Gauthier Lefevre

Alexander Herfurth

Adlane Sayede

Thomas Wylezich

Sacha Welinski

Jean-François Francois Blach

Pedro Duarte Vaz

Stewart F Parker

Philippe Goldner

Nathalie Kunkel

Holger Kohlmann

Electron-Phonon Coupling in Luminescent Europium-Doped Hydride Perovskites Studied by Luminescence Spectroscopy, Inelastic Neutron Scattering, and First-Principles Calculations

Keywords: Electron-Phonon Coupling in Luminescent Europium-Doped Hydride Perovskites Studied by Luminescence Spectroscopy, Inelastic Neutron Scattering, and First-Principles Calculations

come

■ INTRODUCTION

Rare earth-doped compounds play an important role in many optical applications, such as phosphors and plasma screens, [START_REF] Schnick | Shine a Light with Nitrides[END_REF][START_REF] Justel | New Developments in the Field of Luminescent Materials for Lighting and Displays[END_REF][START_REF] Feldmann | Inorganic Luminescent Materials: 100 Years of Research and Application[END_REF][START_REF] Hoppe | Recent Developments in the Field of Inorganic Phosphors[END_REF] optical fibers and waveguides, [START_REF] Eliseeva | Rare Earths: Jewels for Functional Materials of the Future[END_REF] bioimaging and sensors, [START_REF] Bunzli | Taking Advantage of Luminescent Lanthanide Ions[END_REF][START_REF] Binnemans | Lanthanide-Based Luminescent Hybrid Materials[END_REF][START_REF] Bunzli | Intriguing Aspects of Lanthanide Luminescence[END_REF][START_REF] Muller-Buschbaum | MOF Based Luminescence Tuning and Chemical/Physical Sensing[END_REF] or quantum information technology and spectral filtering. [START_REF] Thiel | Rare-Earth-Doped Materials for Applications in Quantum Information Storage and Signal Processing[END_REF][START_REF] Goldner | Chapter Rare Earth-Doped Crystals for Quantum Information Processing[END_REF][START_REF] Kunkel | Recent Advances in Rare Earth Doped Inorganic Crystalline Materials for Quantum Information Processing[END_REF] Whereas the 4f electrons are so well-shielded by the filled 5s 2 and 5p [START_REF] Bunzli | Taking Advantage of Luminescent Lanthanide Ions[END_REF] shells that the crystalline environment can be considered as a weak perturbation of the free-ion level, [START_REF] Thiel | Rare-Earth-Doped Materials for Applications in Quantum Information Storage and Signal Processing[END_REF][START_REF] Macfarlane | High-Resolution Laser Spectroscopy of Rare-Earth Doped Insulators: a Personal Perspective[END_REF] the 5d electrons of the excited state of 4f-5d transitions of ions such as Eu 2+ , Ce 3+ , or Yb 2+ remain unshielded and can therefore show a large energy dependence of the 5d barycenter and the crystal field splitting on the crystalline environment. [START_REF] Blasse | Luminescent Materials[END_REF] As a result, very different excitation and emission energies are found, for example, for Eu 2+ or Ce 3+ , in different host lattices. [START_REF] Dorenbos | Energy of the First 4f 7 -4f 6 5d Transition of Eu 2+ in Inorganic Compounds[END_REF][START_REF] Dorenbos | Ce 3+ 5d-Centroid Shift and Vacuum Referred 4f-Electron Binding Energies of all Lanthanide Impurities in 150 Different Compounds[END_REF] Additionally, except for rare cases of very high lying 5d levels and emission from, for example, the 6 P 7/2 [START_REF] Ellens | 6 I Emission and Vibronic Transitions of Eu 2+ in KMgF 3[END_REF][START_REF] Meijerink | Spectroscopy and Vibronic Transitions of Divalent Europium in LiBaF 3[END_REF] or the 6 I 7/2 17 state of Eu 2+ , the absorption and emission bands in these compounds are rather broad. For such broad 5d-4f emission spectra, it is, even at low temperatures, rare that a well-resolved vibrational fine structure showing coupling to several modes can be observed because the coupling strength is usually intermediate; that is, the Huang-Rhys parameter S has the value 1 < S < 5. [START_REF] Blasse | Vibronic Transitions in Rare Earth Spectroscopy[END_REF] However, some rare examples exist for Ce 3+ , Pr 3+ , and Tb 3+ with well-resolved spectra that show a coupling to two vibrations in double perovskites. [START_REF] Tanner | Absorption and Emission Spectra of Ce 3+ in Elpasolite Lattices[END_REF][START_REF] Duan | 4f5d Transitions of Tb 3+ in Cs 2 NaYF 6 : The Effect of Distortion of the Excited-State Configuration[END_REF][START_REF] Ning | High-Spin and Low-Spin f-d Transitions of Tb 3+ in Elpasolite Hosts[END_REF] Recently, new types of host materials, ionic hydrides, [START_REF] Kunkel | Alkaline-Earth Metal Hydrides as Novel Host Lattices for Eu II Luminescence[END_REF][START_REF] Kunkel | Bright Yellow and Green Eu(II) Luminescence and Vibronic Fine Structures in LiSrH 3 , LiBaH 3 and Their Corresponding Deuterides[END_REF][START_REF] Kunkel | II) Luminescence in the Perovskite Host Lattices KMgH 3 , NaMgH 3 and Mixed Crystals LiBa x Sr 1-x H 3[END_REF][START_REF] Kunkel | Eu 2+ -Containing Luminescent Perovskite-Type Hydrides Studied by Electron Paramagnetic Resonance[END_REF][START_REF] Kunkel | Thermally Stimulated Luminescence and First-Principle Study of Defect