Experimental Phonon Dispersion and Lifetimes of Tetragonal

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Experimental Phonon Dispersion and Lifetimes of Tetragonal CHNHPbI Perovskite Crystals 3

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Hao Ma, Yunwei Ma, Heng Wang, Carla Slebodnick, Ahmet Alatas, Jeffrey J. Urban, and Zhiting Tian J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b03419 • Publication Date (Web): 16 Dec 2018 Downloaded from http://pubs.acs.org on December 17, 2018

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The Journal of Physical Chemistry Letters

Experimental Phonon Dispersion and Lifetimes of Tetragonal CH3NH3PbI3 Perovskite Crystals Hao Ma1, Yunwei Ma2, Heng Wang3,4, Carla Slebodnick5, Ahmet Alatas6, Jeffrey J. Urban3, Zhiting Tian1 1Sibley

School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA

2Department 3Molecular

of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA

Foundry, Lawrence Berkeley National Laboratories, Berkeley, CA 94720, USA

4Department

of Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA

5Department 6Advanced

of Chemistry, Virginia Tech, Blacksburg, VA 24061, USA

Photon Source, Argonne National Laboratory, Argonne, Illinois 64039, USA



Corresponding author. Email: [email protected]

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Abstract Hybrid organic-inorganic perovskites were reported to have ultralow thermal conductivity in recent studies. In this letter, we report the first experimental phonon dispersion and lifetimes of tetragonal CH3NH3PbI3 single crystals at both 200 K and 300 K by high energy resolution inelastic x-ray scattering, which enables a thorough understanding of the underlying mechanisms for the ultralow thermal conductivity. Notably, we observed unusual and significant phonon dips along [100] and [110] directions at both temperatures. The ultralow thermal conductivity can be attributed to small group velocities due to ultrasoft acoustic modes and short phonon lifetimes originating from the strong acoustic-optical coupling. We further provided the structural origins for these peculiar phonon features. Moreover, our results and interpretation are consistent with the reported temperature-dependent trend for thermal conductivity of CH3NH3PbI3. Our work offers critical guidelines for accelerating the design and discovery of novel hybrid materials for energy applications including photovoltaics and thermoelectrics.

Table of Contents (TOC) Graphic

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Organic-inorganic hybrid perovskites have emerged as promising components of future, highly efficient solar cells due to their high-power conversion1-3 and simple solution-based synthesis4. Although a significant number of investigations have been dedicated to understanding their structural stability5-7 and their electrical8-10 and optical properties11-13, their thermal transport properties have received much less attention. Thermal management of hybrid-perovskite-based solar cells is critical to device performance and lifetime because a large fraction of solar energy is converted into heat in the form of phonons. Moreover, phonon dispersion of hybrid perovskites is a critical piece of information that is currently missing to account for phononelectron scattering14-16. However, the interaction of charge carriers with acoustic or optical phonons is currently still under intense debate. On the other hand, hybrid perovskites have shown promising features as thermoelectric materials17-20, where they can leverage the advantages of inexpensive and scalable fabrication and conformal geometries to maximize heat capture compared to traditional inorganic thermoelectrics21,22. Thermal conductivity of hybrid perovskites, which is dominated by phonon transport, plays a significant role in the energy conversion efficiency of thermoelectrics. Fundamental understanding of phonon transport properties of hybrid perovskites can inspire optimal selection and rational design of promising perovskites for more efficient and reliable energy harvesting and conversion.

CH3NH3PbI3 is the most commonly studied hybrid perovskite. Orientational ordering of CH3NH3+ and tilting of the PbI6 octahedra lead to three different phase regions: orthorhombic (330 K)1,

23-25.

CH3NH3PbI3 have shown an

ultralow thermal conductivity of 0.3-0.5 W/mK at room temperature even in single crystals20, 2629,

which is two orders of magnitude lower than that of traditional inorganic perovskites such as

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SrTiO330. Yet, the underlying mechanisms for ultralow thermal conductivity remain poorly understood without reliable phonon information. Experimentally, the vibrational frequencies of CH3NH3PbI3 have been studied by infrared spectroscopy6,31,32, Raman spectroscopy33,34, nuclear magnetic resonance35, and neutron scattering36-38. The only high energy resolution inelastic x-ray scattering (IXS) measurement on CH3NH3PbI3 to date was carried out on the cubic phase at 330380K, which revealed that large-amplitude anharmonic zone edge rotational instabilities of the PbI6 octahedra persist to room temperature and above.39 Computationally, the calculations of phonon properties are non-trivial due to their structural complexity and instability40. Lattice dynamics (LD) calculations based on empirical potential23 or first-principles force fields41 have been carried out to determine the phonon dispersion. Spectral energy density (SED) techniques within classical and ab initio molecular dynamics (MD) frameworks have been applied to calculate phonon dispersion42 and phonon lifetimes23,41,42. However, there are obvious discrepancies in the calculated phonon dispersions and lifetimes23,

