Takashi Suemasu

Laurent Vila

Jean-Philippe Attané

Present status of rare-earth free ferrimagnet Mn 4 N and future prospects of Mn 4 N-based compensated ferrimagnets

The rare-earth-free ferrimagnet Mn 4 N has attractive features for spintronics applications, because it possesses a perpendicular magnetization, due to a relatively large magnetic anisotropy constant of ~10 5 J m -3 and a small spontaneous magnetization of ~100 kA m -1 , and a large spin polarization (P = 0.8). More crucially, it is possible to reach the magnetic compensation at room temperature, by tuning its constituent element in compounds such as Mn 4-x Ni x N and Mn 4-x Co x N. This is particularly interesting for spin-torque-based spintronics applications, because at the vicinity of the magnetization and/or angular momentum compensation points, the switching currents can be reduced significantly, thereby leading to lower switching energies and higher switching speed. In this review article, we emphasize the importance of epitaxial growth of Mn 4 N films by comparing the results obtained on two different substrates, MgO(001) and SrTiO 3 (001). We then present the achievement of ultrafast current-induced domain wall motion (CIDWM) in Mn 4 N microstrips, and study the magnetic compensations in Mn 4-x Ni x N and Mn 4-x Co x N at room temperature, proved by x-ray magnetic circular dichroism measurements. Finally, we offer future prospects for such Mn 4 N-based compensated ferrimagnets.

Introduction

The ability of spin-transfer torques (STTs) and spin-orbit torques (SOTs) to induce magnetization precession and switching is the basis of a whole range of existing or emerging spintronics technologies. 1) In this context, ferrimagnets (FIM) have attracted an increasing attention. [2][3][4][5][6][7][8][9][10][11][12][13][14][15] Their key feature is that their spontaneous magnetizations are much smaller than those of ferromagnets, because the magnetic moments of different sublattices are aligned antiparallel to each other. This parameter is an important asset to develop applications based on STTs and SOTs, in which a flux of angular momentum carried by an incoming spin polarized current acts on the magnetization, inducing magnetization precession and/or switching. In the case of STTs, the spin polarized current is generated within a magnetic layer by the exchange interaction. In the case of SOTs, a pure spin current (i.e., a flow of angular momentum without net charge current) can be generated by spin Hall effect, frequently within a heavy metal layer in contact with the magnetic layer. It can also be produced by the Rashba Edelstein effect, at interfaces breaking the inversion symmetry, or in topological insulators. In all cases, the torque is due to the conservation of angular momentum. When the ferrimagnet is at the vicinity of the magnetic compensation (MC) (and/or angular momentum compensation), the incoming flow of angular momentum affects easily the reduced magnetization, and thus the critical current density necessary for magnetization switching decreases. 5,7,16) . Ferrimagnets are thus appealing materials to develop STTs and SOTs-based devices such as domain wall memories, skyrmion-motion-based devices, three terminal magnetic random-access memories, SOT oscillators, 17) and others. 18,19) The most common route used in spintronics to achieve MC is based on alloys combining rare-earth elements and transition metals such as Gd 0.44 Co 0.56 and Tb 0.21 Co 0.79 . 3,5,6,12,13) When the magnetization of the two species aligns antiparallel, there exists a single concentration at which the compensation occurs at room temperature (RT). Here, we have paid special attention to rare-earth free ferrimagnets as they alleviate the need of critical elements for spintronics. In Mn 4 N, MC can be reached at RT just by tuning its constituent element in Mn 4-x Ni x N and Mn 4-x Co x N films. [20][21][22][23] Anti-perovskite Mn 4 N is ferrimagnetic, and has a Curie temperature of 740 K in bulk Mn 4 N, 24) , while Fe 4 N, Co 4 N, Fe 4-x Co x N, and Fe 4-x Ni x N samples possessing the same structure are ferromagnetic [25][26][27][28][29][30] at RT. On the other hand, Ni 4 N is paramagnetic at RT. 30,31) , except for Ni 4 N. 30) As shown in Fig. 1, there are two inequivalent Mn sites: those at the corner sites, Mn(I), and the others at the face-centered sites, Mn(II). N atoms are positioned at the body-centered sites. Neutron diffraction in bulk Mn 4 N revealed that the magnetic moment of Mn(I) is 3.5 μ B , while that of Mn(II) is .8 μ B at 300 K, 32) where μ B is the Bohr magneton. Thus, the magnetic moments of the Mn(I) atoms determine the direction of magnetization. The electron state of Mn 4 N has been studied extensively. [33][34][35] According to an electron diffraction study using 50-nm-thick polycrystalline Mn 4 N films, the N atom in Mn 4 N was found to behave as an electron acceptor, and the electron state of Mn 4 N was expressed as Mn 0 (Mn +0.2 ) 3 N -0.6 . 34) This is different from the donor model applicable to ferromagnetic Fe 4 N, wherein one electron is donated from the N atom to each of the three face-centered Fe atoms. 36) The interest of this material for spintronics arises from several features.

i)

The combination of a relatively large perpendicular magnetic anisotropy (PMA) with a small Ms leads to perpendicular magnetization, i.e., to the appearance of an out-of-plane easy axis of magnetization. This perpendicular magnetization allows downscaling spintronic devices, and storing data permanently using a bistable magnetization state in STT and SOT-based applications. In this context, Mn 4 N thin films are interesting candidates as they have been reported to have a relatively small spontaneous magnetization M S ~100 kA/m. 32,42,45) , with an anisotropy field value μ 0 H K > 2.5 T. [START_REF] Yasutomi | [END_REF]54) Perpendicular magnetic anisotropy (PMA) has been reported in Mn 4 N films deposited on various substrates, including glass, Si(001), MgO(001), SrTiO 3 [STO](001), (LaAlO 3 ) 0.3 (Sr 2 TaAlO 6 ) 0.7 [LSAT](001), and LaAlO 3 (001), [37][38][START_REF] Tsunoda | International Conference of the Asian Union of Magnetics Societies (ICAUMS) 2012[END_REF][START_REF] Yasutomi | [END_REF][41][42][43][44] and the in-plane tensile strain has been proposed to be the origin of PMA. [START_REF] Yasutomi | [END_REF]44) An interesting point is that Mn 4 N films are under tensile stress even when grown on LSAT(001), which has a smaller lattice constant than Mn 4 N, corresponding to a lattice mismatch of 0.8% 43) which might be considered to induce compressive stress in Mn 4 N layers. The uniaxial magnetic anisotropy constant (K u ) of Mn 4 N thin films has been reported to be of the order of 10 5 J/m 3 . 42,[45][46][47] . A theoretical study has been recently conducted on the contribution of N to the in-plane tensile strain and to the resultant PMA in Mn 4 N. 48) Materials such as Mn 4 N, where the PMA is large enough to overcome the demagnetizing field energy, are perpendicularly magnetized.

ii)

The effective spin polarization extracted from DW velocity measurements in Mn 4 N 16) is relatively high (P=0.8). This allows enhancing the magnetotransport effects used in spintronics such as the Anomalous Hall Effect, the Giant magnetoresistance, and suggests for instance that Mn 4 N could be used as a magnetic soft layer in a Magnetic Tunnel Junction stack.

iii)

The magnetization reversal occurs through nucleation and the motion of Bloch domain walls (DWs). The combination of a relatively large spin polarization with a small Ms leads to high domain wall velocities due to the STT. 16) The current-induced velocity due to the adiabatic torque is indeed given by (1) where v is the DW velocity,  the damping constant, g the Landé factor, e the electron charge, the Bohr magneton, P the current spin polarization and J the current density. Note that the interest of the small magnetization is not restricted to the case of pure STT on domain walls: for both STT through magnetic tunnel junction and for SOTs, the torque efficiency is supposed to vary as the inverse of the free layer magnetization.

iv)

The combination of a high PMA with a reasonable exchange constant leads to relatively sharp Bloch walls. Sharp DWs could lead to an enhanced spin transfer effect through the non-adiabatic contribution 49) and contribute to faster DW motion at smaller currents. 47) The width of the DW (Δ) in the nanowire is given by Eq. (2): 50) (2

)
where A is the exchange stiffness. As K u increases, Δ decreases, leading to the reduction in the threshold current density (j th ) necessary to move the DWs. 47.51) In this respect, materials with PMA are advantageous for current-induced domain wall motion (CIDWM) devices. Furthermore, the DW width needs to be small enough to scale DW-based logic devices, [START_REF] Parveen | IEEE Computer Society Annual Symposium on VLSI (ISVLSI)[END_REF] and three terminal or racetrack memories [START_REF] Fukami | [END_REF] down to the ultimate technology nodes.

v) Mn 4 N does not require chemical elements deemed as critical from geopolitical and environmental points of view, such as heavy metals and rare-earth.

In this review article, we begin by underlining the importance of a high-quality thin-film growth on the magnetic properties, by comparing the epitaxial growth of Mn 4 N films on STO(001) and MgO(001) substrates.

2. Formation and characterizations of Mn 4 N films on STO(001) and MgO(001)

10-nm-thick Mn 4 N layers were grown on MgO(001) and STO(001) substrates at 450 °C, using a molecular beam epitaxy system with an ion-pump (10 -7 Pa), equipped with a high temperature Knudsen cell for Mn and a radio-frequency (RF) N 2 plasma. [START_REF] Yasutomi | [END_REF]54) To prevent oxidation, the samples were capped with 3-nm-thick SiO 2 layers. In the case of STO(001)

substrates, we used a buffered NH 4 F-HF solution with controlled pH values to obtain TiO 2 atomic plane-terminated surfaces, with steps one unit cell in height. 55) The crystalline quality of the Mn 4 N layers was characterized by 20-kV reflection high-energy electron diffraction (RHEED), and X-ray diffraction (XRD) with a Cu Kα radiation source. Magneto-transport properties, such as the magnon-magnetoresistance (MMR) 56,57) and the anomalous Hall effect (AHE), were measured by the Van der Pauw method for Mn 4 N blanket layers at RT. 58) The transverse voltage (V y ) can be expressed as Eq. ( 1): 59) xy AHE H ,

Z y x x B V R I I t t t         (1)
where R H , B Z , t, ρ ΑΗΕ , I x , and ρ xy are the normal Hall coefficient, the magnetic flux density perpendicular to the sample surface, the film thickness, the anomalous Hall resistivity, the longitudinal current, and the Hall resistivity, respectively.

