理论（电子散射、衍射、照相术） - 版本历史

Li.qun：/* 171. micro electron diffraction method, Micro ED */

2020-10-30T02:14:44Z

‎171. micro electron diffraction method, Micro ED

Li.qun：/* 171.micro electron diffraction method, Micro ED */

2020-10-30T02:13:33Z

‎171.micro electron diffraction method, Micro ED

2020年10月30日 (五) 02:11 Li.qun

2020-10-30T02:11:21Z

Li.qun：/* 95. δ fringe */

2020-08-31T02:09:05Z

‎95. δ fringe

Li.qun：/* 95. δ fringe */

2020-08-31T02:08:15Z

‎95. δ fringe

Li.qun：/* 95. δ fringe */

2020-08-31T02:06:06Z

‎95. δ fringe

Li.qun：/* 2. α fringe */

2020-08-28T05:38:36Z

‎2. α fringe

Li.qun：/* 2. α fringe */

2020-08-28T05:37:19Z

‎2. α fringe

Li.qun：/* 2. α fringe */

2020-08-28T05:36:39Z

‎2. α fringe

Li.qun：/* 2. α fringe */

2020-08-28T05:30:29Z

‎2. α fringe

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 The micro electron diffraction method is a method to determine crystal structures using electron diffraction patterns with the help of the kinematical diffraction theory (Fourier transform), where the diffraction patterns are acquired while continuously tilting small crystalline specimens against the incident electron beam to reduce the dynamical diffraction effect.
 A specimen size to be used is a few µm in diameter, and is tilted up to 30 to 60° at a step of 0.1 to 1 deg/sec. Several series of diffraction patterns are taken as movie or frame images. Then, the crystal structures are determined by applying a method broadly used in X-ray crystal structure analysis (the direct method) to the present diffraction data obtained.
 In ordinary electron diffraction, the simultaneous reflection effect (one of dynamical diffraction effects) arises, that is a certain reflection is enhanced via the other reflections simultaneously excited. Thus, X-ray crystallography method based on the kinematical theory (Fourier transform), which does not take account of the dynamical diffraction effect, cannot be applied to electron diffraction. However, when diffraction patterns are acquired while tilting a specimen and summing up the intensities of each diffraction pattern, the diffraction intensity is averaged and the simultaneous reflection effect decreases, and then the obtained diffraction intensities approach to those expected from the kinematical theory. Fig. 1 shows an example of a series of diffraction patterns. Since the angler range and the directions of tilting for one specimen are limited, several series of tilt operations are performed for the specimens with different crystal orientations.Then, the acquired diffraction patterns are combined to form a dataset covering a wide angler range and different orientations. For this data set, the direct method in X-ray crystallography is applied to determine the crystal structure. *1
 The features of Micro ED are as follows.
 The scattering cross section of a crystal for electrons is 104 times larger than that for X-rays. Thus, sufficiently-high electron diffraction intensities are obtained even from a micro-crystal of 1 µm or less in size. Therefore, Micro ED is effective for structural analysis of organic- and inorganic-compounds from which only micro-crystals are prepared. In the case of X-ray structure analysis, a large-crystal of several 10 µm in size is needed. (It is possible to use a crystal with a size down to several µm when a synchrotron radiation light source is used.) For electron diffraction, it should be noted that a radiation damage of a specimen due to electron-beam irradiation can arise. To avoid this problem, it is required to cool the specimen with liquid nitrogen and to decrease the electron dose.
 *1. Note
 An electron, a charged particle, is scattered by the electrostatic potential formed by both the nucleus and electrons of the atoms in a crystal. An X-ray, an electromagnetic wave, is scattered by the electrons of the atoms in a crystal (Thomson scattering). It is noted that an atomic nucleus does not contribute to the X-ray scattering because the nucleus is too heavy to be vibrated by X-rays.
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 [[文件:Micro ed en 01.jpg]]
 Fig. 1 Tilt-series of electron diffraction patterns obtained from an L-histidine micro-crystal.
 Angular tilt range: –16° to +15°. Tilt speed: 0.1°/s. Electron dose: 0.06 e-/Å2/s. Accelerating voltage: 200 kV.
 The angles indicated in each frame are the tilt angles at the start of acquiring each diffraction pattern.
 [[文件:Micro ed en 02.jpg]]
 Fig. 2 For L-histidine with a known molecular structure, the Micro ED method was applied.
 The grid (mesh) pattern shows the equi electrostatic potential planes (potential map) obtained by the method. A molecular model obtained by neutron diffraction is overlaid on the grid pattern. The reconstruction pattern obtained by the Micro ED method is in good agreement with the already reported structural model. (In the model, the respective elements are indicated by the different colors. C: gray, N: blue, O: red, H: white)
 (Reconstruction model: Courtesy of Dr. Yusuke Nishiyama (JEOL RESONANCE Inc.))

