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Fluctuation microscopy – a tool for examining medium-range order in noncrystalline systems
Nuclear Instruments and Methods in Physics Research B 238 (2005) 196–199 www.elsevier.com/locate/nimb
Fluctuation microscopy – a tool for examining medium-range order in noncrystalline systems L. Fan a
a,*
, I. McNulty a, D. Paterson a, M.M.J. Treacy b, J.M. Gibson
a,*,1
Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Ave, Argonne, IL 60439, USA b Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287, USA Available online 2 August 2005
Abstract Fluctuation microscopy examines the spatial variations in coherent microdiffraction from an ensemble of small volumes in noncrystalline systems. The variance of scattered intensity into regions of reciprocal space can be used to give insight into three-body and four-body correlation functions, which are sensitive to medium-range order. The technique was originally developed for transmission electron microscopy and was successfully used to understand medium-range order in amorphous silicon and germanium. Applying this method to X-rays, we have developed a new approach: fluctuation X-ray microscopy (FXM). The approach offers quantitative insight into medium-range correlations in materials at nanometer and larger length scales. The FXM technique can be used to explore medium-range order and subtle structural changes in a wide range of disordered materials from soft matter to nanocomposites, nanowire and quantum dot arrays. We have demonstrated this new technique by studying films of polystyrene latex spheres. Ó 2005 Elsevier B.V. All rights reserved. PACS: 07.85.Tt; 81.05.Lg; 81.07. b Keywords: Fluctuation X-ray microscopy; Medium-range order; Speckle; Nanoscale materials and nanostructures
1. Introduction Characterization of medium-range order (MRO) in disordered materials is a long-standing *
Corresponding author. Tel.: +1 630 252 8368; fax: +1 630 252 0140. E-mail addresses: [email protected] (L. Fan), jmgibson@ aps.anl.gov (J.M. Gibson). 1 Fax: +1 630 252 4599
problem. Recently, fluctuation electron microscopy (FEM) was developed and successfully used for probing MRO in amorphous materials [1–3]. This technique gains its sensitivity to MRO by examining fluctuations (speckle) in the diffracted intensity from very small sample volumes, on a length scale determined by the illuminated radius or associated imaging resolution. The speckle variance depends on two-, three- and four-body atomic correlation functions, whereas the average,
0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.06.048
L. Fan et al. / Nucl. Instr. and Meth. in Phys. Res. B 238 (2005) 196–199
which is just the diffracted intensity, depends only on the two-body pair distribution function (PDF). Higher order correlation functions are more sensitive to medium-range order [4]. By comparison to electrons, X-rays provide access to longer length scales due to their longer wavelengths and offer greater sample penetration with less radiation damage, as well as elemental and chemical sensitivity through resonant effects. Currently, there is no X-ray technique that effectively probes MRO. Consequently, we are developing fluctuation X-ray microscopy (FXM) to study MRO in bulk samples, solutions, and films at nanometer and larger length scales. Compared to FEM, FXM is better suited to materials with larger characteristic length scales such as polymers, biological macromolecules and their complexes, as well as other nanostructured materials, nanocomposites and hybrids.
197
Fig. 1. Definition of medium-range order.
2. Fluctuation X-ray microscopy and experimental setup To extend FEM to the X-ray region, it is helpful to give a working definition of MRO. As shown in Fig. 1, consider a unit (an atomic pair or other extended object) with distance d. Suppose the correlation length of these units (the distance over which they reveal orientational or other correlated ordering) is L. Then a working definition of medium-range order is 5 6 L/d 6 50. In a sense this definition arises from diffraction and the PDF. At short length scales, L/d 6 5, we have shortrange order that is readily detected from the PDF. At L/d P 50 we have well-established longrange order that can be examined by diffraction. The useful energy for X-ray fluctuation microscopy can be determined by two factors: the wavelength must be small enough for diffraction from the unit spacing and the minimum illumination diameter must be smaller than the desired correlation length. It can be seen from Fig. 2 that at present an X-ray energy 2 keV offers the best possibilities for FXM. The minimum illumination radius shown in Fig. 2 is empirical, obtained from an approximate fit to Fresnel zone plate data. Expected improvements in harder X-ray focussing
Fig. 2. Dependence of X-ray wavelength and minimum illumination radius on X-ray energy, revealing the optimal region for examination of medium-range order.