Figures 2(a) and 2(b) show out-of-plane XRD profiles of Mn 4 N epitaxial films on MgO(001) and STO(001) substrates, respectively. 58) Figures 2(c) and 2(d) are their in-plane XRD profiles when the scattering vector was set to be along [100]. In both samples, oriented diffraction peaks such as 002 and 004 together with RHEED streaks are the proof of the epitaxial growth of Mn 4 N films. Superlattice diffractions from N atoms positioned at the body-centered site, marked by arrows, are also present. However, there is a big difference in crystalline quality between them. ω-scan rocking curves are shown in the same figure for (e) Mn 4 N 002 and (f) Mn 4 N 004. We used the higher-order Mn 4 N 004 for Mn 4 N films on STO because the peak position of Mn 4 N 002 is close to STO 002 in Fig. 2(b). According to the fitting by a Lorentzian function, the full-width at half maximum was 2.5 and 0.14 deg. for Mn 4 N films on MgO and STO, respectively. The lattice constant of MgO is 0.421 nm, and that of STO is 0.391 nm. Thereby, the lattice mismatch for Mn 4 N/MgO(001) and Mn 4 N/STO(001) is approximately 7.6% and 0.4%, respectively, assuming that the Mn 4 N films has a cubic structure and a lattice constant of 0.389 nm. 32) Such a small lattice mismatch between Mn 4 N and STO leads to the perfect epitaxial growth of Mn 4 N/STO 16) as shown in Fig. 2(g), whereas misfit dislocations are observed for Mn 4 N/MgO 41) in Fig. 2(h). figures, the magnetoresistance is dominated by the magnon magnetoresistance, typically observed in samples with a strong uniaxial anisotropy. 60) Figures 3(c) and 3(d) show the hysteresis loops measured by AHE. The AHE angle ρ xy /ρ xx is high (-2%), in line with previous reports on Mn 4 N. 61,62) The coercivity of the Mn 4 N/STO sample (0.26 T) is slightly smaller than that of the Mn 4 N/MgO sample (0.44 T). These relatively high coercive fields are due to the small saturation magnetization. The Mn 4 N/MgO sample shows a smooth hysteresis loop. In contrast, the magnetization of the Mn 4 N/STO sample switches very sharply, with a full remanence at zero field. Despite these differences, it is striking that the spontaneous magnetization and all the transport quantities of the two systems are very similar. This result indicates that the Mn 4 N films in the two samples are intrinsically alike, regardless of the different substrates and thus of different lattice mismatches. The increased disorder in the Mn 4 N films on MgO widens the nucleation and DW pinning field distribution associated to the defects, thus leading to a higher coercivity and a slanted hysteresis loop. Figures 3(e) and 3(f) present the hysteresis loops for in-plane and out-of-plane fields, obtained by VSM-SQUID up to 4 and 6 T, respectively. From the out-of-plane hysteresis curves, the M S of Mn 4 N/MgO and Mn 4 N/STO samples was found to be 118 and 105 kA m -1 , respectively. From the in-plane loop of Mn 4 N/STO, the anisotropy field μ 0 H K was estimated to be 4 T. The uniaxial anisotropy K u was calculated to be 1.1 × 10 5 J m -3 , using the integration of the area enclosed between the in-plane and out-of-plane magnetization curves, and taking into account the demagnetization energy. Now we can discuss the magnetic domain configuration in Mn 4 N thin films. The theoretical equilibrium domain size in Mn 4 N layers is determined by the balance between the dipolar energy and the DW energy. From the measured values of M S = 105 kA m -1 , K u = 110 kJ m -3 , and A = 15pJ m -1 (using a rough estimation from the Curie temperature), 63) the DW width can be calculated to be . The resulting equilibrium domain size for a 10-nm-thick Mn 4 N film, calculated using the analytical model of Ref. 64, is of several km. This indicates that the demagnetizing field is negligible because of the small M S , and that in practice the domain size and shape are rather determined by DW pinning on extrinsic defects. 65) Hereafter, we focus on Mn 4 N epitaxial films on STO(001).

Let us examine the domain pattern in Mn 4 N layers on STO substrates. The magnetic The large v DW obtained in Mn 4 N show that the STTs can be competitive with SOTs even though SOTs-driven DW dynamics have been the focus of nearly the entire community in recent years. SOTs have been found to be an efficient mechanism to drive DWs in non-centrosymmetric multilayers, in which a FM is deposited on a heavy metal like Pt. 68,69) The prototypical example is AlO x /Co(0.6nm)/Pt, 70) where the chiral Néel structure acquired by the DWs in the presence of interfacial Dzyaloshinskii-Moriya interaction 71) leads to a high mobility (v DW = 400 m s -1 for j = 3×10 12 A m -2 ). Higher SOT-driven v DW 's were obtained recently in a multilayer structure in which two Co/Ni layers were coupled anti-ferromagnetically through a Ru layer, 72) or in GdCo ferrimagnet layers deposited on top of Pt. 73) In these systems the v DW was clearly observed to vary with the total magnetization. In the former experiment, a maximum velocity of v DW = 750 m s -1 for j = 3 × 10 12 A m -2 was obtained at RT using a Ru spacer layer. Thus, the stack magnetization was reduced to 8% of the M S of a single Co/Ni layer.

In the latter one, a peak velocity of 1300 m s -1 was reported at the compensation temperature, for j = 2 × 10 12 A m -2 and still high even at 300 K with 850 m s -1 . Recently, SOT driven DW motion in insulating ferrimagnetic garnets have also led to similar DW speeds. 74) In this context, the v DW presented here at RT for DWs in Mn 4 N is comparable to the best results obtained using SOTs. Moreover, this constitute the first demonstration of very efficient current-driven DW motion by pure STT using a system with PMA. Another figure of merit of the STT efficiency is the DW mobility = Δ DW /Δ , that can be derived from the v DW versus j curve, and is equal to = 7.1×10 -10 m 3 C -1 . This mobility is also the highest value in all STT-driven systems, and is superior to most SOT-driven records. Above 1.3 × 10 12 A m -2 , many domains nucleate, probably because the sample reaches 745Κ, the Curie temperature of Mn 4 N, and becomes temporarily paramagnetic.

Formation and characterizations of 3d-doped compensated Mn 4 N films

On the basis of the DW experiments presented above, much faster v DW can therefore be expected in the vicinity of the angular momentum compensation point, which is supposed to be close to the MC point in 3d-element-doped Mn 4 N. In the past, Mekata et al. attempted to replace some of the Mn atoms in Mn 4 N by In and Sn, and obtained the MC with appropriate composition ratios and temperature. 75) Here we present our recent results obtained on of KEK in Japan, to find a Ni ratio in Mn 4-x Ni x N and a Co ratio in Mn 4-x Co x N where the MC occurs at RT. These techniques are quite powerful to determine element-specific electronic structures. Among samples, Mn 4-x Co x N (x = 0.8) was measured at the twin helical undulator beamline BL23SU of SPring-8 in Japan, wherein the measurements were performed using the total electron yield (TEY) mode both at the Mn L 2,3 and Co L 2,3 absorption edges. 76) All measurements were performed at RT. We also measured the AHE loops at RT for a magnetic field applied perpendicularly to the plane, using the Van der Pauw method.

Mn substitution by Ni

Approximately 30-nm-thick Mn 4-x Ni x N (x = 0, 0.1, 0.25, and 0.5) thin films were grown on STO(001) substrates at 450 °C by MBE. The deposition rates of Mn and Ni were measured, and independently controlled by changing the crucible temperature of each Knudsen cell. An approximately 3-nm-thick SiO 2 capping layer was used for AHE measurements, while Ti capping layers were used for XAS and XMCD measurements. Figure 6 shows the out-of-plane XRD and RHEED patterns of the Mn 4-x Ni x N (x = 0, 0.1, 0.25, and 0.5) thin films along the STO[100] azimuth. Diffraction peaks of the grown layers appear at small 2θ angles in Fig. 6 and overlap with the intense diffraction peaks of the STO substrate because of the excellent lattice match between the Mn 4-x Ni x N films and the STO(001) substrate. Very sharp, streaky lines together with superlattice lines marked by arrows appeared in the RHEED patterns, and Kikuchi lines also verified the highly c-axis-oriented epitaxial growth of the Mn 4-x Ni x N films. Notably, the diffraction peaks of Mn 4-x Ni x N appear at slightly higher angles than those of cubic STO(001) in Fig. 6, showing the ratio of perpendicular lattice constant c to in-plane lattice constant a, c/a, is smaller than 1. This result indicates the presence of in-plane tensile strain in the Mn 4-x Ni x N films at x≤ 0.5.

Figure 7 shows the AHE loops for Mn 4-x Ni x N (x = 0, 0.1, 0.25, and 0.5) thin films at RT. It is noted that the sign of ρ xy was reversed for Mn 4-x Ni x N films between x = 0.1 and 0.25 in Fig. 7, indicating the crossing of the magnetic compensation point. Such a sign reversal is commonly used to confirm the presence of a MC point in rare-earth ferrimagnets. 4,5) The ratio of the remnant magnetization (M r ) to M S , M r /M S , was almost 1 for x = 0, 0.1, and 0.25. In contrast, Mn 3.5 Ni 0.5 N films showed a much smoother magnetization reversal, and saturating their magnetization required a large magnetic field. The reasons for this behavior could be the degradation of the crystalline quality at x = 0.5 and the decrease of the magnetization, which can both contribute to an increase of the coercivity. We therefore chose the samples x = 0.1 and 0.25, and performed XAS and XMCD measurements. This prevents Ni L 2,3 spectra from overlapping with background signals. Regarding the XAS spectra of Mn 3.9 Ni 0.1 N and Mn 3.75 Ni 0.25 N films, only the sharp main peaks are observed at the L 3 edge (852853 eV) and the L 2 edge (870 eV). Similar peaks were reported for NiFe 3 N. 77) In contrast, we see shoulders in the XAS spectrum of Ni-rich Ni 3 FeN films, 77) wherein Ni atoms unavoidably occupy face-centered II sites. These shoulders are observed approximately 2 eV above the Ni L 2,3 main peaks. Such shoulders are reported for other antiperovskite ferromagnetic nitrides such as Fe 4 N and Co 4 N films above the Fe (Co) L 2,3 main peaks. 78,79) They are interpreted to originate from the electric dipole transition from the metal 2p core level to the hybrid state between the orbitals of the N 2p and metal 3d at II sites, indicating that the objective element is at the face-centered sites in Fig. 1. 78) From these results, we can safely state that Ni atoms preferentially occupy the I sites in Mn 4 N when x ≤ 0.25. Regarding the peak sign of the XMCD spectra, they are opposite at the L 2,3 edges between Mn 3.9 Ni 0.1 N and Mn 3.75 Ni 0.25 N. Thus, the directions of the magnetic moments of Ni(I) in Mn 3.9 Ni 0.1 N films are different from that in Mn 3.75 Ni 0.25 N films with respect to magnetizations.