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 In the structure analysis, so as to minimize the R-factor, the parameters (symmetry, lattice constant, atomic coordinate, etc.) of the crystal structure (structure model) are determined. When the experimentally-obtained crystal structure factor coincides fully with the crystal structure factor calculated from the determined structure, the R-factor becomes 0 (zero). When the crystal structure which provides the highest reproducibility of the experimental value is obtained, the value of the R-factor is about 0.05 for X-ray crystallography and is about 0.2 for electron crystallography.
-==171.micro electron diffraction method, Micro ED==
+==171. micro electron diffraction method, Micro ED==
 The micro electron diffraction method is a method to determine crystal structures using electron diffraction patterns with the help of the kinematical diffraction theory (Fourier transform), where the diffraction patterns are acquired while continuously tilting small crystalline specimens against the incident electron beam to reduce the dynamical diffraction effect.
 A specimen size to be used is a few µm in diameter, and is tilted up to 30 to 60° at a step of 0.1 to 1 deg/sec. Several series of diffraction patterns are taken as movie or frame images. Then, the crystal structures are determined by applying a method broadly used in X-ray crystal structure analysis (the direct method) to the present diffraction data obtained.
@@ 第1,145行： / 第1,145行： @@
 Angular tilt range: –16° to +15°. Tilt speed: 0.1°/s. Electron dose: 0.06 e-/Å2/s. Accelerating voltage: 200 kV.
 The angles indicated in each frame are the tilt angles at the start of acquiring each diffraction pattern.
+[[文件:Micro ed en 02.jpg]]
 Fig. 2 For L-histidine with a known molecular structure, the Micro ED method was applied.
 The grid (mesh) pattern shows the equi electrostatic potential planes (potential map) obtained by the method. A molecular model obtained by neutron diffraction is overlaid on the grid pattern. The reconstruction pattern obtained by the Micro ED method is in good agreement with the already reported structural model. (In the model, the respective elements are indicated by the different colors. C: gray, N: blue, O: red, H: white)
 (Reconstruction model: Courtesy of Dr. Yusuke Nishiyama (JEOL RESONANCE Inc.))

