Romain Viennois

Michael Marek Koza

Régis Debord

Pierre Toulemonde

Hannu Mutka

Stéphane Pailhes

Michael Marek Koza

Stéphane Pailhès

Anisotropic low-energy vibrational modes as an effect of cage geometry in the binary barium silicon clathrate Ba24Si100

INTRODUCTION

Clathrates are representatives of "guest-host" structures and form a wide class of inorganic materials whose crystal structure results in a 3D covalent framework of face-sharing polyhedral cages encapsulating guest cations. Their peculiar crystalline structure offers the possibility of tuning their electronic properties between metallic, semi-conducting and even superconducting for some compositions. Concomitantly, they exhibit a very low thermal conductivity of as low as 1-2 W.m -1 .K -1 at room temperature approximating values found in glassy materials. The conjunction of low electrical resistivity and low thermal conduction are making them promising candidate materials for thermoelectric (TE) applications [START_REF] Nolas | The Physics ans Chemistry of Inorganic Clathrates[END_REF][2][3][4][START_REF]Nano-Cage Structured Materials: Clathrates" T. Takabatake chapter[END_REF][START_REF] Yamanaka | [END_REF].

In clathrates, especially for compositions optimized for TE applications, the heat transport is dominated by lattice thermal conductivity (λL), described microscopically by quasi-particles called phonons.

Despite their low thermal conductivity, inelastic X-ray and neutron spectroscopies (IXS/INS) reveal the existence of well-defined acoustic phonons [START_REF] Yamanaka | [END_REF][7][8][9][10][11]. They are efficient heat carriers propagating their energies with an average sound velocity of about 3 000 m.s -1 over distances of a few tens of nanometers, which correspond to several unit cells (~1 nm) of the type-I clathrate crystals [11]. However, their energies are typically restricted to a range of less than 10 meV (~ 100 K). Indeed, at higher energies, the phonon spectrum consists of nearly non-dispersive optical phonon branches, which "cut through" the acoustic branches [START_REF] Yamanaka | [END_REF][7][8][9][10][11][START_REF] Pailhès | Nanostructured Semiconductors: Amorphization and thermal properties[END_REF]. The low-lying optical bands are dominated by vibrations of the guests in the cages [2]. In the case of the most studied type-I clathrate structure, whose the simplest representative is the binary Ba8Si46, the low-lying optical branches are prevailed by motions of Ba in tetrakaidecahedra Si24 cages. These Ba-weighted optical modes are viewed as well-defined peaks in the phonon density of states (DOS) [START_REF] Reny | [END_REF][14][15][16][17][18] and lead to a broad hump in the temperature dependence of the specific heat (Cp) over the T 3 Debye-dependence [16,[19][20][21][22][23]. Recently, a universal relation has been revealed in type-I clathrates between λL and the product of the average sound velocity by the hump temperature in Cp(T) [23]. This hump temperature is commonly associated in literature to an Einstein temperature (θE) and corresponds in the phonon spectrum to the lowest optical guest phonon energy (E1) such that E1=kBθE.

In the context of the Boltzmann transport equation for phonons, the propagative acoustic component of the lattice thermal conductivity is given by the following spectral integral whose upper limit is locked by E1 [START_REF] Yamanaka | [END_REF][7][8][9][10][11]23]:

𝜆 𝐿 (𝑇) = ∫ 𝜆 𝐿 (𝐸)𝜌(𝐸)𝑑𝐸 𝐸 1 0 (1)
Were 𝜆 𝐿 (𝐸) is the thermal conductivity of acoustic phonons with energies in the range E+dE and 𝜌(𝐸) is the density of states.

Thus, lowering the energy E1 of the guest optical phonons reduces efficiently λL. The nature of the lowlying guest optical phonons is particularly intriguing. Ab initio calculations in the harmonic approximation in type-I clathrates demonstrate that the sole complexity of the 3D framework of cages cannot explain the low value of λL so that the guest vibrations have a particular role [24]. It has been found that these guest optical phonons exhibit very low participation ratios (PR) [9,10,[25][26][27][28].

Furthermore, perturbative ab initio calculations in type-I clathrates show that the existence of nearly non-dispersive optical phonon branches results in a strong enhancement of the phonon-phonon scattering which contribute to lower the lattice thermal conductivity [24,25,29]. An efficient route to reduce λL in clathrates is then to lower the energies of low-lying guest modes. This can be done in type-I clathrates by the substitution of host atoms or the creation of vacancies in the host framework which, by deforming the host cage, can not only smoothen the guest potential but also split the centered guest equilibrium positions into off-centered minima in the cages [2,30].

An alternative route, which is explored in the present work, is to investigate the effect of the cage geometry in the binary clathrate of type-IX, Ba24Si100. The cubic crystal structure of Ba8Si46 (space group Pm-3n) and Ba24Si100 (space group P4132) are shown in the Fig. 1 (a) and (b), respectively. The lattice parameter in the type-IX, of about 14 Å, is much higher than the one of the type-I, of about 10.5 Å. The type-I unit cell consists of six large tetrakaidecahedra 5 12 6 2 Si24 cages and two small pentagonal dodecahedra 5 12 Si20 cages which encapsulate two different barium sites, the BaI(6d) and BaI(2a) respectively. The type-IX unit cell, shown in Fig. 1B, is composed of eight Si20 dodecahedra, four Si8 distorted cubes, and twelve Si20 open cages leading to three different sites for the barium atoms, namely BaIX(8c), BaIX(4b) and BaIX(12d), respectively [32][33][34][35]. The type-I clathrate is composed of sp 3 Si atoms only while, in the type-IX, Si atoms of the distorted Si8 cubic cavity have both sp 3 and sp 2 bond characters [32][33][34][35].

In this paper, we investigate the phonon dynamics in Ba24Si100 mostly in the energy range of the lowlying dispersionless modes. Combining INS and ab initio density functional theory (DFT) calculations, our study reveals the existence of an additional guest optical band around 2.5-4 meV in Ba24Si100, which is not present in Ba8Si46. In general, the DFT results back up the existence of low-energy optical modes in Ba24Si100 and show that they are mostly weighted by Ba displacements in the Si20 dodecahedra cages.

Moreover, the calculations reveal that these modes are characterized by very low values of the PR similar to the ones of the lowest-lying guest phonons in the type-I clathrate. In addition, while the guest potential is nearly harmonic in Ba8Si46 [10,24], a significant deviation from harmonicity is found in Ba24Si100.

EXPERIMENTAL AND COMPUTATIONAL DETAILS

The Ba24Si100 samples were synthesized under high pressure and high temperature conditions in a large volume press with "Conac"-type anvils at the CNRS, Grenoble, France. A mixture of Si and BaSi2 powders in stoichiometric amounts were loaded in a boron nitride crucible within a graphite furnace and were submitted to a pressure of about 1.1 GPa followed by heating to 650°C during one hour. The samples were then thermally quenched and the pressure was slowly decreased. More details can be found in refs. 33 and 36. Our samples contain some amount of secondary phases such as diamond silicon (10-15%) and cubic BaSi2 (3%), however, they are insignificant for the conclusions of this study as confirmed by the comparison with the DFT calculation results.

High-resolution inelastic neutron scattering (INS) experiments were performed with the IN5 time-offlight spectrometer [37] at the Institut Laue Langevin in Grenoble, France. Some preliminary results obtained from previous experiments with the time-of-flight spectrometers IN4 and IN5 in a lowresolution configuration were reported in refs. 16 and 38. The new experiments with higher resolution and improved signal permit to discriminate different low-energy features in the INS spectra. More importantly, our experimental configuration allowed to study the temperature dependence of the lowest energy modes. We have used different incident wavelengths, however, most of the results reported here were obtained with a wavelength of 3 Å resulting in an elastic energy resolution of about 0.3 meV. The generalized density of states (GDOS) G exp (,T) was computed within the incoherent approximation similarly to a recent approach performed for skutterudites [39][40][41]. For the investigation of the temperature dependence of the vibrational spectrum a standard cryostat with a He atmosphere of about 10 mbars at 100 K was used.

Lattice dynamics calculations were carried out with the direct method from the Hellmann-Feynman (HF) forces computed on the relaxed clathrate structures with the Vienna Ab-initio Software Package (VASP). The HF forces were derived by displacing atoms from their equilibrium positions by 0.05 Å along non-equivalent high-symmetry directions. The DFT calculation was based on PAW pseudopotentials and the PBE exchange-correlation functional [42,43]. We have used the finitetemperature smearing first order Methfessel-Paxton method for the band occupancies [44]. For all calculations an energy cut-off of 320 eV and the energy convergence of 10 -6 eV was applied. We applied k-meshes of 5x5x5 and 9x9x9 for Ba24Si100 and Ba8Si46, respectively. The relaxed lattice parameters found are 14.15 Å for Ba24Si100 and 10.39 Å for Ba8Si46. They are slightly larger than the experimental values by about 0.6-0.7 % (14.06-14.07 Å for Ba24Si100 [33,34,36], 10.32-10.33 Å for Ba8Si46 [36,45]) which is typical to PBE exchange correlation functional [46].

