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Book Reprint Characterization of Nanophase Materials Edited by Zhong Lin Wang* (Received: 24 July 2001) This contribution is a preprint of one chapter of Professor Wang’s edited new book ‘‘Characterization of Nanophase Materials’’ (ISBN 3-527-29837-1), published by WILEY-VCH Verlag GmbH, Weinheim, Germany. Engineering of nanophase materials and devices is of vital interest in electronics, semiconductors and optics, catalysis, ceramics and magnetism. Development of nanotechnology involves several steps, of which characterization of nano- particles is indespensable in understanding the behavior and properties of nanoparticles, aiming at implementing nano- technology, controlling their behavior and designing new nanomaterials systems with super performance. The book focuses on structural and property characterization of nanocrystals and their assemblies, with an emphasis on basic physical approach, detailed techniques, data interpretation and applications. Intended as a comprehensive reference work for postgraduate students and researchers in the field who are specialized in materials chemistry, materials physics, and materials science. Introduction Nanomaterials are the fundamental components of nanoscience and nanotechnology, and they are different from the bulk materials in grain sizes, surface=interface-to- volume ratio and grain shapes, which are the origins of their unique electrical, optical, thermodynamic, mechanical and chemical properties. The small size of nanostructures hampers the applications of the well-established testing and measurement techniques, thus new methods and approaches must be developed for their synthesis, property character- ization and device fabrication. The most challenging task in synthesis is how to synthesize structurally, morphologically and surface state controlled nanomaterials. Due to the small sizes of nanomaterials, their characterization may be dif- ferent from that of large-size bulk materials. The most exciting research in characterization is how to measure the physical or chemical properties of individual nano- structures, which is critical in developing new nanomater- ials and exploring their unique and novel applications. The objective of this book is to describe in detail the various techniques used for characterizing the structure and proper- ties of nanomaterials. The first half of the book describes the diffraction and microscopy techniques for characteriz- ing the structures of nanophase materials. The second half of the book focuses on the spectroscopy techniques used for property characterization of nanophase materials. Each chapter was authored by well-known scientists in the field and it covers the fundamental physics, the principle of data interpretation and applications of the technique in charac- terizing the structure and properties of nanophase materials. Each chapter gives a comprehensive introduction about the technique and also gives the updated new results in the field. The book was written for advanced undergraduate students, graduate students and scientists who are interested in nanomaterials. The readers can be physicists, chemists, materials scientists and biological scientists. The contents of the book are listed as following: Chapter 1: Nanomaterials for Nanoscience and Nano- technology (by Z.L. Wang) Chapter 2: X-ray Characterization of Nanoparticles (by D. Zanchet, B.D. Hall and D. Ugarte) Chapter 3: Transmission Electron Microscopy and Spec- troscopy of Nanoparticles (by Z.L. Wang) Chapter 4: Scanning Transmission Electron Microscopy of Nanoparticles (by J. Liu) Chapter 5: Scanning Probe Microscopy of Nanoclusters (by L.F. Chi and C. Rothig) Chapter 6: Electrical and Electrochemical Analysis of Nanophase Materials (by Z. Shi and M. Liu) * Prof. Z. L. Wang, Georgia Institute of Technology, Materials Science and Engineering, Atlanta, GA 30332 – 0245 (USA). E-mail: zhong.wang@mse.gatech.edu # WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2001 0934-0866/01/0306/0142 $17.50þ:50=0 142 Part. Part. Syst. Charact. 18 (2001) 142–165 Chapter 7: Optical Spectroscopy of Nanophase Materials (by C. Burda, T. Green, C. Landes, S. Link, R. Little, J. Patroski and M. A. El-Sayed) Chapter 8: Nuclear Magnetic Resonance–characteriza- tion of Self-assembled Nanostructural Mate- rials (by L.Q. Wang, G.J. Exarhos and J. Liu) Chapter 9: Photoluminescence from Single Semicon- ductor Nanostructures (by S. Empedocles, R. Neuhauser, K. Shimizu and M. Bowandi) Chapter 10: Nanomagnetism (by W.A. de Heer) Chapter 11: Oxide and -sulfide Nanocrystals and Nano- structures (by A. Chamisdee) Chapter 12: Electron Microscopy of Fullerenes and Related Materials (by G. Van Tendoloo and S. Amelinckx). High-resolution transmission electron microscopy (HRTEM) and associated energy dispersive X-ray spectro- scopy (EDS) and electron energy-loss spectroscopy (EELS) are versatile techniques that are among the most powerful tools for structure characterization of nanomaterials. As the imaging resolution approaches 0.1 nm, HRTEM is fully capable of revealing the atomic-scale structures both in the volume and on the surfaces of nanomaterials. The electron probe can be focused to a diameter with sizes smaller than 0.5 nm, thus, the EDS and EELS techniques can provide local chemical information and solid state structural infor- mation from a particle as small as 2 nm. This chapter gives a detailed description on the imaging principle of HRTEM, and its application for determining the particle shape, defect structures and the interface=surface structures of nanoma- terials. It shows how to use EDS and EELS to perform local chemical composition and electronic structures, such as the valence states of some transition metal elements. Chemical mapping using the inelastically scattered signals are also illustrated. The most exciting part of this chapter is the demonstration of using in-situ TEM to observe the struc- tural transformation and melting behaviour of nanoparti- cles, and the measurements of the mechanical and electronic transport properties of nano-wire structures. The measured properties can be correlated one-to-one with the microstructure of the nanowires observed in-situ. Various examples are illustrated for demonstrating the applications of these techniques. The chapter has achieved an objective that TEM is not only a technique for structure analysis but also a tool for quantitative property measure- ments. Chapter 3 Transmission Electron Microscopy and Spectroscopy of Nanoparticles One of the typical characters of nanophase materials is the small particle sizes. Although some structural features can be revealed by x-ray and neutron diffraction, direct imaging of nanoparticles is only possible using transmission electron microscopy (TEM) and scanning probe microscopy. TEM is unique because it can provide a real space image on the atom distribution in the nanocrystal and on its surface [1]. Today’s TEM is a versatile tool that provides not only atomic-resolu- tion lattice images, but also chemical information at a spatial resolution of 1 nm or better, allowing direct identification the chemistry of a single nanocrystal. With a finely focused electron probe, the structural characteristics of a single nanoparticle can be fully characterized. To reveal the cap- abilities of a modern TEM, this chapter is designed to illustrate the fundamentals of TEM and its applications in character- ization of nanophase materials. The fundamentals and appli- cations of scanning transmission electron microscopy (STEM) will be given in Chapter 4. Section 3.1 A Transmission Electron Microscope A modern TEM can be schematically shown in Figure 3.1, which is composed of an illumination system, a specimen stage, an objective lens system, the magnification system, the data recording system(s), and the chemical analysis system. The electron gun is the heart of the illumination system, which typically uses LaB6 thermionic emission source or a field emission source. The LaB6 gun gives a high illumination current but the current density and the beam coherence are not as high as those of a field emission source. Field emission source is unique for performing high coherence lattice imaging, electron holography and high spatial resolution microanalysis. The illumination system also includes the condenser lenses that are vitally important for forming a fine electron probe. Specimen stage is a key for carrying out structure analysis, because it can be used to perform in-situ observations of phenomena induced by annealing, electric field, or mechanical stress, giving the possibility to characterize the physical properties of indi- vidual nanostructures. The objective lens is the heart of a TEM, which determines the limit of image resolution. The magnification system consists of intermediate lenses and projection lenses, and it gives a magnification up to 1.5 million. The data recording system tends to be digital with the use of a charge coupled device (CCD), allowing quantitative data processing and quantification. Finally, the chemical analysis system is the energy dispersive x-ray spectroscopy (EDS) and electron energy-loss spectroscopy (EELS), both can be used complimentary to quantify the chemical composition of the specimen. EELS can also Part. Part. Syst. Charact. 