offer the promise for future studies on smaller unit spacing. FXM examines variations in coherent Xray speckle patterns measured as a function of illumination radius R and sample position. It requires high coherent flux and variable illumination size. We chose the 2-ID-B beamline [5] at the Advanced Photon Source to develop the FXM technique as the beamline is optimized for high coherent flux and coherent scattering experiments, with a unique
198
L. Fan et al. / Nucl. Instr. and Meth. in Phys. Res. B 238 (2005) 196–199
nation radius R and sample position. Speckle patterns are measured at many sample positions by scanning the sample under study. The intensity variance V(q) gives information about the degree and distribution of MRO in the sample. The variance V(R) yields the correlation length.
Fig. 3. A schematic outline of the FXM setup at 2-ID-B.
ability to deliver tuneable, highly coherent 1–4 keV X-rays. A schematic outline of the FXM setup at 2-ID-B is shown in Fig. 3. We use the modified scanning transmission X-ray microscopy configuration. The details of this setup can be found elsewhere [6]. The illumination radius is controlled either by a pinhole or by a Fresnel zone plate. For a system with a characteristic length scale of greater than 100 nm, we use a pinhole setup. An avalanche photodiode detector can be exchanged with the CCD to measure the sample transmission as well as record sample images as it is scanned. This setup is very useful to examine sample regions of interest for FXM measurements. In order to demonstrate FXM we performed measurements on films of disordered polystyrene latex spheres with diameter 277 nm. The spheres were, ultrasonically dispersed in water and then dried on to a Si3N4 membrane. X-ray energy of 1.83 keV is used. Pinholes with diameters of 0.8, 1.6 and 5.5 lm were used to define the coherent illumination on the sample. The CCD detector was placed 1 m from the sample which gave sufficient resolution to resolve individual speckles and provided a sufficient scattering vector (q) range to determine the characteristic length scale of the samples studied.
3. Experimental results and discussion FXM examines variations in coherent X-ray speckle patterns measured as a function of illumi-
Fig. 4. Mean (left) and variance (right) data from 3721 speckle patterns obtained from a film (7 lm thick) of latex spheres, using 1.83 keV radiation and illumination radii of (a) 0.4 lm, (b) 0.8 lm and (c) 2.8 lm.
L. Fan et al. / Nucl. Instr. and Meth. in Phys. Res. B 238 (2005) 196–199
Systematically measuring V(q, R) produces a fluctuation map that contains quantitative information about MRO. By scanning the sample and exchanging pinholes we obtained speckle patterns at various spatial positions and with various illumination radii. Fig. 4 shows mean and variance obtained from these speckle patterns. The mean data on the left of Fig. 4 are equivalent to the average (incoherent) small-angle scattering (SAS) patterns from the sample as spherical particles. In contrast, the variance, shown on the right of Fig. 4, reveals sharp spots which are indicative of medium-range order. As predicted, the variance is far more sensitive to MRO. Conventional SAS produces averaged intensity (two-body correlation) that does not include the subtle structural information reflected by the speckle fluctuations. Therefore, FXM can also give additional structural information that cannot be obtained by conventional SAS techniques. The variance arises from fluctuations in the speckle intensity as the sample position is scanned in the X-ray beam. For completely random samples, the variance is the minimum. For a more heterogeneous structure with local ordering, the variance is larger and varies with sampling conditions. When the sampling volume is comparable to the size of the ordered cluster the variance is the maximum. Changing the illumination size allows extraction of the correlation length quantitatively. As shown on Fig. 4, the variance grows with increasing illumination size until 5 lm, implying a correlation length on the order of 5 lm for this latex sphere ‘‘glass’’ with a sphere diameter of 277 nm. The correlation length can be more accurately defined using the quantitative theory developed by Gibson et al. [7]. However, this theory is currently only applicable to FEM. Consequently the adaptation of the theory to apply to FXM is being conducted.
