Letter pubs.acs.org/NanoLett
Coherent Diffraction Imaging Analysis of Shape-Controlled Nanoparticles with Focused Hard X‑ray Free-Electron Laser Pulses Yukio Takahashi,*,†,‡ Akihiro Suzuki,†,‡ Nobuyuki Zettsu,§ Tomotaka Oroguchi,∥,‡ Yuki Takayama,∥,‡ Yuki Sekiguchi,∥,‡ Amane Kobayashi,∥,‡ Masaki Yamamoto,‡ and Masayoshi Nakasako∥,‡ †
Department of Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan ‡ RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan § Department of Environmental Science and Technology, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan ∥ Department of Physics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan S Supporting Information *
ABSTRACT: We report the first demonstration of the coherent diffraction imaging analysis of nanoparticles using focused hard X-ray free-electron laser pulses, allowing us to analyze the size distribution of particles as well as the electron density projection of individual particles. We measured 1000 single-shot coherent X-ray diffraction patterns of shapecontrolled Ag nanocubes and Au/Ag nanoboxes and estimated the edge length from the speckle size of the coherent diffraction patterns. We then reconstructed the two-dimensional electron density projection with sub-10 nm resolution from selected coherent diffraction patterns. This method enables the simultaneous analysis of the size distribution of synthesized nanoparticles and the structures of particles at nanoscale resolution to address correlations between individual structures of components and the statistical properties in heterogeneous systems such as nanoparticles and cells. KEYWORDS: Shape-controlled synthesis, size distribution, coherent diffraction imaging, X-ray free-electron laser
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particle shape is assumed to be a sphere. On the other hand, imaging analysis in an EM, which has been developed as a result of recent advances in image-processing software, can directly measure the particle size as well as the particle shape without a priori knowledge or assumptions. However, it is difficult to use electrons as a probe to quantitatively visualize the internal structures of metals with thickness more than ∼50 nm owing to the multiple scattering and inelastic scattering of electrons. In contrast to electron beams, X-rays are a useful probe for analyzing local structures buried within bulk materials because of their high penetration power. In particular, coherent X-ray diffraction imaging15,16 (CXDI), which is a lensless X-ray imaging technique based on diffraction-pattern oversampling17,18 and phase retrieval calculation19 is a promising technique for visualizing the electron density distribution and/ or strain distribution of nanoparticles at a high spatial resolution. Thus far, the structures of various nanoparticles such as Pb nanocrystals,20 ZnO nanorods,21 GaN-Ga2O3 core− shell particles,22 and Au/Ag nanoboxes23 have been studied by
anoparticles have been extensively studied for several decades because of the interest in their growth mechanism as well as their fascinating properties.1,2 It is wellknown that the optical properties of a nanoparticle are determined by a number of physicochemical parameters such as size, shape, and surface/internal structures. To enable the application of nanoparticles in catalysis,3 electronics,4 photography,5 information storage,6 photonics,7 sensing,8 imaging,9 and medicine,10 the high uniformity of these parameters is necessary. For instance, shape-controlled synthesis11 is an efficient way to produce nanoparticles with desired physicochemical properties. However, because complete control of the particle size with nanometer resolution is difficult, the bulk properties and inhomogeneity of synthesized particles should mainly depend on the size distribution. Therefore, statistical information on the size and structures of synthesized nanoparticles is crucial to the understanding and control of these properties. The size distribution of particles is usually measured by dynamic light scattering12 (DLS), the laser diffraction13 (LD), or imaging analysis in an electron microscope14 (EM). In wellestablished DLS and LD methods, the coefficient of viscosity and the refractive index of the solvent are prerequisite, and the © 2013 American Chemical Society
Received: August 30, 2013 Revised: November 13, 2013 Published: November 25, 2013 6028
