# Fileset [BL14561.pdf](https://mdr.nims.go.jp/filesets/eb621336-89cd-4790-bc97-adf2b5c52b1b/download) ## Creator H. Tamatsukuri, Y. Murakami, [N. Saito](https://orcid.org/0000-0002-8104-0172), [N. Ohashi](https://orcid.org/0000-0002-4011-0031), S. Tsutsui ## Rights ©2024 American Physical Society[In Copyright](http://rightsstatements.org/vocab/InC/1.0/) ## Other metadata [Lattice dynamics of

CH {({NH}_{2})}_{2} {PbI}_{3}

and

CH {({NH}_{2})}_{2} {SnI}_{3}

investigated by inelastic x-ray scattering and comparison of their elastic properties](https://mdr.nims.go.jp/datasets/95038933-fd60-43b5-9223-fd609154bedb) ## Fulltext main_FPI_IXSph_v7.dviLattice dynamics of CH(NH2)2PbI3 and CH(NH2)2SnI3 investigated by inelastic x-rayscattering and comparison of their elastic propertiesH. Tamatsukuri,1, 2, ∗ Y. Murakami,2, 3 N. Saito,4 N. Ohashi,4, 3 and S. Tsutsui5, 61Materials and Life Science Division, J-PARC Center,Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan2Condensed Matter Research Center (CMRC) and Photon Factory, Institute of Materials Structure Science,High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan3Materials Research Center for Element Strategy,Tokyo Institute of Technology, Yokohama, Kanagawa 226-8503, Japan4National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan5Japan Synchrotron Radiation Research Institute (JASRI), SPring-8, Sayo, Hyogo 679-5198, Japan6Institute of Quantum Beam Science, Graduate School of Science and Engineering,Ibaraki University, Hitachi, Ibaraki 316-8511, Japan(Dated: May 30, 2024)Using the inelastic x-ray scattering (IXS) technique, we investigate the lattice dynamics ofinorganic–organic hybrid iodide perovskites FAPbI3 and FASnI3 (FA ≡ CH(NH2)2, formamidinium)in their cubic α phase and tetragonal β phase. We find that the IXS spectra of FASnI3 are highlybroad at all momentum points, as has been widely observed in the Pb-based halide perovskites. Thespeeds of sound (phonon group velocities) and absolute values of elastic constants of FASnI3 aresmaller than those of FAPbI3 in both phases. In addition, no significant difference in the phononlifetimes of FAPbI3 and FASnI3 is observed. These results correlate better with the reported ten-dency that the lattice thermal conductivity of ASnX3 is lower than that of APbX3. We discuss thatour results also favor the up-conversion mechanism by acoustic phonons in the phonon bottleneckeffect for the long lifetime of hot carriers.I. INTRODUCTIONOver thirty years, metal halide perovskites havebeen extensively studied as candidate materialsfor photovoltaic, optoelectronic, and thermoelectricapplications1–5. They have the general chemical formulaAMX3, where A+ = Cs+, MA+ ≡ CH3NH3+ (methy-lammonium) or FA+ ≡ CH(NH2)2+ (formamidinium);M = Pb2+ or Sn2+; X− = I−, Br−, or Cl−.The ultra-low thermal conductivity and the coherentband transport in this system are helpful for thermo-electric applications3. These properties are attributedto the metal halide perovskites that belong to ‘phononglass electron crystal’ materials6. The concept of thephonon glass electron crystal indicates that charge trans-port is band-like and phonon transport is diffusive6.The phonon glass character appears to stem from arattling-like motion of the A+ ion7,8 and/or the dynam-ical disorder of the MX6 octahedron9,10. These motionswould cause phonon–phonon scattering, especially acous-tic phonons that are the chief causes of dissipation ofheat, and interfere with the thermal transport, leading tothe low lattice thermal conductivity in this system7,8,11.The phonon glass concept is vital for the photo-voltaic and the optoelectronic properties of metal