Fresnel coherent diffractive imaging of elemental distributions in nanoscale binary compounds Chan Kim,1 Yoonhee Kim,1 Sang Soo Kim,1,3 Hyon Chol Kang,2 Ian McNulty,4 and Do Young Noh1,∗ 1 Department
of Physics and Photon Science & School of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju 500-712, South Korea 2 Department of Advanced Materials Engineering, Chosun University, Gwangju 501-759, South Korea 3 Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA 4 Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA ∗ [email protected]
Abstract: We report quantitative determination of elemental distribution in binary compounds with nano meter scale spatial resolution using x-ray Fresnel coherent diffractive imaging (FCDI). We show that the quantitative magnitude and phase values of the x-ray wave exiting an object determined by FCDI can be utilized to obtain full-field atomic density maps of each element independently. The proposed method was demonstrated by reconstructing the density maps of Pt and NiO in a Pt-NiO binary compound with about 18 nm spatial resolution. © 2014 Optical Society of America OCIS codes: (110.1650) Coherence imaging; (340.7460) X-ray microscopy; (160.4236) Nanomaterials.
References and links 1. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999). 2. H. N. Chapman and K. A. Nugent, “Coherent lensless x-ray imaging,” Nat. Photonics 4, 833–839 (2010). 3. H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys. 2, 101–104 (2006). 4. M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006). 5. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008). 6. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010). 7. H. N. Chapman, A. Barty, M. J. Bogan, S. Boutet, M. Frank, S. P. Hau-Riege, S. Marchesini, B. W. Woods, S. Bajt, W. H. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. M. Seibert, F. R.N.C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006). 8. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982). 9. J. Miao, K. O. Hodgson, and D. Sayre, “An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images,” Proc. Natl. Acad. Sci. U. S. A. 98(12), 6641–6645 (2001). 10. A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative x-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
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Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5528
11. I. Robinson and R. Harder, “Coherent x-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291– 298 (2009). 12. A. Tripathi, J. Mohanty, S. H. Dietze, O. G. Shpyrko, E. Shipton, E. E. Fullerton, S. S. Kim, and I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. U. S. A. 108(33), 13393–13398 (2011). 13. J. Miao, J. E. Amonette, Y. Nishino, T. Ishikawa, and K. O. Hodgson, “Direct determination of the absolute electron density of nanostructured and disordered materials at sub-10-nm resolution,” Phys. Rev. B 68, 012201 (2003). 14. K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(2), 529–534 (2010). 15. J. N. Clark. G. J. Williams, H. M. Quiney, L. Whitehead, M. D. de Jonge, E. Hanssen, M. Altissimo, K. A. Nugent, and A. G. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16(5), 3342–3348 (2008). 16. Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102, 018101 (2009). 17. D. Nam, J. Park, M. Gallagher-Jones, S. S. Kim, S. Kim, Y. Kohmura, H. Naitow, N. Kunishima, T. Yoshida, T. Ishikawa, and C. Song, “Imaging fully hydrated whole cells by coherent x-ray diffraction microscopy,” Phys. Rev. Lett. 110, 098103 (2013). 18. V. R. Stamenkovic, B. S. Mun, M. Arenz, K. J. J. Mayrhofer, C. A. Lucas, G. Wang, P. N. Ross, and N. M. Markovic, “Trends in electrocatalysis on extended and nanoscale Pt-bimetallic alloy surfaces,” Nat. Mater. 6, 241–247 (2007). 19. E.-Y. Ko, E. D. Park, H. C. Lee, D. Lee, and S. Kim, “Supported Pt-Co catalysts for selective CO oxidation in a hydrogen-rich stream,” Angew. Chem. Int. Ed. 46, 734–737 (2007). 20. H. Jiang, R. Xu, C-C. Ghen, W. Yang, J. Fan, X. Tao, C. Song, Y. Kohmura, T. Xiao, Y. Wong, Y. Fei, T. Ishikawa, W. L. Mao, and J. Miao, “Three-dimensional coherent x-ray diffraction imaging of molten iron in mantle olivine at nanoscale resolution,” Phys. Rev. Lett. 110, 205501 (2013). 21. H. C. Kang, H. Yan, Y. Chu, S. Y. Lee, J. Kim, E. Nazaretski, C. Kim, O. Seo, D. Y. Noh, A. T. Macrander, G. B. Stephenson, and J. Maser, “Oxidation of PtNi nanoparticles studied by a scanning x-ray fluorescence microscope with multi-layer Laue lenses,” Nanoscale 5, 7184–7187 (2013). 22. C. Song, R. Bergstrom, D. Ramunno-Johnson, H. Jiang, D. Paterson, M. D. de Jonge, I. McNulty, J. Lee, K. L. Wang, and J. Miao, “Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy,” Phys. Rev. Lett. 100, 025504 (2008). 23. Y. Takahashi, H. Kubo, H. Furukawa, K. Yamauchi, E. Matsubara, T. Ishikawa, and Y. Nishino, “Element-specific hard x-ray diffraction microscopy,” Phys. Rev. B 78, 092105 (2008). 24. Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, K. Yamauchi, and T. Ishikawa, “Multiscale element mapping of buried structures by ptychographic x-ray diffraction microscopy using anomalous scattering,” Appl. Phys. Lett. 99, 131905 (2011). 25. J. N. Clark, C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, B. Chen, K. A. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express 18(3), 1981–1993 (2010). 26. S. Kim, C. Kim, S. Lee, S. Marathe, D. Y. Noh, H. C. Kang, S. S. Kim, A. Sandy, and S. Narayanan, “Coherent hard x-ray diffractive imaging of nonisolated objects confined by an aperture,” Phys. Rev. B 81, 165437 (2010). 27. B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20nm,” Appl. Phys. Lett. 93, 214101 (2008). 28. G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006). 29. G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010). 30. I. McNulty, A. M. Khounsary, Y. P. Feng, Y. Qian, J. Barraza, C. Benson, and D. Shu, “A beamline for 1-4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996). 31. D. J. Vine, G. J. Williams, J. N. Clark, C. T. Putkunz, M. A. Pfeifer, “An in-vacuum x-ray diffraction microscope for use in the 0.7-2.9 keV range,” Rev. Sci. Instrum. 83, 033703 (2012). 32. S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003). 33. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapire, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23(5), 1179–1200 (2006).