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CXDI with synchrotron radiation. However, these synchrotron experiments required several minutes to record the diffraction pattern of a single nanoparticle for particle imaging analysis. Therefore, it is difficult to obtain statistical information on the size and structures of synthesized nanoparticles. Thus, from a practical viewpoint the application of CXDI to study the size distribution of synthesized nanoparticles is unrealistic because of the low intensity of coherent X-rays as well as the limited beam time available at synchrotron radiation facilities. X-ray free-electron lasers (XFELs) are a promising X-ray source for imaging analysis in CXDI because they provide almost completely transverse coherent X-rays with an extremely large number of photons in a single pulse with a duration less than 100 fs. XFELs have recently become available at the Linac Coherent Light Source (LCLS) in the U.S.A.24 and the SPring8 Angstrom Compact Free Electron Laser (SACLA) in Japan.25 So far, under the diffract-before-destroy scheme,26,27 large volumes of diffraction data of various specimens have been collected by single-shot diffraction measurements using an aerodynamic focusing system28 at LCLS and then computationally classified,29 and two-dimensional electron density projection maps have been visualized for a submicrometer virus,30 soot, and other aerosols31,32 at resolutions of 24 to 41 nm. In this Letter, we report the first demonstration of imaging analysis based on CXDI with focused hard XFEL pulses at SACLA. We collected a large number of data sets of the singleshot diffraction patterns of Ag nanocubes and Au/Ag nanoboxes with dimensions of 100 nm. The Ag nanocubes, which were prepared by a modified polyol synthesis technique,33,34 were single crystals with facecentered-cubic structures. When the Ag nanocubes were titrated with an aqueous solution of AuCl4−, Au/Ag nanoboxes were formed by the following galvanic replacement reaction35 3Ag + Au(III) → Au + 3Ag(I)
Figure 1. Schematic view of single-shot coherent X-ray diffraction measurement of Ag nanocubes and Au/Ag nanoboxes. XFEL pulses with an energy of ∼5.5 keV were two-dimensionally focused to a ∼1.5 μm spot size using KB mirrors. To block parasitic scattering X-rays from the mirrors, a guard slit (200 μm thick silicon with a 250 × 250 μm2 hole) was used. Forward-diffracted X-ray photons were detected by an MPCCD detector with a pixel size of 50 × 50 μm2 placed 1626.25 mm downstream of the sample. The nanoparticles were supported by a SiN membrane chip. By scanning the SiN membrane relative to the focused XFEL pulses, coherent X-ray diffraction patterns were collected on the MPCCD detector at a frequency of 1 Hz.
subsequent analysis (for details on the data screening please see Supporting Information). The measurement was ∼100 times faster than that in our previous experiments at the thirdgeneration synchrotron radiation facility SPring-8 (ref 39.). Figure 2a,b shows typical diffraction patterns from a single isolated Ag nanocube and a Au/Ag nanobox, respectively. The speckle patterns have high visibility, indicating the almost completely transverse coherence and high peak brilliance of the XFEL pulses. The diffraction patterns composed of a series of fringes perpendicularly crossing the two principal axes are due to the cubic projection densities of the particles and are approximated well by the formula for a diffraction pattern from a rectangular aperture. In the case of the Au/Ag nanobox, other periodic patterns overlaying the fringes appear, as can be seen in Figure 2b, because of the hollow interior of the particles. The relationship between the full width (Δq) of the speckles along a principal axis and the edge length (d) of a particle is simply expressed as 1 d= 2Δq (2)
(1)
The conversion of Ag nanocubes into Au/Ag nanoboxes has not yet been visualized at a resolution of 10 nm despite the need for quality control in the synthesis. Here, we determined the size distribution of the nanoparticles by measuring the edge length and then visualized the electron density projections of individual nanocubes and nanoboxes at resolutions better than 10 nm. Figure 1 shows a schematic layout of the experimental setup at BL3 in SACLA in the present study. XFEL pulses (photon energy: 5.5 keV, pulse duration: ∼10 fs) were focused to a spot of ∼1.5 μm diameter by a pair of Kirkpatrick-Baez (KB) mirrors.36 The X-ray intensity per pulse at the focal position was ∼1 × 1011 photons. The repetition ratio of XFEL pulses was reduced from 10 to 1 Hz by a pulse selector. Nanoparticles were randomly scattered on Si3N4 membranes with a 3 × 3 mm2 window. Each membrane was mounted on a goniometer in the vacuum chamber of a diffraction apparatus (KOTOBUKI-1).37 By raster scanning the membrane relative to the focused XFEL pulses at approximately 25 μm intervals, singleshot diffraction patterns were collected using a multiport charge-coupled device (MPCCD) detector.38 In 2 h, we collected 6400 diffraction patterns for each membrane. Two sets of membranes were used for each nanoparticle. The hit rates of the focused XFEL on a single isolated particle were 9.5% for the Ag nanocubes and 9.7% for the Au/Ag nanoboxes. For each particle, after screening 12 800 diffraction patterns, 1000 diffraction patterns were extracted for