halideperovskites7, although it was initially introduced tosearch for suitable candidates for efficient thermoelectricmaterials. Regarding photovoltaics and optoelectronics,such as solar cells and light emitters, it is crucial to un-derstand the reason for the long lifetime of hot carriersin these materials1,2. Several studies have highlightedthat the phonon glass character promotes the large po-laron formation, which protects charge carriers from thescattering with charged defects and other charge car-riers, elongating their lifetime7,12–17. Furthermore, athigher carrier densities, a phonon bottleneck that fur-ther slows the cooling of the hot carriers occurs in themetal halide perovskites18–23. As a possible origin forthe phonon bottleneck effect, an up-conversion hypoth-esis has been proposed20: if phonon propagation, espe-cially acoustic phonons, is prevented by, for example, an-harmonic phonon–phonon interactions, their energy re-excites low-energy phonons that reheat the carries, lead-ing to the long lifetime of the hot carriers. The phononglass character might be beneficial for the phonon bottle-neck effect because the up-conversion of acoustic phononswould easily occur due to the suppression of thermaltransport and dissipation24.Recently, ASnX3 have been attracted to avoid usingthe toxic element Pb4,25–27. Since the direct bandgapand the carrier mobilities of ASnX3 tend to be narrowerand higher, respectively, than those of their Pb-basedcounterparts25–27, they are potentially more desirable forphotovoltaics and optoelectronics. An extremely longhot carrier lifetime has been reported in FASnI3 thinfilms, where the phonon bottleneck effect and the up-conversion mechanism as its origin are considered to playa critical role22,24. Moreover, the thermal conductivityof MASnI3 is the lowest among the metal halide per-ovskite families3,28. Information on the lattice dynamicsand mechanical properties of ASnX3 is crucial for under-standing their fascinating material performances basedon the ‘phonon glass’.This study investigates the lattice dynamics of FAPbI32c*a*b*M: (1/2, 1/2, 0)X: (0, 1/2, 0)ΓR: (1/2, 1/2, 1/2)FIG. 1. A schematic Brillouin zone of a cubic lattice. High-symmetry points are also shown.and FASnI3 in their cubic α and tetragonal β phases.The speeds of sounds (phonon group velocities) andelastic constants of FASnI3 are smaller than those ofFAPbI3 in both phases, whereas no significant differencein the phonon lifetimes (the reciprocal of the width ofthe phonon peaks) of FAPbI3 and FASnI3 is observed.These results correlate better with the lower thermal con-ductivity of ASnX3 than that of APbX328. Consideringthe reported assumption that the up-conversion of acous-tic phonons easily occurs in materials with lower latticethermal conductivity, our results favor the up-conversionmechanism by acoustic phonons in the phonon bottleneckeffect for the long lifetime of hot carriers.FAPbI3 and FASnI3 crystallize in the cubic structurewith the space group Pm3̄m at room temperature29–32.With decreasing temperature, they undergo sequentialstructural transitions from the cubic α phase to thetetragonal β phase at ∼280 K29,30 and ∼250 K31,32, thento the orthorhombic γ phase at ∼141 K29,30 and ∼150K31,32, respectively. The transition from the α phase tothe β phase is driven by tilting the MI6 octahedrons. Thetilting pattern of the PbI6 octahedrons in FAPbI3 is de-scribed in Glazer notation as a0a0c+, which leads to thespace group P4/mbm in the β phase33. This result dif-fers from the tilting pattern a0a0c− and the space groupI4/mcm in the β phase of MAPbI333. Consequently, thelattice instability in the cubic phase of FAPbI3 is largerat