The lattice dynamics properties and neutron spectra were computed from the HF forces by the diagonalization of the dynamical matrix with the software package Phonon [47]. For a better comparison of the experimental G exp (,T) with the DFT results, the neutron-weighted DOS Z'(E) is calculated using

: 𝑍 ′ (𝐸) = ∑ 𝜎 𝑖 𝑀 𝑖 𝑍 𝑖 (𝐸) 𝑖
, where Zi(E) are the atom-projected density of states, σi are the scattering cross sections and Mi are the atom masses of each atom. The atomic displacement parameters have been computed using the software package Phonon [47] and as described by ref. [49]. The participation ratio p() of the phonons describes the degree of participation of the different atoms to a particular vibrational mode [9,10]. It has been extracted from the above calculations using [9,10]:

𝑝(𝜔) = (∑ |𝑢 ⃗ 𝑖 (𝜔 𝑞 ⃗ )| 2 𝑁 𝑖=1 ) 2 𝑁 ∑ |𝑢 ⃗ 𝑖 (𝜔 𝑞 ⃗ )| 4 𝑁 𝑖=1 ⁄ (2)
Where 𝑢 ⃗ 𝑖 = 𝑒 𝑖 (𝑞 ) √𝑀 𝑖 ⁄ are the atomic amplitudes with the phonon polarization vector 𝑒 𝑖 (𝑞 ) and the mass Mi of atom i.

RESULTS

The ab initio potential energy landscapes (E) probed by Ba atoms in the various cages in type-I and type-IX clathrates have been computed from small displacements x out of the equilibrium position (see Supplemental Material) [50] and reported in Figure 2 along the guest site high-symmetry directions + K3x 3 + K4x 4 , have been performed in order to quantify and compare the deviations from the harmonic potential. The harmonic K2, and the anharmonic cubic K3 and quartic K4 terms are reported in Table 1. Notice that due to the lower symmetry of the BaIX(8c) and BaIX(12d) sites, the cubic terms K3 are non-zero for any direction and along [001], respectively. In any Si cage of the two clathrate types, the potential energy curves take on minimum values at x=0 so that the guest equilibrium positions are at the center of the cages. In both cases, the amplitude of the harmonic term K2 is much lower for Ba than for Si, which is the result of the weaker bonds between Ba-Si than Si-Si. In type-I clathrates, the smallest K2 values are found for BaI(6d) located in the large Si24 cage. Due to the asymmetry of the Si24 cage (see Fig. 1), the BaI(6d)-Si distance varies from 3.5 Å, in the equatorial plane of the cage (parallel to the bc plane in the inset of the Fig. 2. In addition, the potential energy of Ba atoms in the type-IX clathrate, especially that of BaIX(12d), exhibits significant deviations from harmonicity, as illustrated in Fig. 2 where the harmonic (dotted blue points) and anharmonic (red lines) curves are superimposed. On the other hand, no significantly anharmonic term is needed to approximate the BaI(6d) potential in the same range of displacements.

The smoother out-of-plane BaIX(12d) potential compared to the in-plane BaI(6d) potential agrees with the observation of larger Ba atomic displacement parameters (ADPs) in Ba24Si100 than in Ba8Si46 as reported by Toulemonde et al. [34] and by Fukuoka et al. [54]. The G exp () of Ba24Si100 has been measured at several temperatures in the range 5 K -280 K, as reported in the Fig. 4a) in the Debye representation, i.e. G exp ()/ 2 . Owing to the improved instrumental resolution regarding our previous measurements reported in [16,38], we identify three additional lowenergy peaks centered at energies of E1=2.8, E2=3.5 and E3=4 meV at 280 K. Our ab initio calculation of the phonon DOS is shown in Fig. 5 a) in the 0-12 meV energy range. In the energy range above 12 meV, our ab initio calculations reported in the Supplemental Material [50] agree with the previous report [61]. Furthermore, the phonon DOS is better resolved in our calculations thanks to a larger sampling of the reciprocal space. A powder-averaged phonon DOS, G PALD (), has been reconstructed from the ab initio data (see Experimental and computational details) and compared directly to the experimental G exp () as shown in Fig. 3 b). The G PALD () reproduces the low-energy features at E1,2,3 observed in G exp () with a slight energy difference of about 10 %. In previous works [62,63], we have reported a similar difference in energy between ab initio derived and the experimental Raman active phonon energies. The calculated phonon dispersions along the high symmetry directions in Ba24Si100 and the total phonon density of states are shown in Fig. 5 a) and b), respectively, whereas the partial phonon DOS (p-DOS) for each atom is depicted in Fig. 6 a).

Our
Based on this set of theoretical data, the experimental peaks E1,2,3 can be assigned to some specific atomic vibrations. The peak at E1 is ascribed not only to the optical branch of A2 symmetry (optically silent mode) whose calculated energy at Г is 2.1 meV but also to the bending and extensive nondispersive character of the low-energy transverse acoustic (TA1) branch in the vicinity of the Brillouin zone boundary.

The peak at E2 is associated in an analogous way with the bending and extensive non-dispersive character of the high-energy transverse and longitudinal acoustic branches (TA2 and LA, respectively) in the vicinity of the Brillouin zone boundary and to the sum of optical branches with T1 symmetry (infrared active) with energies of about 3.3 meV at the Г point.

The peak at E3 is interpreted as the sum of optical branches with T1 and T2 symmetry (Raman active)

with energies of about 3.6, 3. BaIX(12d) weighted optical phonons perpendicular to this axis are found at higher energies between 5 and 12 meV (see Fig. 6 b)). This anisotropy is a consequence of the Si20 cage geometry as discussed above. The optical phonon branches associated with BaIX (8c) and BaIX (4b) vibrations occupy as well the energy range between 5 and 12 meV (see Fig. 6 a)).

The existence of optical phonons with very low energies around 3 meV in Ba24Si100 was formerly considered in the analysis of the CP of Ba24Si100 [16]. The experimental [16] and calculated temperature dependences of the lattice heat capacity, shown in the Debye representation (CP/T 3 versus T), in Ba24Si100 and in Ba8Si46 are reported in the Fig. 7. As commonly observed in all clathrates, the temperature dependence of CP/T 3 deviates significantly from the Debye behavior and forms a broad peak whose temperature of its maximum is related to the energy of the low-lying optical modes. The temperature of this peak in Ba24Si100 of about 8 K is clearly lower than in Ba8Si46 of about 15 K and thus consistent with the energy downshift of the optical phonons in Ba24Si100 in comparison with those in Ba8Si46. In order to disentangle the atomic contributions to the peak in CP /T 3 , we have computed from the ab initio derived phonon spectrum the heat capacity from each atomic site in both clathrates, see Fig. 7. It shows that the peak in CP/T 3 is dominated by vibrations of BaIX (12d) in Ba24Si100 and by vibrations of BaI(6d) in Ba8Si46.

The phonon participation ratio (PR), which can be interpreted as the relative number of atoms participating to a particular eigenstate with an essentially non-zero amplitude can be as well taken as a measure for the modes localization behavior. Propagating acoustic modes comprise eigenstates with PRs close to unity as they are characterized by a long wavelength in-phase displacement of all atoms.

Localized optic modes, on the other hand, comprise eigenstates with a substantial number of zero or anti-phase atomic displacements, which show a highly dispersed amplitude distribution for a compound with distinctly different atomic masses. In this case and for complex crystal structures, where the optical branches are very flat, the PRs in the optical regime can take on values lower than 0.1. We report in Fig. 5c) the energy-projected phonon PR in Ba24Si100. As expected, in the acoustic limit corresponding to energies lower than about 1.8 meV the PR takes on values of unity. It decreases abruptly when eigenstates with zero and anti-phase amplitudes become prominent. Eigenstates with minimum values of less than 0.04 are observed in the energy range of the low-dispersive modes forming the E3 peak. Recent theoretical works using PDFT in type-I clathrates have related these low PRs values to an effect of phonon localization [24,29]. Now, we discuss the temperature dependence of the low-energy E1,2,3 peaks of the generalized density of states which is reported in the Fig. 4b). The E1 and E2 peaks exhibit a significant softening, of about 0.3-0.5 meV, i. e. about 10-15 %, upon cooling down to 5 K. The E3 peak, viewed as a unique and broad distribution of modes at 280 K, splits in two peaks which are separated by about 0.5 meV at the base temperature. They are labelled E 3 ′ and E 3 ′′ with E 3 ′ < E 3 ′′ . The energy of the E 3 ′ peak decreases upon cooling while that of the E 3 ′′ peak remains almost unchanged in the sampled temperature range. The thermal shift of the mode energies results from the sum of a first term due to the thermal expansion of the unit cell and a second isochoric term caused by the anharmonicity change which, to the first order in perturbation, is given by the quartic component in the potential energy [64,65]. The thermal expansion energy shift (∆𝐸 𝑇𝐸 ) is given by the product of the mode energy (E) by the lattice thermal expansion (α)

and the Grüneisen parameter (γ): ∆𝐸 𝑇𝐸 = -𝛼𝛾∆𝑇. The Grüneisen parameter for the low-lying optical modes in Ba24Si100 and Ba8Si46 have been found positive and of about +2 and the values of their thermal expansion are in the 10 -5 K -1 range [16,66]. Thus, the change in energy due to the thermal expansion is positive upon cooling and counts for about 2.5 % of the mode energy, i.e. less than 0.1 meV in the case of Ba24Si100. On the contrary, we observed a softening of the E1,2,3 with the decrease of the temperature with an amplitude of about ~0.3 meV which cannot be ascribed to the effect of the lattice thermal expansion. In A8Ga16X30 (A = Sr, Ba, Eu and X = Ge,Sn) [2,8,[51][52][53]67] a similar softening of the BaI(6d)-weighted optical phonons was observed, however, by only 0.1-0.2 meV and thus weaker than in Ba24Si100. It was interpreted that the mode softening upon cooling is a signature of an appreciable contribution of the quartic and higher terms of the bonding potential to the mode anharmonicity [29].