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	Here, (hkl) is an index of Bragg reflection (Mirror index) and the sum of the right side of the equation is taken for all of the experimentally measured reflections.		Here, (hkl) is an index of Bragg reflection (Mirror index) and the sum of the right side of the equation is taken for all of the experimentally measured reflections.
	In the structure analysis, so as to minimize the R-factor, the parameters (symmetry, lattice constant, atomic coordinate, etc.) of the crystal structure (structure model) are determined. When the experimentally-obtained crystal structure factor coincides fully with the crystal structure factor calculated from the determined structure, the R-factor becomes 0 (zero). When the crystal structure which provides the highest reproducibility of the experimental value is obtained, the value of the R-factor is about 0.05 for X-ray crystallography and is about 0.2 for electron crystallography.		In the structure analysis, so as to minimize the R-factor, the parameters (symmetry, lattice constant, atomic coordinate, etc.) of the crystal structure (structure model) are determined. When the experimentally-obtained crystal structure factor coincides fully with the crystal structure factor calculated from the determined structure, the R-factor becomes 0 (zero). When the crystal structure which provides the highest reproducibility of the experimental value is obtained, the value of the R-factor is about 0.05 for X-ray crystallography and is about 0.2 for electron crystallography.
		+
		+	==171.micro electron diffraction method, Micro ED==
		+	The micro electron diffraction method is a method to determine crystal structures using electron diffraction patterns with the help of the kinematical diffraction theory (Fourier transform), where the diffraction patterns are acquired while continuously tilting small crystalline specimens against the incident electron beam to reduce the dynamical diffraction effect.
		+	A specimen size to be used is a few µm in diameter, and is tilted up to 30 to 60° at a step of 0.1 to 1 deg/sec. Several series of diffraction patterns are taken as movie or frame images. Then, the crystal structures are determined by applying a method broadly used in X-ray crystal structure analysis (the direct method) to the present diffraction data obtained.
		+	In ordinary electron diffraction, the simultaneous reflection effect (one of dynamical diffraction effects) arises, that is a certain reflection is enhanced via the other reflections simultaneously excited. Thus, X-ray crystallography method based on the kinematical theory (Fourier transform), which does not take account of the dynamical diffraction effect, cannot be applied to electron diffraction. However, when diffraction patterns are acquired while tilting a specimen and summing up the intensities of each diffraction pattern, the diffraction intensity is averaged and the simultaneous reflection effect decreases, and then the obtained diffraction intensities approach to those expected from the kinematical theory. Fig. 1 shows an example of a series of diffraction patterns. Since the angler range and the directions of tilting for one specimen are limited, several series of tilt operations are performed for the specimens with different crystal orientations.Then, the acquired diffraction patterns are combined to form a dataset covering a wide angler range and different orientations. For this data set, the direct method in X-ray crystallography is applied to determine the crystal structure. *1
		+	The features of Micro ED are as follows.
		+	The scattering cross section of a crystal for electrons is 104 times larger than that for X-rays. Thus, sufficiently-high electron diffraction intensities are obtained even from a micro-crystal of 1 µm or less in size. Therefore, Micro ED is effective for structural analysis of organic- and inorganic-compounds from which only micro-crystals are prepared. In the case of X-ray structure analysis, a large-crystal of several 10 µm in size is needed. (It is possible to use a crystal with a size down to several µm when a synchrotron radiation light source is used.) For electron diffraction, it should be noted that a radiation damage of a specimen due to electron-beam irradiation can arise. To avoid this problem, it is required to cool the specimen with liquid nitrogen and to decrease the electron dose.
		+	*1. Note
		+	An electron, a charged particle, is scattered by the electrostatic potential formed by both the nucleus and electrons of the atoms in a crystal. An X-ray, an electromagnetic wave, is scattered by the electrons of the atoms in a crystal (Thomson scattering). It is noted that an atomic nucleus does not contribute to the X-ray scattering because the nucleus is too heavy to be vibrated by X-rays.
		+	Thus, structural analysis using electron diffraction determines the electrostatic potential distribution in a crystal, whereas structural analysis by X-ray diffraction determines the electron density distribution in a crystal. It is known to exist a conversion formula between the electrostatic potential distribution and the electron density distribution in a crystal. Thus, if one is found, the other is found by the conversion.
		+
		+	[[文件:Micro ed en 01.jpg]]
		+	Fig. 1 Tilt-series of electron diffraction patterns obtained from an L-histidine micro-crystal.
		+	Angular tilt range: –16° to +15°. Tilt speed: 0.1°/s. Electron dose: 0.06 e-/Å2/s. Accelerating voltage: 200 kV.
		+	The angles indicated in each frame are the tilt angles at the start of acquiring each diffraction pattern.
		+
		+	Fig. 2 For L-histidine with a known molecular structure, the Micro ED method was applied.
		+	The grid (mesh) pattern shows the equi electrostatic potential planes (potential map) obtained by the method. A molecular model obtained by neutron diffraction is overlaid on the grid pattern. The reconstruction pattern obtained by the Micro ED method is in good agreement with the already reported structural model. (In the model, the respective elements are indicated by the different colors. C: gray, N: blue, O: red, H: white)
		+	(Reconstruction model: Courtesy of Dr. Yusuke Nishiyama (JEOL RESONANCE Inc.))