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Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5529
1.
Introduction
Coherent x-ray diffractive imaging (CDI), in which x-ray wave field exiting an object is retrieved from the corresponding diffraction pattern, has emerged as an ultimate optical imaging method since its resolution is limited in principle only by the probing x-ray wavelength although there are practical limitations such as the numerical aperture of a detector [1–7]. Two key ingredients of the CDI process are measuring the oversampled diffraction intensity, and retrieving its phase by applying appropriate computational algorithms [8, 9]. Non-destructive electron density mappings including three dimensional tomograms have been reported using CDI with great success [10]. Materials properties of an object such as physical morphology, strain field, and magnetic domain structure have also been deduced from the complex object exit wave field [11–17]. Nanoscale alloy particles have received much interest recently due to their excellent catalytic properties and cost-effective applications in fuel and solar cells [18, 19]. Elemental distribution in nanoscale alloys is one of the critical issues in their applications. Recently non-destructive nano scale elemental analysis x-ray methods including variants of CDI and scanning x-ray nano beam fluorescence have been devised to address the needs for elemental analysis [20, 21]. Elemental mappings of alloy compounds using CDI have been carried out by changing x-ray energy across an absorption edge of a specific element [20, 22–24]. In this work, we demonstrate that quantitative element-specific images of a binary compound nano-system can be obtained by the Fresnel coherent diffractive imaging (FCDI) from the magnitude and phase of the object exit wave. The proposed scheme is a full field imaging method and based on that the ratio β /δ in the complex index of refraction, nc ≡ 1 − δ + iβ , is element specific at a given x-ray wavelength independent of atomic density. The ratio has been utilized as an extra constraint in FCDI image reconstructions previously, which aided retrieval of exit wave greatly [15, 25]. Imposing the fixed β /δ constraint, however, is applicable only when one tries to obtain a density map of a single element specimen or an averaged density map of a multi-element specimen. In our work, we retrieved the magnitude and phase of object exit wave separately without imposing the constraint, which made the evaluation of two independent elemental specific images of a binary specimen possible. Reconstructing the object exit wave uniquely was found to be challenging in CDIs using a plane incident wave [7, 13, 26], especially when the exit wave field is complex with both phase and magnitude variations. FCDI utilizes a curved incident wave that offers several advantages over plane wave CDI methods. In FCDI, a hologram of the object, due to interference between the wave scattered by the object and the diverging incident wave, which acts as a reference wave, is measured in addition to high angle diffraction pattern of the object. This hologram facilitates the unique and quantitative reconstruction of a complex object exit wave. The welldefined curvature of the incident wave also serves as a strong constraint on the phase retrieval process, substantially improving the uniqueness of the reconstruction. By comparing the wave field exiting the object with the incident wave field, quantitative values of electron density maps have been obtained [27–29]. 2.
Relationship between exit wave field and elemental density in a binary compound
The complex wave field exiting the object ψe , is expressed as 2π i d ψe (x, y) = ψi (x, y) exp − nc (x, y, z)dz λ 0
(1)
where ψi is the incident wave field, λ is the wavelength, and z is the direction of the x-ray wave propagation. Here, d is the distance from the incident plane to the exit plane that encloses
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Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5530
d FZP with Incident Central stop plane waves
OSA
X-ray CCD Detector
Ȳ Ȳ
Object
Fig. 1. Schematic experimental setup of the Fresnel coherent diffractive imaging employed in this work. A Fresnel zone plate focuses the incident x-ray beam into a curved beam. The object exit plane is defined just downstream of an object.