40-42

even in the acoustic

branches. Experimentally determining phonon dispersion and lifetimes of tetragonal CH3NH3PbI3 single crystal is essential to clearing the cloud and thoroughly understanding the detailed phonon dynamics and observed ultralow thermal conductivity. IXS is uniquely suited to investigate phonon dispersion and lifetimes of CH3NH3PbI3 single crystal. Because of the huge incoherent cross section of neutron for hydrogen (H) atoms, inelastic neutron scattering is inapplicable to measure the phonon dispersion and lifetimes of hybrid materials unless deuterium (D) atoms are used instead of H. Due to the structural complexity, CH3NH3PbI3 single crystal has large numbers of atoms in a unit cell and many phonon branches, and IXS presents the best choice to resolve different phonon modes along the high-symmetry lines.

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In this letter, we report the first experimental data of phonon dispersion and lifetimes for the tetragonal phase of CH3NH3PbI3 at 200 K and 300 K by conducting IXS experiments on single crystals to elucidate the fundamental mechanisms for its ultralow thermal conductivity. We observed peculiar phonon features and correlated them with their unique crystal structures. Notably, there is a profound phonon dip around q=0.6 of the [100] direction for the longitudinal acoustic (LA) branch and strong phonon softening near the zone edge of the [110] direction for both transverse acoustic (TA) and LA modes. Moreover, the acoustic modes are ultrasoft with a frequency range up to 1 THz, and, remarkably, no energy gap is observed between the acoustic and optical branches. All these features are essential to the ultralow thermal conductivity. As temperature increases, the acoustic branches slightly red shift and the lifetimes moderately reduce due to increased phonon-phonon scattering. The important phonon information provided in this study is expected to serve as a benchmark for future studies and guide the rational design of novel hybrid materials for various energy applications.

CH3NH3PbI3 single crystals were grown at the Molecular Foundry at Lawrence Berkeley National Laboratory using an inverted temperature crystallization technique. These crystals were characterized using single-crystal x-ray diffraction (XRD) measurements performed at Virginia Tech. The details of the crystal growth and characterization methods can be found in the Supporting Information (SI). The synchrotron-based IXS technique has high energy resolution and can probe phonons via energy and momentum changes of the scattered photons.43-47 The IXS measurements were performed at the XSD 3-ID beam line of the Advanced Photon Source, Argonne National Laboratory. The wavelength of the x-ray was 0.5725 Å and the focused beam size was 20 µm × 20 µm. The experiment was carried out in the transmission geometry and

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samples were stored in a beryllium dome to prevent visible light exposure during the experiment. Sample 1 and sample 2 (See details about these two samples in SI) were measured at 200 K and 300 K, respectively. A typical IXS spectrum is shown in Figure 1. Instrument resolution was measured separately, and an energy resolution of 2.0 meV (0.48 THz) was determined by fitting with a pseudo-Voigt function. The measured energy spectra were fitted with a model function of Lorentzian peaks convoluted with the pseudo-Voigt function for instrument resolution. We deconvoluted the energy resolution during data fitting to exclude the broadening of elastic peaks from instrument resolution. In this study, the elastic peaks are strong compared to inelastic peaks and we were able to resolve the modes higher than 0.48 THz without ambiguity. The momentum resolution was 0.35 nm−1. To reduce statistical noise, we measured three or four runs and averaged the data for each q point sampled. After fitting the peaks at each q point, we obtained the mode-dependent phonon frequencies and linewidths. The inverse of phonon linewidth gives phonon lifetime. In conducting this study, we paid special attention to the possible role of radiation damage and the details can be found in SI.

Figure 1. Energy spectra from IXS measurement (blue circles) of the LA mode at q=0.6 along [001] for the tetragonal CH3NH3PbI3 single crystal at 300 K characterized by an elastic peak 6


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centered at zero energy and inelastic peaks associated with the creation and annihilation of phonons. Green and red curves represent the instrumental resolution function and fitting core based on Lorentzian function, respectively. The blue solid curve denotes convolution between the resolution function and the fitting core.