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 The symmetry nature above described appears only when the angular difference between the two crystalline regions is several degrees or less. If the angle becomes large, only one crystalline region satisfies the Bragg condition, that is, the excitation error s for the other region becomes large, the symmetry nature of the end stripes or the δ fringe disappears, and instead, equal thickness fringes appear from the former region where the diffraction condition is satisfied. Thus, understanding of the δ fringe together with the α fringe is one of the great successes of the dynamical diffraction theory taking account of the absorption effect. However, the angle between the two crystalline regions is difficult to be measured using the δ fringe.
 It should be noted that the measurement of the angular difference between the two crystalline regions can be performed by the large-angle convergent-beam electron diffraction (LACBED) with a very high accuracy. The following references are referred to detailed LACBED analysis.
 M. Tanaka, M. Terauchi and T. Kaneyama: J. Electron Microscopy 40 (1991) 211-220
 M. Tanaka, M. Terauchi and K. Tsuda: Convergent Beam Electron Diffraction III (1994) pp188-205, JEOL Tokyo

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 ==95. δ fringe ==
 "δ fringe" means the edge fringes showing a specific contrast of the striped interference image obtained from a twin boundary oblique to a crystalline specimen surface, which appears in bright- and dark-field images taken at a two-wave approximation condition. (The twin boundary is formed by two crystalline parts with different orientations.)
 Fig.1(a) shows a schematic of a twin boundary oblique to the specimen surface and the expected striped interference image or the δ fringe from the boundary. The lattice planes change their orientations at the twin boundary. Fig. 1(b) shows the dark-field image of a twin boundary of nickel oxide (NiO). Fig. 1(c) shows an enlarged image of a part of Fig. 1(b).
 The excitation error s of diffracted wave g is different for the two crystalline regions of the twin. The sign of the difference Δs = s1 - s2 between the excitation errors s1 and s2 for the two regions, determines the nature of the end-striped image or the contrast of the δ fringe. The nature and formation of the striped image is explained by the dynamical diffraction theory taking account of the absorption effect. (see Reference: Marc De Graef: Introduction to Conventional Transmission Electron Microscopy, pp507~).
 The end stripes or δ fringes, which appear at the intersection between the twin boundary and the upper and lower surfaces of the specimen, exhibit symmetric contrast in the dark-field image and anti-symmetric contrast in the bright-field image with respect to the center of the striped image (to the half depth position of the specimen). The symmetric contrast (nature) in the dark-field image or a bright (B)- and bright (B)-fringe pair is clearly seen in Fig. 1(b) and (c).
 This symmetry nature reveals the sign of Δs (Δs is positive in Fig. 1(b)), and the sign of the angle between the two crystalline regions (the right region is upward to the left region or downward to the left). The term "δ fringe" is originated from the angular change "δ" between the crystalline regions at the twin boundary.
 The symmetry nature above described appears only when the angular difference between the two crystalline regions is several degrees or less. If the angle becomes large, only one crystalline region satisfies the Bragg condition, that is, the excitation error s for the other region becomes large, the symmetry nature of the end stripes or the δ fringe disappears, and instead, equal thickness fringes appear from the former region where the diffraction condition is satisfied. Thus, understanding of the δ fringe together with the α fringe is one of the great successes of the dynamical diffraction theory taking account of the absorption effect. However, the angle between the two crystalline regions is difficult to be measured using the δ fringe.
 It should be noted that the measurement of the angular difference between the two crystalline regions can be performed by the large-angle convergent-beam electron diffraction (LACBED) with a very high accuracy. The following references are referred to detailed LACBED analysis.
 M. Tanaka, M. Terauchi and T. Kaneyama: J. Electron Microscopy 40 (1991) 211-220
 M. Tanaka, M. Terauchi and K. Tsuda: Convergent Beam Electron Diffraction III (1994) pp188-205, JEOL Tokyo