an object as illustrated in Fig. 1, which should be smaller than the Rayleigh distance or the depth of focus given by 2Δr2 /λ , where Δr is the lateral resolution. In typical soft x-ray FCDI experimental configurations, d is of order 1 μ m. δ and β are related to the real and imaginary parts of atomic scattering factor fi (λ ) = fiR (λ ) + i fiI (λ ) of the elements comprising the object through
δ (x, y, z) =
r0 λ 2 ρi (x, y, z) fiR 2π ∑ i
β (x, y, z) =
r0 λ 2 ρi (x, y, z) fiI , 2π ∑ i
(2)
where ρi (x, y, z) is the local number density of the i-th element in the object and r0 is the classical radius of electron. Using Eqs. (1) and (2), the exit wave can be represented by ψi (x, y)eikd T (x, y) where T (x, y) ≡ A(x, y)eiφ (x,y) is a transmission function whose magnitude and phase are respectively, A(x, y) = exp −λ r0 ∑ ρi (x, y) fiI i
φ (x, y) = −λ r0 ∑ ρi (x, y) fiR ,
(3)
i
where ρi (x, y) ≡ 0d ρi (x, y, z)dz is the atomic number density of the i-th element integrated over the length of a sample in the direction of x-ray propagation. Since both ln A(x, y) and φ (x, y) are proportional to the integrated atomic density with distinct proportionality constants, one might expect to estimate the integrated electron density of a single element specimen from either A(x, y) or φ (x, y). For a binary compound system composed of A and B two elements, the amount of A and B elements, i.e. ρA (x, y) and ρB (x, y), can be determined independently by inverting the following matrix equation, R fA fBR ρA (x, y) φ (x, y) . (4) = − λ r0 lnA(x, y) fAI fBI ρB (x, y)
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Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5531
3.
Experimental results and discussions
We performed an FCDI experiment at the 2ID-B beamline at the Advanced Photon Source at Argonne National Laboratory to verify of the proposed elemental analysis [30, 31]. A coherent ˚ photons was focused by a Fresnel zone plate (FZP) with x-ray beam of 2.185 keV (λ = 5.67A) 160 μ m diameter and 50 nm smallest zone width. The focal length was 14.1 mm. A central stop and a 20 μ m diameter order sorting aperture were employed to select the first order focus of the FZP and to block the direct beam through the FZP. A Pt-NiO binary compound specimen was located about 1 mm downstream of the focal plane. A 2048 × 2048 pixel CCD detector whose pixel size and dynamic range are 13.5 μ m and 16 bits respectively was placed about 590 mm downstream of the specimen to record its diffraction intensity. The experimental setup is schematically illustrated in Fig. 1. To prepare Pt-NiO specimens, Ni and Pt films each with 10 nm thickness were deposited on a SiN substrate using an electron beam evaporator. Then, the specimen was annealed at 750◦C in a N2 environment for 5 min three times to convert it to Pt-Ni alloy nano-particles. Following this, the specimen was further annealed for 5 min at 750◦C in air, during which the Ni atoms out-diffused to form NiO [21]. Shown in Fig. 2(a) is a SEM micrograph of a specimen thus prepared. The sample was intentionally positioned to be illuminated only by the upper left quadrant of the incident beam to avoid the shadow of the central stop. The dotted line indicates the boundary of the incident wave field illuminated on the sample. The far field diffraction intensity, including the holographic region at the center where the diverging incident wave interferes with the wave diffracted by the sample is shown in the inset in Fig. 2(b). The resolution of the holographic region was about 50 nm. We obtained a meaningful diffraction signal up to angles corresponding to 12 nm resolution in real space. The incident wave field (“white field”, not shown) through the SiN substrate without the sample was measured to estimate the reference wave, ψi . The phase and magnitude of the complex transmission function T (x, y), reconstructed using the error reduction algorithm at two reconstruction planes, the sample and the detector plane [3], are displayed in Figs. 2(c) and 2(d) [8]. We imposed the negative phase change as well as the measured diffraction signal as constraints in the phase retrieval algorithm. The boundary of the sample was estimated and determined using the “shrink-wrap” algorithm [32]. No other constraints were employed. The stability of the reconstruction was confirmed by running 30 independent reconstructions each starting with a random initial condition. All the iterations resulted in similar reconstructions without substantial differences. The errors (standard deviations) in the reconstructed phase and logarithm of the magnitude respectively, were 0.01 rad (about 5%) and about 0.01(about 8%) averaged over all pixels. We evaluated the χ 2 by comparing the measured diffraction data and the calculated data from the reconstructed exit wave was about 0.0003, indicating that the reconstruction was reliable [28]. The resolution of the phase image was about 18 nm (at half period resolution), which was estimated by PRTF (Phase Retrieval Transfer Function) [14, 33]. We employed the PRTF for rough estimation of the resolution, which is not quite typical for FCDI analyses. The center of reciprocal coordinate was chosen at the center of the specimen area in the holographic region in evaluating the PRTF. The phase image shown in Fig. 2(c) exhibits a similar morphology as the SEM image shown
Table 1. Atomic scattering factors of Pt and NiO at x-ray energy of 2.185 keV
Material fR fI
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Pt 29.5 26.2
NiO 36.3 5.3
Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5532
(a)
(b)
500 ว 3
(c)
3
(d) 1
1
2
2
500 ว
-1
-0.5 Phase (rad)
0 -0.5
500 ว
-0.25
0
Ln of Magnitude
Fig. 2. (a) SEM image of the Pt-NiO binary compound specimen used in this experiment. The dotted line indicates the boundary of the x-ray illumination. (b) Coherent diffraction pattern recorded by the CCD. An attenuator was used to reduce the intensity of the holographic region in the diffraction pattern, so as to record it together with the much weaker high-angle diffraction data. The inset shows the hologram of the sample. (c,d) Image of the phase (c) and logarithm of the magnitude (d) of the object exit wave reconstructed from the diffraction pattern shown in (b). Particles marked by 1, 2, and 3 were analyzed to obtain elemental maps.