Configurations in the Perovskite-Type Hydrides LiMH 3 :Eu 2+ (M = Sr, Ba) and the Corresponding Deuterides[END_REF] complex hydrides, [START_REF] Marks | Ln(BH 4 ) 2 (THF) 2 ] (Ln = Eu, Yb) -A Highly Luminescent Material. Synthesis, Properties, reactivity, and NMR Studies[END_REF][START_REF] Schouwink | Structure and Properties of Complex Hydride Perovskite Materials[END_REF] and mixed anionic compounds containing hydrides, [START_REF] Kunkel | Variation of the Eu II Emission Wavelength by Substitution of Fluoride by Hydride in Fluorite-Type Compounds EuH x F 2-x (0.20 ≤ x ≤ 0.67)[END_REF][START_REF] Kunkel | Green Luminescence of Divalent Europium in the Hydride Chloride EuHCl[END_REF][START_REF] Kunkel | Ionic Mixed Hydride Fluoride Compounds: Stabilities Predicted by DFT, Synthesis, and Luminescence of Divalent Europium[END_REF][START_REF] Rudolph | Crystal Structure and Luminescence Properties of the First Hydride Oxide Chloride with Divalent Europium: LiEu 2 HOCl 2[END_REF] have been studied as hosts for Eu 2+ luminescence. Here, it was found that replacing less polarizable anions by the polarizable hydride anion can lead to wide shifts of the barycenter of the 5d levels to lower energies. However, besides the interesting properties with regard to the centroid shift and crystal field splitting, hydrides as host lattices can also serve as model systems to study the correlation of the optical properties with lattice phonons. Already in 1980, Judd predicted that vibronic intensities increase with the degree of covalency, [START_REF] Blasse | Vibronic Transitions in Rare Earth Spectroscopy[END_REF][START_REF] Judd | Vibronic Contributions to Ligand-Induced Pseudo-Quadrupole Absorption of Rare Earth Ions[END_REF] which is directly connected to the anion polarizability. Thus, ideal candidates for such studies are compounds with polarizable anions, such as nitrides or hydrides. Moreover, the replacement of [START_REF] Schnick | Shine a Light with Nitrides[END_REF] H by [START_REF] Justel | New Developments in the Field of Luminescent Materials for Lighting and Displays[END_REF] D is an elegant tool for such studies. Knowledge on the relation between lattice phonons and electronic transitions is of great importance because phonons can have a large influence on the optical properties, such as line widths, luminescence quenching, or the efficiency of upconversion processes. [START_REF] Mccumber | Linewidth and Temperature Shift of the R Lines in Ruby[END_REF][START_REF] Equall | Homogeneous Broadening and Hyperfine Structure of Optical Transitions in Pr 3+ :Y 2 SiO 5[END_REF][START_REF] Dorenbos | Thermal Quenching of Eu 2+ 5d-4f Luminescence in Inorganic Compounds[END_REF][START_REF] Ueda | Insight Into the Thermal Quenching Mechanism for Y 3 Al 5 O 12 :Ce 3+ Through Thermoluminescence Excitation Spectroscopy[END_REF][START_REF]From Theory to Applications[END_REF] Here, we present a case study of LiMH 3 and LiMD 3 (M = Sr and Ba), which crystallize in the inverse cubic perovskite structure type in the space group Pm3̅ m (see Figure 1). [START_REF] Kunkel | Bright Yellow and Green Eu(II) Luminescence and Vibronic Fine Structures in LiSrH 3 , LiBaH 3 and Their Corresponding Deuterides[END_REF][START_REF] Greedan | Synthesis and Crystal Growth of SrLiH 3 and EuLiH 3 Ternary Hydrides with the Perovskite Structure[END_REF][START_REF] Messer | Ternary Perovskite Phases in Systems of Lithium Hydride with Barium, Strontium and Calcium Hydrides[END_REF][START_REF] Messer | Systems of Lithium Hydride with Alkaline Earth and Rare Earth Hydrides[END_REF] LiEuH 3 shows the same structure [START_REF] Kohlmann | The Crystal Structure of EuH 2 and EuLiH 3 by Neutron Powder Diffraction[END_REF] with similar lattice parameters as those observed in LiSrH 3 , and we assume that Eu 2+ will occupy the M 2+ site in doped compounds.

The Eu 2+ -doped compounds represent an ideal model system for investigations of the vibrational coupling. In our previous study, [START_REF] Kunkel | Bright Yellow and Green Eu(II) Luminescence and Vibronic Fine Structures in LiSrH 3 , LiBaH 3 and Their Corresponding Deuterides[END_REF] where we reported on the luminescence properties of samples with rather high europium concentrations, we were already able to detect some vibrational fine structure at low temperatures. Here, we use highly diluted samples (europium concentrations of approx. 0.005%) in order to obtain a better resolution of the fine structure. We carried out photoluminescence (PL) measurements on the samples with low europium concentrations as well as inelastic neutron scattering (INS) of the europium-free compounds LiBaH 3 , LiBaD 3 , and LiSrH 3 at 20 K. In an earlier work, we had confirmed the absence of phase transitions down to 10 K. [START_REF] Kunkel | Bright Yellow and Green Eu(II) Luminescence and Vibronic Fine Structures in LiSrH 3 , LiBaH 3 and Their Corresponding Deuterides[END_REF] The obtained results are compared with the phonon dispersion curves and densities of states obtained by first-principles calculations.