The simple model of the anharmonic isolated oscillator, derived by Dahm and Ueda (DUM) [68], is commonly used to compare the strength of the anharmonicity among different materials. In this approach, the renormalization of the eigen-energy of the harmonic oscillator, E, is given by the anharmonic quartic term K4 whose amplitude is expressed by the dimensionless parameter :  = 4K4ħ 4 /E 3 M 2 [68]. This parameter can be extracted from the measurement of the temperature dependence of E. The DUM model has been used to fit the temperature dependence of the peaks E1, E2, E 3 ′ and E 3 ′′ as reported in Fig. 4 b). Due to the uncertainties in the peak definition, only a range of values for of 0.015-0.025 can be approximated for E1, E2, E 3 ′ .  is almost null for the peak E 3 ′′ . The strength of the quartic term in Ba24Si100 is about one order of magnitude lower than in other cage-based systems known as being highly anharmonic, such as the pyrochlore KOs2O6 with ~0.7 [69], the tetrahedrite Cu12Sb2Te2S13 with ~0.1-0.5 [70] and MV2Al20 (M=Al and Ga) with 20 [71]. On the other hand, the range of values for found in Ba24Si100 is slightly higher than the one observed in some other cagebased materials where anharmonicity is assumed to play an important role in the thermal conduction such as in type-I Ba8Ga16Ge30 ( = 0.014) [51], in Cs-osmate pyrochlore ( = 0.025) [69] and in the skutterudite YbFe4Sb12 ( = 0.013) [72]. Thus, if Ba24Si100 can be considered mostly as being harmonic, the anharmonic term of the BaIX(12d) potential is higher than the one of the BaI(6d) potential. This corroborates with the deviation of the ab initio potentials from the quadratic behavior observed for BaIX(12d) and not for BaI (6d), see Fig. 2. As another consequence of the anharmonicity the phonon energies found in experiment at the base temperature are closer to the computed DFT results than the ones observed at room temperature. The harmonic energies, E2 = (K2/M) 1/2 , as well as the anharmonicity parameters, , can be simply estimated from polynomial fits to the ab initio Ba potentials. Along the (100) direction in Ba24Si100, an harmonic energy of 3.3 meV is obtained for BaIX(12d) which matches very well with the peak energy in the directional phonon p-DOS (see Fig. 6 b)). This agreement is another signature of the localized character of the BaIX(12d)-weighted phonons. The values of as extracted from the ab initio BaIX(12d) potential lies in the 0.013-0.014 range depending on the direction which is very close to that obtained experimentally. It is then interesting to notice that, in the case of Ba24Si100, the quartic term can be extracted from the calculated potentials in the harmonic approximation.

On the other hand, in Ba8Si46, an harmonic energy of 6.3 meV is extracted from the BaI(6c) potential along the [100] direction while, in the phonon DOS, the corresponding peak is located at about 7.3 meV (see Fig S-10 in [50]). This difference indicates that BaI(6d)-weighted modes are more extended in the crystal than the BaIX(12d)-weighted modes. For Ba sites in Ba8Si46, the value of  extracted from the ab initio potentials are smaller by a factor of 2 to 3 than in Ba24Si100 which is in agreement with the absence of a temperature effect on the Ba-weighted phonon energies as seen by INS [16] and discussed previously.

CONCLUSION

This work reveals that the phonon spectrum in the binary Ba24Si100 (type-IX clathrate) contains Baweighted modes at significantly lower energies than those found in the binary Ba8Si46 (type-I clathrate).

The energy downshift of the low-energy optical spectrum is ascribed to the difference in the cage In both clathrates, the low-lying Ba-weighted modes result in flat optical bands, which are responsible for a strong bending of the acoustic (transverse and longitudinal) branches and limit their dispersions towards higher energies. In the type-IX clathrate, the BaIX(12d)-weighted phonon band spreads out in the 2.5-4 meV range while, in the type I, the BaI(6c)-weighted band is located at higher energies between 7-9 meV. The available energy range for acoustic phonon states in Ba24Si100 is then shrunk by almost a factor two in comparison to Ba8Si46, which necessarily impacts on the thermal conduction. Indeed, in type-I clathrate, the thermal conductivity is found to depend linearly on the energy of the low-lying guest optical phonon E [23]. From the phonon dispersion curves, we have calculated the sound velocity vS of both type-I Ba8Si46 and type-IX Ba24Si100 (see the supplemental material for the details) [50, 73,74].

In the case of type-I Ba8Si46 and type-IX Ba24Si100, the product E.vS is equal to 26 eV/ms and 12.5 eV/ms, respectively. If we consider the scaling relation found by Ikeda et al [23], this means that the thermal conductivity in the type-IX clathrate is expected to be two times lower than in type-I clathrate, i. e. about 1 W.m -1 .K -1 , which corresponds to an increase in the thermoelectric figure of merit by a factor two.

[

  100] and [010] in type-I clathrate and [100] and [001] in type-IX clathrate, respectively. We report the E of Si atoms in type-IX clathrate in the Supplemental Material [50]. Polynomial fits, ΔE(x) = K2x 2

2

 2

  (d)), to 3.825 Å along the [100] six-fold symmetry axis. The inplane BaI(6d) potential is the smoothest with the lowest K2. As a result, optical phonon branches weighted by in-plane BaI(6d) modes have the lowest energies[51][52][53]. In Ba24Si100, the smallest K2 is found for the out-of-plane BaIX(12d) potential in the Si20 open cage (along the [100] twofold symmetry axis and parallel to the bc plane in the inset of the Fig.2 (c)). Its value is about three times lower than the one of the in-plane BaI(6d) potential Moreover, the Ba motion within the Si20 open cage, with BaIX(12d)-Si distance varying from 3.27 Å to 4.222 Å, is more anisotropic than in the Si24 cage. The largest cage dimension is along the twofold axis, i.e. in the direction of the smoothest K2. This anisotropy difference is best visible when comparing guest potentials along and perpendicular to the high symmetry axes (parallel to the [100] direction) in the open Si20 and Si24 cages as shown in Fig.

  ab initio calculations of the ADPs for the different Ba sites corroborate qualitatively these experimental findings (see Supplemental Material)[50]. The highest ADP value obtained for BaIX(12d), of about 0.03 Å 2 , is almost two times larger than the one obtained for BaI(6d), of about 0.017 Å 2 . The in-plane versus out-of-plane anisotropy of the Ba potential in the Si24 and Si20 cages is also clearly visible in the ab initio derived ADPs shown in Fig.2 c) and d), respectively. The large anisotropy of the ADPs for BaIX(12d) has been already reported experimentally in the type-IX clathrates Ba24Ge100[35,[55][56][57][58] as well as for KIX(12d) in K24Sn100[59]. Its origin is intrinsic to the asymmetric shape of the open X20 cages[60]. On the other hand, the ab initio computed ADPs are almost isotropic for BaIX(8c) and BaIX(4b) in Ba24Si100 and for BaI(2a) in Ba8Si46 in agreement with experiments (see Supplemental Material) [50]. The dynamical structure factor, S(), recorded at 280 K in Ba24Si100 by means of neutron time-of-flight (TOF) spectroscopy (see Experimental and computational details) and the generalized density of states (GDOS, G exp ()), which can be computed from S() [50], are shown in Fig. 3 a) and b) only in the lowenergy range from 0 to 12 meV. The higher energy range is shown in the Supplemental Material [50].

  7 and 4 meV at the Г point. The E1,2,3 optical bands are mostly dominated by BaIX(12d) vibrations in the open Si20 cages as seen in the phonon p-DOS in Fig. 6 a). The lowest-lying optical branch corresponds to out-of-plane vibrations of the BaIX(12d), i.e. along the 2-fold symmetry axis, in open Si20 cages as evidenced in the directional partial PDOS, whereas the in-plane

  geometry and size. The low-lying optical phonons in Ba24Si100 are associated with Ba motions in the open Si20 cage (site 12d) along the twofold axis while, in Ba8Si46, they mostly correspond to Ba motions in the Si24 cages (site 6d). Both open Si20 and Si24 cages are anisotropic with the softest Ba potentials in the direction where the Ba-Si distances are the highest. The guest potential in the open Si20 cage appears much more anisotropic than the one in the Si24 cage. Moreover, the calculated BaIX (12d) potential in the open Si20 cage exhibits an anharmonicity significantly more pronounced that the one of the BaI(6d) in the Si24 cage. It corroborates with the experimental finding of a detectable softening of the BaIX(12d)weighted optical phonon energies upon cooling while no temperature change is identified for the energies of BaI(6d)-weighted optical phonons Ab initio calculations in the harmonic approximation show that the BaIX(12d)-weighted modes are characterized by very low values of their PR going down to 0.0365, lower than the PR values in Ba8Si46 and almost similar to the PR of localized modes in disordered systems. Such low values of the PR, obtained in the harmonic calculations, reveal that the associated eigenstates involve only few atoms with non-zero amplitudes in the unit cell. This is corroborated by the fact that the BaIX(12d)-weighted mode energies are very close to the harmonic energies deduced from the quadratic terms of the ab initio potential.

Figure 1 : 2 Å 3 )

 123 Figure 1: Crystal structures of type-I clathrate Ba8Si46 (a) and of type-IX clathrate Ba24Si100 (b) plotted

Figure 2 :

 2 Figure 2: (Left column) Ab initio calculated atomic potential E vs x displacement of the Ba atoms in

Figure 3 :

 3 Figure 3: Inelastic response of the type-IX clathrate Ba24Si100 measured by INS in the low-energy range

Figure 4 :

 4 Figure 4: (a) Temperature dependence of G exp (,T)/E 2 of Ba24Si100. Temperatures are listed in the figure.

  Right and left sides correspond to the Stokes and anti-Stokes lines, respectively. Arrows are guides for the eye indicating the peak shift upon cooling. (b) Temperature dependence of the peak energies identified and fitted in G exp (,T)/E 2 . Lines correspond to calculations with the DUM[68] characterizing the anharmonicity of the fitted peaks by a dimensionless parameter  whose value is 0.015 for dashed lines and 0.025 for dotted lines.

