1 Type of the Paper (Article) Unusual breathing behavior

Crystals 2020, 10, x; doi: FOR PEER REVIEW www.mdpi.com/journal/crystals

Type of the Paper (Article) 1

Unusual breathing behavior of optically excited 2

Barium Titanate nanocrystals 3

Jiecheng Diao 1, Mathew Cherukara 3, Ross Harder 3, Xiaojing Huang 2, Fucai Zhang 1,4, Bo Chen 4 1,5, Andrew Ulvestad 3, Sanghoon Song 6, Diling Zhu 6, David Keen 7 and Ian Robinson 1,2,*, 5

1 University College, London, WC1E 6BT, UK; [email protected] (I.R.); [email protected] (J.D.) 6 2 Brookhaven National Laboratory, Upton NY 11973, USA; [email protected] (X.H.); 7 3 Argonne National Laboratory, Argonne IL 60439, USA; [email protected] (M.C.); [email protected] 8

(R.H.); [email protected] (A.U.) 9 4 Southern University of Science and Technology, Shenzhen 518055, China; [email protected] (F.Z.) 10 5 Tongji University, Shanghai 201804, China; [email protected] (B.C.) 11 6 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA; [email protected] (S.S.); 12

[email protected] (D.Z.) 13 7 Rutherford Appleton Laboratory, Harwell Oxford, Didcot OX11 0QX, UK; [email protected] 14

(D.K.) 15 * Correspondence: [email protected] 16 Received: date; Accepted: date; Published: date 17

Abstract: Coherent X-ray Diffraction patterns were recorded using an X-ray Free-electron Laser 18 from Barium Titanate nanocrystals as a function of time delay after laser excitation. Rather than 19 seeing any significant thermal expansion effects, the diffraction peaks were found to move 20 perpendicular to the momentum transfer direction. This suggests a laser driven rotation of the 21 crystal lattice. This unusual behavior can be explained as a piezoelectric response coupled with 22 internal twinning of the nanocrystals. 23

Keywords: X-ray pump-probe; coherent imaging; ferroelectric oxide 24 25

1. Introduction 26 Barium Titanate, BaTiO3 (BTO), is an important ferroelectric material, which was first used to 27

explain the coupling of lattice distortions with phonon mode softening, leading to its ferroelectric 28 structure [1]. It has the classical phase diagram for a perovskite oxide material, with a cubic 29 structure at high temperature, becoming tetragonal below TC = 393K and then orthorhombic below 30 T2 = 273K [2]. The room temperature tetragonal phase is ferroelectric with an electric polarization 31 along its c-axis attributed to displacement of the perovskite B-site Ti4+ ion with respect to the A-site 32 Ba2+, locally displaced towards the unit cell corners. 33

Nanosized BTO is an important industrial material for making supercapacitors. BTO’s 34 dielectric constant peaks as a function of size with a maximum around 140nm with a factor of three 35 enhancement of dielectric constant resulting in a big improvement in capacitor performance [3]. A 36 major industry is currently building up for energy storage, which is of significant interest in Energy 37 Sciences. Although BTO has clear structural phase transitions, there are studies showing local 38 rhombohedral distortion even in the cubic phase [4,5]. A powder diffraction study proposed a 39 core-shell structure for the nanoparticles, in which the core is tetragonal and the shell is cubic [6]. 40 The dynamical aspects of this model could in principle explain the enhancement of dielectric 41 constant. 42

Previous experiments on pump-probe diffraction from BTO thin films at the Linac Coherent 43 Light Source (LCLS) showed a small lattice expansion, but no direct piezoelectric response [7]. A 44 fast sub-10ps transient increase of the 003 peak intensity was detected, followed by a shift of the 45

Crystals 2020, 10, x FOR PEER REVIEW 2 of 8

rocking curve to lower angles on an acoustic response time of 15ps. The response indicates a lattice 46 expansion of 0.04% and 0.11% in two different experiments using THz illumination. The expansion 47 was reported to be linear in fluence and attributed to enhanced vibrations of the Ti4+ ion, analogous 48 to transient heating, subsequently relaxing on a time scale of 10ns. 49