the M point than the R point (Fig. 1) in contrast toMAPbI3. The space group in the β phase of FASnI3 is thesame as FAPbI331,32. Note that the crystal structure andthe space group of the γ phase in both compounds, andeven structural transitions from the β phase in FAPbI3are still controversial29–32.II. EXPERIMENTAL DETAILSA single crystal of FAPbI3 with typical dimensions of 4× 4 × 2 mm3 was synthesized by an inverse-temperature-crystallization method. A single crystal of FASnI3 withtypical dimensions of 0.3 × 0.3 × 0.3 mm3 was grownby the aqueous solution process using phosphinic acid(H3PO2). Details of the crystal growth of the samples aredescribed in the Supplemental Material34. We employthe cubic unit cell in this paper.The IXS experiments were conducted at BL35XU ofSPring-8 in Japan. Using a Si(11 11 11) backscattering,the incident x-ray energy was tuned to 21.747 keV withenergy resolution of 1.5 meV. Resolutions of a momen-tum transfer in FAPbI3 and FASnI3 were (0.09, 0.09,0.04) and (0.09, 0.09, 0.05) in reciprocal lattice units(r.l.u.). The sample temperature was controlled using aHe closed-cycle refrigerator. The IXS experiments wereperformed at room temperature (RT) and 200 K forFAPbI3 and RT and 180 K for FASnI3, where both sam-ples exhibited the α and β phases, respectively29–31. Inour IXS measurements, the lattice constants a of FAPbI3and FASnI3 are 6.360 Å and 6.315 Å at RT, and 6.311Å at 200 K and 6.267 Å at 180 K, respectively, whichare used to estimate mass densities and sound speeds.These values are consistent with those in the literature[27, 29–31]. No x-ray damage to the samples could beseen during and after the IXS experiments. The phononenergies were obtained by fitting the measured IXS spec-tra using the Lorentz function with the Bose factor,I(Q, E) = Ie(Q) +∑iIi(Γi/2)2(E ∓ Ei)2 + (Γi/2)2× (n(Ei) + 1/2± 1/2)/Ei, (1)where Ii, Ei, Γi, and n(E) is the intensity, energy, thefull width at half maximum of the phonon mode withindex i, and the Bose factor, respectively. Upper andlower signs of ∓ (±) correspond to the energy loss side(E > 0) and the energy gain side (E < 0), respectively.The elastic part Ie(Q) is also described by the Lorentzfunction, Ie(Q) = I ′(Q)(Γ/2)2/(E2 + (Γ/2)2). Takingthe energy resolution into account, Γ is fixed as 1.5 meV.A yellow polymorph of these compounds exists calledthe δ phase, as exemplified by δ-CsPbI335,36. The yellowpolymorph adopts the nonperovskite structure, whichmight be the most stable state in air35,36. However, thesamples used in this study are black and as well-definedas the cubic perovskite structure at RT, even though thesamples are exposed to air within a few hours for checkingthe principal axes of the crystals and the sample mount-ing before the IXS experiments. Moreover, they remainblack for a few days even after the IXS experiments.3FAPbI3Γ ↔ M LongitudinalE (meV)Intensity (arb.units)0 5−5 201510−10E (meV)0 5−5 201510−10E (meV)0 5−5 201510−10E (meV)0 5−5 201510−10FASnI30 0 0 0000000000000121112 2123246642426811121251012243148161220(a) (6.071, 6.071, 0.001)Γ ↔ M LongitudinalΓ ↔ X Longitudinal Γ ↔ X Longitudinal(6 + q, 6 + q, 0)(6.154, 6.166, 0.053)(6.334, 6.325, −0.027)(6.416, 6.419, 0.027)(8.110, 0.006, 0.001)(8.237, −0.031, −0.033)(8.363, −0.069, −0.068)(8.488, −0.109, −0.104)(6.089, 6.097, 0.000)(6.196, 6.166, 0.046)(6.393, 6.428, −0.045)(6.500, 6.496, 0.003)(0.000, 8.112, −0.005)(0.026, 8.237, 0.038)(0.054, 8.362, 0.082)(0.082, 8.487, 0.127)(6 + q, 6 + q, 0)(8 + q, 0, 0) (0, 8 + q, 0)Obs.FittingElasticPh1Ph2(b) (c) (d)MΓMΓXΓXΓFIG. 