Therefore, one can easily estimate the edge length of a particle from its diffraction patterns. For instance, the diffraction pattern of a Ag nanocube with a ΔqAg value of 3.11 μm−1 indicates that the edge length is 161 nm, and the edge length of the Au/Ag nanobox was determined to be 170 nm from the ΔqAu/Ag value of 2.94 μm−1 (Figure 2). The determination accuracy of Δq in our data analysis is ∼0.05 μm−1, equivalent to that for d ∼ 3 nm. Although the XFEL pulses randomly hit the nanoparticles, the 1000 diffraction patterns had sufficient intensity to apply this procedure. The distribution of edge lengths in each specimen was derived from the 1000 diffraction patterns as illustrated for the Ag nanocube (Figure 3a) and Au/Ag nanobox (Figure 3b). When the size distributions are approximated by Gaussian functions, the standard deviation (σ) values are similar for the Ag nanocube (14.5 nm) and Au/Ag nanobox (14.1 nm), suggesting that the size-controlled synthesis of the particles is possible. In contrast, the average edge length (daverage) of the 6029
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defined as the peak position in the distribution. Because Au layers have been reported to epitaxially grow on Ag nanocubes during the formation of Au nanocages,33 this difference suggests that the surface of Ag nanocubes is covered by a Au layer with a thickness of approximately 5.7 nm. From the difference in the size of the two nanoparticles, we estimated that approximately 77% of the interior Ag is oxidized and removed to form the nanocage. Thus, the distribution of edge lengths provides a statistical view of the structural changes during the epitaxial growth of a Au/Ag nanobox from a Ag nanocube. The nanostructures of individual particles were visualized by reconstructing projection electron density images, which were retrieved from the best eight diffraction patterns by the hybridinput−output method19 with the oversampling smoothness algorithm40 and shrink-wrap algorithm41 (for details on the iterative phasing method please see Supporting Information). Because these diffraction patterns had significant diffraction intensities, we consider that the illumination field across each nanoparticle was uniform. Figure 4a shows the projection maps of Ag nanocubes at the peak and slope positions in the size distribution (Figure 3). From a cross-sectional plot through line P in Figure 4a, the edge resolution of a 160 nm size particle was found to reach approximately 7 nm, which is the highest resolution of single-shot CXDI using an XFEL pulse reported thus far. The resolution of the other images is better than 10 nm. The projection maps indicate a uniform electron density over the particles except for at the edges and suggest a small size-dependent variation in the internal structures. It is considered that the contrast at the edges is due to the facet structures of the nanocube itself.33 In contrast to the Ag nanocubes, the projection maps of the Au/Ag nanoboxes have low-density regions, indicating hollow interiors (Figure 4c). We found that the size of the hollow strongly depends on the size of the Au/Ag nanobox. For particles with an edge length less than 130 nm, a small lowdensity region was observed. When a particle grows to an edge length of approximately 155 nm, the low-density region occupies 20−40% of the area of the projection map. From the edge-length distribution shown in Figure 3, more than half the particles synthesized in this study possess hollow interiors. When the edge length of the particle exceeds 170 nm, only
Figure 2. Single-shot coherent diffraction patterns of isolated (a) Ag nanocube and (b) Au/Ag nanobox with size of 501 × 501 pixels. q is defined as |q| = 2sin(Θ/2)/λ, where Θ is the scattering angle and λ is the X-ray wavelength. The pattern in the low-q region is displayed on the right. ΔqAg and ΔqAu/Ag are the speckle widths along the expanding direction for the Ag nanocube and Au/Ag nanobox, respectively.
