Directional Negative Thermal Expansion and Large Poisson Ratio in

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Directional Negative Thermal Expansion and Large Poisson Ratio in CHNHPbI Perovskite Revealed by Strong Coherent Shear Phonon Generation 3

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Pierre-Adrien Mante, Constantinos C. Stoumpos, Mercouri G. Kanatzidis, and Arkady Yartsev J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 28 May 2018 Downloaded from http://pubs.acs.org on May 28, 2018

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is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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Directional Negative Thermal Expansion and Large Poisson Ratio in CH3NH3PbI3 Perovskite Revealed by Strong Coherent Shear Phonon Generation Pierre-Adrien Mante,1, 2, * Constantinos C. Stoumpos,3 Mercouri G. Kanatzidis,3 and Arkady Yartsev2, * 1

Department of Applied Physics, Hong Kong Polytechnic University, Hung Hom, Kowloon,

Hong Kong. 2

Division of Chemical Physics, Department of Chemistry, Lund University, 221 00 Lund,

Sweden. 3

Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA.

AUTHOR INFORMATION Corresponding Author *[email protected] * [email protected]


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ABSTRACT

Despite the enormous amount of attention CH3NH3PbI3 has received, we are still lacking an indepth understanding of its basic properties. In particular, the directional mechanical and structural characteristics of this material have remained elusive. Here, we investigate these properties by monitoring the propagation of longitudinal and shear phonons following the absorption of a femtosecond pulse along various crystalline directions of a CH3NH3PbI3 single crystal. We first extract the sound velocities of longitudinal and transverse phonons along these directions of the crystal. Our study then reveals the negative directional thermal expansion of CH3NH3PbI3, which is responsible for a strong coherent shear phonon generation. Finally, from these observations, we perform the elastic characterization of this material, revealing large directional Poisson’s ratio, which reaches 0.7, and that we associate to the weak mechanical stability of this material. Our results also provide guidelines to fabricate transducer of high frequency transverse phonons.

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The incredible performance of methylammonium lead iodide, CH3NH3PbI3, in optoelectronics applications has attracted a large attention.1-6 In just a few years, the efficiency of solar cells based on this material has exploded.2-6 CH3NH3PbI3 has a perovskite structure with organic and inorganic sub-lattices. Due to this exotic structure and despite the huge level of attention received, an in-depth understanding of many properties is still lacking and numerous questions remain open, from charge transport to stability.7 To solve these issues, detailed investigations of the basic physical properties of CH3NH3PbI3 is needed. A multitude of optical and electronic characterizations have been performed,8-11 but the weak stability and the wealth of fabrication processes greatly hamper the acquisition of a unified picture of the properties of this material.12, 13 Mechanical properties, such as elastic constants, are important in understanding the physical properties of this perovskite, as they provide key information on electrical transport,9 and the stability of the material.7,

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A deeper knowledge of the mechanical properties of

CH3NH3PbI3 is also required to achieve the long-term prospects of this material as many of its foreseen applications depend on its robustness and thermal stability.15 Experimental studies of the mechanical properties of CH3NH3PbI3 are scarce and have been mostly limited to nano-indentation,14,

16, 17

which only gives access to a limited set of

information, i.e. the Young’s modulus and the hardness.18 The limitations of this approach forbid to obtain a deeper understanding of the mechanical behavior of this material. In particular, thermal expansion and Poisson’s ratio cannot be obtained with nano-indentation, despite their importance to understand the stability of this material. Additionally, the value of these properties for different crystalline orientation has not been explored in details. The Poisson’s ratio, which represents the ratio of transverse to longitudinal strain due to a compression, is often considered