■ METHODS

Synthesis. Eu 2+ -doped samples LiMH 3 and LiMD 3 (M = Sr and Ba) for PL measurements were prepared by hydrogenation of the alloys. Alloys were synthesized by melting reactions of the elements (strontium, Alfa Aesar, distilled dendritic pieces 99.8%; europium rod, Alfa Aesar 99.8%,; barium rod, Chempur, 99.3% (rest strontium); and lithium, Alfa Aesar 99.8%; all were mechanically surface-cleaned) in niobium ampoules (at approx. 1100 K, depending on the metals used). In order to obtain low europium concentrations, samples of Sr:Eu with 0.5 mol % were prepared first and then diluted in order to reach the desired concentrations. Then, the alloys were hydrogenated in a hydrogen resistant autoclave (Inconel 718) at approx. 750 K and 100 bar H 2 -pressure for 2-3 days (H 2 Praxair 99.8%, D 2 Praxair 99.8%). These samples contained no or only small amounts of the binary hydrides. Large amounts of europiumfree LiMH 3 and LiMD 3 (M = Sr and Ba) samples for INS experiments were prepared from the binary hydrides (MH 2 had been obtained by hydrogenation of the metal before; starting materials: LiH, abcr, 99.0%; LiD, abcr, 99.4%; barium, Chempur, 99.3%; and strontium, Chempur, 99.0%). The binary hydrides were mixed and heated in a hydrogen resistant autoclave (Inconel 718) at approx. 850 K and 20-40 bar for 2-5 days. Some of these samples contained more than 25% of the binary hydrides (compositions of the samples are given in the Supporting Information, Table S2). As large amounts of samples are needed for INS, the first synthesis approach was not suitable here, and the presence of unreacted binary hydrides could not be avoided completely. Because of moisture sensitivity, all starting materials and products were handled in an argon-filled glovebox.

X-ray Diffraction. Laboratory powder X-ray diffraction (PXRD) data of the samples used for INS were collected on a Huber G670 diffractometer with Guinier geometry at T = 297(2) K with Cu Kα 1 radiation. Laboratory PXRD data of the samples used for PL measurements were collected on a STOE Stadi P powder diffractometer (Stoe & Cie GmbH) with Cu Kα 1 radiation (Ge(111) monochromator) and a Dectris Mythen DCS 1K detector. For both cases, flat transmission samples with Apiezon grease between two Kapton foils were used. Crystal structures were refined using the program TOPAS (TOPAS version 5; Bruker AXS, www.bruker-axs.com). Refined lattice parameters and the amount of residual binary hydride (deuteride) are given in the Supporting Information (Table S2).

PL Measurements. PL spectra were recorded on a setup constructed in-house with a tunable optical parametric oscillator pumped by an Nd:YAG laser (Ekspla NT342B-SH with 6 ns pulse length) as the excitation source, a Jobin-Yvon HR250 monochromator, and a PI-Max ICCD camera for detection. Samples (enclosed in silica tubes of about 5 mm diameter) were placed in a closed-cycle helium cryostat (Janis CTI-Cryogenics Model CCS-150, together with a LakeShore temperature controller) and attached to the sample holder using high purity silver paint and copper sheets. Decay curves were recorded using a Jobin-Yvon HR250 monochromator and a photomultiplier tube.

Inelastic Neutron Scattering. INS experiments were carried out at the high-resolution broad-band spectrometer TOSCA (an indirect geometry time-of-flight spectrometer) [START_REF] Colognesi | TOSCA Neutron Spectrometer: The Final Configuration[END_REF][START_REF] Parker | Recent and Future Developments on TOSCA at ISIS[END_REF] at the ISIS Facility at 20 K. The signal was collected by detector banks in forward and backward scattering, and for data analysis, the arithmetical average of those was used. To minimize the background, short-time high-energy neutrons and the Γ-flash were removed by a NIMONIC chopper. Additionally, the tail cutter of the chopper also removes low-energy neutrons in order to prevent frame overlap. The beam size of the instrument is about 4 × 4 cm 2 . Samples were loaded into indium-wire-sealed, flat-plate aluminum cans in an argon-filled glovebox. Because MH 2 and MD 2 (M = Sr and Ba) were present in the corresponding samples, spectra of the binary hydrides were taken from the literature [START_REF] Barrera | LDA or GGA? A Combined Experimental Inelastic Neutron Scattering and Ab Initio Lattice Dynamics Study of Alkali Metal Hydrides[END_REF][START_REF] Colognesi | Hydrogen Self-Dynamics in Orthorhombic Alkaline Earth Hydrides Through Incoherent Inelastic Neutron Scattering[END_REF] for subtraction or comparison.