Au/Ag nanobox (155.4 nm) is significantly larger than that of the Ag nanocube (144.0 nm), where the average edge length is
Figure 3. Edge-length distributions of Ag nanocubes and Au/Ag nanoboxes, which were derived from speckle size of 1000 coherent diffraction patterns. 6030
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general use of the proposed method of analysis including industrial use and for studies on dynamics in chemical reactions, we are planning to further develop the instruments and data acquisition scheme so that several thousand diffraction patterns can be collected within a few minutes. We believe that coherent diffraction imaging analysis with XFELs will open up a new frontier in the imaging of heterogeneous systems such as cells, aerosols, and nanomaterials.
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ASSOCIATED CONTENT
S Supporting Information *
Details of data screening and post analysis and iterative phasing method. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The experiments were performed at SACLA with the approval of JASRI and the Program Review Committee (Nos. 2012A8001, 2012B8037, and 2013A8043). This work was supported by the X-ray Free Electron Laser Priority Strategy Program and Grants-in-Aid for Young Scientists (A) (Grant 25709057) and JSPS Fellows (Grant 25·2959) from the Ministry of Education, Culture, Sports, Science, and Technology. The authors would like to thank Mr. Shin Furutaku for the preparation of the nanoparticle samples, and the beam line development and data acquisition teams for technical support in the XFEL experiments.
Figure 4. (a) Projection images of Ag nanocubes reconstructed from single-shot coherent diffraction patterns measured using XFEL pulses. The image of a nanocube with an edge length (EL) of ∼160 nm was reconstructed from the diffraction pattern in Figure 2a. (b) Crosssectional plot through line P in (a). (c) Projection images of Au/Ag nanoboxes. The image of a nanobox with EL ∼ 173 nm was reconstructed from the diffraction pattern in Figure 2b. The scale bar in (a) and (c) is 100 nm.
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cubic nanoframes appear in the retrieved images. The simultaneous analysis of the size distribution and the electron density map of the particles in this study has clearly revealed the conversion process of Au/Ag nanoboxes, in which a pinhole is formed in the initial process of the reaction and serves as a site for Ag dissolution, and then the hollow interior is formed and the Au/Ag replacement reaction is completed through the direct deposition of Au near the pinhole.35 This is the first demonstration of multiple analyses of the edge-length distribution of particles more than 100 nm in size and their surface/internal nanostructures to the best of our knowledge. Such simultaneous measurements to determine the size and size-dependent variation of structures in a short period of time are expected to have crucial importance for controlling the physicochemical properties of Au/Ag nanoboxes and Au nanocages, particularly in their application as contrast agents for optical imaging in early tumor detection and as therapeutic agents for photothermal cancer treatment.42 In conclusion, we have demonstrated the coherent diffraction imaging analysis of nanoparticles with respect to both the size distribution and individual projection structures using focused XFEL pulses. We obtained a statistical description of the structural change from a Ag nanocube to a Au/Ag nanobox and the relationship between the edge-length distribution of Au/Ag nanoboxes and the nanostructures of their hollow interiors. The present imaging analysis can also be applied to grain analysis in polycrystalline materials in the Bragg geometry. This will provide the relationship between the grain-size distribution and the crystallographic orientation of individual grains and/or the strain distribution with nanoscale resolution. Toward the
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Coherent Diffraction Imaging Analysis of Shape-Controlled Nanoparticles with Focused Hard X‑ray Free-Electron Laser Pulses Yukio Takahashi,*,†,‡ Akihiro Suzuki,†,‡ Nobuyuki Zettsu,§ Tomotaka Oroguchi,∥,‡ Yuki Takayama,∥,‡ Yuki Sekiguchi,∥,‡ Amane Kobayashi,∥,‡ Masaki Yamamoto,‡ and Masayoshi Nakasako∥,‡ †