2. Typical IXS spectra of [(a),(b)] FAPbI3 and [(c),(d)] FASnI3, at room temperature (RT), respectively. The data of(a) and (c) are measured at the longitudinal geometries along the Γ-M direction, and those of (b) and (d) are measured at thelongitudinal geometries along the Γ-X direction.III. RESULTS AND DISCUSSIONFigures 2(a) and 2(b) show the typical IXS spectra ofFAPbI3 for the longitudinal mode along the Γ-M and Γ-X directions, respectively, at RT. These spectra rangingto 20 meV are considerably broad, and overall featuresin the transverse modes are similar. These features agreewell with the previous studies on the lattice dynamics ofthe halide perovskites37–46. Figures 2(c) and 2(d) showsimilar datasets for FASnI3. We find that the IXS spec-tra of FASnI3 are also broad. Broad phonon spectra canbe attributed to phonon anharmonicity43,44, which alsocauses the short mean free paths of phonons, namelyphonon glass behavior. Since the anharmonic potentialcreates an instant large atomic displacement that canbe coupled with the charge carriers, these broad phononspectra due to phonon anharmonicity would be advan-tageous to the large polaron formation in the APbX3systems7,45.We estimate phonon energies by analyzing the mea-sured IXS spectra using the eq.(1). Figure 2 shows thefitted curves, thereby obtaining the phonon dispersionrelations (Fig. 3). In these dispersion relations, quarterwidth at half maximum of phonon peaks are depicted asvertical bars instead of the fitting uncertainty. Althoughthe overall dispersion relations are similar in FAPbI3 andFASnI3, a remarkable difference can be seen in the trans-verse mode with the [001] polarization along the Γ-M di-rection. In this mode, the energies of the lowest phononexcitations near the zone center in FASnI3 are muchsmaller than those in FAPbI3. This result is also evi-dent from the spectra shown in Figs. 4(a) and 4(c). Thisresult indicates that the speed of transverse sound alongthis direction in FASnI3 is much smaller than in FAPbI3,although the mass of Pb is two times larger than thatof Sn. Note that the previous neutron scattering studieshave reported quasielastic scatterings owing to the FA orMA molecular rotations, whose relaxation times are theorder of nano second corresponding to the energy reso-lution of 1 ∼ 10 µeV37,47. However, such a quasielasticscattering owing to the FA molecular rotations can notbe extracted from our data, because the energy resolu-tion of our IXS experiments is 1.5 meV and x-rays is notsensitive to the FA molecule.We estimate the speeds of sound and the elastic con-stants from the dispersion relations to extract the elasticproperties of these systems. From a continuous approx-imation viewpoint, we use the longitudinal mode dataalong the Γ-X direction, the transverse mode data (thepolarization is parallel to the [001] direction) along theΓ-M direction, and the longitudinal mode data alongthe Γ-M direction to calculate the speeds of sound, vΓXLA ,vΓMTA , and vΓMLA , respectively. For the cubic lattice, theelastic constants are related to the speeds of sound as40 0.1 0.2 0.3 0.4 0.5q (r.l.u.)RΓMΓXΓ024681012E(meV)024681012E(meV)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)024681012E(meV)024681012E(meV)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)RLongitudinal Transverse [1-10]LongitudinalΓMΓ MΓ MΓXΓ XΓTransverse [001]Transverse [001]0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)0 0.1 0.2 0.3 0.4 0.5q (r.l.u.)XΓMΓ MΓLongitudinalLongitudinalTransverse [001] Transverse [1-10]Transverse [001]FAPbI3FASnI3FIG. 3. Phonon dispersion relations along the Γ-X (red), Γ-M (blue), and Γ-R (green) directions in FAPbI3 (left panels) andFASnI3 (right panels), respectively, at RT. Note that (i) the data along the Γ-R direction correspond to neither