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as an isotropic property in CH3NH3PbI3.16, 19 To the best of our knowledge, there are no reports of Poisson’s ratio along different crystalline directions of this perovskite crystal. Regarding the thermal expansion coefficients, some investigations have reported negative directional thermal expansion along the crystallographic c-axis for the tetragonal β-phase.20, 21 It is thus critical to use experimental methods that allow the retrieval of mechanical and structural properties in the various crystalline direction of this material. This task is well suited for picosecond ultrasonics,22-30 a technique based on femtosecond pump-probe spectroscopy. This experimental method allows monitoring the propagation of phonons and gives direct access to the sound velocities and to the elastic constants. It has, in particular, been applied already on another hybrid halide perovskite, CH3NH3PbBr3, to highlight its strong anisotropy.29 Moreover, the investigation of the phonon generation mechanism offers a window in the complex interaction between photons, electrons and phonons,9 and further improves the characterization possibilities of this approach. In this letter, we have applied the picosecond ultrasonics method22-30 to investigate the directional thermal expansion coefficient and Poisson’s ratio of CH3NH3PbI3. First, we derive the model for the generation of coherent phonons, both shear and longitudinal, induced by the absorption of a femtosecond laser pulse in a material exhibiting negative directional thermal expansion. Our analysis reveals that in such materials, the generation of shear phonons can be much stronger than the generation of longitudinal phonons. We then experimentally investigate coherent phonons propagation in a single CH3NH3PbI3 crystal. We observe coherent shear and longitudinal phonons and extract the sound velocities in multiple directions of the crystal. Then, by comparing the amplitude of those signals, we confirm the negative directional thermal expansion of this material. We then take advantage of the observation of these multiple phonon


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polarizations to perform an elastic characterization of CH3NH3PbI3. In particular, we show that for specific crystalline orientation, the Poisson’s ratio can be extremely anisotropic and can surpass the isotropic limit of 0.5. These results also show the possibility to develop efficient high frequency shear phonon transducer with CH3NH3PbI3 which are much needed to understand the structural relaxation of liquids and glass-forming materials.30, 31 We consider a sample in a coordinate system (x1, x2, x3), with x3 parallel to the normal to the sample surface. The stress, σij, induced by the absorption of a femtosecond pulse in a material can be written as:22, 23 = + − 3 ∆, (1) where Cijkl is the elasticity tensor, ηkl is the strain tensor, N is the density of photoexcited carrier, dij is the deformation potential tensor, B is the bulk modulus, βij is the linear thermal expansion tensor and ∆T is the temperature increase induced by the absorption of the laser pulse. There are two sources of stress in equation 1. The transition of electrons from valence to conduction band induces a stress through the deformation potential and the thermalization of these photogenerated carriers creates a stress through thermal expansion. Experimentally, the laser spot size is usually much larger than the penetration depth of light. As a consequence, we have translational invariance, and the stress only varies along x3.22, 23 We obtain the simplified equation of motion:

= , (2)

where ui is the displacement in the i direction. From Eq. 2, we see that in order to generate a shear wave, i.e. a wave propagating along x3, but with displacement in the (x1, x2) plane, we need the off-diagonal term of the stress tensor to be non-zero. In other words, the deformation


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potential and thermal expansion tensors should have non-vanishing off-diagonal terms. Experimentally, we can achieve these conditions by using a material with anisotropic thermal expansion and/or deformation potential and orienting it in a direction of low symmetry.24-27 Injecting Eq. 1 in Eq. 2, we obtain the following wave equation:24-27 ! 1 − = − 3 , (3) with α, the phonon polarization and v, the sound velocity. The values of the effective deformation potential constant, dα, and thermal expansion coefficient, βα, depend on the material properties and the orientation of the crystal relative to the normal to the sample’s surface. At room temperature, CH3NH3PbI3 has a tetragonal crystalline structure,9 and, therefore, the deformation potentials and thermal expansion coefficients have different values along the aand c-axis of the crystal. The tensor of these properties takes the following form: # "0 0

0 # 0

0 0&. (4) %

Due to the structure of this tensor, we limit our investigation to the effect of a rotation by an angle θ along one of the a-axis, as shown in Fig. 1.