We next discuss the XAS (blue) and XMCD (black) spectra of Mn 3.9 Ni 0.1 N and Mn 3.75 Ni 0.25 N films at the Mn L 2,3 absorption edges in Figs. 8(c) and 8(d). Here we focus on the XMCD spectra. In Fig. 8(c), in Mn 3.9 Ni 0.1 N the signs of the XMCD signals around the Mn L 3 edge are positive, negative, and positive from low to high photon energy. The superposition of spectra with different signs indicates that the magnetic moments of Mn(I) and Mn(II) are aligned antiparallel to each other. In our previous studies on Fe 4 N films, the transition metals at the I(II) site exhibited localized (itinerant) states, which is supported by first-principles calculation using the all-electron full-potential linearized augmented-plane-wave (FLAPW) method and Fermi's golden rule with E1 transitions. 78) Similar results are also observed for Mn 4 N using FLAPW calculation. 76) Therefore, the XMCD spectra of Mn 3.9 Ni 0.1 N and Mn 3.75 Ni 0.25 N films can also be viewed as an overlap of such localized and itinerant components characterized by features α and β, respectively, with opposite signs. In Mn 3.9 Ni 0.1 N, the broad positive peak (β) near 642 eV likely originates from Mn(II) atoms, caused by the hybridization between Mn(II) 3d and N 2p orbitals. In contrast, the sharp negative peak (α) near 640 eV likely comes from Mn(I), which is remote from the body-centered N atom, and therefore entails less hybridization. On the other hand, the signs of the XMCD signals near the Mn L 3 absorption edges in Fig. 8(d) are negative, positive, and negative from low to high photon energy in Mn 3.75 Ni 0.25 N, which is the opposite to the results obtained for the Mn 3.9 Ni 0.1 N films. We attribute this to magnetization reversal at both the I and II sites of Mn atoms. Such behavior of the spectra was reported in ferrimagnets at the vicinity of the compensation temperature. 80,81) It is also notable that the XMCD signal at the Ni L 3 absorption edge has the opposite sign of the sharp peak (α) for the Mn L 3 edge at 640 eV regardless of x, and has the same sign as that of the broad spectrum (β) at 642 eV. Thus, the magnetic moments of Ni(I) align in parallel with those of Mn(II) in the studied range of Ni content x. From these discussions, we conclude that the Ni atoms preferentially occupy the I site in Mn 4-x Ni x N thin films, and that the magnetic moments of Ni atoms are parallel to those of Mn(II). The simplified schematics of the magnetic structures in Mn 4-x Ni x N below the MC composition ratio in Fig. 8(e) and above it in Fig. 8(f). Therefore, we can safely state that the MC occurs at a certain value x between 0.1 and 0.25 at RT.

Mn substitution by Co

30-nm-thick Mn 4-x Co x N (x = 0 1.3) thin films were grown on STO(001) substrates at approximately 450 °C by MBE. The deposition rates of Mn and Co were independently measured and controlled by changing the crucible temperature of each Knudsen cell. An approximately 3-nm-thick SiO 2 capping layer was used for AHE measurements, while Ta capping layers were employed for XAS and XMCD measurements. Both a magnetic field of ±5

T and circularly polarized X-rays with left or right polarization were applied at an angle of 54.7° to the plane. 82) The X-ray polarization was switched at every energy point with a frequency of 10 Hz using five kicker magnets. The energy of the incident soft X-rays was adjusted to include the L 2 and L 3 absorption edges of Mn and Co. The XAS spectra were obtained in TEY mode and TFY mode at the Mn L 2,3 and Co L 2,3 absorption edges, respectively.

Figure 9 shows the out-of-plane XRD profiles and RHEED patterns of the Mn 4-x Co x N thin films along the STO[100] azimuth. c-axis-oriented XRD peaks such as 001, 002, and 004 of Mn 4-x Co x N appeared at slightly higher angles compared to those of STO. For samples with x = 01.1, the diffraction peaks of Mn 4-x Co x N 002 and 004 with RHEED streaks confirm the epitaxial growth of Mn 4-x Co x N films. Superlattice diffractions from N atoms at the body-centered site are also present for samples with x = 00.8, as indicated by the white arrows.

With increasing x, however, the XRD peak intensity decreased, the RHEED streaks were blurred at x = 1.2, and the diffraction peak of 004 was not observed at x = 1.1 and 1.2, meaning that the crystalline quality degraded. The in-plane lattice constant a decreased from 0.389 nm (x = 0) to 0.384 nm (x = 1.3). The out-of-plane lattice constant c also decreased from 0.386 nm to 0.381 nm, keeping the in-plane tetragonal distortion (c/a ~ 0.99). Figures 10(a)10(h) shows the ρ AHE vs. μ 0 H curves at RT. The magnitude of ρ AHE decreases with x, and its sign reverses between x = 1.1 and 1.2. In the case of Mn 4-x Ni x N films, the sign reverses between x = 0.1 and 0.25 in Fig. 7, which is consistent with the MC composition for this material. We therefore chose the two samples (x = 0.8 and 1.

3) together with one more sample (x = 0.2), and performed XAS and XMCD measurements. (d,e), respectively, we conclude that all magnetic moments of Mn(I), Mn(II), and Co(I) reverse between these two compositions, and that the MC occurs in the range of 0.2 < x < 0.8. At present, we do not have sufficient data to discuss the reason why the sign reversal in ρ AHE was absent between x = 0.2 and 0.8 in Fig. 10, and further studies are mandatory on this issue. The XMCD spectrum of Co atoms at x = 1.3 in Fig. 11(c) is more complex than those of the other two compositions. This spectrum can be viewed as an overlap of two sets of components (A-A' and B-B'), which have opposite signs. It is notable that the sign of the peak A(A') at x = 1.3 is opposite to that at x = 0.8, meaning that the magnetic moments of Co(I) atoms reversed between these two compositions. Considering that the Co composition x is 1.3, higher than 1, some of the Co atoms are likely to be positioned at II sites, Co(II). The peak position of B (B') was slightly shifted from that of A(A'), similar to peaks α and β in Figs. 11(d) and 11(e). Thus, we interpret peaks B and B' in Fig. 11(c) to originate from Co(II) atoms with their magnetic moments aligned antiparallel to those of Co(I). We can therefore state that all the magnetic moments of Mn and Co atoms reverse between x = 0.8 and x = 1.3, suggesting that MC occurs in the range of 0.8 < x < 1.3. This is consistent with the sign reversal of ρ AHE between x = 1.1 and 1.3 in Fig. 10. Figure 11(g) shows simplified schematic illustrations of the magnetic structures in Mn 4-x Co x N, based on the above discussions. We used x = 0.2, 0.8, and 1.3 samples in this work; however, the Co compositions are 0.25, 0.75, and 1.25 to simplify the representation in Fig.

11(g).

Please note that we do not mean to exclude the possibility that all I sites are occupied with Co atoms when x = 1.3. Our findings show that the MC presumably occurs both between x = 0.2 and 0.8, and between x = 0.8 and 1.3. Observation of a MC at two low temperatures have already been reported 83) and have been studied theoretically. 84) However, to our knowledge there has been no report thus far of the existence of two MC compositions at RT just by doping.

Future prospects of Mn 4 N-based ferrimagnets

At the vicinity of MC in Mn 4-x Ni x N and Mn 4-x Co x N, much faster v DW than those obtained in Mn 4 N can be expected, at RT, asthe efficiency of STT in these systems is primarily due to the low magnetization. The combination of SOTs to STTs in these layers, for instance by adding a neighbouring spin Hall effect layer, might be beneficial for inducing DW motion and magnetization switching. To develop spintronics applications, it would also be worthwhile to check if the relatively high spin polarization of Mn 4 N-based ferrimagnets could be used to obtain significant Tunnel Magnetoresistance ratios. Also, the double MC at RT found in is relatively high, probably caused by a large damping constant α. It was measured to be around 0.10.2 at RT from the linewidth of microwave absorption spectra and the oscillation frequency of time-resolved MOKE signals. [START_REF] Isogami | JSAP Spring Meeting 10a-M101-7[END_REF] This value is much greater than those reported on Fe 4 N(α ~ 0.03), [START_REF] Isogami | [END_REF] and higher by two orders of magnitude than those of MnGa alloys. 87) We are not sure why α is so large for Mn 4 N at the moment. Thus extensive studies are mandatory to solve this issue. As j th is proportional to α, we have to consider how to reduce α in Mn 4 N-based materials.

In any case, the results presented in this article prove the versatility of doped Mn 4 N thin films, and open up a rare-earth free platform for ferrimagnetic spintronics.

An unexplored aspect is the use of heavy metal to induced Dzyaloshinskii Moriya interaction (DMI) and to take benefit of SOT altogether with the STT. Thin layers of the Mn 4 N family can be covered by a heavy metal in order to induce DMI and generate a transfer of angular momentum to enhance the current induced domain wall motion. It would be interesting to find a material combination where the direction of motion of STT and SOT adds up. If DMI could be large, it would be possible to obtain small skyrmions in thin Mn 4 N layers.

Finally, the large tuning of the coercivity observed under a gate application through the STO substrate [ref. 16] is another route to tailor the magnetic state of Mn 4 N. This is a very appealing way to achieve a very energy efficient control of its magnetic properties, yet the origin; strain, charge transfer or ionic migration; has to be elucidated.

Conclusion

In this article, we review the potential of rare-earth free Mn 4 N for spintronics, from the fundamental properties of Mn 4 N such as the excellent epitaxial growth on STO(001) substrates, the AHE loops, and the domain structures observed by MOKE, to the latest results on CIDWM in Mn 4 N microstrips, in which v DW reaches 900 m s -1 . Mn 4 N shows perpendicular magnetic anisotropy, and has a high magnetic anisotropy constant of ~10 5 J m -3 , a small spontaneous magnetization of ~100 kA m -1 and a large spin polarization as inferred from the large DW velocity. One of the striking features of this material is that magnetic compensation occurs at RT just by tuning its constituent element by doping. The sign reversal of the XMCD signals was observed in Mn 4-x Ni x N and Mn 4-x Co x N epitaxial films between below and above the MC compositions. The two different MC compensations appearing in Mn 4-x Co x N should also exist Mn 4 N-based ferrimagnets. To further develop applications based on STTs and/or SOTs, several material properties have to be studied more detailedly, such as the spin current polarization and the damping parameter. Also, using and enhancing spin-orbit effects such as the SOTs or the Dzyaloshinskii Moriya interaction will require depositing ultrathin films of Mn 4 N-based ferrimagnets, with a very high quality. These material developments could help confirming the potential of Mn 4 N beyond DW manipulation by pure STT, from SOTs 88,89) to skyrmions 7,90) or THz switching. . 91,92) We therefore hope that many researchers will be interested in using this material.

experiments and fruitful discussions.