in Fig. 2(a), which was attributed to fact that the value of fNiO and fPt are rather similar at 2.185 keV. The atomic scattering factors of Pt and NiO at the x-ray energy used in this experiment are summarized in Table 1. The phase image, therefore, reflects mostly the total atomic density, the weighted summation of ρPt and ρNiO , which should be similar to the SEM image but much more quantitative. By contrast, the magnitude map in Fig. 2(d) shows a rather different morphology. I is much larger than f I , Pt should be weighted more strongly in the magnitude Because fPt NiO map, and it should be close to the elemental map of Pt. In fact, the x-ray energy was chosen to enhance the contrast in β /δ between Pt and NiO. Figure 3 shows the Pt and NiO distributions in the selected particles 1, 2, and 3 as indicated in Figs. 2(c) and 2(d). They were evaluated from the values of the transmission function T (x, y) shown in Fig. 2, using Eq. (4). As seen in Figs. 3(a) and 3(b), the Pt particles are segregated and surrounded by NiO. This is consistent with out-diffusion and oxidation of Ni atoms while annealing in an oxygen environment [21]. The elemental maps, however, showed that the separation was not complete and was limited kinetically in this specific sample preparation process. Figure 3(c) displays SEM images taken under the composition mode in which heavy Pt atoms are more strongly weighted. The images are similar and consistent with the Pt maps shown in Fig. 3(b). The elemental maps obtained by FCDI are clearer and much more quantitative.
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Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5533
NiO molecules /nm2 (104)
(a)
1.4
NiO
1
0.7
NiO
0
NiO
2
3
200 ว Pt atoms/nm2 (104)
(b)
1.4
Pt
1
Pt
2
0.7
0
Pt
3
200 ว
(c)
200 ว
Fig. 3. (a, b) Density map of NiO (a) and Pt (b) integrated along the beam direction of the selected particles, 1, 2, and 3. They are calculated from the reconstructed phase and magnitude images. (c) SEM images of the corresponding particles obtained in the composition mode in which heavy Pt element is weighted more strongly.
4.
Conclusion
We presented a novel and quantitative method of determining the elemental distribution in binary nano-systems using FCDI. We demonstrated that the absolute phase and magnitude of the object exit wave reconstructed from an FCDI measurement provides quantitative element specific atomic density maps. We applied this method to analyze the elemental distribution of binary Pt-NiO nano-particles quantitatively. The elemental analysis presented in this work may be compared with recent scanning fluorescence x-ray microscopy results in which a nanofocused x-ray beam was used [21]. Although the spatial of about 20 nm is comparable, our full-field imaging approach is significantly faster and offers several advantages in handling samples. It is also much less sensitive to precise focusing, and the resolution can potentially be improved to 1 nm level. Although FCDI is not as free of vibration as plane wave CDI due to the focusing optics, it is still much less sensitive to the vibration of the sample stage than scanning x-ray fluorescence microscopy, which is a critical issue as the image resolution improves below 10 nm. The vibration problem [31] should be improved more to achieve the spatial resolution of 1 nm level. As for scanning fluorescence methods, the elemental sensitivity can be enhanced by tuning the x-ray energy close to an absorption edge of a specific element. In future, this method can be extended by tomographic techniques to provide threedimensional images of elemental distributions. We expect that the three-dimensional FCDI will be much more powerful because there is no need to integrate the atomic densities along the beam propagation, enabling exact identification of specific elements in each voxel. This work
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Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5534
may expand applications of the FCDI method to broad class of alloy and core-shell nano systems. Acknowledgments We would like to acknowledge La Trobe University & ARC Centre of Excellence for Coherent X-ray Science group for providing the FCDI instrument. This research was supported by the National Research Foundation of Korea(NRF) grant funded by the Korean government(MSIP) through NCRC (No. 2008-0062606, NCRC-CELA), and general user program (2010-0023604). We also acknowledge the GSG Project through a grant provided by GIST in 2014 and the support by Institute for Basic Science (IBS). Use of the Advanced Photon Source was supported by the U.S. Department of Energy under Contract No. DE-AC02- 06CH11357.
