fractions of Type-II boundaries, thus the undulation of grain boundary serration would be more pronounced. HT-3 sample contained 76.20% of Type-II boundary, the fraction of Type-II boundary was further increased to 99.13% in HT-4 sample. Aa a result, the amplitude of the grain boundary increased from 29.16 μm to 135.27 μm.

Figure. 7 .

 7 Figure. 7. (a) Average diameter and number density of γ' phase in four different specimens, (b) The correlation between fractions of two different types of serrated grain boundaries versus the amplitude in four different specimens.

Figure. 8 .

 8 Figure. 8. (a) Stress-strain curve of four specimens tested at 1000 °C with a strain rate of 0.1s -1 and the macroscopic view of deformed samples (b) HT-1, (c) HT-2, (d) HT-3, (e) HT-4.

Figure. 9 .

 9 Figure. 9. SEM images showing compressed microstructures of (a) HT-1, (b, c) HT-2, (d, e) HT-3, (f) HT-4.

Figure. 10 .

 10 Figure. 10. IPF maps of (a) HT-1 compressed to 20% reduction ratio (0.22 strain), (b) HT-2 compressed to 31% reduction ratio (0.37 strain), (c) HT-3 compressed to 45% reduction ratio (0.6 strain), (d) HT-4 sample compressed to 70% reduction ratio (1.2 strain) at 1000 °C and 0.1 s -1 .

  (b) & (c)).

Figure. 11

 11 Figure. 11. (a) SEM image, (b) EBSD forward scatter diodes(FSD) image and its corresponding (c) IPF image showing the compressed microstructure in HT-4 sample deformed at 1000°C and 0.1s -1 to 70% reduction ratio (1.2 strain).

Figure. 12 .

 12 Figure. 12. IPF and KAM maps of (a), (b) HT-1, (c), (d) HT-2, (e), (f) HT-3, (g), (h), HT-4 sample tested at

Figure. 13 .

 13 Figure. 13. Schematic illustration of the formation of (a) Type-I and (b) Type-II serrated grain boundary.

Figure. 14 .

 14 Figure. 14. MD simulation of strain distribution along (a) straight grain boundary and (b) serrated grain boundary compressed at 1000 o C to about 6% strain.

Table . 1

 . . Chemical composition of as-received U720Li (in wt. %).

	Al	Co	Cr	Mo	Ni	Ti	W	Others (ppm)
								B: 135 ± 2
	2.55 ± 0.05 14.72 ± 0.02 16.42 ± 0.06 2.97 ± 0.02 57.20 ± 0.27 4.88 ± 0.01 1.24 ± 0.02	C: 65 ± 2
								Zr: 289 ± 7

Acknowledgments

Authors would like to acknowledge funding support from Gloria Material Technology Corporation and S-Tech Corporation. This work was also financially supported by the "High Entropy Materials Center" from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) and from the Project NSTC 111-2634-F-007-008,111-2224-E-007-003,110-2221-E-007-020-MY3 by National Science and Technology Council (NSTC) in Taiwan.