longitudinalnor transverse modes because of the scattering geometry, and (ii) the vertical bars are quarter width at half maximum phononpeaks, not the uncertainty of fitting; the gray solid lines are a guide for the eyes.TABLE I. Speeds of sound estimated in FAPbI3 and FASnI3; all values are given in m/s.Temperature vΓXLA vΓMTA vΓMLAFAPbI3 RT (Cubic α phase) 2000 ± 120 1400 ± 80 1500 ± 150200 K (Tetragonal β phase) 1730 ± 70 690 ± 30 1200 ± 100FASnI3 RT (Cubic α phase) 1890 ± 60 600 ± 90 1170 ± 90180 K (Tetragonal β phase) 1430 ± 80 610 ± 80 1100 ± 100follows50: vΓXLA =√C11/ρ, vΓMTA =√C44/ρ, and vΓMLA =√(C11 + 2C44 + C12)/ρ, where ρ is the mass density. Ta-ble I summarizes the estimated speeds of sound and Ta-ble II provides the estimated elastic constants. To seethe temperature variation, the speeds of sound and theelastic constants in the β phase are also estimated usingthe cubic notation.The elastic constants of FAPbI3 at RT, except for C44,agree well with a previous report42. Also, these con-stants within the uncertainties satisfy the so-called Bornstability criteria, the generic requirement for the elas-tic stability of cubic crystals42,50,51: C11 > 0, C44 > 0,C11 − C12 > 0, C11 + 2C12 > 0. A previous study re-ported that C44 of MAPbBr3 smoothly decreases withthe decreasing temperature from RT42. Accordingly, C44of FAPbI3 at 200 K in our data reduces significantly, alsoapparent from the IXS spectra shown in Figs. 4(a) and4(b), and its value is consistent with previous results.Therefore, the larger C44 of FAPbI3 at RT than in theprevious one might result from the slight difference ofthe measurement temperature. We add that the lower q-resolution of our data than that in Ref. [42] may lead tolarger differences in the speeds of sound and the elasticconstants beyond the fitting errors for the broad peaks.As expected from the IXS spectra shown in Fig. 4,the C44 of FASnI3 at RT is significantly smaller thanthat of FAPbI3. Furthermore, the absolute values of theother elastic constants of FASnI3 are smaller than those5TABLE II. Elastic constants and bulk moduli B of FAPbI3 and FASnI3; all values are given in GPa.Temperature (phase or structure) C11 C44 C12 B = (C11 + 2C12)/3FAPbI3 RT (α phase) 15.9 ± 3.9 8.0 ± 1.8 −12.4 ± 6.6 −2.9 ± 4.6200 K (β phase) 12.5 ± 1.0 2.0 ± 0.2 −3.5 ± 2.5 1.8 ± 1.7FASnI3 RT (α phase) 12.9 ± 1.6 1.3 ± 0.8 −5.6 ± 3.5 0.5 ± 2.4180 K (β phase) 7.6 ± 0.8 1.4 ± 0.4 −1.8 ± 2.3 1.3 ± 1.6FAPbI3 [42] RT (α phase) 11.1 ± 2.0 2.7 ± 0.3 −5.5 ± 2.2 0.0 ± 2.4FAPbI3 (Calc.) [48] (a pseudo-cubic structure) 30.15 2.03 2.99 13.25FAPbI3 (Calc.) [49] (the cubic structure) 20.5 4.8 12.3 15.3FASnI3 (Calc.) [48] (a pseudo-cubic structure) 29.96 2.35 6.85 12.96E (meV)0 1−1 432−2 Intensity (arb.units)0001122123(8, −q, q)FAPbI3 (RT)q = 0.094q = 0.195q = 0.295E (meV)0 1−1 432−2000FASnI3 (RT) (q, 8, −q)q = 0.101q = 0.215q = 0.330 MΓObs.FittingElasticPh1Ph2FAPbI3 (200 K) (8, −q, q)130100532102010155E (meV)0 1−1 432−2315132q = 0.094q = 0.195q = 0.295(a) (b) (c)FIG. 4. IXS spectra in the range relevant to the sound velocity for the transverse[001] mode along the Γ-M direction in (a)FAPbI3 at RT, (b) FAPbI3 at 200 K, and (c) FASnI3 at RT.of FAPbI3, although the error margin is large. The resultcorrelates well with the theoretical prediction, showingthat the Pb-I bonds in FAPbI3 are stronger than the Sn-I bonds in FASnI348. This result suggests that the solidstate stability of FASnI3 is less than that of FAPbI3. Thesingle crystal of FASnI3 prepared in this study is verysmall in size as described in Sec. II, whereas the largesingle crystal of FAPbI3 is available. As well as the elas-tic constants, the speeds of sound of FASnI3 are