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Figure 1. Schematic diagram illustrating the rotation of the crystal along one of the a-axis and the geometry of the experiments. Taking into account this rotation, we expect three polarizations of acoustic phonons: one pure transverse mode with displacement along x1, as well as one quasi-longitudinal mode and one quasi-shear mode, both with displacement in the (x2, x3) plane. In general, the displacements are not strictly parallel or perpendicular to the direction of propagation. The phonons with displacement closest to the direction of propagation are called quasi-longitudinal, and the ones with displacement closest to the perpendicular to the direction of propagation are called quasitransverse.32 The pure transverse mode is not expected since the projection of driving force along x1 is zero. We then obtain the effective deformation potential constant, dα, and thermal expansion coefficient, βα, responsible for the generation of quasi-shear (α=QS) and quasi-longitudinal modes (α=QL):26


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)*+ = (# − %) cos(/) sin(/), (5)

)*3 = # . sin (/) + % . cos (/), (6) where A represents either the deformation potential constant, dα, or the thermal expansion coefficient, βα. From these equations, we observe that for quasi-longitudinal phonons, and contrarily to quasi-shear waves, the contributions from the a- and c-axis add up. It also means that if a material has properties of different sign along these axes, which we will refer to as negative directional properties in the following, it will be possible to generate strong quasi-shear phonons. This idea was evidenced recently in BiFeO3 that have piezoelectric coefficients of different signs along different crystalline directions.26 In Ref. 26, it was shown that it is possible to generate transverse phonons that induced changes of reflectivity six times stronger than for longitudinal phonons. To investigate the generation of shear phonons in tetragonal CH3NH3PbI3, we prepared single crystals as reported previously.9, 33 CH3NH3PbI3 single crystals exhibit naturally the (100) and (112) facets.34 We then performed transient reflectivity experiments on these different facets (see Methods). In Fig. 2a, we present the experimental transient reflectivity obtained on the (112) facet of the CH3NH3PbI3 single crystal with a pump wavelength of 550 nm and a probe wavelength of 850 nm.


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Figure 2. (a) Transient reflectivity obtained on a (112) facet for a pump wavelength of 550 nm and a probe wavelength of 850 nm. (b) Transient reflectivity after removal of the electronic


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contribution on the (100) and (112) facets for pump and probe wavelengths of 550 and 850 nm, respectively. (c) Fourier transform of the transient reflectivity signals revealing the enriched spectrum in the direction. We observe a sharp rise of the reflectivity at zero time delay corresponding to the photoexcitation of carriers. The signal then decays due to thermalization of electrons and holes with the lattice followed by charge recombination. On top of this signal, we observe oscillations that correspond to the propagation of coherent acoustic phonons. We extract the signal arising from coherent phonons by fitting the electronic contribution with a double exponential function and then subtracting this fit from the measured kinetics. We performed this procedure on transient reflectivity signals obtained on (100) and (112) facets (Fig. 2b). The oscillations, known as Brillouin oscillations, are due to the interference between the part of the probe pulse reflected at the free surface and the part reflected by the propagating acoustic wave.28 The shape of oscillations varies greatly between different facets. For the (100) direction, we observe exponentially decaying oscillations, while for the (112) direction, the signal is more complex. To obtain a better understanding of these signals, we performed their Fourier transform (Fig. 2c). For the (100) facets, we observe a single frequency at 12.0 GHz. We attribute this frequency to the Brillouin oscillations arising from longitudinal phonons. Indeed, the frequency of the Brillouin oscillations f is given by f=2nv/λ,28 with n the refractive index at the wavelength λ. Here, using n = 2.4 at 850 nm,35 we measure a longitudinal sound velocity of 2125 m.s-1, close to literature value of 2135 m.s-1.19 In the case of the (112) facets, we observe three frequencies at 3.5, 7.2 and 11.5 GHz. The attribution of these frequencies to Brillouin oscillations is confirmed by the probe wavelength dependence of the phonon frequencies (see Supplementary information). Using the same principle as for the (100) direction we can calculate the sound


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velocities of each of these contributions. We obtain sound velocities of 700, 1100 and 2050 m.s1

. These values are in good agreement with the expected values of the shear, quasi-shear and

quasi-longitudinal phonons as can be seen in the slowness curves of the (110) plane calculated with elastic constants from Ref. 19 and presented in Fig. 3. The angle between the (112) and (110) direction where found using a dot product and assuming that the lattice constant along the c-axis is √2 times longer than along the a-axis.21

Figure 3. Slowness curves representing the sound velocity of shear, quasi-shear and quasilongitudinal phonons in the (110) plane and the experimentally determined sound velocity measured on the (112) facet.