199
4. Conclusions We have demonstrated that FXM is useful for studying disordered materials with relatively large length scales. The current FXM pinhole setup at 2-ID-B allows us to study ordering in systems with structural units on length scales of 100 nm–2 lm. With future development of nanofocusing optics, we will be able to study length scales down to 10–100 nm and correlation lengths of 50–500 nm. This range is particularly interesting for soft matter such as polymers, biological systems, selfassembled nanostructures, nanocomposite and hybrid materials. Furthermore, this technique can help us to understand the mechanisms of order-disorder transitions and may lead to better control of ordering. X-ray optics improvements for focusing hard-X-rays at the nanometer scale would make this an exciting frontier for study of inorganic glasses and disordered materials.
Acknowledgment Use of the Advanced Photon Source was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109-Eng-38. References [1] M.M.J. Treacy, J.M. Gibson, Acta Cryst. A 52 (1996) 212. [2] J.M. Gibson, M.M.J. Treacy, Phys. Rev. Lett. 78 (1997) 1074. [3] P.M. Voyles, J.E. Gerbi, J.M. Gibson, J.R. Abelson, Phys. Rev. Lett. 86 (2001) 5514. [4] M.M.J. Treacy, P.M. Voyles, J.M. Gibson, J. Non-Cryst. Sol. 150 (1999) 266. [5] I. McNulty et al., Rev. Sci. Instrum. 9 (1996) 67, CD-ROM. [6] I. McNulty et al., J. Phys. IV France 104 (2003) 11. [7] J.M. Gibson, M.M.J. Treacy, P.M. Voyles, Ultramicroscopy 83 (2000) 169.
Fluctuation microscopy – a tool for examining medium-range order in noncrystalline systems L. Fan a
a,*
, I. McNulty a, D. Paterson a, M.M.J. Treacy b, J.M. Gibson
a,*,1
Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Ave, Argonne, IL 60439, USA b Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287, USA Available online 2 August 2005
Abstract Fluctuation microscopy examines the spatial variations in coherent microdiffraction from an ensemble of small volumes in noncrystalline systems. The variance of scattered intensity into regions of reciprocal space can be used to give insight into three-body and four-body correlation functions, which are sensitive to medium-range order. The technique was originally developed for transmission electron microscopy and was successfully used to understand medium-range order in amorphous silicon and germanium. Applying this method to X-rays, we have developed a new approach: fluctuation X-ray microscopy (FXM). The approach offers quantitative insight into medium-range correlations in materials at nanometer and larger length scales. The FXM technique can be used to explore medium-range order and subtle structural changes in a wide range of disordered materials from soft matter to nanocomposites, nanowire and quantum dot arrays. We have demonstrated this new technique by studying films of polystyrene latex spheres. Ó 2005 Elsevier B.V. All rights reserved. PACS: 07.85.Tt; 81.05.Lg; 81.07. b Keywords: Fluctuation X-ray microscopy; Medium-range order; Speckle; Nanoscale materials and nanostructures
1. Introduction Characterization of medium-range order (MRO) in disordered materials is a long-standing *
Corresponding author. Tel.: +1 630 252 8368; fax: +1 630 252 0140. E-mail addresses: [email protected] (L. Fan), jmgibson@ aps.anl.gov (J.M. Gibson). 1 Fax: +1 630 252 4599
problem. Recently, fluctuation electron microscopy (FEM) was developed and successfully used for probing MRO in amorphous materials [1–3]. This technique gains its sensitivity to MRO by examining fluctuations (speckle) in the diffracted intensity from very small sample volumes, on a length scale determined by the illuminated radius or associated imaging resolution. The speckle variance depends on two-, three- and four-body atomic correlation functions, whereas the average,
0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.06.048
L. Fan et al. / Nucl. Instr. and Meth. in Phys. Res. B 238 (2005) 196–199
which is just the diffracted intensity, depends only on the two-body pair distribution function (PDF). Higher order correlation functions are more sensitive to medium-range order [4]. By comparison to electrons, X-rays provide access to longer length scales due to their longer wavelengths and offer greater sample penetration with less radiation damage, as well as elemental and chemical sensitivity through resonant effects. Currently, there is no X-ray technique that effectively probes MRO. Consequently, we are developing fluctuation X-ray microscopy (FXM) to study MRO in bulk samples, solutions, and films at nanometer and larger length scales. Compared to FEM, FXM is better suited to materials with larger characteristic length scales such as polymers, biological macromolecules and their complexes, as well as other nanostructured materials, nanocomposites and hybrids.