Department of Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan ‡ RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan § Department of Environmental Science and Technology, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan ∥ Department of Physics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan S Supporting Information *
ABSTRACT: We report the first demonstration of the coherent diffraction imaging analysis of nanoparticles using focused hard X-ray free-electron laser pulses, allowing us to analyze the size distribution of particles as well as the electron density projection of individual particles. We measured 1000 single-shot coherent X-ray diffraction patterns of shapecontrolled Ag nanocubes and Au/Ag nanoboxes and estimated the edge length from the speckle size of the coherent diffraction patterns. We then reconstructed the two-dimensional electron density projection with sub-10 nm resolution from selected coherent diffraction patterns. This method enables the simultaneous analysis of the size distribution of synthesized nanoparticles and the structures of particles at nanoscale resolution to address correlations between individual structures of components and the statistical properties in heterogeneous systems such as nanoparticles and cells. KEYWORDS: Shape-controlled synthesis, size distribution, coherent diffraction imaging, X-ray free-electron laser
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particle shape is assumed to be a sphere. On the other hand, imaging analysis in an EM, which has been developed as a result of recent advances in image-processing software, can directly measure the particle size as well as the particle shape without a priori knowledge or assumptions. However, it is difficult to use electrons as a probe to quantitatively visualize the internal structures of metals with thickness more than ∼50 nm owing to the multiple scattering and inelastic scattering of electrons. In contrast to electron beams, X-rays are a useful probe for analyzing local structures buried within bulk materials because of their high penetration power. In particular, coherent X-ray diffraction imaging15,16 (CXDI), which is a lensless X-ray imaging technique based on diffraction-pattern oversampling17,18 and phase retrieval calculation19 is a promising technique for visualizing the electron density distribution and/ or strain distribution of nanoparticles at a high spatial resolution. Thus far, the structures of various nanoparticles such as Pb nanocrystals,20 ZnO nanorods,21 GaN-Ga2O3 core− shell particles,22 and Au/Ag nanoboxes23 have been studied by
anoparticles have been extensively studied for several decades because of the interest in their growth mechanism as well as their fascinating properties.1,2 It is wellknown that the optical properties of a nanoparticle are determined by a number of physicochemical parameters such as size, shape, and surface/internal structures. To enable the application of nanoparticles in catalysis,3 electronics,4 photography,5 information storage,6 photonics,7 sensing,8 imaging,9 and medicine,10 the high uniformity of these parameters is necessary. For instance, shape-controlled synthesis11 is an efficient way to produce nanoparticles with desired physicochemical properties. However, because complete control of the particle size with nanometer resolution is difficult, the bulk properties and inhomogeneity of synthesized particles should mainly depend on the size distribution. Therefore, statistical information on the size and structures of synthesized nanoparticles is crucial to the understanding and control of these properties. The size distribution of particles is usually measured by dynamic light scattering12 (DLS), the laser diffraction13 (LD), or imaging analysis in an electron microscope14 (EM). In wellestablished DLS and LD methods, the coefficient of viscosity and the refractive index of the solvent are prerequisite, and the © 2013 American Chemical Society
Received: August 30, 2013 Revised: November 13, 2013 Published: November 25, 2013 6028