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Specific orientation with low symmetry, such as the (112) facet of the CH3NH3PbI3 crystal, allows the generation of shear and quasi-shear phonons, while for highly symmetric direction, only longitudinal phonons are observed, as is the case for the (100) facet. Contrarily to our expectation, we are able to detect not only quasi-shear phonons but also shear phonons. The quasi-shear phonon generation can stem from the difference of thermal expansion coefficients and deformation potential along the a- and c-axis. On the other hand, the observation of the pure shear mode is surprising, as it would imply that the deformation potential constants or the thermal expansion coefficients are not the same along the and the directions, which should not occur in tetragonal crystals. There are to the best of our knowledge, no reports of such difference for thermal expansion coefficients, but such discrepancy has been reported for the deformation potential, and could thus explain the observation of a pure shear mode.36 If we now consider the intensity of the detected signal, we observe that the amplitude of the quasi-shear phonons is the largest one. In particular, for these specific experimental conditions, the quasi-shear phonon signal is almost two times larger than the longitudinal one. We have shown previously that the observation of a large shear phonon signal, larger than the quasi-longitudinal one is a sign of directional negative properties. Since the deformation potential constants of CH3NH3PbI3 have the same sign along various directions,36 we can conclude that the large generation of quasi-shear phonons results from the strong anisotropy of the thermal expansion, and more precisely, given the strong amplitude of shear phonons, from directional negative thermal expansion. However, it is important to note that at this stage, it is not possible to perform a quantitative analysis of the directional thermal expansion. Indeed, the measured signals are proportional to the longitudinal and transverse strain multiplied by the relevant component of the photo-elastic tensor. This tensor, which relates the change in


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refractive index along one direction to the strain in another one, is still unknown for CH3NH3PbI3. In our results, the shear phonon signal stronger than the longitudinal one is attributed to the opposite sign of the thermal expansion coefficients along the a- and c-axis, a feature that has been seen in numerous perovskite structures,37 including CH3NH3PbI3.21 The mechanisms responsible for negative thermal expansion depend on the material and are still under debate.38 In general, a phase transition to a smaller volume phase is one of the mechanisms that could be responsible for such behavior. CH3NH3PbI3 exhibits such a phase transition near 330 K from the tetragonal to the cubic phase.21 The transformation from the tetragonal to the more symmetric cubic crystal phase implies that while the a-axis undergoes an expansion, the c-axis contracts.21 These are the exact conditions required for generation of strong transverse phonons, as showcased in Eq. 5. These results highlight the potential of CH3NH3PbI3 as an efficient coherent shear phonon transducer. In this material, the ratio of the signal induced by quasi-shear phonons to the one from quasi-longitudinal phonons is increased by one order of magnitude, compared to materials without directional negative properties.24 Additionally, in Fig. 3, we notice a large difference between the sound velocity of transverse and longitudinal waves for certain specific crystalline direction. In isotropic materials, the ratio of velocities is related directly to the Poisson’s ratio, which represents the ratio of transverse to longitudinal strain due to a longitudinal compression, and is bounded between -1 and 0.5. The large difference in sound velocities hints at some peculiarities of the Poisson’s ratio. It is thus appealing to extract its value for various crystal orientations. Using the elastic constants of Ref. 19, which are in good agreement with the sound velocities we measured, we calculated these values for different orientation of the crystal (Fig. 4).39