Figure 5 :

 5 Figure 5: Phonon dispersion curves (a), phonon density of states (PDOS) (b) and phonon participation

Figure 6 :

 6 Figure 6: (a) Partial phonon density of states (PDOS) for the different Ba atoms and for all the Si atoms

Figure 7 :

 7 Figure 7: Total and partial heat capacity Cv(T) derived from DFT calculations plotted in a Debye plot C/T 3 vs T and compared to experimental data Cp(T) [16] for Ba24Si100 (a) and Ba8Si46 (b).

Figures

  Figures

Table 1 :

 1 Characteristic energy and potential parameters of Ba guests in type-IX (top) and type-I (bottom) Ba-Si clathrates derived from DFT results. K2, K3, and K4 are harmonic and anharmonic potential parameters from the fitting of Ba potentials with the polynomial function y = K2x 2 + K3x 3 + K4x 4 .E2 corresponds to the characteristic energy calculated from K2, and the dimensionless anharmonic parameter  is computed from the quartic force constant K4 according to the DUM[68].

	Tables

Table 1

 1

Acknowledgements

SP and RV acknowledge support from the French National Research Agency (ANR-13-PRGE-0004) and the Lyon IDEX Scientific Breakthrough program for funding of the project IPPON. We acknowledge the Institut Laue Langevin (ILL) for beam-time and computation resources. RV acknowledges the ILL for its financial support for several stays at the ILL. RV and PT acknowledge C. Godart from ICMPE in Thiais for the preparation of the BaSi2 precursor and C. Goujon and M. Legendre from CNRS Grenoble for their help in the HP-HT synthesis of the samples studied here by INS. RV acknowledges P. Hermet for the program of calculations of participation ratio.


Rémy Roca
email: remy.roca@legos.obs-mip.fr

Estimation of extreme daily precipitation thermodynamic scaling using gridded satellite precipitation products over tropical land

Keywords: extreme precipitation, tropics, satellite observations

This study explores the tropical land distribution of precipitation and its extremes focusing on the daily 1°×1°scale. A common period of 5-year over the tropical belt (30°s-30°n) corresponding to more than 39 million data points, is used to highlight the robust (and non-robust) observed features. A set of 10 observational products is analyzed ranging from satellite only to rain gauges only products and various blended intermediates as well as a sub ensemble of satellite-based products relying upon microwave observations. Overall, the various datasets show a small diversity of response as far as tropical land mean precipitation is concerned. When sorted by surface temperature, the spread in mean rainfall is also well below 10% over a large span of the surface temperature regime. The consistency between the surface temperature and the extreme precipitation is further investigated by computing the thermodynamic scaling of daily precipitation extreme with surface temperature. The wet days' 99.9th and 99th percentiles are considered and corresponds to 'extreme' extremes (∼110 mm d -1 ) and 'moderate' extremes (∼60 mm d -1 ), respectively. The analysis reveals three regimes over the 287-305 K 2 m temperature range. In the cold regime, 287-293 K, extremes exhibit no dependence to surface temperature while in the warm regime, 299-305 K, the extremes decrease with temperature as identified in previous studies. Over the 293-299 K regime, the scaling of the sub ensemble of satellite products is ∼5.2 K/% for the 'extremes' extremes and 5.0% for the 'moderate' extremes, and is robust throughout the sub ensemble. This analysis fills the regional gap of previous conventional data based studies and further confirms the Clausius-Clapeyron theoretical expectation for the tropical land regions.

Introduction

Global energy budget considerations provide a strong constraint of global precipitation owing to the coupling between energy and water budgets and offer a physically sound theoretical pathway to explore the future evolution of precipitation under climate warming through changes of the atmospheric water vapor content (Ramanathan 1981). Thermodynamics indeed dictates an increase of the atmospheric water vapor content under warming at a rate of 6%-7%/K which translates in a 2%-3%/K increase in global mean precipitation via the induced radiative cooling closure enforcement of the water and energy budget (Stephens and Ellis 2008). This thermodynamically constrained alteration of the atmospheric water vapor also has consequence on local precipitation events and a moister atmosphere is expected to yield stronger local precipitation (Trenberth 2011 and reference therein). The scaling of the high rainfall percentiles to surface temperature as depicted by the conventional observations (rain gauges), have been extensively used to explore the recent evolution of the precipitation extremes over land and its associated scaling with temperature (e.g. Westra et al 2013). Extreme precipitation from the gauges have further been shown to well agree with theoretical expectations and climate models results at least in the mid-latitudes (Fischer and Knutti 2016). Indeed, these observations are by essence mainly concentrated over data rich areas of the globe, leaving an unsatisfactory appraisal of the evolution of intense rainfall over conventional data poor regions like the tropical land regions [START_REF] Becker | A description of the global land-surface precipitation data products of the global precipitation climatology centre with sample applications including centennial (trend) analysis from 1901-present[END_REF], Kidd et al 2017, Taylor et al 2017). The lack of data yields to a series of non-robust results about the scaling of daily extreme precipitation to temperature in the tropics (Utsumi et al 2011, [START_REF] Eiji | Decreasing precipitation extremes at higher temperatures in tropical regions[END_REF], Vittal et al 2016[START_REF] Bao | The robust relationship between extreme precipitation and convective organization in idealized numerical modeling simulations[END_REF][START_REF] Barbero | Temperature-extreme precipitation scaling: a two-way causality[END_REF], Wang et al 2017[START_REF] Ali | Global observational evidence of strong linkage between dew point temperature and precipitation extremes[END_REF]. A large number of multisource gridded precipitation products, including multiple satellites observations and microwave constellation-based products, has emerged in the recent decade (Levizzani et al 2018) that could help to alleviate this regional gap and clarify the observational relationship between precipitation extremes and surface temperature in the tropics. At daily scale satellite gridded products indeed exhibit significant skills at documenting meteorological variability in the tropics (Roca et al 2010, Gosset et al 2013, Guilloteau et al 2016), if not for the documentation of the extremes, and are characterized by improvements of the recent generation of products over the previous ones (Maggioni et al 2016, [START_REF] Beck | Global-scale evaluation of 22 precipitation datasets using gauge observations and hydrological modeling[END_REF]. Despite the importance of the local scaling at daily scale, studies addressing tropical landwide statistics using gridded data based are not numerous with the exception of (Wasko et al 2016) for which a single gridded product is used that suggests the satellite observations are offering an alternative to stations based estimates.

The scaling of extreme precipitation to surface temperature can be derived from physical considerations. Precipitation at the surface results from the condensation of water vapor in the atmosphere and subsequent fall out to the ground. The net condensation rate of the atmosphere is indeed the outcome of the complex interplay between the thermodynamic profiles of the column, the intensity of convection, the cloud and rain microphysics and in particular to the tropics, the mesoscale dynamics of the cloud system (e.g. Roca et al 2017). Despites this complexity, in the tropics, following atmosphere dry static energy budget considerations and focusing on extreme conditions, extreme precipitation rate (P e ) can be expressed (O'Gorman and Schneider 2009) as

P dq dp , 1 e e s *  w = - q ⎪ ⎪ ⎪ ⎪ ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ ( )
where ω ε is the vertical velocity in pressure coordinates, q s the specific humidity at saturation at constant equivalent potential temperature (θ * ) and ε is the measure of the precipitation efficiency related to the microphysics of the rain and the {.} sign indicates the vertical averaging operator. At daily scales, the sensitivity of P e to efficiency can be neglected (Singh and O'Gorman 2014) and the physical scaling (1) further simplifies to a dynamical and a thermodynamical contributions. For tropical conditions, idealized cloud resolving model simulations suggest a weak dynamical response to large perturbations of surface temperature The near surface air saturation humidity is a function of temperature alone and pressure and equation (2) simply states that the fractional change of extreme precipitation scales with near surface air temperature at the rate of change of the Clausius-Clapeyron law with near surface air temperature. Under typical tropical conditions, this thermodynamic scaling is close to 6%-7%/K (Trenberth et al 2003). Therefore, near surface temperature is used to assess the scaling within the gridded precipitation products. By essence, the physical scaling hence is valid under assumptions that restrict its use to the regime for which surface humidity increases with surface temperature. Indeed, at the warm end of the range of surface air temperature (like Sahara) rain rarely occurs. Hence, it should be considered that the near air temperature is only a proxy for near surface air humidity at saturation and the range of meaning of the physical scaling is further discussed below. The estimation of the physical scaling does not need to reflect the time evolution of the extreme precipitation under recent climate change. The physical scaling is a way to 'map' the precipitation distribution over regimes of surface air temperature (rather than geographical locations) that further links the precipitation to its local environment. Such physical scaling is not to be misinterpreted or compared with other proposed scaling in the literature based on co-variability of precipitation extremes with various surface temperature indicators ranging from globally averaged surface temperature, global ocean surface mean temperature or regional composite of temperature (Westra and Sisson 2011, Liu et al 2012). The estimated thermodynamic scaling of precipitation extreme with surface temperature for the current climate should nevertheless be used with caution to discuss the evolution of extreme events with future climate change. Indeed, unaccounted for chan- The main objective of this paper is hence to fill the regional gap over the tropical land using a large set (and a sub set) of gridded products and to investigate the robust and non-robust features among the products for various metrics of the tropical precipitation distribution and its extremes. A secondary aim of this paper is to explore the ability of the gridded products to provide a robust (or not) perspective on the thermodynamic scaling of precipitation extremes to the surface temperature over the tropical land in the current climate.