18 (2001) 142–165 143 provide information about the electronic structure of the specimen. Section 3.2 High-resolution TEM Lattice Imaging Section 3.2.1 Image Formation As a start, we first illustrate the image formation process in an TEM [2]. For easy illustration, an TEM is simplified into a single lens microscope, as given in Figure 3.2, in which only a single objective lens is considered for imaging and the intermediate lenses and projection lenses are omitted. This is because the resolution of the TEM is mainly determined by the objective lens. The entrance surface of a thin foil specimen is illuminated by a parallel or nearly parallel electron beam. The electron beam is diffracted by the lattices of the crystal, forming the diffracted beams which are propagating along different directions. The electron-specimen interaction results in phase and ampli- tude changes in the electron wave that are determined by quantum mechanical diffraction theory. For a thin specimen and high-energy electrons, the transmitted wave function C(x, y) at the exit face of the specimen can be assumed to be composed of a forward-scattered wave. The non-near-axis propagation through the objective lens is the main source of non-linear information transfer in TEM. The diffracted beams will be focused in the back-focal plane, where an objective aperture could be applied. An ideal thin lens brings the parallel transmitted waves to a focus on the axis in the back focal plane. Waves leaving the specimen in the same direction (or angle y with the optic axis) are brought together at a point on the back focal plane, forming a diffraction pattern. The electrons scattered to angle y experience a phase shift introduced by the chro- matic and spherical aberrations of the lens, and this phase shift is a function of the scattering angle, thus, the dif- fraction amplitude at the back-focal plane is modified by c 0ðuÞ ¼ cðuÞ exp½iwðuފ ð3:1Þ wherec(u) is the Fourier transform of thewaveC(r) at the exit face of the specimen, u is the reciprocal space vector that is related to the scattering angle by u ¼ 2 sin y=l , and w(u) is determined by the spherical abberation coefficient Cs of the objective lens and the lens defocusDf [3] wðuÞ ¼ p 2 Csl3 u4 ÿ pDf l u2 ð3:2Þ where l is the electron wavelength. The aberration and defocus of the lens is to modulate the phases of the Bragg beams distributed in reciprocal space. The electron image is the interference result of the beams scattered to different angles, and this interference pattern is affected by the phase modulation introduced by the aber- Fig 3.1: Schematic structure of a transmission electron microscope. Fig 3.2: Abbe’s theory of image formation in an one-lens trans- mission electron microscope. This theory is for a general optical system in TEM. 144 Part. Part. Syst. Charact. 18 (2001) 142–165 ration of the objective lens. The image is calculated according to Iðx; yÞ ¼ jCðrÞ tobjðx; yÞj2 ð3:3Þ where indicates a convolution calculation of (x, y), tobj(x,y) is the inverse Fourier transform of the phase function exp[iw(u)]. The convolution of the lens transfer function introduces the non-linear information transfer characteristics of the objective lens, leading to complexity in image interpretation. Section 3.2.2 Contrast Mechanisms Images in TEM are usually dominated by three types of contrast. First, diffraction contrast [4], which is produced due to a local distortion in the orientation of the crystal (by dislocations, for example), so that the diffracted intensity of the incident electron beam is perturbed, leading to contrast observed in bright-field image. The nanocrystals oriented with their low-index zone-axis parallel or nearly parallel to the incident beam direction usually exhibit dark contrast in the bright field image, that is formed by selecting the central transmitted beam. Since the diffraction intensities of the Bragg reflected beams are strongly related to the crystal orientations, this type of image is ideally suited for imaging defects and dislocations. For nanocrystals, most of the grains are defect-free in volume, while a high density of defects are localized at the surface or grain boundary, dif- fraction contrast can be useful for capturing strain dis- tribution in nanocrystals whose sizes are larger than 15 nm. For smaller size nanocrystals, since the resolution of dif- fraction contrast is in the order of 1–2 nm, its application is limited. Secondly, phase contrast is produced by the phase mod- ulation of the incident electron wave when transmits through a crystal potential [1]. This type of contrast is sensitive to the atom distribution in the specimen and it is the basis of high-resolution TEM. To illustrate the physics of phase contrast, we consider the modulation of a crystal potential to the electron wavelength. From the de Brogli relation, the wavelength l of an electron is related to its momentum, p, by l ¼ h p : ð3:4Þ When the electron goes through a crystal potential field, its kinetic energy is perturbed by the variation of the potential field, resulting in a phase shift with respect to the electron wave that travels in a space free of potential field. For a specimen of thickness d, the phase shift is f � sVpðbÞ ¼ s …d 0 dzV ðrÞ ð3:5Þ where s ¼ p=lU0; b ¼ ðx; yÞ;U0 is the acceleration voltage, and Vp(b) the thickness-projected potential of the crystal. Therefore, from