Density Functional Calculations. Density functional calculations were carried out using the Vienna Ab initio Simulation Package (VASP) [START_REF] Kresse | Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set[END_REF][START_REF] Kresse | Efficiency of Ab-Initio Total Energy Calculations For Metals and Semiconductors Using Plane-Wave Basis Sets[END_REF][START_REF] Hafner | Ab initio Simulations of Materials Using VASP: Density-Functional Theory and Beyond[END_REF] Version 5.4.1 together with projector augmented wave (PAW). [START_REF] Blochl | Projector-Augmented Wave Method[END_REF][START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF] The Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] was used to evaluate the exchange and correlation energies. PAW potentials with the valence electrons 5s 2 5p 6 6s 2 for Ba and 4s 2 4p 6 5s 2 for Sr atoms were used. In order to guarantee the reliability of the results, an optimization of the cutoff energies as well as the k-point meshes was carried out. For lithium strontium and lithium barium hydride, convergence for the total energy was obtained with a 9 × 9 × 9 Monkhorst-Pack grid centered at the Γ-point, resulting in 35 k-points in the first irreducible Brillouin zone and a plane-wave expansion cutoff of 1000.0 eV. Lattice parameters and atomic positions were optimized by the minimization of the Hellmann-Feynman forces using a quasi-Newton algorithm. Criteria of 10 -6 eV per Å and 10 -9 eV were adopted for the convergence of the total energy and Hellmann-Feynman forces, respectively. All performed calculations were non-spin-polarized because the compounds are known to be nonmagnetic. Phonon dispersion curves were calculated with the PHONOPY code [START_REF] Togo | First Principles Phonon Calculations in Materials Science[END_REF] using the density functional perturbation theory.

■ RESULTS Vibronic Transitions. Theoretical Considerations. Electron-phonon interactions can give rise to vibronic transitions, which are optical transitions that simultaneously show a change in the electronic state and the vibrational state of the system. [START_REF] Blasse | Vibronic Transitions in Rare Earth Spectroscopy[END_REF] For weak electron-phonon interactions, rather sharp lines can be observed, 10 whereas a strong electron-phonon interaction yields broad bands and the influence of phonons also shows a temperature dependence. [START_REF] Mccumber | Linewidth and Temperature Shift of the R Lines in Ruby[END_REF] For a transition between two electronic states Ψ (electronic ground state, n) and Ψ (electronic excited state, n′) with different initial and final vibrational states, the matrix element is given as follows:

μ ⟨Ψ |⃗ |Ψ ⟩ ′ n n (electronic ground state, ) (electronic excited state, ) (1)
with the transition electric dipole operator μ⃗ . [START_REF] Blasse | Vibronic Transitions in Rare Earth Spectroscopy[END_REF] The optical transition can consist of a number of vibronic transitions for the vibrational states n′-n. However, in the present study, we consider the case of low temperature, where we assume that only the lowest vibrational level of the initial electronic state will be occupied. As a consequence, we only need to consider transitions between the vibrational states 0-n. The 0-0 transition is the zero phonon line, ZPL.

A symmetry analysis for the inverse cubic perovskite structure of LiMH 3 (M = Sr, Ba) in the space group type Pm3̅ m (corresponding to the point group O h in Schonflies notation) yields one acoustic mode of the irreducible representation T 1u and four optical modes, [START_REF] Aroyo | Bilbao Crystallographic Server I: Databases and Crystallographic Computing Programs[END_REF][START_REF] Aroyo | Bilbao Crystallographic Server II: Representations of Crystallographic Point Groups and Space Groups[END_REF][START_REF] Hunt | Far-Infrared and Transmittance of Potassium Magnesium Fluoride and Magnesium Fluoride[END_REF][START_REF] Maeland | Ternary Hydrides Possessing the Cubic Perovskite Structure. II. Vibration Spectra by the Inelastic Scattering if Cold Neutrons[END_REF] which are all triply degenerate. Three of the optical modes belong to the IRactive representation T 1u , whereas one mode is hyper-Ramanactive and belongs to the representation T 2u . The representations Γ of the acoustic and optical modes are given by

Γ =T u acoustic 1
(2)

Γ = + T T 3 u u optic 2 1
(3)

Because we can expect Eu 2+ to occupy the strontium or barium site 1b, its surrounding consists of a cuboctahedron and consequently the lowest lying 5d 1 level will be the two-folddegenerate 2 E g state. To determine if an optical transition is electric-dipole-allowed, the matrix element from eq 1 can be evaluated as a product of irreducible representations with μ⃗ transforming as T 1u . [START_REF] Blasse | Vibronic Transitions in Rare Earth Spectroscopy[END_REF][START_REF] Henderson | Optical Spectroscopy of Inorganic Solids[END_REF] Because in our case, the Eu 2+ 4f 7 -5d 1 transition is parity allowed, we can assume that this product contains A 1g :

Γ × ×Γ ⊃ T A [ ] electronic ground state 1u electronic excited state 1g (4)
The matrix element of a vibronic transition that couples with phonons belonging to the representation T 1u corresponds to the product

Γ × × × Γ × T T T [ ] u u u electronic ground state 1 1 electronic excited state 1 (5)
and because

× ⊃ T T A [ ] u u 1 1 1 g (6)
we conclude that the product in eq 5 contains A 1g and therefore the vibronic transition is allowed. If we repeat this procedure for the hyper-Raman mode that belongs to the representation T 2u , we find that a transition involving a coupling of the electronic transition and the hyper-Raman mode belonging to T 2u is forbidden. In the PL spectra of the Eu 2+ -doped perovskites showing the electric dipole 4f 7 ( 8 S 7/2 )-4f 6 5d 1 (e g ) transition, we therefore expect to only observe a coupling of the electronic transition with the IRactive modes of the representation T 1u .