Fig. 1 Crystal structure of anti-perovskite-type Mn 4 N. The magnetic moment of the corner-site Mn atoms, Mn(I), is antiparallel to that of the face-centered Mn atoms, Mn(II), and parallel to the overall magnetization (black arrow).

Figures 3 (

 3 Figures 3(a) and 3(b) show the dependence of the longitudinal resistance R xx with the magnetic field normal to the sample surface. The resistivity ρ xx is 187 μΩ cm for the Mn 4 N/MgO sample, and 181 μΩ cm for the Mn 4 N/STO sample at RT. As shown in these

3 .

 3 domain configuration was observed by magneto-optical Kerr effect (MOKE) microscopy. The observation was performed both for the as-deposited state in Fig.4(a) and for a partially reversed state in Fig.4(b), corresponding to the red dot state in the magnetization curve shown in Fig.4(c). In Fig.4(a), the magnetic domain size d p is as large as 20 μm, with smooth magnetic DWs. This value is comparable with the equilibrium value of ultrathin CoFeB (1.1 nm)/MgO(1) and Pt(2.4)/Co(0.27) system, with d p values of respectively 14 and 6.5 μm obtained after thermal demagnetization.66,67) Figure4(b) presents the domain configurations in partially reversed states. The domain size in Mn 4 N/STO reaches a value as large as one millimeter. MOKE images show the presence of very few nucleation centers, showing that the magnetization switching occurs by nucleation, followed by an easy propagation of DWs. This observation is consistent with the fact that the hysteresis loop is square. Note that the use of MgO substrate leads to much smaller sub-micrometric domains, which is consistent with the observation of a larger disorder using structural and magnetic characterizations[ref. 58]. On the basis of these results, we can state that the selection of a well-matching substrate is crucial to improve the magnetic properties of Mn 4 N layers, and notably its suitability for current-induced DW propagation. Evaluation of DW speed and spin transfer efficiency 10-nm-thick Mn 4 N epitaxial films were processed by ion milling into sets of twenty 1 or 2 µm wide microstrips, connected to two electric pads. The current flows through the microstrips in order to induce DW motion. After saturation of the magnetization, magnetic field pulses were applied to nucleate a domain in a pad and to inject DWs into the microstrips. The DWs were then pushed by current pulses. The DW displacement during the current pulses was measured using a differential MOKE imaging technique, consisting in subtracting the MOKE image before pulse injection from the image obtained after the pulse injection, to highlight the difference between them and showing the corresponding magnetization reversal by DW displacement. Figure5(a) shows the differential MOKE image after domain nucleation using a field pulse of 0.6 T for 300 μs, and Fig.5(b) shows the differential MOKE image taken after injection of several 1 ns current pulses. The area through which the DW propagated appears in black. The DW motion direction is opposite to the current, and thus follows the electrons flow.

Figure 5 (

 5 Figure5(c) presents the current density dependence of the DW velocity v DW . The threshold current density for 1-ns-width pulse is 3.0 × 10 11 A m -2 . Above 8 × 10 11 Am -2 in 1-μm-wide strips, the trend of the v DW versus j curve becomes linear. In the studied range of current densities, the DW reached an average velocity of 900 m s -1 , for a current density of 1.3 × 10 12 A m -2 in both 1-μm and 2-μm-wide strips. This value is the highest in all materials and structures whose DW was driven by only pure STTs. The velocities observed in Mn 4 N can thus be considered as a milestone in the history of STTs.

Mn 4 -

 4 x Ni x N and Mn 4-x Co x N epitaxial films grown on STO(001). Preparation details are given in Refs. 21 and 23. We performed x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) measurements at the twin APPLE-II undulator beam line BL16A

Figures 8 (

 8 Figures 8(a) and 8(b) show the XAS (blue) and XMCD (black) spectra of Mn 3.9 Ni 0.1 N and Mn 3.75 Ni 0.25 N films at the Ni L 2,3 absorption edges, respectively. Both a magnetic field of ±3 T and circularly polarized x-rays with left or right polarization were applied perpendicularly to the plane. The x-ray polarization was switched at every energy point with a frequency of 10Hz using five kicker magnets. Spectra at the Mn L 2,3 absorption edges were acquired in the TEY mode, while those at the L 2,3 absorption edges in the total fluorescence yield (TFY) mode.

Figures 11 (

 11 Figures 11(a)11(c) show the XAS and XMCD spectra of Mn 4-x Co x N films (x = 0.2, 0.8, and 1.3) at the Co L 2,3 absorption edges, and Figs. 11(d)11(f) show those at the Mn L 2,3 absorption edges, respectively. Here, we focus on the XMCD spectra. The peaks A and A' in Figs. 11(a) and 11(b) have opposite signs. According to our previous work, 75) Co atoms were found to preferentially occupy I sites, Co(I), when x = 0.8 in Mn 4-x Co x N, and the magnetic

Mn 4 -

 4 x Co x N is very attractive from application perspectives, because the observed double MC mechanism might constitute a route to preserve the MC within a relatively wide range of Co concentrations, providing that one can find compensation concentrations close enough to each other. This is important because several magnetic quantities such as v DW change sharply at the vicinity of the MC, and slight concentration variations may induce undesirable results. From the fundamental viewpoint, it would be interesting to compare the magnetic and spintronic properties such as SOT, STT, AHE, and polarization at the vicinity of the two MC concentrations. It is notable that double MC may occur also in Mn 4-x Ni x N at RT, when Ni atoms start to occupy the face-centered sites with their magnetic moments aligned with Mn(I) atoms when x > 0.5. In this context, double MCs are likely to occur in other Mn 4 N-based ferrimagnets. As shown in Fig.5(c), the DW mobility is quite high in Mn 4 N, compared to those achieved in SOTs. However, the threshold current density, j th , for DWs to start moving in Mn 4 N

Fig. 2

 2 Fig. 2 XRD profiles of Mn 4 N films on (a, c, e) MgO(001) and (b, d, f) STO(001) substrates. (a, b) Out-of-plane XRD patterns. The insets show the stack structures. Copyright 2018 Japan Society of Applied Physics. (c, d) In-plane XRD patterns. The incident angle is ω = 0.4°, and the scattering vector is along the [100] of Mn 4 N films. The insets show the RHEED images of the Mn 4 N layers along the [100] direction of each substrate. Arrows indicate the superlattice diffractions from N atoms at the body-centered site. (e, f) ω-scan rocking curves for Mn 4 N films on MgO(001) and STO(001), respectively. (g, h) TEM cross sections of Mn 4 N films on MgO(001) 41) (Copyright 2014 AIP Publishing) and STO(001). 16) Copyright 2019 American Chemical Society.

Fig. 3 (Fig. 4 (

 34 Fig. 3 (a, b) Longitudinal resistance against magnetic field normal to the plane. (c, d) Anomalous Hall effect hysteresis loops. (e)(f) Out-of-plane hysteresis loops measured by VSM.(a, c, e) correspond to the Mn 4 N films on MgO(001), and (b, d, f) to the Mn 4 N films on STO(001).58) Copyright 2018 Japan Society of Applied Physics.

Fig. 5 (Fig. 6

 56 Fig. 5 (a) Differential MOKE image after domain nucleation using a field pulse of 0.6 T. (b) Differential MOKE image after several 1 ns current pulses. The area through which the DW propagated appears in black. The DW motion direction is opposite to the current, and thus follows the electrons flow. 16) (c) Current density dependence of v DW measured at RT. Both the 1and 2-μm-wide strips possess similar behaviors.16) The DW mobility is calculated to be 7.1 × 10 -10 m 3 C -1 . Copyright 2019 American Chemical Society.

5 Fig. 7

 57 Fig. 7 Dependence of the Hall resistivity ρ AHE on a perpendicular magnetic field for Mn 4-x Ni x N (x = 0, 0.1, 0.25, 0.5) films on STO(001) at RT.

  Photon energy [eV]Photon energy [eV] 630 640 650 660 670

Fig. 8

 8 Fig. 8 XAS (blue) and XMCD (black) spectra in (a, c) Mn 3.9 Ni 0.1 N films and (b, d) Mn 3.75 Ni 0.25 N films at (a, b) Ni-L 2,3 edges and (c, d) Mn-L 2,3 edges. 21) The sharp peak (α) and broad peak (β) in (c, d) originate mainly from Mn(I) and Mn(II), respectively. The reversal of the XMCD signals between (a) and (b) and between (c) and (d) means that the direction of magnetic moments of Mn and Ni is reversed between them. Copyright 2020 AIP Publishing.

Fig. 9 Fig. 10

 910 Fig. 9 Out-of-plane XRD profiles of Mn 4-x Co x N (x = 0, 0.4, 0.8, 1.0, 1.1, 1.2) films on STO(001). 23) The insets show the RHEED patterns taken along the [100] azimuth. The arrows indicate the superlattice diffractions from N atoms at the body-centered site. Copyright 2020 American Physical Society.

Fig. 11 XAS

 11 Fig. 11 XAS (blue) and XMCD (black) spectra in (a, d) Mn 3.8 Co 0.2 N films, (b, e) Mn 3.2 Co 0.8 N films, and (c, f) Mn 2.7 Co 1.3 N films at (a, b, c) Co-L 2,3 edges and (d, e, f) Mn-L 2,3 edges. 23) The sharp peak (α) and broad peak (β) in (d, e, f) originate mainly from Mn(I) and Mn(II), respectively. The reversal of the XMCD signals between (a) and (b) and between (d) and (e) means that the direction of magnetic moments of Mn and Co is reversed between them. In (c), the sign of the XMCD signal of Co(I) (A-A') reverses again and another signal with the opposite sign (B-B') of Co(II), appears, meaning that the magnetic moment of Co(II) is antiparallel to that of Co(I). Copyright 2020 American Physical Society.