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Figure 4. Poisson’s ratios of tetragonal CH3NH3PbI3 for rotation about (a) the z direction, (b) the x direction and (c) the y direction. For each curve, a compression is applied along the x’ axis and the ratio of displacement along the y’ and x’ axis (blue curves) and along the z’ and x’ axis (red curves) are measured. In these plots, we study the effect of a compression along one axis on the displacement in perpendicular directions. For that, we consider the coordinate system (x,y,z) that corresponds to the crystal lattice. We then perform a rotation of this system and obtain the (x’,y’,z’) system as described in Fig. 4. We calculate the Poisson’s ratio corresponding to the ratio of displacement along x’ and y’ (blue curves, ν12) and to the ratio of displacement along x’ and z’ (red curves, ν13), after the application of a compression along x’.39 These plots of the directional Poisson’s ratios in CH3NH3PbI3 reveal strong anisotropy, similar to what has been observed for CH3NH3PbBr3.29 For instance, we see in Fig. 4a, that for θ=0°, by applying a compression along one of the a-axis, the displacement is 7 times larger along the c-axis than in the perpendicular a-


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axis. Furthermore, for numerous orientations, the Poisson’s ratio is extremely large and can even surpass the isotropic limit of 0.5. Our study shows that, in addition to its numerous extraordinary electronic and optical properties, CH3NH3PbI3 also displays unusual mechanical properties. The strong Poisson’s ratio values we observe could be related to the weak mechanical stability of this perovskite material. Poisson’s ratio is an indicator of the stability of a material, in particular to its capacity to absorb acoustic energy.40, 41 Using the Poisson’s ratio, we can classify materials as ductile or brittle. A transition from brittle to ductile occurs around a value of 0.3.40, 41

Material with larger Poisson’s ratio are ductile and can be easily deformed elastically. On the

other hand, materials with lower Poisson’s ratio are brittle. These materials are extremely hard but can break easily. The anisotropy of the Poisson’s ratio in CH3NH3PbI3 shows that along certain specific directions, this perovskite can easily break, in particular along the c-axis, as shown by the large value of ν13. In conclusion, we have investigated the directional thermal expansion and Poisson’s ratio of CH3NH3PbI3 using picosecond ultrasonics. We observe the propagation of longitudinal and shear phonons along multiple directions of the crystal and retrieved their sound velocities. By comparing the amplitudes of the shear and longitudinal phonon signals, we were able to show the negative directional thermal expansion of this material, that we attributed to the light absorption induced local heating and a consequential tetragonal to cubic phase transition of the single crystal. Finally, we calculated the Poisson’s ratio of CH3NH3PbI3, revealing large values for specific orientations. We then correlated these large values of Poisson’s ratio to orientation in which the mechanical stability is low. Our results demonstrate the possibility to use materials with directional negative thermal expansion for efficient generation of high frequency coherent transverse phonons and offer a new platform for the investigation of phase transitions.


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METHODS Femtosecond pump-probe experiments. Experiments were carried out using a regeneratively amplified, mode-locked Yb:KGW (Ytterbium-doped potassium gadolinium tungstate) based femtosecond laser system (Pharos, Light conversion) operating at 1030 nm with pulse duration of 200 fs. The repetition rate of the laser is 2 kHz. The output is then split in two and is used to pump two non-collinearly phase-matched optical parametric amplifiers (NOPAs). The first one (Orpheus-N, Light Conversion), was used to generate pump pulses centered at 550 nm with pulse duration of about 35 fs. With the second NOPA (Orpheus-N, Light Conversion), we generated probe pulses at 850 nm with 40 fs pulse duration. A mechanical delay stage controls the delay between the pump and probe pulses. The pump beam was chopped at the frequency of 1 kHz, allowing measuring the reflectivity of the sample with and without pump and obtaining ∆R. Both beams were focused on the sample and the modification of the probe reflectivity induced by the pump was time-resolved. AUTHOR INFORMATION The authors declare no competing financial interests. ACKNOWLEDGMENT The work at Lund University was supported by the Crafoord Foundation, the Knut and Alice Wallenberg Foundation, and grant 2017-05150 from the Swedish Research Council (VR). The work at Northwestern University was supported by grant SC0012541 from the U.S. Department of Energy, Office of Science. SUPPORTING INFORMATION Probe wavelength dependent transient reflectivity on the (112) facets of CH3NH3PbI3 REFERENCES


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