Bragg Coherent Diffraction Imaging (BCDI) is a powerful X-ray technique for investigating the 50 structures of nanocrystals in three dimensions on the 30nm resolution scale [8]. By using an area 51 detector far enough from the sample, the fringes surrounding a Bragg diffraction peak, due to the 52 external shape of the crystals, can be oversampled with respect to their spatial Shannon-Nyquist 53 frequency. Such data can be inverted to images using iterative algorithms, namely the Error 54 Reduction and Hybrid Input-Output method [9]. These methods depend on a well-defined spatial 55 support function, used as the real-space constraint, which can be provided by a “shrink-wrap” 56 approach [10]. The feature of BCDI, which is important here, is its high sensitivity to strain [11]. In 57 this work, BCDI is combined with laser excitation of the samples in a pump-probe approach to 58 obtain ultrafast time-resolved images of internal strain fields [12]. 59

2. Materials and Methods 60 Barium Titanate (BTO) nanocrystals were obtained commercially from Sigma-Aldrich and were 61

assumed to have been fabricated by hydrothermal synthesis. The crystals were found by Scanning 62 Electron Microscopy (SEM) to have roughly spherical shapes and a size distribution centered at 63 200nm. Crystals were drop-cast from ethanol suspension onto a Si3N4 (SiN) window array 64 provided by Silson. The crystals were bonded to the substrate using 1% Tetraethyl Orthosilicate 65 (TEOS) as an adhesive and calcined in air at 723K [8]. No particular care was taken to ensure that 66 the crystals were separated from each other on the substrate; this was found to have consequences 67 for the laser excitation described below. 68

The transmission geometry was used to measure Coherent X-ray Diffraction patterns of the 69 samples. We had previously found [13] this led to slightly higher damage thresholds for the 70 samples to become detached from the substrate by radiation pressure, at least with respect to the 71 commonly-used grazing incidence geometry [14]. The samples were mounted on the Huber 72 diffractometer of the X-ray Pump-Probe (XPP) station of the LCLS X-ray Free Electron Laser (XFEL) 73 at Stanford. The 9keV X-ray beam was focused with in-line X-ray Compound Refractive Lenses 74 (CRLs) and 10-15% attenuators were used to stay below the X-ray damage threshold, as detected by 75 sudden loss of diffraction peaks. 120Hz repetition rate was used. 2D and 3D Bragg Coherent 76 Diffraction Imaging (BCDI) data at a range of delay times were collected on the CS-Pad detector 77 (pixel size 110µm) placed 1.575m from the sample at 27° Bragg angle in the vertical scattering-plane 78 geometry. After mapping the general behavior, discussed below, we selected about six 79 nano-crystals for detailed BCDI measurement over 36 hours of “standard configuration” operations 80 at LCLS. 81

The XPP Ti-sapphire laser was synchronized with the X-ray beam via a motorized delay line, 82 allowing pump-probe delays up to several nanoseconds. The beam came down through the hutch 83 roof and was directed onto the sample by the final focusing mirror in a collinear geometry with 84 about 2° inclination. Temporal overlap was calibrated with a Bi standard. Spatial overlap was set 85 with phosphor screens and checked using diffraction effects seen from the actual samples, as well as 86 with some Au standard crystals [14]. The laser was used on the third harmonic, with wavelength 87 266nm, to excite the sample above its band gap of 5eV. Manual adjustments were made initially of 88 the time delay and the beam position on the sample to explore the response to the laser with a 89 real-time display. Then time-delay scans were made on aligned samples to extract quantitative 90 values for the Bragg peak position on the detector to learn about the laser induced changes of the 91 crystal structure. 92

3. Results 93 Previous experiments on metal nanocrystals have measured radial oscillatory Bragg peak 94

movements on the detector. These are identified as breathing modes of crystal vibration in which 95


the crystal expands and contracts with a period given by the ratio of the speed of sound to the crystal 96 size [14]. These vibrations represent the impulse response of the crystal to a short thermal pulse 97 applied homogeneously throughout the crystal. The Two Temperature Model (2TM) [15] is 98 invoked to explain how the optical excitation reaches the entire nanocrystal faster than the sound 99 velocity: the optical absorption is relayed by hot electrons which travel rapidly through the crystal 100 before equilibrating their temperature with the lattice. Both the electron transport and 101 electron-phonon coupling take place on a time scale of around 1ps, significantly faster than the 102 acoustic response of the crystal, for which the vibration period is consistent with the speed of sound 103 in the material. 104