the phase point of view, the electron wave is modulated by a phase factor QðbÞ ¼ exp½isVpðbފ: ð3:6Þ This is known to be the phase object approximation. (POA), in which the crystal acts as a phase grating filter. If the incident beam travels along a low-index zone-axis, the variation of Vpðb) across atom rows is a sharp function because an atom can be approximated by a narrow potential well and its width is in the order of 0.2–0.3 A˚. This sharp phase variation is the basis of phase contrast, the funda- mental of atomic-resolution imaging in TEM. Finally, mass-thickness or atomic number produced con- trast. Atoms with different atomic numbers exhibit different powers of scattering. If the image is formed by collecting the electrons scattered to high-angles, the image contrast would be sensitive to the average atomic number along the beam direction. This type of imaging is usually performed in STEM (see Chapter 4). Section 3.2.3 Image Interpretation In high-resolution TEM (HRTEM) images, one usually wonders if the atoms are dark or bright. To answer this question one must examine the imaging conditions. For the clarity of following discussion, the weak scattering object approximation (WPOA) is made. If the specimen is so thin that the projected potential satisfies jsVpðbÞj << 1, the phase grating function is approximated by CðbÞ � 1þ isVpðbÞ: ð3:7Þ From Eq. (3.3) and ignoring the s2 term, the image inten- sity is calculated by Iðx; yÞ � 1ÿ 2sVpðbÞ tsðbÞ ð3:8Þ where tsðbÞ ¼ Im½tobjðbފ. The second term in Eq. (3.8) is the interference result of the central transmitted beam with the Bragg reflected beams. Any phase modulation intro- duced by the lens would result in contrast variation in the observed image. Under the Scherzer defocus, ts(b) is approximated to be a negative Gaussian-like function with a small oscillating tail, thus, the image contrast, under the WPOA, is directly related to the two-dimensional thickness- projected potential of the crystal, and the image reflects the projected structure of the crystal. This is the basis of structure analysis using HRTEM. On the other hand, the contrast of the atom rows is determined by the sign and real space distribution of ts(b). The convolution of ts(b) with the potential changes the phases of the Bragg reflected beams, which can be explicitly illustrated as following. Part. Part. Syst. Charact. 18 (2001) 142–165 145 A Fourier transform is made to the both sides of Eq. (3.8), yielding FT½IpŠ � dðuÞ ÿ 2sFT½VpðbފTsðuÞ: ð3:9Þ The d(u) function represents a strong central transmitted (000) beam. The Fourier transform of the crystal potential, FT[Vp(b)], is the diffraction amplitude of the Bragg beams under the kinematic scattering approximation. The con- tribution from each diffracted beam to the image is mod- ified by the function Ts(u)¼ sinw E(u), and E(u) is the envelope function due to a finite energy spread of the source, the focus spread, beam convergence, the mechanical vibration of the microscope, the specimen drift during the recording of the image, and electric voltage and lens current instability. The envelope function defines the maximum cut- off frequency that can be transferred by the optic system. Ts(u) is known as the phase-contrast transfer function (PCTF), characterizing the information transfering property of the objective lens. To illustrate this result, we consider a fcc structured crystal which gives {111}, {200}, {220} and {311} reflections. The angular distribution of these beams are schematically shown on the horizontal u axis. The dif- fraction amplitudes f{111} and f{220} of beams {111} and {220}, respectively, are chosen as two representatives to show the characteristics of phase transfer. When the defocus is zero (Figure 3.3a), f{111} is transferred with positive sign (sinw > 0), while f{220} is transferred with negative sign (sinw < 0). The sign reverse of f{220} with respect to f{111} results in a contrast reversal in the interference pattern due to the destructive summation of the two. At Df¼ 20 nm (Figure 3.3b), the two amplitudes are transferred with the same sign except the relative weight factor of the two is changed. At Df = 40.5 nm (Figure 3.3c), f{111} and f{220} are both transferred with the negative sign, and there is no relative phase change between f{111} and f{220}, thus, the interferences between f{000}, f{111} and f{220} give the image that is directly related to the crystal structure (i.e., the atom rows and planes). The PCTF depends sensitively on the defocus of the objective lens. The interpretable image resolution that is directly associated with the crystal structure (e.g., the structural resolution) is determined by the width of the information passing band. It was first investigated by Scherzer [5] that the highest structural resolution of R¼ 0.66 l3=4 Cs1=4 would be obtained at defocus Df = (4/3 Csl)1=2. In this focus condition, the ts(