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Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5535
of Physics and Photon Science & School of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju 500-712, South Korea 2 Department of Advanced Materials Engineering, Chosun University, Gwangju 501-759, South Korea 3 Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA 4 Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA ∗ [email protected]
Abstract: We report quantitative determination of elemental distribution in binary compounds with nano meter scale spatial resolution using x-ray Fresnel coherent diffractive imaging (FCDI). We show that the quantitative magnitude and phase values of the x-ray wave exiting an object determined by FCDI can be utilized to obtain full-field atomic density maps of each element independently. The proposed method was demonstrated by reconstructing the density maps of Pt and NiO in a Pt-NiO binary compound with about 18 nm spatial resolution. © 2014 Optical Society of America OCIS codes: (110.1650) Coherence imaging; (340.7460) X-ray microscopy; (160.4236) Nanomaterials.
References and links 1. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999). 2. H. N. Chapman and K. A. Nugent, “Coherent lensless x-ray imaging,” Nat. Photonics 4, 833–839 (2010). 3. H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys. 2, 101–104 (2006). 4. M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006). 5. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008). 6. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010). 7. H. N. Chapman, A. Barty, M. J. Bogan, S. Boutet, M. Frank, S. P. Hau-Riege, S. Marchesini, B. W. Woods, S. Bajt, W. H. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. M. Seibert, F. R.N.C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006). 8. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982). 9. J. Miao, K. O. Hodgson, and D. Sayre, “An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images,” Proc. Natl. Acad. Sci. U. S. A. 98(12), 6641–6645 (2001). 10. A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative x-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
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Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5528
11. I. Robinson and R. Harder, “Coherent x-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291– 298 (2009). 12. A. Tripathi, J. Mohanty, S. H. Dietze, O. G. Shpyrko, E. Shipton, E. E. Fullerton, S. S. Kim, and I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. U. S. A. 108(33), 13393–13398 (2011). 13. J. Miao, J. E. Amonette, Y. Nishino, T. Ishikawa, and K. O. Hodgson, “Direct determination of the absolute electron density of nanostructured and disordered materials at sub-10-nm resolution,” Phys. Rev. B 68, 012201 (2003). 14. K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(2), 529–534 (2010). 15. J. N. Clark. G. J. Williams, H. M. Quiney, L. Whitehead, M. D. de Jonge, E. Hanssen, M. Altissimo, K. A. Nugent, and A. G. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16(5), 3342–3348 (2008). 16. Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102, 018101 (2009). 17. D. Nam, J. Park, M. Gallagher-Jones, S. S. Kim, S. Kim, Y. Kohmura, H. Naitow, N. Kunishima, T. Yoshida, T. Ishikawa, and C. Song, “Imaging fully hydrated whole cells by coherent x-ray diffraction microscopy,” Phys. Rev. Lett. 110, 098103 (2013). 18. V. R. Stamenkovic, B. S. Mun, M. Arenz, K. J. J. Mayrhofer, C. A. Lucas, G. Wang, P. N. Ross, and N. M. Markovic, “Trends in electrocatalysis on extended and nanoscale Pt-bimetallic alloy surfaces,” Nat. Mater. 6, 241–247 (2007). 19. E.-Y. Ko, E. D. Park, H. C. Lee, D. Lee, and S. Kim, “Supported Pt-Co catalysts for selective CO oxidation in a hydrogen-rich stream,” Angew. Chem. Int. Ed. 46, 734–737 (2007). 20. H. Jiang, R. Xu, C-C. Ghen, W. Yang, J. Fan, X. Tao, C. Song, Y. Kohmura, T. Xiao, Y. Wong, Y. Fei, T. Ishikawa, W. L. Mao, and J. Miao, “Three-dimensional coherent x-ray diffraction imaging of molten iron in mantle olivine at nanoscale resolution,” Phys. Rev. Lett. 110, 205501 (2013). 21. H. C. Kang, H. Yan, Y. Chu, S. Y. Lee, J. Kim, E. Nazaretski, C. Kim, O. Seo, D. Y. Noh, A. T. Macrander, G. B. Stephenson, and J. Maser, “Oxidation of PtNi nanoparticles studied by a scanning x-ray fluorescence microscope with multi-layer Laue lenses,” Nanoscale 5, 7184–7187 (2013). 22. C. Song, R. Bergstrom, D. Ramunno-Johnson, H. Jiang, D. Paterson, M. D. de Jonge, I. McNulty, J. Lee, K. L. Wang, and J. Miao, “Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy,” Phys. Rev. Lett. 100, 025504 (2008). 23. Y. Takahashi, H. Kubo, H. Furukawa, K. Yamauchi, E. Matsubara, T. Ishikawa, and Y. Nishino, “Element-specific hard x-ray diffraction microscopy,” Phys. Rev. B 78, 092105 (2008). 24. Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, K. Yamauchi, and T. Ishikawa, “Multiscale element mapping of buried structures by ptychographic x-ray diffraction microscopy using anomalous scattering,” Appl. Phys. Lett. 99, 131905 (2011). 25. J. N. Clark, C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, B. Chen, K. A. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express 18(3), 1981–1993 (2010). 26. S. Kim, C. Kim, S. Lee, S. Marathe, D. Y. Noh, H. C. Kang, S. S. Kim, A. Sandy, and S. Narayanan, “Coherent hard x-ray diffractive imaging of nonisolated objects confined by an aperture,” Phys. Rev. B 81, 165437 (2010). 27. B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20nm,” Appl. Phys. Lett. 93, 214101 (2008). 28. G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006). 29. G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010). 30. I. McNulty, A. M. Khounsary, Y. P. Feng, Y. Qian, J. Barraza, C. Benson, and D. Shu, “A beamline for 1-4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996). 31. D. J. Vine, G. J. Williams, J. N. Clark, C. T. Putkunz, M. A. Pfeifer, “An in-vacuum x-ray diffraction microscope for use in the 0.7-2.9 keV range,” Rev. Sci. Instrum. 83, 033703 (2012). 32. S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003). 33. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapire, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23(5), 1179–1200 (2006).