197
Fig. 1. Definition of medium-range order.
2. Fluctuation X-ray microscopy and experimental setup To extend FEM to the X-ray region, it is helpful to give a working definition of MRO. As shown in Fig. 1, consider a unit (an atomic pair or other extended object) with distance d. Suppose the correlation length of these units (the distance over which they reveal orientational or other correlated ordering) is L. Then a working definition of medium-range order is 5 6 L/d 6 50. In a sense this definition arises from diffraction and the PDF. At short length scales, L/d 6 5, we have shortrange order that is readily detected from the PDF. At L/d P 50 we have well-established longrange order that can be examined by diffraction. The useful energy for X-ray fluctuation microscopy can be determined by two factors: the wavelength must be small enough for diffraction from the unit spacing and the minimum illumination diameter must be smaller than the desired correlation length. It can be seen from Fig. 2 that at present an X-ray energy 2 keV offers the best possibilities for FXM. The minimum illumination radius shown in Fig. 2 is empirical, obtained from an approximate fit to Fresnel zone plate data. Expected improvements in harder X-ray focussing
Fig. 2. Dependence of X-ray wavelength and minimum illumination radius on X-ray energy, revealing the optimal region for examination of medium-range order.
offer the promise for future studies on smaller unit spacing. FXM examines variations in coherent Xray speckle patterns measured as a function of illumination radius R and sample position. It requires high coherent flux and variable illumination size. We chose the 2-ID-B beamline [5] at the Advanced Photon Source to develop the FXM technique as the beamline is optimized for high coherent flux and coherent scattering experiments, with a unique
198
L. Fan et al. / Nucl. Instr. and Meth. in Phys. Res. B 238 (2005) 196–199
nation radius R and sample position. Speckle patterns are measured at many sample positions by scanning the sample under study. The intensity variance V(q) gives information about the degree and distribution of MRO in the sample. The variance V(R) yields the correlation length.
Fig. 3. A schematic outline of the FXM setup at 2-ID-B.
ability to deliver tuneable, highly coherent 1–4 keV X-rays. A schematic outline of the FXM setup at 2-ID-B is shown in Fig. 3. We use the modified scanning transmission X-ray microscopy configuration. The details of this setup can be found elsewhere [6]. The illumination radius is controlled either by a pinhole or by a Fresnel zone plate. For a system with a characteristic length scale of greater than 100 nm, we use a pinhole setup. An avalanche photodiode detector can be exchanged with the CCD to measure the sample transmission as well as record sample images as it is scanned. This setup is very useful to examine sample regions of interest for FXM measurements. In order to demonstrate FXM we performed measurements on films of disordered polystyrene latex spheres with diameter 277 nm. The spheres were, ultrasonically dispersed in water and then dried on to a Si3N4 membrane. X-ray energy of 1.83 keV is used. Pinholes with diameters of 0.8, 1.6 and 5.5 lm were used to define the coherent illumination on the sample. The CCD detector was placed 1 m from the sample which gave sufficient resolution to resolve individual speckles and provided a sufficient scattering vector (q) range to determine the characteristic length scale of the samples studied.