smallerthan those of FAPbI3. In addition, no significant differ-ence in the phonon lifetimes (the reciprocal of the widthof the phonon peaks) of FAPbI3 and FASnI3 is observedin our data. Since the lattice thermal conductivity is pro-portional to the speeds of sound (phonon group veloci-ties) and the phonon lifetime, these lower speeds of soundwould directly correspond to the lower lattice thermalconductivity of ASnX3 than its APbX3 counterparts8,28.Note that the width of the acoustic phonon peaks tend tobecome broader near the zone boundaries in both FAPbI3and FASnI3. This tendency is also reported for the sev-eral metal halide perovskites39,41,43,52,53, in which the im-portance of the contribution from the A site molecules issuggested, such as the molecular dynamics through thehydrogen bonding54 or anharmonic effect due to low en-ergy optical modes arising from the A site molecules43.However, M. Songvilay et al. have recently demonstratedthat the width of the acoustic phonons are similar inMAPbCl3 and CsPbBr3, which indicates that the roleof the organic molecules and the difference in the halideX− ions are not crucial for the broadening of the acousticphonon peaks52. Taking this study into account, thereare possibility that the difference in the Pb2+ and Sn2+6ions also does not affect the acoustic phonon lifetimes inFAPbI3 and FASnI3.As briefly described in Sec. I, the microscopic origin ofthe long carrier lifetime in this system must be elucidatedmore clearly for photovoltaic and optoelectronic applica-tions. Several explanations for the long relaxation timehave been proposed, including the (dynamical) Rashbaeffect55–57 and the large polaron formation12–17. More-over, the phonon bottleneck effect occurs in this systemat higher carrier densities18–23. Some mechanisms statedabove could coexist with the phonon bottleneck effectand might cowork to elongate the relaxation, becausethere are several characteristic time scales in the relax-ation process of the hot carriers20–22. The phonon bot-tleneck effect indicates some factors due to phonons thathinder the energy dissipation of the hot carriers. As oneof the possible origins of the phonon bottleneck effect,Yang et al. proposed the up-conversion mechanism oflow-energy acoustic phonons20. In this mechanism, it isassumed that blocking acoustic phonon propagation dueto anharmonic scattering suppresses thermal transportand thermal (vibrational) energy dissipation, and thenthe recycled vibrational energy reheats the carries20. Ashighlighted in the literature [20, 22, and 24], this up-conversion of acoustic phonons occurs easily in materialswith lower lattice thermal conductivity, where acousticphonon propagation is more strongly prevented. This as-sumption is in line with the lower thermal conductivityof FASnI3, corroborated by our results that the speeds ofsound in FASnI3 are lower than in FAPbI3, and the re-sulting longer relaxation time in FASnI322,24. Therefore,in terms of their mechanical properties, our results fa-vor the up-conversion mechanism, where acoustic phononmodes are involved.Another explanation exists for the phonon bottleneckeffect, and thus, the origin of the phonon bottleneck ef-fect is still controversial. For example, J. Fu et al. haveproposed that at moderate carrier densities, the bottle-neck effect results from the suppression of the Klemensrelaxation which involves the longitudinal optical (LO)phonon decay. At higher carrier densities, the Augerheating process occurs and further reduces the coolingrate21. However, F. Sekiguchi et al. recently provided di-rect evidence of the phonon bottleneck effect, where theexcitation of transverse optical (TO) phonons