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Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5529
1.
Introduction
Coherent x-ray diffractive imaging (CDI), in which x-ray wave field exiting an object is retrieved from the corresponding diffraction pattern, has emerged as an ultimate optical imaging method since its resolution is limited in principle only by the probing x-ray wavelength although there are practical limitations such as the numerical aperture of a detector [1–7]. Two key ingredients of the CDI process are measuring the oversampled diffraction intensity, and retrieving its phase by applying appropriate computational algorithms [8, 9]. Non-destructive electron density mappings including three dimensional tomograms have been reported using CDI with great success [10]. Materials properties of an object such as physical morphology, strain field, and magnetic domain structure have also been deduced from the complex object exit wave field [11–17]. Nanoscale alloy particles have received much interest recently due to their excellent catalytic properties and cost-effective applications in fuel and solar cells [18, 19]. Elemental distribution in nanoscale alloys is one of the critical issues in their applications. Recently non-destructive nano scale elemental analysis x-ray methods including variants of CDI and scanning x-ray nano beam fluorescence have been devised to address the needs for elemental analysis [20, 21]. Elemental mappings of alloy compounds using CDI have been carried out by changing x-ray energy across an absorption edge of a specific element [20, 22–24]. In this work, we demonstrate that quantitative element-specific images of a binary compound nano-system can be obtained by the Fresnel coherent diffractive imaging (FCDI) from the magnitude and phase of the object exit wave. The proposed scheme is a full field imaging method and based on that the ratio β /δ in the complex index of refraction, nc ≡ 1 − δ + iβ , is element specific at a given x-ray wavelength independent of atomic density. The ratio has been utilized as an extra constraint in FCDI image reconstructions previously, which aided retrieval of exit wave greatly [15, 25]. Imposing the fixed β /δ constraint, however, is applicable only when one tries to obtain a density map of a single element specimen or an averaged density map of a multi-element specimen. In our work, we retrieved the magnitude and phase of object exit wave separately without imposing the constraint, which made the evaluation of two independent elemental specific images of a binary specimen possible. Reconstructing the object exit wave uniquely was found to be challenging in CDIs using a plane incident wave [7, 13, 26], especially when the exit wave field is complex with both phase and magnitude variations. FCDI utilizes a curved incident wave that offers several advantages over plane wave CDI methods. In FCDI, a hologram of the object, due to interference between the wave scattered by the object and the diverging incident wave, which acts as a reference wave, is measured in addition to high angle diffraction pattern of the object. This hologram facilitates the unique and quantitative reconstruction of a complex object exit wave. The welldefined curvature of the incident wave also serves as a strong constraint on the phase retrieval process, substantially improving the uniqueness of the reconstruction. By comparing the wave field exiting the object with the incident wave field, quantitative values of electron density maps have been obtained [27–29]. 2.
Relationship between exit wave field and elemental density in a binary compound
The complex wave field exiting the object ψe , is expressed as 2π i d ψe (x, y) = ψi (x, y) exp − nc (x, y, z)dz λ 0
(1)
where ψi is the incident wave field, λ is the wavelength, and z is the direction of the x-ray wave propagation. Here, d is the distance from the incident plane to the exit plane that encloses
#203978 - $15.00 USD (C) 2014 OSA
Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5530
d FZP with Incident Central stop plane waves
OSA
X-ray CCD Detector
Ȳ Ȳ
Object
Fig. 1. Schematic experimental setup of the Fresnel coherent diffractive imaging employed in this work. A Fresnel zone plate focuses the incident x-ray beam into a curved beam. The object exit plane is defined just downstream of an object.