Acknowledgment

This work was supported in part by the Japan Society for the Promotion of Science KAKENHI (Grants No. 19K21954, No. 19KK0104, and No. 19K21954). We acknowledge funding from the IDEX of University Grenoble Alpes, through the International Strategic Partnership Project DOMINO, and from the ANR project CONTRABASS. The XMCD experiment was performed at beamline BL-16A of KEK-PF with the approval of the Photon Factory Program Advisory Committee (Proposal No. 2018P011 and No. 2019G574) with the help of Professor K. Amemiya. Special thanks are given to Associate Professor K. Toko, Dr S. Pizzini, Dr J. Vogel, Dr. H. Okuno, Dr. T. Gushi, Dr. K. Ito (Tohoku University at present), Mr. S. Ghosh, Mr. T. Komori, Mr. T. Hirose, Ms. H. Mitarai, and past students of the University of Tsukuba for their


Sylvie Pierre

Philippe Cassette

Benoit Sabot

C Fréchou

A Antohe

C Barna

P Blahušiak

F Cardellini

R Dersch

A Honig

F Juget

M Krivošík

A Luca

F J Maringer

F Mertes

S Röttger

M Sahagia

J Slučiak

M Stietka

L Szűcs

C Teodorescu

comparison of activity measurements of radon 222

Introduction 222

Rn is a radioactive noble gas decaying through alpha transition to short half-life progenies and is one of the main sources of natural radioactivity. It can be monitored with commercial instruments to evaluate radon activity concentrations in individual rooms, water or soil. National standards of 222 Rn are available from National Metrology Institutes (NMIs) and comparisons of these standards are necessary to ensure the traceability of this radionuclide and to support the CMC's of the NMIs and Designated Institutes (DIs). This comparison of activity per unit volume of 222 Rn was organised within the framework of the MetroRADON project under the auspices of EURAMET. Samples were made available to the participants by the LNE-LNHB.

The reference measurement method is Defined Solid Angle alpha counting (DSA) with a frozen disc source of 222 Rn which is a primary measurement method. This method was used by two laboratories. Other methods such as comparison by a scintillation cell with 222 Rn extracted from standard 226 Ra solution or comparison by a scintillation cell with 222 Rn in glass ampoules previously measured with an NaI detector, were used by other participants. Another laboratory used a LSC method (Cassette, 2006), [START_REF] Sahagia | The Rn-222 standard system established at IFIN-HH, Romania[END_REF], [START_REF] Sahagia | Establishment of the Rn-222 traceability chain with the Romanian Standard System[END_REF].

Relevant information about the comparison

The list of the participants is given in Table 1. IRA (Switzerland) received a sample too. Unfortunately, when IRA started the measurement, a problem happened with the vacuum pump, so the measurement could not be completed. Metal cells containing 222 Rn at low pressure (below 10 -3 hPa) were prepared by the LNE-LNHB and dispatched to the participants. A container (105 cm 3 ) and its dimensions can be seen in Figure 1 and Figure 2. Each volume is measured by comparison with a certified volume, as described in Section 4.2 of [START_REF] Sabot | Experimental facility for the production of reference atmosphere of radioactive gases (Rn, Xe, Kr, and H isotopes)[END_REF]. 2 gives information about the volume of the containers.

The relative standard uncertainty on each volume measurement is less than 0.4%, and the relative standard deviation of the volume of all containers is 0.4%. This uncertainty of 0.4% was quadratically added to the uncertainty of the activity given by the participants to calculate the uncertainty on the activity concentration. LNE-LNHB divides the activity given by each laboratory by the appropriate volume to calculate the activity per unit volume. The homogeneity of the filling of the containers was verified by gamma-ray spectrometry using an HPGe detector, to measure the activity of the radon daughters. The relative standard deviation of the results from these measurements of the daughter products was 0.3%, so the containers are considered homogeneous.

The half-life value T1/2 = 3.8232 (8) d (Bé, 2008) was used and the results were evaluated on the reference date 15 April 2019 at 12:00 UTC. Table 3 provides the list of the methods used, together with the laboratories who applied these methods. Acronyms of the methods are also given according to the CCRI(II) rules (BIPM-2).

BFKH

4P-IC-AP-00-00-00

The measurements were carried out with two AlphaGUARD radon measuring instruments. One of them was calibrated by the PTB, the other has a manufactural calibration.

ENEA-INMRI

4P-SC-AP-00-00-HE calibrated by 4P-NA-GR-00-00-HE Glass ampoule measured by Scintillation Cell previously calibrated for 222 Rn by a 4-integral counting method.

IFIN-HH

Arithmetic mean of the values obtained by: 4P-LS-MX-00-00-TD Absolute measurement by liquid scintillation counting of an ampoule containing an amount of 222 Rn transferred in a quantitative mode from the gas container (Cassette, 2006) [START_REF] Sahagia | The Rn-222 standard system established at IFIN-HH, Romania[END_REF]).

UA-GH-GR-00-00-00 4P-IC-MX-00-00-00, both calibrated by 4P-LS-MX-00-00-TD Relative measurements of a gas vial, using the calibration figures for the HPGe and Ionisation chamber [START_REF] Sahagia | Establishment of the Rn-222 traceability chain with the Romanian Standard System[END_REF].

LNE-LNHB

SA-PS-AP-00-00-00 Alpha Counting in Defined Solid Angle.

PTB

SA-PS-AP-00-00-00 Alpha Counting in Defined Solid Angle.

SMU

4P-IC-AP-00-00-00

Continual monitoring of a volume activity of 222 Rn in a radon chamber with a volume of ̴ 1 m 3 with AlphaGUARD DF2000 in diffusion 60 min mode.

The Italian 222 Rn Reference Measurement System at ENEA INMRI

The INMRI radon reference measurement system (RRMS) for radon in air is shown in Figure 3. All the elements of this system are connected in a closed circuit in which the air can circulate by means of a micro-pump placed in the aluminium flask. In the circuit are also a flow-meter, a manometer, a vial-holder and a hygrometer. The exact configuration of the radon source assembly (labelled as "radon source" in the figure) depends on the measurement that is carried out: in some experiments, the source to be measured is in the left bubbler, while the right bubbler is only a trap; in other measurements, the radon source is in the right bubbler and the left bubbler contains only water. The bubbler may be easily removed and replaced by any other suitable vessel containing radon.

The system is calibrated using bubblers (BBL) containing a 226 Ra reference solution of known activity, referred to a NIST standard (National Institute of Standards and Technology, USA) (De Felice, 1996). The 222 Rn activity inside the sources is in equilibrium with the activity of the 226 Ra solution. The BBL containing the 226 Ra solution is put on the right (see Figure 3), while the BBL on the left humidifies the air to ensure that the 226 Ra source does not dry out.

The circulation of the air through the BBL extracts the 222 Rn from the 226 Ra source and forces it into the circuit, giving rise to a 222 Rn reference atmosphere, i.e., a volume where the 222 Rn concentration value is known. When the circuit is calibrated with the standard sources, it can be used to measure the activity of other 222 Rn sources of unknown activity. This can be achieved simply by comparing the count rate given by the reference bubbler with the one produced by the 222 Rn from the unknown source.

Alternatively the system may be calibrated by the use of glass vials containing a known activity of 222 Rn. The system is equipped with a proper vial-holder used to break the vials and introduce the radon into the system without leakage (shown in Figure 4). The small vertical cylinder on the top of the vial holder is used to break the vial and transfer the radon into the circuit.

The activity of the 222 Rn gas inside the glass vials was measured by the 4π-γ integral counting method using the ENEA-INMRI well-type NaI(Tl) 5" x 5" scintillator detector. The total counting efficiency, with which the count rate was normalized, was computed by the GEANT4 Monte Carlo code (Caponi, 2012). The two methods (reference bubblers and radon in glass vials) are in agreement within 0.5%. A set of experiments was carried out to evaluate the reproducibility of the RRMS and to calibrate a fixed Ionization Chamber (IC) for 222 Rn measurement. 222 Rn gas was collected and sealed in a glass vial and the vial was measured with the IC.

After some days the 222 Rn activity of the vial was measured in the 222 Rn reference circuit with the procedure described in the previous paragraph. The obtained activity value was corrected for decay at the date of measurement in the ionization chamber and related to the ionization current. A series of 8 measurements were carried out obtaining reproducibility within 0.5%.

The procedure and minor features of the 222 Rn measurement circuit were refined and a new set of 5 experiments was carried out. For these experiments the average calibration factor of the ionization chamber is K = 15543 (26) nA/kBq.

The French 222 Rn Reference Measurement System at LNE-LNHB

This method is based on a Defined Solid Angle (DSA) measurement of solid alpha-emitting sources widely used for primary standardization of activity. In the case of 222 Rn, which is a noble gas, the use of a cold finger surface allows the deposition of 222 Rn to produce a pure 222 Rn disk source under vacuum (below 10 -5 hPa). The cold finger is a 6 mm diameter nickel rod, laser-welded to a 6 cm diameter stainless steel disk of 100 µm thickness. The nickel rod, which allows good thermal conduction, is cooled down at 80 K, while the stainless steel disk of lower conductivity and its periphery are heated to 293.15 (7) K (Figure 5). The stainless steel disk is also used as a membrane to separate the volume containing the cold head and the measurement chamber. These two volumes have the same pressure (vacuum of 1•10 -5 hPa) to prevent mechanical deformation. At this pressure 222 Rn will be deposited on the cold surface as long as the temperature is lower than 100 K.

As the emission of alpha particles is isotropic, we assume that only the alpha particles passing through the collimator are counted (Fig. 4). Every alpha particle reaching the detector is counted by the silicon detector, and a spectrum is obtained in which radon and its daughters are well separated. The detection efficiency of the measuring system is simply equal to the geometry factor G defined by:

G= Ω eff 4 π ,
where Ωeff is the solid angle shown in Figure 6. In this device, G = 2.019•10 -3 with a relative standard uncertainty of 0.28%.

Figure 6 -Scheme of the DSA measurement system at LNE-LNHB:a, radius of the collimator; b, radius of the source; z, distance between source and diaphragm; e, eccentricity, if the source and collimator axes are different.

The geometry factor has been characterized by precise distance and diameter measurements by the French national metrology institute LNE. As a result, these quantities are directly traceable to national standards. The activity A of the measured source is then given by:

𝐴 = 𝐶𝑅 𝐺 (1)
With CR meaning "counting rate".

The solid angle Ωeff can be calculated using different kinds of software such as Anglesol from LNE-LNHB. As a result, with this kind of system, it is possible to obtain a small uncertainty as long as the counting statistical uncertainty is negligible and the dimensions of the apparatus are precisely known.

After the activity measurement, if needed, the 222 Rn is transferred by cryo-diffusion into a storage vial (Figure 7), which can be metal or glass. To perform this transfer, this storage vial is cooled with liquid nitrogen and the cold finger is heated to room temperature. A second measurement after the transfer, once the storage vial is closed, is performed in order to determine the background (e.g. 210 Po contamination, which varies over time). Initially, a quantity of radon is selected by opening a radium source and waiting for the approximate activity required. The activity is measured and transferred. The aim is to ensure that all the radon on the cold finger is transferred, so enough time is allowed so that there is no residual radon in the chamber. Any radon left in the tubes is measured and the value deducted from the first measurement. If required, it is possible to transfer only part of the radon on the cold finger by closing the valve before all the radon is transferred. The remaining radon can then be condensed on the cold finger and deducted from the radon inside the container by calculating the difference between the two measurements.