To simplify the reading of the letter, the description of the full products ensemble and the rationale for selecting a subset ensemble are discussed in the supplementary material data section. Similarly, the methodological aspects of the scaling computation are detailed in the Supplementary Material Methods section. The analysis of the full distribution of dailyaccumulated precipitation is presented next. Section 3 is devoted to the results of the scaling and the papers ends with a conclusion/discussion section.

The tropical land precipitation distribution

2.1. The tropical precipitation distribution over land Mean conditional precipitation, i.e. mean precipitation when precipitation is greater than 1 mm -1 , over tropical land is remarkably consistent among the various products (table 1) with a mean value of 9.8 mm d -1 +-10% for the entire ensemble. The sub-ensemble products exhibit the same average value with even less spread among the products (3%). The occurrence of daily accumulated precipitation at 1°×1°over tropical land for the 2012-2016 period spans 5-6 order of magnitude over the 0-275 mm d -1 range for each product (figure 1 top). All the products share a similar shape for the distribution. Above 25 mm d -1 , the GPCC product occurrence is systematically higher than all the other products while the PERSIANN record shows the lowest occurrence systematically.

While the mean value is very robust among the products, the distribution is not. We note that here the distribution is explored up to 275 mm d -1 which correspond to very heavy rain accumulation. The relationship between the tropical wide rainfall accumulation and the percentiles of the distribution is presented in figure S1 is available online at stacks.iop. org/ERL/14/095009/mmedia.

The spread among the whole ensemble of products increases with the daily accumulated precipitation amount (figure 1 bottom) from 10%-25% up to 50 mm d -1 (∼99th percentile), and asymptotes around 100% from 100 mm d -1 (∼99.9th) and above. The spread is considerably less when the sub-ensemble of satellite-based products that includes microwave observations is concerned. Up to 75 mm d -1 , the spread is below 10%. Above 75 mm d -1 , the normalized standard deviation increases log-linearly with the daily-accumulated precipitation at 25% for 150 mm d -1 (∼99.99th) and up to 50% at 200 mm d -1 (∼99.999th) and just below 100% at the end of the distribution.

The tropical precipitation distribution sorted by surface temperature over land

When daily-accumulated precipitation is sorted with respect to 2 m temperature regimes, the contribution to the total precipitation peaks around 298 K at a value of ∼18% for all of the products (figure 2 top). The distribution from the coldest and the warmest regimes are very similar across the products. The spread among the various products is very small (figure 2 bottom), less than 10% up to 303 K and there is hardly any difference between the ensemble mean distribution and the one from the sub ensemble. This very robust feature of the gridded products can also be interpreted in terms of the various products having a similar geographical distribution of the precipitation. This is expected to some extent, at least for the sub-ensemble, since the products share some of the raw satellite observations. Compared to the ensemble members, the CHIRPS product appears to overestimate slightly the contribution to total rainfall up to 297 K where it peaks and then shows underestimations in the warmer regime. The TAPEER dataset reveals a distribution close to the ensemble mean but with a slightly underestimated maximum contribution at 299 K. 3. The scaling of the extreme of tropical precipitation with surface temperature

The extremes are characterized via the upper wet day percentiles of the distribution for various surface temperature bins (see Supplementary materials: method section). 'Extreme' extremes and the 'moderate' extremes are defined by the 99.9th and the 99th percentile, respectively. The magnitude of these percentiles are ∼110 and ∼60 mm d -1 (figure 3). The use of other metrics or indices to qualify the extremes can limit the considered magnitude of the range of precipitation. For instance, the quasi-global analysis of (Herold et al 2017) relies upon the Rx1day index to characterize the 'extreme' extremes which ranges, at the 1°×1°daily scale, between 35 and 50 mm d -1 depending upon the product, much less than the magnitude considered here. Note that statistics for the 90th percentiles are also reported although the intensity under considerations (∼25 mm d -1 ) is generally not associated with the notion of an extremely intense rain event.

The relationship between the extremes of precipitation and the surface temperature for all of the individual products, the entire and the sub ensemble are presented in figures S2, S3 and S4 for the 99.9th, the 99th and the 90th percentiles, respectively. Figure 3 summarizes the results for the 99.9th and the 99th percentiles for the mean of the sub ensemble of products. A spread around 20% for 99.9th and 99th percentiles, and around 15% for the 90th percentile characterize the distribution of the extremes. When the sub ensemble is considered, the spread is reduced significantly around 5% or less over a large part of the temperature range under considerations. For the three percentiles values and for most of the products, the extreme exhibits a 'peak' structure in agreement with previous findings based on rain gauges' data (Hardwick Jones et al 2010), reanalysis or climate models (Wang et al 2017). The peak is observed around 299-300 K. For most of the products, the 90th percentiles distribution (figure S4) shows two regimes with temperature, increasing up to the peak and decreasing for higher temperature; a feature already identified in various previous studies. On the other hand, for the 99.9th and the 99th percentiles, three temperature regimes can be distinguished for most of the products and for the product ensemble and sub ensemble means that differs from point gauges analysis (Westra et al 2014) and are detailed next.

The 'cold' regime (287 K<t2m<293 K)

This regime corresponds to ∼6% of the total precipitation (figure 2). In this regime, the extreme precipitation (both at the 99.9th and 99th percentiles) shows little to no variations with surface temperature. At the 99.9th percentile, the ensemble mean value is around 90 mm d -1 with a 16% spread among the products. The sub ensemble is characterized by the same mean value and a 8% average spread over the regime. Similar behavior of the products is found at the 99th percentile, with a mean value of 49 mm d -1 and an ensemble (sub ensemble) spread of 13% (6%). Unlike the other products, the GPCC estimate expresses an increase of the two extreme percentile values with temperature within this regime.

The 'warm' regime (299 K<t2m <305 K)

This corresponds to ∼17% of the total precipitation (figure 2). This regime is characterized by an overall decrease of the extreme precipitation with temperature attributed to the limited supply of moisture over these arid land regions (Westra et al 2014). For this regime, the more complex relationship between surface temperature, surface humidity and column humidity could also explain the negative scaling of the extreme precipitation (Roderick et al 2019). It is also important to note that this regime could be driven not only by thermodynamics but also by changes in the dynamics of the storms, with increasing surface temperature. While this negative scaling was explored with rain gauges data in the literature, it is well reproduced by the gridded products. The spread among the products of the ensemble is larger than for the previous regime especially at the warm end of the range for which very low sample is available (figure 2). 3.3. The 'Clausius-Clapeyron' regime (293 Kt2m 299 K) This regime accounts for ∼73% of the total precipitation (figure 2) and is characterized by an overall increase of the extreme precipitation with temperature across the regime. The spread among the products for the entire ensemble spans the 15%-25% range for all the three percentiles. The GPCC and PERSIANN products provides the highest and the lowest percentile values, respectively for the three cases contributing to the relative large spread of the whole ensemble. On the other hand, the sub ensemble again shows strong consistency with a small spread of 4%, 3% and 3% for the 99.9th, 99th and 90th percentiles. As discussed in the Introduction, theoretical considerations suggest that the rate of increase of the extreme precipitation in this regime is close to Clausius-Clapeyron that is 6%-7%/K. The slope of the regression (see Method in supplementary material) has been computed for each product for the 99.9th, 99th and 90th percentiles (table S2). The highest estimate is 6.2%/K for GSMArtg and the lowest 0.5%/K for GPCC. The entire ensemble mean slope is around ∼3%-4%/K for each percentiles values with a spread between 25% and 75%. When the sub ensemble is concerned, the 90th percentile scaling is 4.7%±17%. For the 99.9th and the 99th percentiles the spread among the products is reduced to ∼20% compared to the entire ensemble and the mean value of the slope is 5.2%/K. When the 299 K upper bound is changed to 300 or 298 K, the mean value of the slope becomes 4.7%/K or 5.6%/K showing little sensitivity to the precise location of the peak. Changing the lower bound to 292 K yields to a slightly lower 4.4%/K value also indicating the robustness of the 'Clausius-Clapeyron' regime for the sub ensemble of products.

Conclusions and discussion

Mean conditional precipitation (mean precipitation when precipitation is greater than 1 mm d -1 ) is very consistent among the various products over the tropical land in agreement with previous analysis at a quasi-global scale (Herold et al 2017). The sub ensemble is significantly more robust than the entire ensemble. On the other hand, the full precipitation distribution, while looking alike within the ensemble members, can exhibit significant variance among the products, in particular at the high end of the precipitation spectrum. Sub setting the ensemble to a restricted selection of satellite products that includes microwave observations from a constellation of satellites partly mitigate this issue. In particular, up to 75 mm d -1 , the spread among the sub ensemble members is less than 10%. When sorted by surface temperature, the ensemble of gridded precipitation observations reveals a mean conditional precipitation distribution with a relatively small spread of the values well below 10% over a large span of the surface temperature regime. According to this metric, both the entire and the sub ensembles exhibit the same level of robustness.