an object as illustrated in Fig. 1, which should be smaller than the Rayleigh distance or the depth of focus given by 2Δr2 /λ , where Δr is the lateral resolution. In typical soft x-ray FCDI experimental configurations, d is of order 1 μ m. δ and β are related to the real and imaginary parts of atomic scattering factor fi (λ ) = fiR (λ ) + i fiI (λ ) of the elements comprising the object through
δ (x, y, z) =
r0 λ 2 ρi (x, y, z) fiR 2π ∑ i
β (x, y, z) =
r0 λ 2 ρi (x, y, z) fiI , 2π ∑ i
(2)
where ρi (x, y, z) is the local number density of the i-th element in the object and r0 is the classical radius of electron. Using Eqs. (1) and (2), the exit wave can be represented by ψi (x, y)eikd T (x, y) where T (x, y) ≡ A(x, y)eiφ (x,y) is a transmission function whose magnitude and phase are respectively, A(x, y) = exp −λ r0 ∑ ρi (x, y) fiI i
φ (x, y) = −λ r0 ∑ ρi (x, y) fiR ,
(3)
i
where ρi (x, y) ≡ 0d ρi (x, y, z)dz is the atomic number density of the i-th element integrated over the length of a sample in the direction of x-ray propagation. Since both ln A(x, y) and φ (x, y) are proportional to the integrated atomic density with distinct proportionality constants, one might expect to estimate the integrated electron density of a single element specimen from either A(x, y) or φ (x, y). For a binary compound system composed of A and B two elements, the amount of A and B elements, i.e. ρA (x, y) and ρB (x, y), can be determined independently by inverting the following matrix equation, R fA fBR ρA (x, y) φ (x, y) . (4) = − λ r0 lnA(x, y) fAI fBI ρB (x, y)
#203978 - $15.00 USD (C) 2014 OSA
Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5531
3.
Experimental results and discussions
We performed an FCDI experiment at the 2ID-B beamline at the Advanced Photon Source at Argonne National Laboratory to verify of the proposed elemental analysis [30, 31]. A coherent ˚ photons was focused by a Fresnel zone plate (FZP) with x-ray beam of 2.185 keV (λ = 5.67A) 160 μ m diameter and 50 nm smallest zone width. The focal length was 14.1 mm. A central stop and a 20 μ m diameter order sorting aperture were employed to select the first order focus of the FZP and to block the direct beam through the FZP. A Pt-NiO binary compound specimen was located about 1 mm downstream of the focal plane. A 2048 × 2048 pixel CCD detector whose pixel size and dynamic range are 13.5 μ m and 16 bits respectively was placed about 590 mm downstream of the specimen to record its diffraction intensity. The experimental setup is schematically illustrated in Fig. 1. To prepare Pt-NiO specimens, Ni and Pt films each with 10 nm thickness were deposited on a SiN substrate using an electron beam evaporator. Then, the specimen was annealed at 750◦C in a N2 environment for 5 min three times to convert it to Pt-Ni alloy nano-particles. Following this, the specimen was further annealed for 5 min at 750◦C in air, during which the Ni atoms out-diffused to form NiO [21]. Shown in Fig. 2(a) is a SEM micrograph of a specimen thus prepared. The sample was intentionally positioned to be illuminated only by the upper left quadrant of the incident beam to avoid the shadow of the central stop. The dotted line indicates the boundary of the incident wave field illuminated on the sample. The far field diffraction intensity, including the holographic region at the center where the diverging incident wave interferes with the wave diffracted by the sample is shown in the inset in Fig. 2(b). The resolution of the holographic region was about 50 nm. We obtained a meaningful diffraction signal up to angles corresponding to 12 nm resolution in real space. The incident wave field (“white field”, not shown) through the SiN substrate without the sample was measured to estimate the reference wave, ψi . The phase and magnitude of the complex transmission function T (x, y), reconstructed using the error reduction algorithm at two reconstruction planes, the sample and the detector plane [3], are displayed in Figs. 2(c) and 2(d) [8]. We imposed the negative phase change as well as the measured diffraction signal as constraints in the phase retrieval algorithm. The boundary of the sample was estimated and determined using the “shrink-wrap” algorithm [32]. No other constraints were employed. The stability of the reconstruction was confirmed by running 30 independent reconstructions each starting with a random initial condition. All the iterations resulted in similar reconstructions without substantial differences. The errors (standard deviations) in the reconstructed phase and logarithm of the magnitude respectively, were 0.01 rad (about 5%) and about 0.01(about 8%) averaged over all pixels. We evaluated the χ 2 by comparing the measured diffraction data and the calculated data from the reconstructed exit wave was about 0.0003, indicating that the reconstruction was reliable [28]. The resolution of the phase image was about 18 nm (at half period resolution), which was estimated by PRTF (Phase Retrieval Transfer Function) [14, 33]. We employed the PRTF for rough estimation of the resolution, which is not quite typical for FCDI analyses. The center of reciprocal coordinate was chosen at the center of the specimen area in the holographic region in evaluating the PRTF. The phase image shown in Fig. 2(c) exhibits a similar morphology as the SEM image shown
Table 1. Atomic scattering factors of Pt and NiO at x-ray energy of 2.185 keV
Material fR fI
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Pt 29.5 26.2
NiO 36.3 5.3
Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5532
(a)
(b)
500 ว 3
(c)
3
(d) 1
1
2
2
500 ว
-1
-0.5 Phase (rad)
0 -0.5
500 ว
-0.25
0
Ln of Magnitude
Fig. 2. (a) SEM image of the Pt-NiO binary compound specimen used in this experiment. The dotted line indicates the boundary of the x-ray illumination. (b) Coherent diffraction pattern recorded by the CCD. An attenuator was used to reduce the intensity of the holographic region in the diffraction pattern, so as to record it together with the much weaker high-angle diffraction data. The inset shows the hologram of the sample. (c,d) Image of the phase (c) and logarithm of the magnitude (d) of the object exit wave reconstructed from the diffraction pattern shown in (b). Particles marked by 1, 2, and 3 were analyzed to obtain elemental maps.