by a tera-hertz pulse laser elongates the carrier lifetime23. Sincethe Fröhlich interaction between carriers and the LOphonons is dominant in these materials58–60, they arguedthat the up-conversion from the excited TO phonons toLO phonons possibly occurs23. Although it is still unclearwhether the up-conversion from excited TO phononsto LO phonons occurs directly or through the acous-tic phonons23, some up-conversion might occur betweenphonons in the metal halide perovskites.In general, the elastic constants increase with decreas-ing temperature50, corresponding to the hardening of asolid as the temperature decreases. As shown in TableII, the C44 of FAPbI3 shows an opposite temperature de-pendence, whereas that of FASnI3 is almost unchanged.As described above, this tendency has also been reportedin MAPbBr342. The authors of the literature [42] high-lighted that this softening of C44 is related to the prox-imity of a ferroelastic transition61, but it is independentof the cubic-to-tetragonal transition. The change in C44of MAPbBr3 weakens before the phase transition fromthe cubic α to the tetragonal β phases, or rather it isblocked by the cubic-to-tetragonal transition. The lowervariation in C44 of FASnI3 might be due to a similarsituation, which would result from the lower cubic-to-tetragonal transition temperature. It is helpful to mea-sure the elastic constants of FASnI3 at higher tempera-tures to confirm this point. We add that the temperaturedependence of C11 of FASnI3 also contradicts the generaltendency, whereas that of FAPbI3 is unclear due to thelarge uncertainties.Finally, we compare the elastic constants deduced bythe experiments with those of the calculations. TableII shows that the calculations estimate that C11 is largerthan the experiments. Also, a significant difference existsbetween the experimental and calculated results of C12in both compounds48,49. First-principles calculations forthe instability of tilting the MX6 octahedron in CsMX3revealed that the cubic structure is realized as a time-average structure due to the dynamical disorder of theoctahedral tilting9,10. Subsequently, the dynamical dis-order of the octahedral tilting was experimentally verifiedin CsPbBr346, which would be a common feature in themetal halide perovskites. Therefore, the discrepancy inthe elastic constants might be due to the use of the staticcubic structure in the calculations. We note that the neg-ative values of C12 are seen only in FAPbI3 and FASnI3among the metal halide perovskites. Combining FA andI, which are common to both compounds, might enhancethe dynamical disorder of the octahedron.IV. SUMMARY AND CONCLUSIONSWe performed IXS experiments to investigate the lat-tice dynamics of FAPbI3 and FASnI3 in their cubic α andtetragonal β phases. The speeds of sound and elastic con-stants of FASnI3 are smaller than those of FAPbI3 in bothphases. These results corroborate the reported tendencythat the thermal conductivity and the hot carrier lifetimeof ASnX3 are lower and longer, respectively, than those ofAPbX3. Our results also favor the up-conversion mecha-nism by acoustic phonons in the phonon bottleneck effectobserved in the metal halide perovskites. A more sophis-ticated theoretical calculation for the elastic constants,which might need to include the effect of the dynamicaldisorder of the MX6 octahedron, is desirable.7ACKNOWLEDGMENTSWe thank T. Tadano and K. Miyano for fruitful dis-cussions, and H. T. thanks S. Kawachi and J. Yamaurafor their support for preparations of experiments. M.Atsumi is acknowledged for her excellent assistance forcrystal growth process. 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