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CXDI with synchrotron radiation. However, these synchrotron experiments required several minutes to record the diffraction pattern of a single nanoparticle for particle imaging analysis. Therefore, it is difficult to obtain statistical information on the size and structures of synthesized nanoparticles. Thus, from a practical viewpoint the application of CXDI to study the size distribution of synthesized nanoparticles is unrealistic because of the low intensity of coherent X-rays as well as the limited beam time available at synchrotron radiation facilities. X-ray free-electron lasers (XFELs) are a promising X-ray source for imaging analysis in CXDI because they provide almost completely transverse coherent X-rays with an extremely large number of photons in a single pulse with a duration less than 100 fs. XFELs have recently become available at the Linac Coherent Light Source (LCLS) in the U.S.A.24 and the SPring8 Angstrom Compact Free Electron Laser (SACLA) in Japan.25 So far, under the diffract-before-destroy scheme,26,27 large volumes of diffraction data of various specimens have been collected by single-shot diffraction measurements using an aerodynamic focusing system28 at LCLS and then computationally classified,29 and two-dimensional electron density projection maps have been visualized for a submicrometer virus,30 soot, and other aerosols31,32 at resolutions of 24 to 41 nm. In this Letter, we report the first demonstration of imaging analysis based on CXDI with focused hard XFEL pulses at SACLA. We collected a large number of data sets of the singleshot diffraction patterns of Ag nanocubes and Au/Ag nanoboxes with dimensions of 100 nm. The Ag nanocubes, which were prepared by a modified polyol synthesis technique,33,34 were single crystals with facecentered-cubic structures. When the Ag nanocubes were titrated with an aqueous solution of AuCl4−, Au/Ag nanoboxes were formed by the following galvanic replacement reaction35 3Ag + Au(III) → Au + 3Ag(I)
Figure 1. Schematic view of single-shot coherent X-ray diffraction measurement of Ag nanocubes and Au/Ag nanoboxes. XFEL pulses with an energy of ∼5.5 keV were two-dimensionally focused to a ∼1.5 μm spot size using KB mirrors. To block parasitic scattering X-rays from the mirrors, a guard slit (200 μm thick silicon with a 250 × 250 μm2 hole) was used. Forward-diffracted X-ray photons were detected by an MPCCD detector with a pixel size of 50 × 50 μm2 placed 1626.25 mm downstream of the sample. The nanoparticles were supported by a SiN membrane chip. By scanning the SiN membrane relative to the focused XFEL pulses, coherent X-ray diffraction patterns were collected on the MPCCD detector at a frequency of 1 Hz.
subsequent analysis (for details on the data screening please see Supporting Information). The measurement was ∼100 times faster than that in our previous experiments at the thirdgeneration synchrotron radiation facility SPring-8 (ref 39.). Figure 2a,b shows typical diffraction patterns from a single isolated Ag nanocube and a Au/Ag nanobox, respectively. The speckle patterns have high visibility, indicating the almost completely transverse coherence and high peak brilliance of the XFEL pulses. The diffraction patterns composed of a series of fringes perpendicularly crossing the two principal axes are due to the cubic projection densities of the particles and are approximated well by the formula for a diffraction pattern from a rectangular aperture. In the case of the Au/Ag nanobox, other periodic patterns overlaying the fringes appear, as can be seen in Figure 2b, because of the hollow interior of the particles. The relationship between the full width (Δq) of the speckles along a principal axis and the edge length (d) of a particle is simply expressed as 1 d= 2Δq (2)
(1)
The conversion of Ag nanocubes into Au/Ag nanoboxes has not yet been visualized at a resolution of 10 nm despite the need for quality control in the synthesis. Here, we determined the size distribution of the nanoparticles by measuring the edge length and then visualized the electron density projections of individual nanocubes and nanoboxes at resolutions better than 10 nm. Figure 1 shows a schematic layout of the experimental setup at BL3 in SACLA in the present study. XFEL pulses (photon energy: 5.5 keV, pulse duration: ∼10 fs) were focused to a spot of ∼1.5 μm diameter by a pair of Kirkpatrick-Baez (KB) mirrors.36 The X-ray intensity per pulse at the focal position was ∼1 × 1011 photons. The repetition ratio of XFEL pulses was reduced from 10 to 1 Hz by a pulse selector. Nanoparticles were randomly scattered on Si3N4 membranes with a 3 × 3 mm2 window. Each membrane was mounted on a goniometer in the vacuum chamber of a diffraction apparatus (KOTOBUKI-1).37 By raster scanning the membrane relative to the focused XFEL pulses at approximately 25 μm intervals, singleshot diffraction patterns were collected using a multiport charge-coupled device (MPCCD) detector.38 In 2 h, we collected 6400 diffraction patterns for each membrane. Two sets of membranes were used for each nanoparticle. The hit rates of the focused XFEL on a single isolated particle were 9.5% for the Ag nanocubes and 9.7% for the Au/Ag nanoboxes. For each particle, after screening 12 800 diffraction patterns, 1000 diffraction patterns were extracted for