The distribution of 'extreme' (∼110 mm d -1 ) and 'moderate' (∼60 mm d -1 ) extremes sorted by surface temperature regime again reveals a robust behavior among the products, in particular for the sub ensemble that is characterized by less than ∼10% relative spread in the highest percentile all through the considered surface temperature range from 287 to 305 K. Within that range, three distinct regimes are found in most of the product and in both the ensemble means that exhibit only a slight sensitivity to the percentile considered to delineate the temperature range of each regimes. The cold regime extends from 287 to 293 K, the increasing regime spans 293-299 K and the decreasing regime is found over the warmest region from 299 to 305 K. Our results confirm previous elaboration about the decreasing regime after a peak temperature (Westra et al 2014). In our case, for the tropical land as a whole, a robust peak is observed around 299-300 K which is warmer than previous tropical rain gauges based analysis (Hardwick Jones et al 2010) although the difference between local observations and 1°×1°area averaged 2 m temperature analysis could explain this warm shift. Our analysis further indicates that a 'flat' regime characterizes the 'extreme' and 'moderate' extremes at the cold end of the temperature spectrum. From 287 to 293 K indeed the extremes show no dependence to surface temperature. Note also that for the 90th percentile, no such flat regime is observed; the range of value of this low percentile follow a bell shaped distribution. While the decreasing regime has been associated to limited humidity supply, the reasons for the flat regime are not clear. The 287-293 K regions could be related to orography or some seasonal features over tropical land areas that contribute to a steady value of the extreme, although high (∼90 mm d -1 for the 'extreme' extremes case), over that range of surface temperature conditions. This new result warrants further investigation of these large daily rainfall accumulation extremes on the cold end of the spectrum.

In between these two regimes, across the 'increasing' regime, from 293 to 299 K, the scaling of the extreme precipitation to the surface temperature is investigated. For the entire ensemble, the 'extreme' extremes mean scaling is around 3%/K with a 75% spread within the ensemble. For the moderate extremes, the mean value is 3.4%/K respectively and the spread decrease to 45% consistent with the distribution spread variation with precipitation intensity (figure 1). When the sub ensemble is considered, a different perspective emerges with mean value ∼5%/K close to the tropical Clausius-Clapeyron for both the 'extreme' and the 'moderate' extremes. The robustness of the estimates is also better than for the entire ensemble with a relative spread of 19% and 20% for the 99.9th and 99th percentiles. This result are based on a renewed observational set of gridded products, depicted by recent versions of mainly satellite precipitation products and rules out any super-cc scaling for the 1°×1°daily extremes precipitation as well as the earlier proposed negative scaling (Utsumi et al 2011) or lack of scaling (Vittal et al 2016). This analysis further confirms the theoretical expectation (O'Gorman and Schneider 2009) for the tropical regions. As discussed in the Introduction, these results are valid for present climate conditions and should not be straight forwardly extrapolated for future climate conditions as the drivers for climate change in extreme may not be the same as the one acting in the present climate (Li et al 2019).

The three regimes identified here are linking the upper tail of the precipitation distribution to the surface temperature conditions. These are part of a larger scale co-variability of precipitation and temperature (Trenberth and Shea 2005) related to the large scale circulation. The analysis of the spatial and temporal distribution of these regimes and links to largescale circulation shifts requires further studies. It is out of the scope of this Letter to explore these regimes further and it is deferred as a direction for future works.

(

  Muller et al 2011, O'Gorman 2015 its figure 3; Pfahl et al 2017). Considering weak variations in the vertical velocity and further assuming a simple tropical divergence profile, the fractional change in P e scales with fractional change of saturation humidity at the surface (O'Gorman and Schneider 2009) and further reads

  ges in precipitation frequency (Schär et al 2016) or the limited scope of the underlying physical framework to characterize the future evolution of precipitation extremes (Pfahl et al 2017) prevents a straight forward interpretation of the scaling. When carefully interpreted the scaling has nevertheless proven itself as a useful metric to narrow the spread in climate models responses (O'Gorman 2012, Bao et al 2017), to relate past observed variations of precipitation to surface conditions (Westra et al 2014) or to serve as an emerging constraint to climate model ensembles (Allan and Liu 2018). At daily scales, the scaling of high percentile with surface temperature has been vastly used in various previous studies (O'Gorman 2015 and references therein).

Figure 1 .

 1 Figure 1. (Top) Distribution of occurrence of daily 1°×1°accumulated precipitation over the tropical (30°s-30°n) land for the period 2012-2016. The colors correspond to various precipitation datasets listed on the right. (Bottom) the normalized standard deviation of the above distribution across the ensemble of all the products (ENS) and for the sub-set of the ensemble defined in the text (sENS). In the bottom figure, the horizontal dashed gray lines corresponds to the 10%, 25%, 50% and 100% level.

Figure 2 .

 2 Figure 2. (Top) Contribution (in %) to the total accumulated precipitation over the tropical (30°s-30°n) land for the period 2012-2016 as a function of the 2 m daily temperature. The colors correspond to various precipitation datasets listed on the right. (Bottom) the normalized standard deviation of the above distribution across the ensemble of all the products (ENS) and for the subset of the ensemble defined in the text (sENS).

Figure 3 .

 3 Figure3. The value of the 99.9th and 99th percentiles of the 1°× 1°daily-accumulated precipitation over the tropical (30°s-30°n) land for the period 2012-2016 as a function of the 2 m daily temperature for the sub-set of the ensemble defined in the text (sENS). Shading is the standard deviation of the ensemble. The dashed dot gray lines correspond to the Clausius-Clapeyron 6.5%/K rate.

Table 1 .

 1 Conditional mean precipitation (>1 mm d -1 ) for the 2012-2016 period over tropical land. Mean, standard deviation and coefficient of variation (or normalized standard devitation) are also reported for the ensemble of all the products and for the sub-set of the ensemble defined in the text.

	Name	Conditional mean (mm d -1 )
	TAPR	10.0
	TMPA	9.8
	GSMArtg	9.3
	CMORg	9.5
	MSWE	9.7
	GPCPun	10.9
	PERS	8.2
	CHIRg	9.2
	GPCC	11.9
	GPCCfg	9.1
	Ens Mean	9.8
	Ens std	1.0
	Ens cvar (%)	10.6
	sEns Mean	9.7
	sEns std	0.3
	sEns cvar (%)	2.7

Environ. Res. Lett. 14 (2019) 095009

Acknowledgments

This study benefited from the IPSL mesocenter ESPRI facility, which is supported by CNRS, UPMC, Labex L-IPSL, CNES and Ecole Polytechnique. The author acknowledges the CNES and CNRS support under the Megha-Tropiques program. The author thanks an anonymous reviewer and Dr Richard Allan for interesting comments that help improve this letter.

Data availability statement

The data that support the findings of this study are openly available. Precipitation datasets originates from the FROGS database DOI: https://doi.org/ 10.14768/06337394-73A9-407C-9997-0E380DAC5598. The ERA-interim surface temperature can be obtained from ECMWF.


P Tourneur

Fabien Lucas

Cassandre Quinton

Y Olivier
email: yoann.olivier@unamur.be

R Lazzaroni

P Viville
email: pascal.viville@materianova.be

J Cornil

Cyril Poriel
email: cyril.poriel@univ-rennes1.fr

White-light electroluminescence from a layer incorporating a single fully-organic spiro compound with phosphine oxide substituents

come

White-light electroluminescence from a layer incorporating a single fully-organic spiro compound with phosphine oxide substituents

Introduction

Despite the tremendous commercial success of the organic light-emitting diode (OLED) technology, the field is still searching for strategies to build devices incorporating fully-organic emitters together with a small number of layers in order to reduce the production costs. 1,2 On the one hand, the first challenge stems from the need to replace the widely used organometallic complexes due to the toxicity and/or low earth abundance of the metallic centres, such as iridium, platinum, or osmium. 3 Nevertheless, the substitutes should preserve the huge benefit accompanying the use of organometallic dopants, namely the full harvesting of the electron-hole pairs into triplet excitons exploitable for phosphorescence emission thanks to the large spin-orbit coupling provided by the metallic centers, 4 leading to external quantum yields frequently reported above 25% for red, green, and blue emission. [5][6][7][8][9][10] This has stimulated recently a large amount of work dedicated to Thermally Assisted Delayed Fluorescence (TADF). 3,[11][12][13] Here, the key idea is to design fully-organic molecules featuring a small energy gap DE ST (typically below 200 meV) between the lowest singlet and triplet excited state in order to convert by thermal activation the triplet excitons into singlet excitons via a reverse intersystem crossing process (RISC); [14][15][16] the singlet excitons can then decay radiatively with a short lifetime component linked to the intrinsic fluorescence decay (i.e. the prompt fluorescence) and a long-lived component originating from the triplet exciton reconversion (i.e. the delayed fluorescence). A small DE ST is typically achieved by designing molecules with a pronounced charge-transfer character in the lowest excited state, i.e., with a distinct spatial localization of the HOMO and LUMO wavefunctions 3 in order to reduce the exchange energy term.