PL Emission Spectra. As already reported in previous results, [START_REF] Kunkel | Bright Yellow and Green Eu(II) Luminescence and Vibronic Fine Structures in LiSrH 3 , LiBaH 3 and Their Corresponding Deuterides[END_REF] for M = Sr, the inverse perovskites LiMH 3 :Eu 2+ and LiMD 3 :Eu 2+ show an intense broad band emission in the yellow region, whereas the barium compounds emit in the green region. Below approximately 80 K, a vibrational fine structure starts to appear, which becomes very well-resolved at low temperatures. Decay times were in the range of those reported in the literature [START_REF] Kunkel | Bright Yellow and Green Eu(II) Luminescence and Vibronic Fine Structures in LiSrH 3 , LiBaH 3 and Their Corresponding Deuterides[END_REF] or slightly longer, which is probably due to the low europium concentrations. In Figure 2, the emission spectra at 20 K under laser excitation at 350 nm are shown. Doped with only 0.005% Eu 2+ , all compounds show more resolved vibrational fine structures than those observed in previous results with higher doping levels, [START_REF] Kunkel | Bright Yellow and Green Eu(II) Luminescence and Vibronic Fine Structures in LiSrH 3 , LiBaH 3 and Their Corresponding Deuterides[END_REF] and the resolution is especially good for M = Sr. As observed before, the vibronic fine structures are more pronounced for the hydrides than for the deuterides. To determine the phonon energies, the energy of the ZPL was subtracted from the spectra. The energies of the vibronic lines are listed in Table 1, and a pictorial assignment is shown for LiSrH 3 :Eu 2+ in Figure 3.

The well-resolved vibronic pattern shows a coupling with at least three vibrations. For LiSrH 3 :Eu 2+ , three lines separated by about 100 cm -1 are repeated at about 370 cm -1 . The 100 cm -1 line is not affected by replacing hydride by deuteride. Upon substitution of hydrogen by deuterium, we expect vibration frequencies to decrease by the square root of the reduced mass ratio, for example, approximately square root of two, if hydrogen or deuterium atoms are strongly involved in these modes. We therefore conclude that mainly the metal atoms contribute to the mode. At approximately 960 cm -1 , another strong line is observed, which shows replicas separated by approximately 100 cm -1 . Additionally, overtones involving further combinations of the modes are found. We have labeled the lines using the notation ν x-y-z , where x, y, and z stand for the number of vibrations involved in the 100 cm -1 (x), 370 cm -1 (y), and 960 cm -1 modes, respectively. On the basis of our considerations regarding the allowed coupling of modes to the electronic transition in section Vibronic Transitions Theoretical Considerations, we assume that the 370 and 960 cm -1 modes belong to the optical T 1u representations. A comparison with vibrational spectra in the literature [START_REF] Maeland | Ternary Hydrides Possessing the Cubic Perovskite Structure. II. Vibration Spectra by the Inelastic Scattering if Cold Neutrons[END_REF] suggests that one additional mode belonging to one of the optical T 1u representations should be found at around 1100 cm -1 . However, in this spectral region, several lines from different overtones coincide so that it is difficult to correctly assign the fourth allowed vibration. Thus, we limited the assignment to the vibrational couplings that we believe can be safely identified. We repeated the assignment for LiSrD 3 :Eu 2+ as well as the barium compounds. In the latter, we refrained from assigning the higher overtones because the spectra are less well-resolved.

Inelastic Neutron Scattering. In contrast to the vibrational coupling in the electronic spectra, no selection rules hold for INS, and INS is also not restricted to the center of the Brillouin zone. Because of the large incoherent neutron scattering cross section of hydrogen, it is an especially powerful tool for studying hydrides. According to ref 60, the incoherent neutron scattering cross sections for 1 H, 2 D, nat Li, nat Sr, and nat Ba are 80.27(6), 2.05(3), 0.92(3), 0.06 (11), and 0.15 (11) barn, respectively. However, because the cross section for 1 H is so much larger than those of the other elements involved, vibrations involving a high degree of hydrogen motion in the spectra will lead to enhanced signals, which can act as an effective selection rule. [START_REF] Maeland | Vibration Spectra of the Orthorhombic Alkaline-Earth Hydrides by the Inelastic Neutron Scattering of Cold Neutrons and Infrared Transmission Measurements[END_REF] Small amounts of 1 H impurities in 2 D 2 might also have a large influence on the spectral properties. Furthermore, in INS, multiple scattering processes (overtones and combinations) involving two or more 1-0 transitions are allowed and may also be observed.

In Figure 4, the INS spectrum of LiSrH 3 is displayed. Because the samples contained SrH 2 (as detected by PXRD; see the Supporting Information), the spectrum of SrH 2 was subtracted from the measured data.