Therefore, one can easily estimate the edge length of a particle from its diffraction patterns. For instance, the diffraction pattern of a Ag nanocube with a ΔqAg value of 3.11 μm−1 indicates that the edge length is 161 nm, and the edge length of the Au/Ag nanobox was determined to be 170 nm from the ΔqAu/Ag value of 2.94 μm−1 (Figure 2). The determination accuracy of Δq in our data analysis is ∼0.05 μm−1, equivalent to that for d ∼ 3 nm. Although the XFEL pulses randomly hit the nanoparticles, the 1000 diffraction patterns had sufficient intensity to apply this procedure. The distribution of edge lengths in each specimen was derived from the 1000 diffraction patterns as illustrated for the Ag nanocube (Figure 3a) and Au/Ag nanobox (Figure 3b). When the size distributions are approximated by Gaussian functions, the standard deviation (σ) values are similar for the Ag nanocube (14.5 nm) and Au/Ag nanobox (14.1 nm), suggesting that the size-controlled synthesis of the particles is possible. In contrast, the average edge length (daverage) of the 6029
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defined as the peak position in the distribution. Because Au layers have been reported to epitaxially grow on Ag nanocubes during the formation of Au nanocages,33 this difference suggests that the surface of Ag nanocubes is covered by a Au layer with a thickness of approximately 5.7 nm. From the difference in the size of the two nanoparticles, we estimated that approximately 77% of the interior Ag is oxidized and removed to form the nanocage. Thus, the distribution of edge lengths provides a statistical view of the structural changes during the epitaxial growth of a Au/Ag nanobox from a Ag nanocube. The nanostructures of individual particles were visualized by reconstructing projection electron density images, which were retrieved from the best eight diffraction patterns by the hybridinput−output method19 with the oversampling smoothness algorithm40 and shrink-wrap algorithm41 (for details on the iterative phasing method please see Supporting Information). Because these diffraction patterns had significant diffraction intensities, we consider that the illumination field across each nanoparticle was uniform. Figure 4a shows the projection maps of Ag nanocubes at the peak and slope positions in the size distribution (Figure 3). From a cross-sectional plot through line P in Figure 4a, the edge resolution of a 160 nm size particle was found to reach approximately 7 nm, which is the highest resolution of single-shot CXDI using an XFEL pulse reported thus far. The resolution of the other images is better than 10 nm. The projection maps indicate a uniform electron density over the particles except for at the edges and suggest a small size-dependent variation in the internal structures. It is considered that the contrast at the edges is due to the facet structures of the nanocube itself.33 In contrast to the Ag nanocubes, the projection maps of the Au/Ag nanoboxes have low-density regions, indicating hollow interiors (Figure 4c). We found that the size of the hollow strongly depends on the size of the Au/Ag nanobox. For particles with an edge length less than 130 nm, a small lowdensity region was observed. When a particle grows to an edge length of approximately 155 nm, the low-density region occupies 20−40% of the area of the projection map. From the edge-length distribution shown in Figure 3, more than half the particles synthesized in this study possess hollow interiors. When the edge length of the particle exceeds 170 nm, only
Figure 2. Single-shot coherent diffraction patterns of isolated (a) Ag nanocube and (b) Au/Ag nanobox with size of 501 × 501 pixels. q is defined as |q| = 2sin(Θ/2)/λ, where Θ is the scattering angle and λ is the X-ray wavelength. The pattern in the low-q region is displayed on the right. ΔqAg and ΔqAu/Ag are the speckle widths along the expanding direction for the Ag nanocube and Au/Ag nanobox, respectively.