On the other hand, standard TADF and phosphorescent OLED devices include host-guest systems to reduce the detrimental impact of intermolecular interactions on the solid-state luminescence properties [17][18][19] thus requiring a critical choice of the components to ensure a proper energy level alignment of the electronic levels (HOMO/LUMO) and excited states (S 1 and T 1 ) to transfer the excitons efficiently to guest species. Moreover, the experimental processing conditions should be finely tuned so that the host-guest systems feature a good dispersion of the emitting dopants within the matrix. One strategy reported in the early days of the field to alleviate this drawback is to exploit spiro compounds to limit the impact of intermolecular interactions thanks to their cumbersome 3D shapes. 20 This strategy has also been successfully employed, with the flagship 9,9 0 -spirobifluorene molecule, for the design of ACCEPTED MANUSCRIPT high-triplet-energy host materials for phosphorescent OLEDs. 21,22 Recently, this molecular approach has been adopted with some spiro-based TADF compounds used in a single emissive layer 23 in contrast to many previous works involving spiro-based TADF emitters in a host matrix. [24][25][26] The above considerations have motivated us to explore the potential of single-component layers based on a donor-acceptor spiro compound for light emission in OLED devices. Actually, some of us have recently synthesized a compound matching all requirements, namely the spirophenylacridine-2,7-(diphenylphosphineoxide)-fluorene compound (SPA-F(POPh 2 ) 2 , Fig. 1), which connects via a central spiro carbon an electron-rich phenylacridine unit (acting as electron donor) and an electron-deficient 2,7-bis-(diphenylphosphine oxide)-fluorene, acting as electron acceptor. Note that this compound was initially designed for a completely different purpose, namely as host matrix for green and blue singlelayer phosphorescent OLEDs. 27 In this work, we report a detailed characterization of the unusual absorption and emission properties of this compound both in solution and thin films. The experimental results have been further rationalized with the help of theoretical modelling. Strikingly, when inserted in OLED devices as a single emissive layer, this compound yields a white light emission that we interpret as originating from the contributions of a mixture of emitting intramolecular and intermolecular charge-transfer excited states. This clearly represents a huge benefit in terms of stability and processing compared to white emitting OLED devices typically incorporating several emitters. 28

Results and discussion

We have first explored the electronic and optical properties of this compound by computing its electronic levels and excited states at the (Time-Dependent) Density Functional Theory -(TD)-DFT -level. These calculations have been performed using the hybrid PBE0 functional and a 6-31G** basis set; the TD-DFT calculations have been performed within the Tamm-Dancoff approximation; its validity has been assessed in previous studies. [29][30][31] As expected, the HOMO of the molecule is strongly localized on the acridine group and the LUMO localized on the fluorene group (Fig. 1). The lowest singlet excited state S 1 is calculated at 3.32 eV in the gas phase and is only weakly optically coupled to the ground state (oscillator strength = 0.002); this also holds true for the singlet states from S 2 to S 4 , with oscillator strengths of 0.031, 0.004, and 0.001, respectively. The first singlet state strongly coupled to the ground state is the fifth excited state (S 5 ) lying 0.92 eV above S 1 . The lowest triplet state is computed at 3.15 eV, thus leading to a small DE ST of 0.17 eV. We have also used the detachment/attachment formalism to visualize the electronic density removed in the ground state upon excitation (detachment) and the way it is rearranged in the excited state (attachment). 32 In this framework, the overlap F S between the electron and hole density is a useful parameter to gauge the degree of charge-transfer (CT) character in an excited state; 31,33,34 F S = 1 for a purely localized character (over either the donor or the acceptor part) and 0 for a pure CT excitation. In the case of this spiro compound, F S = 0.99 in T 1 and 0.19 in S 1 (Fig. 1), clearly pointing to the difference in the nature of those two states, which favors efficient reverse intersystem crossing in the TADF mechanism according to El Sayed rules. 35 At the same level theory, the prototypical 2CzPN TADF emitter (see chemical structure in Fig. 9) exhibits a larger S 1 -T 1 splitting (0.34 eV) than SPA-F(POPh 2 ) 2 . The S 1 state of 2CzPN lies about 0.3 eV below the value computed for the spiro compound; a major difference is, however, the large oscillator strength associated to the S 1 state in 2CzPN (0.08 versus 0.002 in SPA-F(POPh 2 ) 2 ). This is readily explained by the fact that the donor and acceptor branches are orthogonal in the spiro compound, thus strongly limiting the electronic coupling between the HOMO and LUMO orbitals mostly involved in the S 0 -S 1 excitation; this coupling is more pronounced in 2CzPN featuring torsion angles around 601 between the donor and acceptor units. The F S value of the S 1 state of 2CzPN amounts to 0.42, thus pointing to a weaker charge-transfer character compared to SPA-F(POPh 2 ) 2 (F S = 0.19).

Fig. 2 displays the absorption spectrum of SPA-F(POPh 2 ) 2 recorded in THF together with the corresponding TD-DFT simulated spectrum; note that the spectrum simulated in gas phase has been shifted rigidly by 0.42 eV to higher energy to best match the most intense experimental absorption bands. The comparison between the experimental and theoretical spectra indicates that the first intense absorption band at 324 nm (3.82 eV) corresponds to S 5 and that the S 1 state is not observed in the spectra due to its very low oscillator strength (as can be understood from its pronounced chargetransfer character and the orthogonality of the donor and acceptor units imposed by the spiro centre). S 5 is an excited state mostly centred over the acceptor part with an F S = 0.73 (Fig. 1). The intramolecular character of S 5 is consistent with its large oscillator strength and F S index, as well as the absence of significant solvatochromic effects (see Fig. S1,ESI †).

The emission properties of SPA-F(POPh 2 ) 2 are extremely unusual. The emission spectrum recorded at room temperature in THF at a concentration of 4.4 Â 10 À5 mol L À1 displays a broad band centred around 490 nm. When the solution is warmed above 40 1C before recording spectra back at room temperature, the absorption spectrum remains unchanged while the emission spectrum exhibits an additional weak and broad band at higher energy, at ca. 400 nm (Fig. 3 and Fig. S2,ESI †). This new band keeps increasing with the heating time (Fig. 3), possibly suggesting that reaching another molecular conformation higher in energy might be required to observe that emission signal. The band systematically persists upon cooling down the solution to room temperature. At higher concentration (above 6.0 Â 10 À5 mol L À1 ), the band at 400 nm is not observed, even at reflux of THF. Although this high-energy band does not play any role in the electroluminescence properties (vide infra), we performed some additional measurements to shed further light on its origin. We also emphasize that 2CzPN does not display such a dual emission both in THF solution and film, see Fig. S3 (ESI †). This is most probably due to the larger electronic coupling between the donor and acceptor moieties ensuring that the system rapidly relaxes down to the S 1 state before emission occurs.

At a concentration of 4.8 Â 10 À5 mol L À1 , the excitation spectrum generated from the emission at 520 nm matches fairly well the shape of the absorption spectrum (Fig. 4, right). The high intensity of the excitation spectrum below 320 nm indicates that most electron-hole pairs photogenerated above

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this energy threshold decay non-radiatively down to S 1 before emission occurs from that state. Strikingly, the excitation spectrum recorded at 385 nm (Fig. 4, left) overlaps poorly with the absorption spectrum and displays actually a high intensity in an energy range below the onset of the first intense absorption band, thus suggesting that the emission occurs from one (or several) excited state(s) lying higher than S 1 . This is further supported by the variations in the emission spectra measured at different excitation wavelengths (Fig. 5): exciting above the energy of the first intense absorption band (o330 nm) favours the emission around 500 nm while excitation at higher wavelength (4330 nm) triggers the emission at 385 nm. Note that chemical degradation can be ruled out as an explanation for the appearance of the emission band at 385 nm because the absorption spectrum is not affected by heating.

The emission at low energy exhibits a significant solvatochromic effect (Fig. S4, ESI †), thus pointing to a strong chargetransfer character, as fully supported by the calculations (Fig. 1). Adding water progressively (from 0 to 38%) to the THF solution previously warmed above 40 1C leads to an increase and a red shift of the low energy emission band (Fig. S5,ESI †), which we associate to an interplay between the formation of aggregates induced by hydrophobic effects and the increase in the medium polarity. In contrast, the band at 385 nm is reduced in intensity but is not shifted, thus pointing to a locally excited character for this band.

The fluorescence decay curve of SPA-F(POPh 2 ) 2 measured in THF at l em = 485 nm (l exc = 310 nm, see Fig. S6,ESI †) is dominated by a long lifetime of 11.5 ns; at l em = 354 nm, the fluorescence decays with a very short lifetime of 2.4 ns. This is once again coherent with the fact that S 1 has a strong chargetransfer character, in contrast to the state(s) at the origin of the emission at 385 nm. Interestingly, the same two emission bands are also observed when recording the spectra under argon (Fig. S7, ESI †); noteworthy, the intensity of the band at 500 nm is significantly increased in the absence of oxygen, thus pointing to the active role of triplet excitons in that band. 36 The quantum yield, using quinine sulfate as reference, is increased from below 1% under air to 4% under argon (see Fig. S7,ESI †). For the sake of comparison, the quantum yield of 2CzPN has been reported at 28% in toluene. 37 This major difference is attributed to the large oscillator strength between S 0 -S 1 in 2CzPN, which makes fluorescence competitive with nonradiative decay channels, in contrast to the situation prevailing for SPA-F(POPh 2 ) 2 .

However, the absence of a long tail extending up to the microsecond timescale in the decay emission profile of the band at 500 nm suggests the absence of a delayed fluorescence mechanism both in air and under argon in the present experimental conditions (see Fig. S5,ESI †). Altogether, we can conclude that the emission at 385 nm competes with the emission from S 1 at 480 nm following a branching ratio extremely sensitive to the excitation wavelength, temperature, time (possibly via conformational effects), and aggregation/concentration effects (possibly via electrostatic effects associated to the polar phosphine groups).

We have next deposited SPA-F(POPh 2 ) 2 on glass both by spin coating at room temperature and by thermal sublimation. Fig. 6 compares the emission spectrum of the compound in solution (concentration below 6.0 Â 10 À5 mol L À1 ) versus the solid state. In these experimental conditions, the two emission bands are observed in solution and in the vacuum-deposited thin films. In contrast, only the low energy band is observed for the spin-coated films, with a slight red shift of 19 nm (0.1 eV) compared to the solution, thus suggesting that the film morphology varies as a function of the processing method. We also typically observe an increased broadening of the main emission band on the low energy side in the solid state. This behaviour can be rationalized by the fact that an intermolecular chargetransfer state between the donor branch of one molecule and the acceptor branch of another (also referred to as exciplex) can significantly contribute to the spectra in the solid state, in addition to the intramolecular charge-transfer state characteristic of the isolated molecules in solution. 38 The large diversity of possible exciplex contact geometries is consistent with the larger spectral width observed in the thin film.