The frequency distribution measured for LiSrH 3 shows vibrational modes at approximately 100, 360, 560, 650, 970, and 1160 cm -1 . The modes at 100, 360, and 970 cm -1 are in very good agreement with the data obtained from the analysis of the vibrational coupling to the Eu 2+ 4f-5d transition and can be assigned to the modes ν 1-0-0 , ν 0-1-0 , and ν 0-0-1 , respectively, where ν 0-1-0 and ν 0-0-1 are optical modes belonging to the representation T 1u . The mode at 560 cm -1 can be assigned to Table 1. Vibronic Transitions in the PL Emission Spectra at 20 K for the Eu 2+ Transition 4f 6 5d 1 -4f 7 ( 8 S 7/2 ) in LiMH a Energies are given with respect to their ZPLs. Assignments in LiSrH 3 were made based on very well-resolved spectra, whereas the spectra for M = Ba are less well-resolved so that larger errors in the correct assignment may be expected. the replica ν 2-1-0 . Furthermore, the mode at 1160 cm -1 is assigned to a further optical mode of the representation T 1u , which cannot be clearly identified in the PL spectrum because of overlaying replicas. Consequently, we assign the mode at 650 cm -1 to the optical mode of the representation T 2u with a hyper-Raman activity, which cannot couple to the electric dipole transition of Eu 2+ . We also studied LiBaH 3 and LiBaD 3 by means of INS (data are given in the Supporting Information, Figure S1). For both compounds, a mode at 90 cm -1 is found, which is in good agreement with the optical spectra. Furthermore, the ν 0-1-0 mode can be assigned at 340 cm -1 for the hydride and 300 cm -1 for the deuteride. For LiBaH 3 , also the ν 0-0-1 is observed at ∼890 cm -1 . However, the quality of the data is not as good as in the case of the strontium compound.

Density Functional Calculations. For further clarifications, we also carried out first-principles calculations using a supercell approach, as described in section MethodsDensity Functional Calculations. The equilibrium lattice constants determined from Birch-Murnaghan fourth-order equation of states and the corresponding mechanical properties (bulk, Shear, and Young's moduli) are summarized in Table 2. The results are in good agreement with experiments and other theoretical work. [START_REF] Ghebouli | First-Principles Study of Structural, Elastic, Electronic and Optical Properties of Perovskite Hydrides XLiH 3 (X = Ba and Sr) Under Pressure[END_REF][START_REF] Yalcin | Investigation of Structural, Mechanical, Electronic, Optical, and Dynamical Properties of Cubic BaLiF 3 , BaLiH 3 , and SrLiH 3[END_REF] Figures 5 and6 show the dispersion and the phonon density of states (phonon DOS) of LiSrH 3 and LiSrD 3 . For both the hydride and the deuteride, a low-energy acoustic branch is observed, which appears at ∼110 cm -1 (0 cm -1 at the Γ-point). This is in good agreement with the mode found in the INS data (100 cm -1 ). At 360 cm -1 , another intense mode can be found in the calculated LiSrH 3 spectra and assigned to the T 1u optical representation. This is also in good agreement with the mode found for the vibrational coupling to the Eu 2+ electronic transition (367 cm -1 ) and the mode found in the INS spectra (360 cm -1 ). In the calculated phonon DOS for the deuteride LiSrD 3 , the agreement with the vibronic coupling of this mode is not as good as in the case of the hydride; the calculated mode at around 310 cm -1 seems to correspond to the ν 0-1-0 mode found at 260 cm -1 in the experimental data. In the calculated spectra, this corresponds to a decrease in energy of about 13% from hydride to deuteride. Further modes can be found at ∼620, ∼730, ∼920, and ∼1160 cm -1 in the calculated spectra of LiSrH 3 . The mode at 620 cm -1 likely corresponds to the mode observed at 650 cm -1 by INS. Modes at 920 and 1160 cm -1 are likely to correspond to the 970 and 1160 cm -1 modes, respectively, found by PL and INS measurements.

Comparison of the calculated spectra of the hydride LiSrH 3 and LiSrD 3 (Figure 7) shows an approximate ratio of 2 for the frequencies of the higher energy modes, which is expected for optical phonons. [START_REF] Kittel | Einfuḧrung in die Festkorperphysik[END_REF] The corresponding phonon distributions and phonon DOSs for the barium compounds are shown in the Supporting Information (Figures S2-S4). Furthermore, the partial phonon DOSs for LiBaH 3 (a), LiBaD 3 (b), LiSrH 3 (c), and LiSrD 3 (d) are shown in Figure 8. As expected, the heavy atoms barium and strontium have their quasi-global contribution to the acoustical region, whereas the contributions of lithium and hydride are found in the optical region. For deuterides, the lithium vibrations seem to be more spread to higher optical phonon frequencies.