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 lattice vibration, Bragg reflection</pre>
 ==95. δ fringe ==
-"δ fringe" means a fringe contrast, which is observed in bright- and dark-field images under a two-beam approximation condition in the case where the orientations of the upper and lower crystals are different to each other (for example, twin boundary) at an interface oblique to the surface of a crystalline specimen. The fringe contrast, which appears at two positions (edges) where the interface intersects the upper and lower surfaces, exhibits symmetric contrast in the dark-field and anti-symmetric contrast in the bright-field with respect to the center of the fringe (specimen).
+"δ fringe" means the edge fringes showing a specific contrast of the striped interference image obtained from a twin boundary oblique to a crystalline specimen surface, which appears in bright- and dark-field images taken at a two-wave approximation condition. (The twin boundary is formed by two crystalline parts with different orientations.)
 <pre>Related term
 twins, boundary, two-beam approximation, bright-field image, dark-field image, α fringe</pre>
 ==96. charge and orbital ordering ==
 "Charge and orbital ordering" states the charge-ordered state and the orbital-ordered state for 3d electrons in transition metals in a crystal. The charge-ordered state means that two charge states are alternately and regularly arranged. The orbital-ordered state means that orbitals, for example eg orbitals, with one orientation and the other orientation are alternately and regularly arranged. These states emerge in perovskite oxides containing transition metals when composition or temperature is changed. Such super structures in electronic systems are reflected in lattice systems, thus these structures are observed by superlattice reflections in an electron diffraction pattern.

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	S. Yamada and M. Tanaka: J. Electron Microscopy 46 (1997) 67-74		S. Yamada and M. Tanaka: J. Electron Microscopy 46 (1997) 67-74
		+
	M. Tanaka, M. Terauchi and K. Tsuda: Convergent Beam Electron Diffraction III (1994) pp156-177, JEOL Tokyo		M. Tanaka, M. Terauchi and K. Tsuda: Convergent Beam Electron Diffraction III (1994) pp156-177, JEOL Tokyo

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 The nature and formation of the striped image depending on the phase angle α is explained by the dynamical diffraction theory taking account of the absorption effect (see Reference: Marc De Graef: Introduction to Conventional Transmission Electron Microscopy, pp499~). The term "α" fringe is originated from the phase angle α.
 It should be noted that it is difficult to determine quantitatively the displacement vector between the two crystalline regions from analysis of the fringe intensity profile. For quantitative analysis, it is essential to use large-angle convergent-beam electron diffraction (LACBED). The following references are referred to detailed LACBED analysis.
 S. Yamada and M. Tanaka: J. Electron Microscopy 46 (1997) 67-74
 M. Tanaka, M. Terauchi and K. Tsuda: Convergent Beam Electron Diffraction III (1994) pp156-177, JEOL Tokyo
 [[文件:Alpha fringe 01.png]]
 Fig.1(a) Two striped images or α fringes oblique to the specimen surface (dark-field image of stacking faults). Specimen: PbTiO3. Accelerating voltage: 200 kV. The upper fringe of the stripe is bright (B) and the lower fringe is dark (D), showing a characteristic asymmetrical contrast. It is noted that the zigzag images appearing left and right is due to zigzag overlap of two stacking faults.
 Fig.1(b) Enlarged image of a part of the stripe in Fig.1(a). A pair of dark (D) and bright (B) fringes is seen. The (top and bottom) fringes show anti-symmetric contrast nature with respect to the center of the stripes.

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 ==2. α fringe==
-"α fringe" means a fringe contrast, which is observed in bright- and dark-field images under a two-beam approximation condition in the case where the upper and lower crystals are shifted to each other (for example, stacking faults) at an interface oblique to the surface of a crystalline specimen. The end fringes, which appear at the intersection between the interface and the upper and lower surfaces, exhibit symmetric contrast in the bright-field and anti-symmetric contrast in the dark-field with respect to the center of the fringe (specimen).
+"α fringe" means the edge fringes showing a specific contrast of the striped interference image obtained from a stacking fault oblique to a crystalline specimen surface, which appears in the bright- and dark-field images taken at a two-wave approximation condition. (The stacking fault is a planer defect at which an atomic displacement takes place between the two crystalline regions sandwiching the fault plane.)
 <pre>Related term
 stacking fault, two-beam approximation, bright-field image, dark-field image, δ fringe</pre>