The complete details of the measurement device are given in reference [START_REF] Sabot | An absolute radon 222 activity measurement system at LNE-LNHB[END_REF], which is an upgraded version of an earlier system developed by LNE-LNHB in 1995 [START_REF] Picolo | Absolute measurement of radon 222 activity[END_REF].

The 222 Rn Measurement System at IFIN-HH

The method used by IFIN-HH is the 4π LSC-TDCR system for absolute activity measurement of an ampoule with transferred 222 Rn into a LS solution (Cassette, 2006). This measurement is completed by γ-ray spectrometry using an HPGe detector to measure net counting rates of the original receptacle GAZ 7 before and after the transfer of 222 Rn into the LS ampoule.

The original GAZ 7 receptacle from LNE-LNHB was measured successively over two days, at a distance of 45.5 cm from the surface of the HPGe detector, in vertical position, for both 352 keV and 609 keV Full Absorption Peaks (FAPs). These peaks are coming from the 222 Rn progenies ( 214 Pb and 214 Bi, respectively). Two mean net counting rates of N352 and N609, counts per second (s -1 ), were calculated (after background subtraction).

A quantity of 222 Rn was transferred to the LS type Ultimagold LLT ampoule N° 38, cooled with nitrogen vapour from liquid nitrogen (77 K) using the 222 Rn standard system at IFIN-HH (the system is described in reference [START_REF] Sahagia | The Rn-222 standard system established at IFIN-HH, Romania[END_REF]. The remaining quantity of 222 Rn was quantitatively recovered in the GAZ 7 receptacle, cooled as described above. The recovery was verified several times, as mentioned in section 4.1 of the reference [START_REF] Sahagia | Establishment of the Rn-222 traceability chain with the Romanian Standard System[END_REF]. The method used, including the complete recovery of 222 Rn are also confirmed by the results of IFIN-HH within the K2 type comparison, CCRI(II)-K2. Rn-222, 2015(BIPM-2015); this comparison was also piloted by the LNHB but the activity range was higher.

After the equilibrium was re-established in the GAZ 7 receptacle, it was again measured with the HPGe detector in the same initial geometry and new mean net counting rates, N'352 and N'609, (s -1 ), were registered. Two values of the counting rate ratios: R352 = N'352 / N352 = 0.926 (41) and R609 = N'609 / N609 = 0.894 (42) were calculated. Their mean value is R = 0.910 (29), u = 3.2%.

After the equilibrium was reached, the activity of LS ampoule N° 38, was repeatedly measured in the LSC TDCR system, obtaining the activity value A38 = 913 Bq, u = 1.6%. The uncertainty of the activity of LS ampoule N° 38 has several components due to: counting statistics (measurement and background of D), detection efficiency and decay correction, respectively (see Table 5). More details about this type of measurements are presented in reference (Antohe, 2011).

The activity of the initial GAZ 7 receptacle at the reference date of the comparison, 15 April 2019, 12:00 UTC, was calculated as: AGAZ 7 = A38/(1-R) = 10 144 Bq = 10.14 kBq. The uncertainty was calculated as the quadratic summation of the activity of A38, (1-R), instability and recovery uncertainties. A value for the combined relative standard uncertainty of u = 32.3% was obtained.

A comparative measurement (estimation) by Monte Carlo simulation (GESPECOR software) for calculation of the HPGe efficiency for the two types of receptacles: GAZ 7 and LS ampoule, measured in vertical position, at 45.5 cm from the detector surface. The determined activity of (GAZ 7) before transfer is 10 696 Bq, the relative difference from the reported value (10 140 Bq), being about 5.5%.

Two problems were identified:

 Low transfer of the 222 Rn from the container into the ampoule (only about 10%): in vacuum (the pressure in the container was about 10% higher than in the radon transfer installation, approximately 3 Pa), with a transfer time of only about 5 min.  Non-reproducible volume distribution of the 222 Rn daughters in the container (before and after transfer).

The arithmetic mean of the mean of the net counting rate ratios for 214 Pb and 214 Bi (two measurements before and two measurements after transfer) was used to compute the activity, which was 10 140 Bq at the reference time (15 April 2019, 12:00 UTC) as mentioned above. The results for the different sets of measurements (two before transfer and two after transfer) lead to four values of R, which were from 0.87 to 0.95; for (1-R), which is used to calculate the reported 222 Rn activity in GAZ 7 receptacle, result in a wide range, from 0.05 to 0.13.

The reported relative uncertainty of 32.3% resulted from quadratic summation of the following relative uncertainties: 1.6% (LS counting), 32.2% (relative uncertainty of the value of (1-R)) and 0.47% (supplementary due to recovery). It should be noted that the absolute standard uncertainty of (1-R) is equal to that of R, i.e. 0.029; so, the relative uncertainty of (1-R) is very high, 0.029/0.090=0.322 (32.2%), which can explain the large relative difference between the IFIN-HH result and the reference value of this comparison.

In conclusion, the main reason identified for the rather large relative uncertainty in the result reported by IFIN-HH is the too low transfer of 222 Rn from the metallic recipient into the glass ampoule with LS solution. Consequently, the reported result had a very strong dependence of the relative measurements performed by gamma-ray spectrometry -measurements which might be affected by a non-reproducible volume distribution of the radon progenies ( 214 Pb, 214 Bi) before and after the radon transfer.

For the future, a better way to transfer the 222 Rn gas from the metallic container (100 cm 3 ) into a glass vial with LS solution (20 cm 3 ) should be identified, tested and implemented. The use of an air pump and a significantly longer time for the radon transfer might improve this type of radon activity measurement at IFIN-HH.

The Radon Measurement System at BEV

The measurement is done by complete exhalation of the 222 Rn from the small sample container into a big calibration container barrel with a net air volume Vc of 204.2 (3) L. The 222 Rn is completely exhaled from the small sample container into the absolute airtight calibration container barrel, homogenized and measured with the traceable calibrated Austrian national standard for 222 Rn activity concentration in air. The diffusion inlet of the ionization chamber has been positioned in the middle of the calibration container to ensure a highly representative measured 222 Rn activity concentration and reduce potential wall effects.

Before starting the exhalation and measurement of the 222 Rn activity concentration in the calibration container, the blank background rate r0 (s -1 ) of the used traceable calibrated ionization chamber (Genitron AlphaGuard PQ 2000 Rn/Tn, S/N 1338) is determined. For this purpose, the calibration container is flushed with outdoor air at low 222 Rn activity concentration < 5 Bq•m -3 . The blank background count rate is determined over a measurement period of 3 600 s (1 h) in six 10 min subperiods. The ionization chamber with an active measurement volume of 0.56 L is used in diffusion mode and operated in alpha particle impulse count mode.

After determination of the blank background count rate, the small sample container is placed inside the calibration container barrel (Genitron Typ EV, S/N 03211, D 56 cm, H 86 cm, 210.1 L gross empty nominal volume) and carefully opened. The net air volume of the container had been adjusted by subtracting the volumes of all entered solid parts (e.g. ionization chamber, Rn-222 sample container). A small degassing hose -connected to an air pump (Genitron Alpha Pump) -is then put onto the small sample container. Then the calibration container is closed gastight and the air pump is switched on with a flow rate of 1 L•min -1 (Figure 8). The air circulates and degasses the 222 Rn from the small sample container into the barrel air volume. After about 20 min of air circulation, 222 Rn is almost completely exhaled from the sample container and distributed homogeneously by a fan into the air volume of the calibration container.

c A ( T m ) = A ( T 0 ) V c • K ∆ t = A ( T 0 ) V c • e -ln (2)• ∆t T 1/2
 cA(Tm), 222 Rn activity concentration in the container at the time of measurement Tm.  A(T0), 222 Rn activity of the radon sample at the reference time T0 (Bq).  Vc, air volume of the calibration container (m³).  Kt, correction factor for the radioactive decay of 222 Rn.  t, time span between reference time and measurement (Tm -T0) (d).  T1/2, half-life of 222 Rn: 3.8232 (8) d.

Details of the measured quantities (e.g. measured ionization current, calibration factor for ionization chamber) and detailed uncertainty calculation are given in [START_REF] Maringer | An innovative quick method for traceable measurement of radon 222 in drinking water[END_REF].

The German Radon Reference Measurement System at PTB

For the absolute determination of the activity of 222 Rn gas samples several methods are applied in the radioactivity laboratory of PTB. A primary method based on the Defined Solid Angle alpha spectrometry of condensed 222 Rn on a cold point (device Id.: M19) [START_REF] Picolo | Absolute measurement of radon 222 activity[END_REF]. A gamma spectrometric method using an HPGe detector which is calibrated against PTB's Hönigschmid standard source [START_REF] Schötzig | Photon emission probabilities per decay of 226Ra and 232Th in equilibrium with their daughter products[END_REF]) and a fast secondary standard system, applying an integral counting technique with dead time correction of an NaI(Tl) detector (device Id.: M07) together with selected, calibrated stainless steel containers.

During this EURAMET intercomparison the primary method and the fast secondary method were applied. The primary method was used to determine the activity of the 222 Rn source supplied by LNE-LNHB. The secondary method was used as a fall back, in case of vacuum problems and to determine the transfer losses of the vacuum system during the handling of the 222 Rn gas, in between the different measuring systems.

In the course of this activity determination, the 222 Rn activity supplied by LNE-LHNB was measured in the stainless steel container sent by LNE-LNHB. Then the activity was transferred to the PTB calibrated stainless steel container (Id. RN12) and measured again. Afterwards the activity was transferred to the primary measuring device M19, to determine the activity. In order to understand any transfer losses, the 222 Rn was retransferred to RN12 and measured again with the secondary standard M07 (a calibrated NaI(Tl) system).

The results from the secondary standard are in perfect agreement with the primary method results, which were reported as PTB results of this intercomparison. The secondary results from M07 of (12.90 ± 0.12) kBq (k = 1) have slightly higher uncertainty and prove that the transfer losses during this intercomparison can be neglected with the given frame of uncertainty. They also prove the usefulness of this stabilised secondary method, since the calibration factors, dating back to the year 2004, are still valid.

In Defined Solid Angle device, the detector is placed at the opposite side of the condensed 222 Rn source where only the alpha-particles passing through the diaphragm are detected. As the inner radius of the diaphragm is known and source-todiaphragm distance as well as the source diameter, a defined geometry allowing the solid angle to be exactly calculated using standard elliptic integrals is achieved [START_REF] Ruffle | The geometric efficiency of a parallel-disc source and detector system[END_REF].