Au/Ag nanobox (155.4 nm) is significantly larger than that of the Ag nanocube (144.0 nm), where the average edge length is
Figure 3. Edge-length distributions of Ag nanocubes and Au/Ag nanoboxes, which were derived from speckle size of 1000 coherent diffraction patterns. 6030
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general use of the proposed method of analysis including industrial use and for studies on dynamics in chemical reactions, we are planning to further develop the instruments and data acquisition scheme so that several thousand diffraction patterns can be collected within a few minutes. We believe that coherent diffraction imaging analysis with XFELs will open up a new frontier in the imaging of heterogeneous systems such as cells, aerosols, and nanomaterials.
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ASSOCIATED CONTENT
S Supporting Information *
Details of data screening and post analysis and iterative phasing method. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The experiments were performed at SACLA with the approval of JASRI and the Program Review Committee (Nos. 2012A8001, 2012B8037, and 2013A8043). This work was supported by the X-ray Free Electron Laser Priority Strategy Program and Grants-in-Aid for Young Scientists (A) (Grant 25709057) and JSPS Fellows (Grant 25·2959) from the Ministry of Education, Culture, Sports, Science, and Technology. The authors would like to thank Mr. Shin Furutaku for the preparation of the nanoparticle samples, and the beam line development and data acquisition teams for technical support in the XFEL experiments.
Figure 4. (a) Projection images of Ag nanocubes reconstructed from single-shot coherent diffraction patterns measured using XFEL pulses. The image of a nanocube with an edge length (EL) of ∼160 nm was reconstructed from the diffraction pattern in Figure 2a. (b) Crosssectional plot through line P in (a). (c) Projection images of Au/Ag nanoboxes. The image of a nanobox with EL ∼ 173 nm was reconstructed from the diffraction pattern in Figure 2b. The scale bar in (a) and (c) is 100 nm.
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cubic nanoframes appear in the retrieved images. The simultaneous analysis of the size distribution and the electron density map of the particles in this study has clearly revealed the conversion process of Au/Ag nanoboxes, in which a pinhole is formed in the initial process of the reaction and serves as a site for Ag dissolution, and then the hollow interior is formed and the Au/Ag replacement reaction is completed through the direct deposition of Au near the pinhole.35 This is the first demonstration of multiple analyses of the edge-length distribution of particles more than 100 nm in size and their surface/internal nanostructures to the best of our knowledge. Such simultaneous measurements to determine the size and size-dependent variation of structures in a short period of time are expected to have crucial importance for controlling the physicochemical properties of Au/Ag nanoboxes and Au nanocages, particularly in their application as contrast agents for optical imaging in early tumor detection and as therapeutic agents for photothermal cancer treatment.42 In conclusion, we have demonstrated the coherent diffraction imaging analysis of nanoparticles with respect to both the size distribution and individual projection structures using focused XFEL pulses. We obtained a statistical description of the structural change from a Ag nanocube to a Au/Ag nanobox and the relationship between the edge-length distribution of Au/Ag nanoboxes and the nanostructures of their hollow interiors. The present imaging analysis can also be applied to grain analysis in polycrystalline materials in the Bragg geometry. This will provide the relationship between the grain-size distribution and the crystallographic orientation of individual grains and/or the strain distribution with nanoscale resolution. Toward the
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