The measured phonon dispersion in three high-symmetry directions is shown in Figure 2. It uncovers unique phonon features in hybrid perovskites. I. LA curves show a prominent dip around q=0.6 in the [100] direction at both 200 K and 300 K, as marked by the green arrows in the Figure 2a and Figure 2b, which was barely captured by previous calculations of CH3NH3PbI323, 41 as shown in Figure 2c. The original fitting data around q=0.6 are shown in SI (Figure S2). The evident dip is likely a feature of weak electrostatic interaction between CH3NH3+ and PbI3- cages along [100] direction because weak electrostatic interaction can soften phonon modes. In CH3NH3PbI3, the inorganic component is a three-dimensional framework of corner sharing PbI6 octahedra, with CH3NH3+ in the framework cages and separating octahedra along [100] direction. Therefore, the weak electrostatic interactions between inorganic cages and organic cations are expected to be profound along the [100] direction. LA modes in the [100] direction correspond to atomic vibrations along [100] and thus exemplify the weak interactions. We did not observe phonon dip for TA modes along [100] direction because TA modes corresponds the atomic vibrations perpendicular to [100] direction and the impact from the weak interactions is supposedly less significant. LA modes become even a bit lower than TA modes at the dip. Note that LA modes can be lower than TA modes when they are away from Γ point, as observed in other materials48,49. II. We observed phonon softening at the zone boundary of the [110] direction at both 200 K and 300 K. The original fitting data around X point are shown in SI

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(Figure S3 and S4). It is similar to a soft-mode behavior for the TA branch in [111] of Pu-Ga alloy at 𝛿 phase due to 𝛿 to 𝛾 phase transition50. The face-centered cubic (fcc) 𝛿-phase Pu-Ga alloy transforms into the face-centered orthorhombic 𝛾 phase at lower temperature by distorting hexagonally packed atomic layers. The phase transition of CH3NH3PbI3 from cubic to orthorhombic is mainly attributed to the PbI6 octahedra rotation in parallel to [001]. This rotation results in different alignments of I- anions with respect to Pb2+ cations along the [110] direction and softens the high-frequency acoustic modes near the zone edge of the [110] direction (Figure 3). This structure change that eventually leads to phase transition is a continuous process. In other words, the soft phonon modes exist even though not right at the phase transition temperature. Therefore, we observed phonon softening at both 200 K and 300 K. A similar but weaker softening in LA branch of [110] direction was also observed by a recent simulation of CH3NH3PbI341 but has never been experimentally verified before, as shown in Figure 2c. III. We did not observe any obvious phonon softening along [001] direction because there is continuous strong ionic bonding of PbI3- cages as illustrated in Figure 3. IV. The acoustic branches are, in general, ultrasoft. The acoustic modes are associated with inorganic cage PbI3-.41,

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If we

compare the acoustic modes of CH3NH3PbI3 with those of PbTe or PbSe49, we found that the frequency range of CH3NH3PbI3 is only up to ~1 THz compared to that of ~3 THz for PbTe or PbSe despite the fact that these materials share the same predominant heavy element (Pb). The acoustic modes are much less stiff in CH3NH3PbI3 due to the weak electrostatic interaction between CH3NH3+ and PbI3- cages. These ultrasoft acoustic modes have small group velocities, which are essential for the ultralow thermal conductivity of CH3NH3PbI3 single crystals. V. There is, in general, no gap between acoustic and optical branches, which can be attributed to the interplay between organic molecular orientation and the corner-sharing octahedral inorganic

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networks40. Due to low intensity and possible overlapping of optical modes, we include optical modes in the Figure S5 of SI. This gapless feature can lead to strong acoustic-optical phonon scattering and correspondingly short phonon lifetimes, contributing to the ultralow thermal conductivity of CH3NH3PbI3.

Comparing the acoustic modes at the 200 K and 300 K in Figure 2d, we observed phonon softening with respect to temperature, especially along the [110] direction. Compared to 200 K, the structure of CH3NH3PbI3 at 300 K is closer to the highly symmetric cubic phase that commonly displays soft modes due to structural instability.52-54 Therefore, temperaturedependent phonon softening can be attributed to the random distortion and rotation of the PbI6 octahedra due to temperature change.

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Figure 2. Phonon dispersion curves of CH3NH3PbI3 at (a) 300 K and (b) 200 K; the triangle markers are the measured data from IXS experiment; the green solid line (LA) and orange solid line (TA) curves are the best fitted curves based on the green and orange markers, respectively; the green arrows mark the position of phonon dips; (c) Comparison between IXS data and simulations; the blue solid lines denote LA modes from our IXS data, while the pink and black dashed lines are LA modes from harmonic LD calculation results based on a classical model potential (Wang et al.23) and density functional theory (DFT) force constants (Yue et al.41), respectively. The arrows denote the position of phonon dips. Note that the reference data (Wang et al.23 and Yue et al.41) were plotted based on the first Brillouin zone of a cubic cell and we converted them into a body-centered tetragonal cell to directly compare with our IXS data. The

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detailed conversion can be found in SI. (d) Comparison between phonon dispersion of CH3NH3PbI3 measured by IXS at 300 K (red dashed lines) and 200 K (blue solid lines). The high-symmetry directions are plotted based on the first Brillouin zone of the body-centered tetragonal cell with c>a. Z is (0 0 1), Σ is (0.75 0 0), and X is (0.5 0.5 0) in terms of (2π/a, 2π/a, 2π/c).