The cooling of the cold surface where the 222 Rn is condensed is created by a cryogenic system in which the cold head of the cryogenerator is connected to the cold surface with a flexible copper braid and a nickel rod of about 6 mm in diameter and 20 mm length. One end of the nickel rod serves as the cold surface and is welded to the centre of a thin circular stainless steel foil 75 m thick. The construction from the cryogenic system to the cold point uses good thermal conductors of copper and nickel to ensure good thermal transfer.

At the cold head of the cryogenerator, there is a similar temperature regulating system allowing the temperature at the cold point to be adjusted. The coldest temperature available is 25 K.

The stainless steel foil with a thickness of 75 µm forms the bottom of the measurement chamber and is welded in the centre to the nickel rod and outside to the end of the UHV-flange. Measurements of the system dimensions were carried out at the PTB Coordinate Metrology Section. The dimensional quantities have been determined as (7.997 ± 0.005) mm for the diaphragm radius and (168.40 ± 0.0 7) mm for the sourcediaphragm distance. Specific investigations showed that the difference in the distance to the cold point does not change more than a few micrometres from room temperature to a temperature of less than 100 K.

The solid angle was evaluated first by calculation of the temperature distribution derived from the conduction of heat transfer described by Fourier's law, which show that radon cannot be condensed at a radius of more than 4 mm, considering the 3 mm radius of the nickel rod. An experiment using radiographic image was used to confirm the calculation results. It shows that the radius of the 222 Rn source is (4.9 ± 1.0) mm. Using all of these data, the geometry factor /(4) can be calculated to be (5.626 ± 0.010)•10 -4 (Dersch, 2004).

With the DSA method, the relative standard uncertainty is reduced to less than 1%, where the most important components are: geometry factor = 0.18%, scattering of the alpha particles at the edge of the diaphragm = 0.3%, and peak evaluation of the 222 Rn spectrum = 0.6%. The secondary measurement system with a digital dead time unit of the non-extendable type [START_REF] Schönfeld | Precise measurement of dead time[END_REF] and an NaI(Tl) detector is used with integral counting of pulses [START_REF] Dersch | Production and Measurement of 222Rn Standards[END_REF] for the confirmation of the absolute measurements. It was developed as an independent system for the activity determination of gaseous 222 Rn sources. To control the stability of the system, a 226 Ra point source is measured at regular intervals. From these measurements also a possible decrease of the detector efficiency can be observed and corrected for, guaranteeing the reliability of the radon activity determination.

The 222 Rn Measurement System at SMU

For the determination of the reference value of the 222 Rn gas sample No. GAZ 9 obtained from LNE-LNHB, a new SMU radon secondary standard (AiRneSt) was used (Figure 9 and Figure 10). This system will be used for calibration and verification of customers' devices as well as SMU standards in the future.

The standard consists of two main parts, a radon chamber and a measuring device. The chamber is a horizontal cylinder made from stainless steel with a diameter of 0.78818 (44) m, length of 2.00130 (10) m, thickness of the stainless sheet is 5.0 mm and inner volume of 0.9757 (23) m 3 (Figure 9). All dimensions (radius, diameter, length), inner volume and inner surface of the chamber were determined at SMU and are traceable to the Slovak National Standard of Length No. 002/97. The measuring device AlphaGUARD DF2000 was used as a reference device and the measurement system using Lucas cells as a parallel control device. Both systems are traceable to Czech National Standard via calibration in SÚJCHBO in Czech Republic.

Before starting measurements, the container with 222 Rn gas was connected to the chamber and 222 Rn gas was transferred through a HEPA filter and daughter products filter into the chamber by evacuating. The filling air (inner atmosphere of laboratory (air with background volume activity of radon less than 20 Bq.m -3 ) comes through the zero filter (a box with a volume of 30 l filled with activated charcoal), a dryer vessel with silica, a HEPA filter (acrylic copolymer on a non -woven support) to the container with 222 Rn (flushing of container with 222 Rn) and then is finally transferred to the radon chamber. Inside the chamber 222 Rn gas was mixed and homogenized with the inner atmosphere by a set of fans. Thermodynamic parameters like temperature (T), pressure (p) and humidity (h) were measured during measurement via calibrated monitors.

Then a long-term measurement was performed with a slight vacuum against ambient atmospheric pressure (about 1.5 kPa lower) to ensure the airtightness of the chamber. After transfer of radon to chamber is started, it is necessary to wait about 2 h to stabilize conditions inside the chamber to stabilize the AlphaGUARD response. Stable conditions are considered when the variance of measured values falls below 2%. Reference value of 222 Rn volume activity (RAC) was determined as a weighted mean of 21 specifically selected measured values in the chosen range. Selected measured data comes from stable AlphaGUARD response. The weight of each value was determined from the uncertainty of each value obtained directly from the radon monitor (AlphaGUARD). Each value was corrected for pressure (kp) and temperature (kT) measured directly in the chamber during measurement. Even though AlphaGUARD can measure p and T, these climatic data were not taken into account. Efficiency correction, decay correction and recalculation to the reference date were applied.

  RAC = RAC k k m p T                             p-1013 p k = 1+ A p 1013 p-620                             T -20 130 k = 1+ B T 293 130 -T
The radon monitor is connected to the PC via the KF system in order to collect measured data. There are two possibilities of a placement of radon monitor, either inside the chamber, mostly in diffusion mode, or outside the chamber in flow mode. Comparison measurements of volume activity of radon were performed in the radon atmosphere of the chamber in diffusion mode. The data from AlphaGUARD, RACm -measured volume activity of radon (Bq m -3 ), were subsequently corrected by pressure kp and temperature factors kT, using the previous formula according to recommendations from Bertin Technologies [START_REF] Technologies | Bertin Technologies "Exchange with technical staff from Bertin Technologies from 02[END_REF]. A and B coefficients are taken from Bertin Technologies and are dependent on the measurement range. This work at SMU was supported by the Slovak Research and Development Agency under the contract No. APVV-15-0017.

Measurement system from BFKH

The equipment consists of an airtight stainless steel chamber, a 222 Rn source (type RF 500 from Czech Metrological Institute), a leakproof gas pump (Alpha Pump, rate flows 0.3, 0.5 and 1 L•min -1 ), a nitrogen gas-cylinder, a controller unit with computer and an environmental parameters (temperature, air pressure and relative humidity) measuring unit. The volume of the chamber is 840 L. The activity of the radium source is 630.4 kBq with a very high emanation factor (99%). The homogeneity of the radon gas in the chamber is ensured by two continuously running fans. The radon chamber's distinctive features are the two gas circuits which have a common branch. The common branch consists of the radon generator and the pump. Figure 11 shows the scheme of the measuring system. In the figure, the blue lines indicate the gas paths and the red one the electrical control lines. The radon measuring system was flushed with nitrogen gas after being sealed. The radon gas container after its arrival at BFKH was connected to one of the inlet valves of the chamber. The radon was then transferred (flow through) to the measuring volume. Two internal fans assisted in homogenization. Once the radon concentration values measured by a calibrated (reference) AlphaGUARD in the chamber was stabilized, data were collected every 10 minutes.

The reference measuring device is a GENITRON AlphaGUARD PQ 2000 (serial number is 1150), calibrated in PTB.

The number of measurement readings was 830. An exponential function was fitted to the data. Extrapolation of the fitted function to the loading time gave the initial activity concentration of the transferred gas. To determine the total activity of the radon gas this value was multiplied by the volume of the radon chamber to give the reported value.

A very important parameter is the volume of the radon chamber. As AlphaGUARD only measures the radon concentration the volume is required to obtain the total activity. It is not easy to determine the volume, since the value calculated from the side edges may be different from the actual one (side swell, etc ...). The radon chamber volume was determined by CO concentration measurement. The advantage of this method is that the walls of the chamber do not deform under high or low pressure. A well-known amount of CO was introduced into the chamber and circulated through a CO concentration meter.

The volume can be determined using the universal gas law : pV=nRT where p is the gas pressure, V the volume, n the amount of chemical substance (mol), R the universal gas constant, T the gas temperature.

The measured volume of the measuring chamber is Vchamber= (844.9 ± 5.9) L. Of course, the minimum (828.6 L) and the maximum (849.1 L) volume have been determined from the side edges as well.

As the volume determined by CO concentration measurement is within the minimum-maximum range, it has been accepted as the volume value.

Results and evaluation

Seven laboratories took part in this comparison providing results in kBq, as shown in Table 4, where the combined uncertainties are also given. A Grubbs test (5725-2:1994) was performed on the results submitted by the participants, which showed no outliers were identified (Table 6). The final results submitted by the participants in Bq•cm -3 together with the arithmetic mean and weighted mean values are shown in Figure 12. The details of the weighted mean, arithmetic mean, median and PMM value are given in Table 7. ) Laboratory results (Bq•cm -3 ) k = 1

Following the policy of the KCWG(II), the Power-Moderated Mean (PMM) [START_REF] Pommé | Determination of a referernce value, associated standard uncertainty and degrees of equivalence for CCRI(II) key comparison, European Commission[END_REF] was used to calculate the reference value of the comparison: 125.4 (35) Bq•cm -3 and details of PMM calculations are given in Figure 13. D corresponds to each value minus the mean and S50 corresponds to the standard deviation divided by the z-score for the middle 50% of normal distribution.

Conclusion

All results are consistent, within the uncertainties. No outliers were identified by the Grubbs test (Table 6). Nevertheless, five results are in very good agreement whereas two others are quite discrepant (about 20% from the weighted mean). The relative standard deviation between the seven results is 11.4%. A 369 (1996A 369 ( ) 445-451. 1996A 369 ( , pp. 445-451. Dersch, R.,. 2004. Primary and secondary measurements of 222Rn. . ARI 60 (2004), 387-390. 2004, pp. 387-390.

Figure 1 :

 1 Figure 1: Picture of a container

Figure 2 :

 2 Figure 2: Dimensions of the containers

Figure 3 -

 3 Figure 3 -Primary 222 Rn Reference Measurement System operating at INMRI-ENEA. It is used to measure the activity of 222 Rn sources and to calibrate all the reference monitors of the INMRI (De Felice, 1996) (Cardellini, 2016). It consists of an aluminium flask whose volume is 111.77 L (the larger volume in the figure), one radon monitor based on a Lucas Scintillation Cell and a group of 222 Rn sources.All the elements of this system are connected in a closed circuit in which the air can circulate by means of a micro-pump placed in the aluminium flask. In the circuit are also a flow-meter, a manometer, a vial-holder and a hygrometer. The exact configuration of the radon source assembly (labelled as "radon source" in the figure) depends on the measurement that is carried out: in some experiments, the source to be measured is in the left bubbler, while the right bubbler is only a trap; in other measurements, the radon source is in the right bubbler and the left bubbler contains only water. The bubbler may be easily removed and replaced by any other suitable vessel containing radon.