We observed two clear Debye-Scherrer (DS) rings of spots corresponding to the tetragonally 105 distorted (110) and (101) diffraction peaks. The spots from individual nanocrystals were 106 well-separated and the number of peaks on the outer (110) ring was roughly half the number on the 107 inner (101) ring, consistent with the multiplicity. Unexpectedly, during real-time monitoring of the 108 diffraction pattern during laser excitation, we found that some of the diffraction spots moved 109 around the DS ring, transverse to the scattering vector direction. This motion reversed when the 110 laser was turned off. Some other spots showed a blinking behavior, becoming less or more intense 111 upon excitation. There were also many diffraction spots which did not respond at all to the laser, a 112 behavior we attribute to blocking of the laser by other nanocrystals within the clusters of crystals 113 seen in the SEM. No significant radial spot motion was detected in this real-time preliminary 114 investigation. 115

We attribute both responses to crystal rotations, as shown in Figure 1. The transverse motion 116 corresponds to a component of rotation around the forward direction, denoted “X-axis” in the 117 figure, while the blinking corresponds to transverse rotations on or off the Bragg condition, denoted 118 “Z-axis”. Rotations of crystals about their third axis, denoted “Y-axis”, the scattering vector 119 direction, would not have been detected. 120

121 Figure 1. Illustration of the set-up for the X-ray pump-probe experiment performed at LCLS. A 0.5m 122 delay stage is used for making laser pulse time delays up to 3000ps. The wave plate is used to control 123 the fluence of laser pulses. The X, Y and Z axis of the crystal under Bragg condition is shown. The 124 rotation of crystal on X-axis causes the diffraction pattern to move in X direction on detector, which is 125 along the (110)/(101) powder ring. The rotation around the Z-axis results in a scanning of crystal 126 around its Bragg condition and leads to intensity difference. This is the “blinking” phenomenon seen 127 in the experiment. 128

Crystals were then selected for further investigation using two approaches. Time delay scans 129 were performed after centering a selected nanocrystal in the X-ray beam and on the maximum of its 130 rocking curve; these allowed detailed measurement of the Bragg peak position on the detector with 131


sub-pixel accuracy as a function of time delay. Figure 2a shows the rotation angle variation of 132 diffraction pattern comparing with the position at the start of measurement, along the X and Y 133 directions of the detector. Zone 1 and Zone 2 were acquired from different scans and combined 134 together. The waterfalls of these position changes can be seen in Figure 2c to 2f. Figure 2b shows the 135 intensity plot over different delay times. There is a clear difference between Zone 1 and Zone 2. In 136 Zone 1, the intensity is higher and the period of oscillation is shorter, around 100ps. While in Zone 2, 137 there is a 450ps periodic oscillation when time delay is over 1500ps. 138

139 Figure 2. (a) The rotation of a BTO diffraction pattern along the X and Y directions of the detector as a 140 function of laser pulse delay. (b) Intensity plot of diffraction pattern for different laser-pulse delays. 141 Zone 1 and Zone 2 were recorded before and after a BCDI measurement. (c)-(f) Waterfall plot of 142 transverse (X) and radial (Y) slices through the diffraction pattern for different time delays. The first 143 and second column display positions in the X and Y directions, respectively. 144

The time scale for both these rotations was the same, so we conclude it was just due to its chance 145 orientation of the crystal around the (110) Q-vector of the measurement. There is an interesting 146 delayed onset of the motion in Figure 2a, around 250ps, seen on this crystal and several others. This 147 can be understood as the laser and X-ray beam are not hitting the same crystal in the BTO aggregates 148 and acoustic coupling between them. Figure 3 is a sketch to show there can be a delay between X-ray 149 illumination and laser heating. The crystal inside (colored blue) is illuminated by X-ray and been 150


imaged, while the laser is heating another crystal on bottom. It takes time for the mechanical 151 response to the laser to transfer from bottom side to the top, which explains the time gap before 152 onset of the motion. 153