Finally, we have introduced a single layer of SPA-F(POPh 2 ) 2 in bottom-emitting OLED devices. Since the present work does Fig. 4 Excitation (black lines) and absorption (blue lines) spectra of SPA-F(POPh 2 ) 2 in THF. Excitation spectra have been recorded at l em = 385 nm (left) and l em = 520 nm (right) at a concentration of 4.8 Â 10 À5 mol L À1 ; note that we have not measured the excitation spectra at energies corresponding to the maxima of the two emission bands in order to avoid any bias due to their overlap. not aim at optimizing the efficiency of the OLEDs, the devices were fabricated by thermal sublimation in a glovebox in a way inspired by the architecture typically used for the benchmark 2CzPN TADF emitter (see chemical structure in Fig. 9): 11 a layer of 25 nm of a hole-injecting N,N-bis(naphthalen-1-yl)-N,N 0 -bis-(phenyl)-2,2 0 -dimethylbenzidine (a-NPD) compound was deposited on a commercial ITO (indium tin oxide)-covered glass substrate used as the anode, followed by 5 nm of a hole-transporting 1,3bis(N-carbazolyl)benzene (mCP) layer, a 20 nm-thick layer of the SPA-F(POPh 2 ) 2 emitter, 5 nm of bis[2-(diphenylphosphino)phenyl] ether oxide (DPEPO) as electron transport and hole-blocking material, 25 nm of 2,2 0 ,2 00 -(1,3,5-benzinetriyl)-tris(1-phenyl-1-Hbenzimidazole) (TPBi) as electron transport layer. Finally, a very thin layer (1 nm) of lithium fluoride facilitating electron injection and a 100 nm-thick Al layer as the cathode were deposited to complete the stack (Fig. 7). A detailed protocol for the fabrication of the devices is provided in the ESI. † Ultimately, 30 nm of Al 2 O 3 were deposited by Atomic Layer Deposition (ALD) on top of the stack in order to encapsulate the devices prior to measurements of the performances outside the glovebox. We display in Fig. 7 the chemical structures of those compounds, as well as the relative alignment of their frontier electronic levels based on typical values reported in the literature. 39 Strikingly, white light is generated by the OLEDs containing SPA-F(POPh 2 ) 2 , with CIE chromatic coordinates of (0.26; 0.40). The spectral range of the electroluminescence signal is broad (from 400 nm to 750 nm, see blue curve in Fig. 6) and is very similar to that of the low energy photoluminescence signal obtained for thermally sublimed thin films. The electroluminescence spectrum also displays a more pronounced tail on the low energy side, suggesting that the concomitant emission from intramolecular and intermolecular excited states is at the origin of the white light. The electroluminescence signal is vibronically-resolved, in contrast to the photoluminescence spectra (both in solution and in films); this is most probably due to the fact that the injected carriers are thermalized in the emitting layer before they recombine radiatively from the low-energy CT states. Interestingly, the emission at 375 nm is not observed in the electroluminescence signal, as also expected from the fact that the thermalized injected electrons and holes do not recombine into the emitting high-lying excited state(s). Fig. 8 shows the evolution of the electroluminescence spectra as a function of the applied bias and points to the stability of the device at high voltage. At 8 volts, the current density reaches a value close to 200 mA cm À2 (see Fig. 9) while maintaining the shape of electroluminescent signal quite stable.

Finally, we have compared the electrical characteristics of OLEDs made from SPA-F(POPh 2 ) 2 with those obtained for the prototypical 2CzPN TADF blue emitter in a mCP matrix (see chemical structure in Fig. 9). The comparison is here performed with home-made devices fabricated with an architecture similar to that described in ref. 6 (namely a-NPD (30 nm)/mCP:2CzPN (25 nm-10 wt%)/TPBi (70 nm)/LiF (1 nm)/Al (100 nm)). We stress Fig. 6 Photoluminescence spectra of SPA-F(POPh 2 ) 2 in THF (at a concentration of 4.75 Â 10 À5 mol L À1 ) and in films deposited by spincoating or thermal sublimation together with the electroluminescence signal recorded at 7 volts. The photoluminescence spectra have been recorded upon excitation at 310 nm. Fig. 7 Chemical structure of the compounds used in the different layers (a-NPD, mCP, DPEPO and TPBi, respectively) and scheme of the level alignment in the devices, based on typical values reported in the literature. 37 Fig. 8 Electroluminescence spectra recorded at different voltages.

that the device fabrication with 2CzPN was carried out in order to guarantee that the two series of devices under comparison have the same area (0.21 cm 2 ) and operate in the same experimental conditions, without optimization steps.

The devices based on SPA-F(POPh 2 ) 2 show a low turn-on voltage (V ON ) of 4.5 V, very similar to that obtained when using 2CzPN/mCP as emitting layer, with a higher current density (around 160 mA cm À2 in comparison with only 6.5 mA cm À2 for 2CzPN at 7 V). The fact that a much higher current is observed can be linked to the architecture of the SPA-F(POPh 2 ) 2 devices, which only comprise homogeneous layers rather than host-guest structures as in standard devices. The luminance measured at 7 V reaches 270 cd m À2 for SPA-F(POPh 2 ) 2 and is slightly higher than with 2CzPN (260 Cd m À2 at 7 V). The EQE reaches a value at 0.35% at 7 V, which is lower than the EQE obtained with 2CzPN at the same bias (2.9%); note also that the EQE value obtained for 2CzPN is fully consistent with that reported by Adachi and coworkers. 11 These results illustrate a disadvantage of the single-component layer, namely the fact the absence of a guest species strongly reduces the possibility of the charge trapping, and hence their more efficient recombination. There is a clear interest of using a single-component emissive layer for the fabrication of white light-emitting device, although a compromise appears necessary at this stage between the device efficiency and the easiness of device fabrication.

Conclusions

In this work, we unravelled the spectroscopic properties of an organic semi-conductor SPA-F(POPh 2 ) 2 built on the association of an electron-rich (phenylacridine) and an electron-poor (diphenylphosphine oxide fluorene) fragment. In particular, we evidenced a very unusual dual emission, with the relative intensities of the two bands strongly affected by many factors such as the concentration and the

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temperature in solution or the processing method in thin films. Theoretical calculations were further exploited to shed light on the nature of the lowest singlet excited states and to rationalize the spectroscopic measurements. When used as emitter in a singlecomponent layer within an OLED, SPA-F(POPh 2 ) 2 yields surprisingly a white light emission. This behaviour is attributed to the simultaneous occurrence of emission from intramolecular and intermolecular charge-transfer excited states, giving rise to a large distribution of electron-hole separations and hence of chargetransfer state energies at the origin of the spectral broadening in the film. With respect to white-emitting OLEDs typically incorporating several emitters, 28 the present work offers an alternative strategy, which needs to be optimized to ultimately fabricate devices with attractive quantum yield combined with simplified processing.

Fig. 1

 1 Fig. 1 (a) Shape of the HOMO (bottom) and LUMO (top) levels of SPA-F(POPh 2 ) 2 in its ground state geometry, (b) chemical structure of the compound, (c) energies of the lowest singlet and triplet excited states and oscillator strengths associated to the singlet states, (d) plots of the electron detachment/ attachment densities of S 1 , T 1 , and S 5 . These results have been obtained at the (TD-)DFT level with the PBE0 functional and the represented surfaces have been obtained using an isocontour value of 0.02.

Fig. 2

 2 Fig. 2 Experimental absorption spectrum of SPA-F(POPh 2 ) 2 in THF and corresponding TD-DFT simulated spectrum (full width at half maximum set to 0.1 eV).

Fig. 3

 3 Fig. 3 Evolution as a function of heating time of the emission spectrum of SPA-F-(POPh 2 ) 2 in THF at a concentration of 4.4 Â 10 À5 mol L À1 (with an excitation wavelength at 310 nm). The solution is heated at a constant temperature of 50 1C; 10 mL are extracted every 5 minutes and the emission spectra are recorded once the extracted solution has cooled down to room temperature.

Fig. 5

 5 Fig. 5 Emission spectra of SPA-F(POPh 2 ) 2 in THF at a concentration of 4.8 Â 10 À5 mol L À1 , as a function of the excitation wavelength.

Fig. 9

 9 Fig. 9 Structure of 2CzPN (a); luminance and current density curves of SPA-F-(POPh 2 ) 2 and 2CzPN (b and c, respectively); external quantum efficiency calculated from the electroluminescence spectra for SPA-F-(POPh 2 ) 2 and 2CzPN (d and e, respectively).

Acknowledgements

This study benefited from the European Union through the Interreg V initiative France-Wallonie-Vlaanderen -projet LUMI-NOPTEX -and has been supported in Mons by the Belgian National Fund for Scientific Research (FRS-FNRS). Computational resources were provided by the Consortium des E ´quipements de Calcul Intensif (CE ´CI) funded by F. R. S.-FNRS under Grant 2.5020.11. J. C. is an FNRS research director. The authors would like to thank the ANR (no. 19-CE05-0024) and the Region Bretagne (DIADEM project) for PhD grant (Fabien Lucas).

Notes and references

Conflicts of interest

There are no conflicts to declare.