Figure 4 -

 4 Figure 4 -Vial holder used to introduce the radon contained in glass vials into the radon reference measurement system.The small vertical cylinder on the top of the vial holder is used to break the vial and transfer the radon into the circuit.

Figure 5 -

 5 Figure 5 -Scheme of the DSA measurement chamber and picture of the cold finger used at LNE-LNHB.

Figure 7 -

 7 Figure 7 -Radon measurement system at LNE-LNHB (a) photograph and (b) simplified schematic representation.

Figure 8 -

 8 Figure 8 -Scheme of 222 Rn measurement inside the gastight radon calibration container at BEV. Thirty minutes after the start of the 222 Rn emanation from the sample container into the air of the closed calibration container, the diffusion of 222 Rn into the ionization chamber is completed. Then the 3 600 s (1 h) measurement period starts. After finishing the data processing, the calibration container is opened and flushed again with low 222 Rn fresh outdoor air establishing the blank background situation in the calibration container.The 222 Rn activity concentration in the container is calculated as follows:

Figure 9 -

 9 Figure 9 -Simplified block diagram of the radon chamber at SMU, where SF -silica gel filter, RS -source of 222 Rn, DFdaughters products filter, HF -HEPA filter, FM -flow meter, AG -AlphaGUARD, LC -Lucas cell, pTh -monitoring system for thermodynamic parameters, PC -personal computer.

Figure 10 -

 10 Figure 10 -SMU radon chamber, AiRneSt

Figure 11 -

 11 Figure 11 -Scheme of the measuring system.

Figure 12 -

 12 Figure 12-Individual results of the international comparison of activity per unit volume (7 individual results) in Bq•cm -3

Figure 13 -

 13 Figure 13 -PomPlot of the participants' results for the 222 Rn intercomparison.

Figure 1 :Figure 2 :Figure 5 -

 125 Figure 1: Picture of a container ............................................................................................................................................... 2 Figure 2: Dimensions of the containers ................................................................................................................................... 2 Figure 3 -Primary 222 Rn Reference Measurement System operating at INMRI-ENEA. ........................................................ 4 Figure 4 -Vial holder used to introduce the radon contained in glass vials into the radon reference measurement system. The small vertical cylinder on the top of the vial holder is used to break the vial and transfer the radon into the circuit. ....... 4 Figure 5 -Scheme of the DSA measurement chamber and picture of the cold finger used at LNE-LNHB. .......................... 5 Figure 6 -Scheme of the DSA measurement system at LNE-LNHB:a, radius of the collimator; b, radius of the source; z, distance between source and diaphragm; e, eccentricity, if the source and collimator axes are different. ............................... 5 Figure 7 -Radon measurement system at LNE-LNHB (a) photograph and (b) simplified schematic representation. ........... 6 Figure 8 -Scheme of 222 Rn measurement inside the gastight radon calibration container at BEV. ........................................ 8 Figure 9 -Simplified block diagram of the radon chamber at SMU, where SF -silica gel filter, RS -source of 222 Rn, DFdaughters products filter, HF -HEPA filter, FM -flow meter, AG -AlphaGUARD, LC -Lucas cell, pTh -monitoring system for thermodynamic parameters, PC -personal computer. .......................................................................................... 10 Figure 10 -SMU radon chamber, AiRneSt .......................................................................................................................... 10 Figure 11 -Scheme of the measuring system. ....................................................................................................................... 11 Figure 12-Individual results of the international comparison of activity per unit volume (7 individual results) in Bq•cm -3 14 Figure 13 -PomPlot of the participants' results for the 222 Rn intercomparison. ................................................................... 15

Table 1 :

 1 List of participants

	BEV	Bundesamt für Eich-und Vermessungswesen, Austria
	BFKH	Budapest Főváros Kormányhivatala, Budapest, Hungary
	ENEA	Instituto Nazionale di Metrologia delle Radiazioni Ionizzanti (INMRI), Italy
	IFIN-HH	Horia Hulubei National Institute for Research and Development in Physics and Nuclear
		Engineering, Romania
	LNE-LNHB	Laboratoire National de métrologie et d'Essais -Laboratoire National Henri Becquerel,
		France
	PTB	Physikalisch-Technische Bundesanstalt, Germany
	SMU	Slovenský metrologický ústav, Slovakia

Table 2 :

 2 Container volumes

		Container	Volume	Absolute standard	Relative standard
	Laboratory	number	(cm 3 )	uncertainty (cm 3 )	uncertainty (%)
	PTB	GAZ 1	105.84	0.31	0.30
	BFKH	GAZ 2	104.37	0.44	0.42
	BEV	GAZ 3	104.93	0.44	0.42
	IRA	GAZ 6	104.70	0.46	0.44
	IFIN-HH	GAZ 7	104.87	0.41	0.39
	ENEA-INMRI	GAZ 8	105.29	0.41	0.39
	SMU	GAZ 9	105.03	0.42	0.40
	LNE-LNHB	GAZ10	104.76	0.42	0.40
	Mean		104.97
	Standard deviation (cm 3 )		0.44
	Relative standard deviation		0.41%

Table 3 :

 3 List of the methods used as reported by participants

	Laboratory	Method Acronym	Description of the method
			Exhalation of the 222 Rn activity into the air of a traceable
	BEV	4P-IC-AP-00-00-00	volume calibration container and measurement of the 222 Rn activity concentration in air by a traceable calibrated
			secondary standard 222 Rn ionisation chamber.

Table 4 :

 4 Measurement results evaluated on 15 April 2019 12:00 UTC. Values as reported by participants Total uncertainty also includes the uncertainty on the volume, cf. § 2. § Mean of four values measured.

	Laboratory	Activity (kBq)	Combined standard uncertainty (kBq)	Combined relative standard uncertainty (%)	Activity concentration (Bq•cm -3 )*	Total relative standard uncertainty (%)**
	BEV 4P-IC-AP-00-00-00	13.0	0.4	3.1	123.9	3.1
	BFKH 4P-IC-AP-00-00-00	15.11	0.6	3.8	145	3.8
	ENEA-INMRI 4P-IC-GR-00-00-00	13.056	0.155	1.19	124.0	1.3
	IFIN-HH 4P-LS-MX-00-00-TD	10.14 §	3.28	32.3	97	32
	UA-GH-GR-00-00-00
	LNE-LNHB SA-PS-AP-00-00-00	12.710	0.054	0.42	121.3	0.6
	PTB SA-PS-AP-00-00-00	12.90	0.10	0.8	121.9	0.9
	SMU 4P-IC-AP-00-00-00	13.14	0.49	3.75	125.1	3.8
	* The activity concentration is the result of the activity (measured by each laboratory) divided by the volume given in Erreur ! Source
	du renvoi introuvable. Table 2.

**

Table 5

 5 presents the detailed uncertainty budget as provided on the reporting forms of the participants for all individual parameters included in the measurement process..

Table 5 :

 5 Relative standard uncertainty components as reported by participants for their activity measurement, where u(x)i is the uncertainty of the i th input quantity, xi, and u(y)i is the corresponding contribution to the output quantity (activity) from input quantity i.

	Laboratory Method	Uncertainty components, xi	u(x)i (%)	u(y)i (%)	Evaluation type
	BEV	K_decay	0.09		A
	4P-IC-AP-00-00-	Mean activity concentration at ref. date (Bq/m³)	0.7		A
	00	Background (Bq)	41		A
		Calibration factor	3.0		B
		Air volume	0.10		B
	BFKH	Volume of radon chamber (m 3 )	0.69		B
	4P-IC-AP-00-00-00	Statistical uncertainty of measured values (kBq/m 3 )	3.8		A
	ENEA-INMRI	Activity of reference 226 Ra solution for calibration	0.60		A
	4P-SC-GR-00-00-	Radon emanation factor of reference radium solution	0.80		A
	HE	Reproducibility of calibration	0.40		B
		Reproducibility of the measurement of 222 Rn gas	0.50		B
	IFIN-HH	Statistical uncertainty of the LSC-TDCR measurement	0.25	0.25	A
	4P-LS-MX-00-00-	Statistical uncertainty of the background of D (LSC-	1.1	1.1	A
	TD;	TDCR)
	UA-GH-GR-00-00-	Detection efficiency (LSC-TDCR)	1.1	1.1	B
	00	Decay correction (LSC-TDCR)	0.11	0.11	B
		Statistical uncertainty of the calculation of R	3.2	32.2	A
		Recovery of radon in the receptacle GAZ 7 after the	0.47	0.47	B
		transfer in the LS ampoule
		counting statistics	0.20	0.21	B
		dead time	0.001	0.001	B
		background	4.1	0.02	B
		pile-up	0.001	0.001	B
	LNE-LNHB	counting-time	0.0023	0.0023	B
	SA-PS-AP-00-00-	decay-scheme	0.016	0.016	B
	00	other effects (G)	0.32	0.32	B
		decay correction during measurement	0.042		B
		backscattering	0.0000001		B
		repeatability	0.01	0.01	B
		reproducibility	0.18	0.18	B
		solid angle	0.68	0.68	A
		counting statistics	0.15	0.16	A
		dead time	0.46	0.47	A
	PTB SA-PS-AP-00-00-00	decay correction during measurement background frequency standard time to start of measurement	0.000004 1.2 0.02 0.17	0.000004 0.078 0.02 0.012	A A B A
		nuclear data	0.014	0.014	B
		time to reference date	0.04	0.0073	A
		transfer losses	0.13	0.13	A
		temperature	0.082		A/B
	SMU 4P-IC-AP-00-00-00	pressure calibration factor volume of radon chamber decay correction (half-life)	0.034 3.7 0.27 0.021		B B B B
		weighted mean	0.0072		A

Table 6 :

 6 Grubbs test

	Nb of results	7
	Gmin	1.846
	Gmax	1.590
	Critical value at 5%	2.02
	Critical value at 1%	2.14
	Test	Correct

Table 7 :

 7 PMM results, median, weighted mean, arithmetic mean for the activity concentration, CA

		170
	Activity per unit volume (Bq•cm -3	70 90 110 130 150
		50
			CA (Bq•cm -3 )	uCA (Bq•cm -3 )
		Weighted mean	122.0	0.9 (external)
		Arithmetic mean	122.6	5.3
		Median	123.9	1.6
		PMM value	125.4	3.5

Table 1 :

 1