in Fig. 2(a), which was attributed to fact that the value of fNiO and fPt are rather similar at 2.185 keV. The atomic scattering factors of Pt and NiO at the x-ray energy used in this experiment are summarized in Table 1. The phase image, therefore, reflects mostly the total atomic density, the weighted summation of ρPt and ρNiO , which should be similar to the SEM image but much more quantitative. By contrast, the magnitude map in Fig. 2(d) shows a rather different morphology. I is much larger than f I , Pt should be weighted more strongly in the magnitude Because fPt NiO map, and it should be close to the elemental map of Pt. In fact, the x-ray energy was chosen to enhance the contrast in β /δ between Pt and NiO. Figure 3 shows the Pt and NiO distributions in the selected particles 1, 2, and 3 as indicated in Figs. 2(c) and 2(d). They were evaluated from the values of the transmission function T (x, y) shown in Fig. 2, using Eq. (4). As seen in Figs. 3(a) and 3(b), the Pt particles are segregated and surrounded by NiO. This is consistent with out-diffusion and oxidation of Ni atoms while annealing in an oxygen environment [21]. The elemental maps, however, showed that the separation was not complete and was limited kinetically in this specific sample preparation process. Figure 3(c) displays SEM images taken under the composition mode in which heavy Pt atoms are more strongly weighted. The images are similar and consistent with the Pt maps shown in Fig. 3(b). The elemental maps obtained by FCDI are clearer and much more quantitative.
#203978 - $15.00 USD (C) 2014 OSA
Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5533
NiO molecules /nm2 (104)
(a)
1.4
NiO
1
0.7
NiO
0
NiO
2
3
200 ว Pt atoms/nm2 (104)
(b)
1.4
Pt
1
Pt
2
0.7
0
Pt
3
200 ว
(c)
200 ว
Fig. 3. (a, b) Density map of NiO (a) and Pt (b) integrated along the beam direction of the selected particles, 1, 2, and 3. They are calculated from the reconstructed phase and magnitude images. (c) SEM images of the corresponding particles obtained in the composition mode in which heavy Pt element is weighted more strongly.
4.
Conclusion
We presented a novel and quantitative method of determining the elemental distribution in binary nano-systems using FCDI. We demonstrated that the absolute phase and magnitude of the object exit wave reconstructed from an FCDI measurement provides quantitative element specific atomic density maps. We applied this method to analyze the elemental distribution of binary Pt-NiO nano-particles quantitatively. The elemental analysis presented in this work may be compared with recent scanning fluorescence x-ray microscopy results in which a nanofocused x-ray beam was used [21]. Although the spatial of about 20 nm is comparable, our full-field imaging approach is significantly faster and offers several advantages in handling samples. It is also much less sensitive to precise focusing, and the resolution can potentially be improved to 1 nm level. Although FCDI is not as free of vibration as plane wave CDI due to the focusing optics, it is still much less sensitive to the vibration of the sample stage than scanning x-ray fluorescence microscopy, which is a critical issue as the image resolution improves below 10 nm. The vibration problem [31] should be improved more to achieve the spatial resolution of 1 nm level. As for scanning fluorescence methods, the elemental sensitivity can be enhanced by tuning the x-ray energy close to an absorption edge of a specific element. In future, this method can be extended by tomographic techniques to provide threedimensional images of elemental distributions. We expect that the three-dimensional FCDI will be much more powerful because there is no need to integrate the atomic densities along the beam propagation, enabling exact identification of specific elements in each voxel. This work
#203978 - $15.00 USD (C) 2014 OSA
Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5534
may expand applications of the FCDI method to broad class of alloy and core-shell nano systems. Acknowledgments We would like to acknowledge La Trobe University & ARC Centre of Excellence for Coherent X-ray Science group for providing the FCDI instrument. This research was supported by the National Research Foundation of Korea(NRF) grant funded by the Korean government(MSIP) through NCRC (No. 2008-0062606, NCRC-CELA), and general user program (2010-0023604). We also acknowledge the GSG Project through a grant provided by GIST in 2014 and the support by Institute for Basic Science (IBS). Use of the Advanced Photon Source was supported by the U.S. Department of Energy under Contract No. DE-AC02- 06CH11357.
#203978 - $15.00 USD (C) 2014 OSA
Received 2 Jan 2014; revised 7 Feb 2014; accepted 8 Feb 2014; published 3 Mar 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005528 | OPTICS EXPRESS 5535