■ DISCUSSION

In order to summarize the results obtained by different methods, a comparison of the values and the assignment of the fundamental modes found in the PL spectra, the inelastic neutron spectra, and the density functional calculations are given in Table 3. Whereas the vibrational modes are clearly resolved in the PL spectra for the strontium compounds, the resolutions are less good for the barium compounds. Thus, the assignment of the modes for the barium compounds can be expected to be less exact. As already mentioned in section ResultsPL Emission Spectra, comparison of the vibrations in the different compounds shows that the mode ν 1-0-0 and its replicas do not show any decrease of their frequencies by a factor of 2 upon replacing hydride by deuteride. We explain this observation by the fact that acoustic modes will be less affected by isotope effects than optical modes [START_REF] Kittel | Einfuḧrung in die Festkorperphysik[END_REF] because the isotopic shift will be proportional to the total mass of all ions in the unit cell because they all participate in the mode; thus, deuteration will have a negligible effect on the transition energy. However, there is a significant change in the intensity of the ZPL when hydrides and deuterides are compared. Moreover, the 100 cm -1 mode in the PL spectra seems to correspond to an acoustic mode, even though it is unexpected to observe it in the optical spectra. The nature of these transitions remains unclear. For the higher energy modes ν 0-1-0 , ν 0-0-1 and their replicas, a decrease of the frequencies by a factor of 2 upon replacing hydride by deuteride can be approximately observed. For example, in the optical spectra, we find about 370 cm -1 for ν 0-1-0 in LiSrH 3 :Eu 2+ and only ∼260 cm -1 in the corresponding deuterides. In the optical spectra of the barium compound, the ν 0-1-0 mode can be found at 340 cm -1 for the hydride and ∼270 cm -1 for the deuteride. For the third mode ν 0-0-1 , ∼960 cm -1 is found in LiSrH 3 :Eu 2+ and 690 cm -1 for LiSrD 3 :Eu 2+ . In the barium compound, ν 0-0-1 appears at 890 cm -1 in the hydride and 630 cm -1 in the deuteride. In conclusion, we assign the optical mode in LiSrH 3 at 370 cm -1 , which can also be observed in both INS and PL data, to a Sr-(LiH 3 ) stretching mode (T 1u ) and the mode at 1160 cm -1 , which could only clearly be identified in the INS data, to a Li-H stretching mode (T 1u ). Both assignments are in good agreement with the literature data for cubic perovskites. [START_REF] Hunt | Far-Infrared and Transmittance of Potassium Magnesium Fluoride and Magnesium Fluoride[END_REF][START_REF] Maeland | Ternary Hydrides Possessing the Cubic Perovskite Structure. II. Vibration Spectra by the Inelastic Scattering if Cold Neutrons[END_REF] For the two remaining modes at 650 (only observed in the INS, not the optical spectra) and 970 cm -1 , which both correspond to Li-H-bending modes, we propose a different assignment. In contrast to earlier suggestions [START_REF] Maeland | Ternary Hydrides Possessing the Cubic Perovskite Structure. II. Vibration Spectra by the Inelastic Scattering if Cold Neutrons[END_REF] and on the basis of the selection rules for the coupling of vibrational modes to the electric dipole 4f-5d transition of Eu 2+ , we suggest to assign the mode at 650 cm -1 to the T 2u representation and the mode at 970 cm -1 to T 1u . The assignment in the deuteride and the barium compounds can be carried out accordingly; however, the resolution of the optical spectra is not as good as for the strontium compounds, and also the quality of our INS data is lower. The low-energy modes assigned to acoustic modes do not show any decrease of their frequencies by a factor of 2 upon replacing hydride by deuteride, whereas the modes assigned to optical modes do.

a 0 (Å) B (GPa) a G (GPa) b E (GPa) c ν d LiBaH 3 calc.
Information on the vibrational modes can also be interesting for the understanding of the optical thermal stabilities of the

The phonon energies are directly related to the photoionization behavior because thermal quenching in such systems follows an Arrhenius relation, where the temperature dependence of the luminescence emission intensity is given as follows: [START_REF] Kunkel | Thermally Stimulated Luminescence and First-Principle Study of Defect Configurations in the Perovskite-Type Hydrides LiMH 3 :Eu 2+ (M = Sr, Ba) and the Corresponding Deuterides[END_REF][START_REF] Dorenbos | Thermal Quenching of Eu 2+ 5d-4f Luminescence in Inorganic Compounds[END_REF] = + Γ Γ -Δ ν ( )

I T I ( ) (0)
1 exp

E k T 0 B (8)
where k B is Boltzmann's constant, ΔE is the energy barrier for thermal quenching, Γ ν is the radiative decay rate of the Eu 2+ 5d states, and Γ 0 is the attempt rate for thermal quenching. It is well-known that the attempt rate has a magnitude similar to that of the maximum phonon frequency. [START_REF] Ueda | Insight Into the Thermal Quenching Mechanism for Y 3 Al 5 O 12 :Ce 3+ Through Thermoluminescence Excitation Spectroscopy[END_REF] Consequently, the observed higher phonon energies in hydrides are responsible for the observed slightly faster thermal quenching in hydrides. The situation is less clear for the substitution of strontium with barium. It may be suggested that the slightly higher phonon frequencies in the strontium compounds also play a role; however, the different sizes of the band gaps or the different position of the conduction band may have a larger impact.

■ CONCLUSIONS

In summary, the combination of highly well-resolved vibrational fine structures in the Eu 2+ 5d-4f luminescence emission, especially for LiSrH 3 :Eu 2+ , INS experiments, and density functional calculations allowed the assignment of several vibrational modes, and we observed a decrease in the energies of the optic modes upon replacing hydride by deuteride. Because substitution of hydride by deuteride leads to a doubling of the anion mass, hydrides are ideal candidates for such studies, and the results show that the combination of resolved fine structures in rare earth-doped samples showing PL and INS, as well as calculations, represent a powerful tool for the investigation of lattice phonons in ionic hydrides. It is also possible to directly relate the photoionization behavior to the changes in the vibrational frequencies which result from the substitution of hydride by deuteride. To gain a better overview, it may be worthwhile to extend the combination of studies using INS as well as the determination of optical properties, such as the luminescence quenching temperature, to other hydride-and deuteride-containing host materials as well as other materials with polarizable anions, such as nitrides, in the future.