154 Figure 3. Illustration of the time delay between laser heating and x-ray illumination. The crystal 155 colored blue is been illuminated by the X-ray beam and gives out X-ray diffraction profile. 156

At strategic points on these time delay scans, BCDI data were taken by collecting rocking curves 157 with angular steps fine enough to oversample the coherent diffraction pattern. These 3D datasets 158 were inverted to real-space images using standard iterative algorithms, alternating cycles of error 159 reduction and hybrid input-output [9], using a “shrink-wrap” support [10] and partial coherence 160 correction [16]. The data inversion was carried out in the detector-pixel-angle coordinate system 161 and then transformed to the laboratory coordinates in the standard way [11]. The first column of 162 Figure 4 shows the central slice of the 3D diffraction patterns at different time delays, while the 163 second and third columns shows their corresponding reconstructed Bragg density slice and 164 displacement slice, respectively. The displacement shown at each point in the crystal is derived 165 from the phase of the complex image f, and given as the projection of the 3D displacement u along 166 the Q-vector, using the relation f = Q·u. For a perfect single crystal, the Bragg density map would 167 have only one center in the middle and monotonically decrease towards the surface. In this case, 168 however, there are several high-density regions distributed inside the single crystal, indicating a 169 complex nature. The displacement map is also seen to be changing with time delay. The crystal has a 170 positive displaced region seen before the laser pump at -50ps. After +50ps of pump-probe delay, the 171 positive displaced region diminishes, while there are negative displaced regions appearing at the 172 surface, which could arise from contacts with surrounding crystals showing a compressive strain. 173 When the laser pump delay reaches +500ps to +700ps, a positive displaced region is showing up on 174 the surface. Upon +900ps laser delay, the positive region inside crystal comes back. 175


176 Figure 4. Diffraction patterns and reconstructed images of the same BTO crystal shown in Figure 2 177 after different pump-probe delays. The first column shows the diffraction patterns, while the second 178 and third columns are Bragg density and phase slices in which the phase is expressed as the 179 component of crystal displacement along the Q-vector (shown in red). 180

4. Discussion 181 Our XFEL experiment clearly shows that rotations of the BTO nanocrystals are induced by laser 182

excitation on a 100ps time scale, appropriate for an acoustic response of the material. The time 183 delay on a similar time scale could be attributed to generation of the acoustic waves at some distance 184 from the part of the sample probed with the X-ray diffraction. The longitudinal and transverse 185


speeds of sound of BTO (in sintered ceramics) are 4800m/s and 2400m/s [17,18], so the 250ps time 186 delay corresponds to a distance between the excitation and its observation of 1.2µm or 0.6µm. The 187 apparent vibration period of 450ps would correspond to the breathing of a slab of crystal 1.1µm or 188 0.55µm thick. Both these lengths are greater than the 200nm size of the particles being measured 189 with the X-rays, so we consider this represents a collective response of several nanocrystals bonded 190 together, as seen in SEM images of the samples used. 191

192

Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: Waterfall of 193 diffraction pattern over different time delays. 194 Author Contributions:. All authors contributed to planning, executing the experiment, analysis of data and 195 writing the manuscript. 196 Funding: The work was supported by the UK EPSRC grant EP/I022562/1. Work at Brookhaven National 197 Laboratory was supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy 198 Sciences, under Contract No. DE-SC0012704. Work at Argonne National Laboratory was supported the DOE 199 Office of Science by under Contract No. DE-AC02-06CH11357. Work at the SLAC National Accelerator 200 Laboratory, was supported by the DOE Office of Science, Office of Basic Energy Sciences under Contract No. 201 DE-AC02-76SF00515. 202 Acknowledgments: The x-ray pump-probe experimental work was carried out at the Linac Coherent Light 203 Source, a National User Facility operated by Stanford University on behalf of the U.S. Department of Energy, 204 Office of Basic Energy Sciences. We are grateful for useful discussions about this work with Jesse Clark, Aaron 205 Lindenberg, Mariano Trigo, David Reis and Wen Hu. 206 Conflicts of Interest: The authors declare no financial conflict of interest. 207

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1 Type of the Paper (Article) Unusual breathing behavior