3. Experimental results and discussion FXM examines variations in coherent X-ray speckle patterns measured as a function of illumi-
Fig. 4. Mean (left) and variance (right) data from 3721 speckle patterns obtained from a film (7 lm thick) of latex spheres, using 1.83 keV radiation and illumination radii of (a) 0.4 lm, (b) 0.8 lm and (c) 2.8 lm.
L. Fan et al. / Nucl. Instr. and Meth. in Phys. Res. B 238 (2005) 196–199
Systematically measuring V(q, R) produces a fluctuation map that contains quantitative information about MRO. By scanning the sample and exchanging pinholes we obtained speckle patterns at various spatial positions and with various illumination radii. Fig. 4 shows mean and variance obtained from these speckle patterns. The mean data on the left of Fig. 4 are equivalent to the average (incoherent) small-angle scattering (SAS) patterns from the sample as spherical particles. In contrast, the variance, shown on the right of Fig. 4, reveals sharp spots which are indicative of medium-range order. As predicted, the variance is far more sensitive to MRO. Conventional SAS produces averaged intensity (two-body correlation) that does not include the subtle structural information reflected by the speckle fluctuations. Therefore, FXM can also give additional structural information that cannot be obtained by conventional SAS techniques. The variance arises from fluctuations in the speckle intensity as the sample position is scanned in the X-ray beam. For completely random samples, the variance is the minimum. For a more heterogeneous structure with local ordering, the variance is larger and varies with sampling conditions. When the sampling volume is comparable to the size of the ordered cluster the variance is the maximum. Changing the illumination size allows extraction of the correlation length quantitatively. As shown on Fig. 4, the variance grows with increasing illumination size until 5 lm, implying a correlation length on the order of 5 lm for this latex sphere ‘‘glass’’ with a sphere diameter of 277 nm. The correlation length can be more accurately defined using the quantitative theory developed by Gibson et al. [7]. However, this theory is currently only applicable to FEM. Consequently the adaptation of the theory to apply to FXM is being conducted.
199
4. Conclusions We have demonstrated that FXM is useful for studying disordered materials with relatively large length scales. The current FXM pinhole setup at 2-ID-B allows us to study ordering in systems with structural units on length scales of 100 nm–2 lm. With future development of nanofocusing optics, we will be able to study length scales down to 10–100 nm and correlation lengths of 50–500 nm. This range is particularly interesting for soft matter such as polymers, biological systems, selfassembled nanostructures, nanocomposite and hybrid materials. Furthermore, this technique can help us to understand the mechanisms of order-disorder transitions and may lead to better control of ordering. X-ray optics improvements for focusing hard-X-rays at the nanometer scale would make this an exciting frontier for study of inorganic glasses and disordered materials.
Acknowledgment Use of the Advanced Photon Source was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109-Eng-38. References [1] M.M.J. Treacy, J.M. Gibson, Acta Cryst. A 52 (1996) 212. [2] J.M. Gibson, M.M.J. Treacy, Phys. Rev. Lett. 78 (1997) 1074. [3] P.M. Voyles, J.E. Gerbi, J.M. Gibson, J.R. Abelson, Phys. Rev. Lett. 86 (2001) 5514. [4] M.M.J. Treacy, P.M. Voyles, J.M. Gibson, J. Non-Cryst. Sol. 150 (1999) 266. [5] I. McNulty et al., Rev. Sci. Instrum. 9 (1996) 67, CD-ROM. [6] I. McNulty et al., J. Phys. IV France 104 (2003) 11. [7] J.M. Gibson, M.M.J. Treacy, P.M. Voyles, Ultramicroscopy 83 (2000) 169.