Figure 1 .

 1 Figure 1. Crystal structure of LiSrH 3 showing the cuboctahedral surrounding of strontium and the octahedral coordination of lithium.

Figure 2 .

 2 Figure 2. PL emission spectra of Eu 2+ (0.005%) in LiMH 3 and LiMD 3 (M = Sr and Ba) at 20 K. λ ex = 350 nm.

  3 and LiMD 3 (M = Sr and Ba) (Eu 2+ 0.005%)a line LiSrH 3 [cm -1 ] LiSrD 3 [cm -1 ] LiBaH 3 [cm -1 ] LiBaD 3 [cm -1 ] ν 1

Figure 3 .

 3 Figure 3. PL emission spectrum of Eu 2+ (0.005%) in LiSrH 3 at 20 K. λ ex = 350 nm. Energies ΔE are given with respect to the ZPL.Figure 4. Frequency distributions for LiSrH 3 as measured and LiSrH 3 after subtracting the spectra of SrH 2 and LiH. Recorded at TOSCA at 20 K.

Figure 4 .

 4 Figure 3. PL emission spectrum of Eu 2+ (0.005%) in LiSrH 3 at 20 K. λ ex = 350 nm. Energies ΔE are given with respect to the ZPL.Figure 4. Frequency distributions for LiSrH 3 as measured and LiSrH 3 after subtracting the spectra of SrH 2 and LiH. Recorded at TOSCA at 20 K.

Figure 5 .

 5 Figure 5. Phonon dispersion and DOS of LiSrH 3 as calculated by using VASP.

Figure 6 .

 6 Figure 6. Phonon dispersion and DOS of LiSrD 3 as calculated by using VASP.

Figure 7 .

 7 Figure 7. Comparison of the phonon DOSs of the hydride LiSrH 3 and the deuteride LiSrD 3 as calculated by using VASP.

Figure 8 .

 8 Figure 8. Comparison of the partial phonon DOSs for LiBaH 3 (a), LiBaD 3 (b), LiSrH 3 (c), and LiSrD 3 (d) as calculated by using VASP.

Table 2 .

 2 Calculated Structural and Elastic Parameters of LiBaH 3 , LiBaD 3 , LiSrH 3 , and LiSrD 3 at Zero Pressure

Table 3 .

 3 Comparison of the Fundamental Modes Found in the PL Emission Spectra at 20 K for the Eu 2+ Transition 4f 6 5d 1 -4f 7 ( 8 S 7/2 ), the Inelastic Neutron Spectra, and the Density Functional Calculations Given in cm -1 . A comparison of the luminescence quenching temperatures for the different perovskites[START_REF] Kunkel | Thermally Stimulated Luminescence and First-Principle Study of Defect Configurations in the Perovskite-Type Hydrides LiMH 3 :Eu 2+ (M = Sr, Ba) and the Corresponding Deuterides[END_REF] obtained from luminescence emission lifetime measurements yielded luminescence quenching temperatures (T 50% ) of 165 K for LiSrH 3 , 175 K for LiSrD 3 , 210 K for LiBaH 3 , and 230 K for LiBaD 3 . From the luminescence quenching temperatures (T 50% ), it is possible to estimate the energy barrier ΔE for thermal quenching (difference between the relaxed lowest d-states and the conduction band) using the simple equation[START_REF] Dorenbos | Thermal Quenching of Eu 2+ 5d-4f Luminescence in Inorganic Compounds[END_REF]

		PL	INS	DFT
		LiSrH 3
	T 1u acoustic	105	100	110
	T 1u optic	367	360	360
	T 2u optic		650	620
	T 1u optic	956	970	920
	T 1u optic		1160	1160
		LiSrD 3
	T 1u acoustic	105		110
	T 1u optic	258		310
	T 2u optic			460
	T 1u optic	690		660
	T 1u optic			820
		LiBaH 3
	T 1u acoustic	92	90	90
	T 1u optic	340	340	330
	T 2u optic		650	650
	T 1u optic	890	890	890
	T 1u optic		950	930
		LiBaD 3
	T 1u acoustic	92	90	90
	T 1u optic	270	300	330
	T 2u optic		450	440
	T 1u optic	630	620	625
	T 1u optic		670

compounds

■ ACKNOWLEDGMENTS

The authors would like to thank the ISIS Neutron and Muon Source for beamtime at TOSCA and Jean-Francois Engrand for constructing a sample holder for low-temperature PL measurements using ampoules. N.K. and T.W. would like to thank the Fonds der Chemischen Industrie for a Liebig and a doctoral fellowship (Li 197/02) and Prof. Fassler for hosting our group. A.H. and H.K. would like to thank the DFG for financial support (KO1803/7-1). P.G., N.K., S.W., and T.W. thank the Bavarian-French Academy Center for a mobility aid for their French-German collaboration (Az. FK03-2017). Furthermore, A.S., H.K., and N.K. thank the Universitéd'Artois for financial support for a French-German exchange.