Figure 3. Crystal structure illustration of CH3NH3PbI3, (a) top view and (b) side view. Orange arrows mark the orientation of [100], [110] and [001]. There are weak electrostatic interactions between PbI3- cages (green and brown) and CH3NH3+ (grey and purple) along [100] direction while there is continuous strong ionic bonding between Pb2+ (green) and I- (brown) along [110] and [001] directions.

The measured lifetimes of acoustic modes as a function of frequency are shown in Figure 4. All the lifetimes drop slightly faster than a -2 dependence based on the Klemen’s prediction55, indicating the difference between a hybrid crystal and a pure inorganic crystal. The variation in

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extracted phonon lifetimes at similar frequencies comes from the existence of different phonon modes within that frequency range. This variation is a common feature that has also been observed in the previous calculation for CH3NH3PbI323 and other materials, such as PbSe49, PbTe49 and Si56. The lifetimes at 300 K are slightly smaller than those at 200 K due to increased anharmonic phonon-phonon scattering. The smaller lifetimes, together with the smaller group velocities due to phonon softening, lead to smaller thermal conductivity at 300 K compared to that at 200 K. Although this temperature trend for thermal conductivity of CH3NH3PbI3 has been measured23, 57, it was not deeply understood before. This work provides the physical groundwork for understanding the temperature dependent trend of CH3NH3PbI3, which can benefit designing novel hybrid materials for various energy applications. Notably, the overall lifetimes are between 0.5-30 ps, which are comparable to previous measurements on the cubic phase of CH3NH3PbI3 (0.8-20 ps)39 and the residence time of CH3NH3+ in different preferred orientations measured by quasielastic neutron scattering36. The previous calculation moderately underestimated phonon lifetimes and resulted in a calculated thermal conductivity of 0.31 W/mK23, which is close to lower bound of the experimental value of 0.3-0.5 W/mK26.

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Figure 4. Phonon lifetimes as a function of frequency for acoustic modes along the [001], [100], and [110] directions measured at 300 K (red circles) and 200 K (blue triangles). The black dashed line denotes a 𝜔 ―2 dependence trend. The red and blue ellipses guide the decreasing trend of phonon lifetimes at 300 K and 200 K, respectively.

In summary, we performed high energy resolution IXS measurements to obtain the experimental phonon dispersion and lifetimes of tetragonal CH3NH3PbI3 at both 200 K and 300 K. This work provides the benchmark data for future studies on phonon properties of CH3NH3PbI3 and offers the underlying mechanisms governing ultralow thermal conductivity. We discovered profound phonon dip in LA branch along [100] and phonon softening in the acoustic branches along [110] direction at both 200 K and 300 K. These peculiar phonon softening behaviors uncover the unique atomic interactions in the hybrid perovskites. The ultralow thermal conductivity can be attributed to small group velocities due to ultrasoft acoustic modes and short phonon lifetimes caused by the strong acoustic-optical phonon scatterings originating from the gapless feature between acoustic and optical branches. These key phonon features for ultralow thermal conductivity revealed in this study can serve as useful criteria of designing the novel hybrid materials. For example, machine learning techniques can be applied to search for these features to design and discover new materials with ultralow thermal conductivity. As temperature increases, acoustic phonons soften and phonon lifetimes reduce due to increased phonon-phonon scattering. We expect this work to set a solid foundation for phonon properties of hybrid perovskites and profoundly impact their energy applications including photovoltaics and thermoelectrics.

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Acknowledgements This work was funded by Z.T.’s NSF CAREER Award (CBET-1839384). Z.T. was also supported by a 3M Non-Tenured Faculty Award. This work was supported by the Molecular Foundry at Lawrence Berkeley National Laboratory, a user facility supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy (DOE) under Contract No. DE-AC02-05CH11231. This research used resources of the Advanced Photon Source, a U.S. DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

Supporting Information Available Sample preparation and characterization, radiation damage analysis, original fitting data for phonon dip around q=0.6 in the [100] and phonon softening at the zone boundary of the [110] direction, direction conversion between cubic and body-centered tetragonal CH3NH3PbI3, and optical phonon modes of tetragonal CH3NH3PbI3 single crystals.

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Experimental Phonon Dispersion and Lifetimes of Tetragonal

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