Lab 05: Transmission Electron Microscopy

Transcription

1 Lab 05: Transmission Electron Microscopy Author: Mike Nill Alex Bryant Contents 1 Introduction Imaging Modes Electromagnetic Lenses Experimental Procedures 4 3 Results Indexing the Diffraction Pattern Crystal Orientation Relative Rotation Discussion Digital Microscopy Balancing Act Conclusions 7 1

2 Abstract A sample of molybdenum trioxide crystals deposited on a lacy carbon substrate was used to determine the image rotation in a Transmission Electron Microscope. Bright-field images were taken at 30k, 150k, and 400k magnification and compared to a diffraction pattern resulting primarily from a single crystal of interest. The orientation of the diffraction pattern was compared with knowledge about the crystal facets of MoO 3 to determine the angular rotation in each case. 1 Introduction The Transmission Electron Microscope shares more characteristics with its optical cousins than with the similarly named Scanning Electron Microscope. Although the SEM also uses a set of electromagnetic lenses to focus the electron beam onto a small spot, the lenses do not participate in image formation. Objects are spatially resolved by scanning the beam rapidly across the sample surface and measuring the plume of ejected electrons to generate a signal at each point. The tall beam column of the TEM, much taller than that of the SEM, houses a filament from which electrons are extracted by thermal excitation, a series of electromagnetic lenses for focusing the electron beam, a limiting aperture, and of course the sample stage itself. The image is formed at the base of the column where the electrons cause a phosphorous screen to fluoresce, or are imaged directly by a digital CCD camera. 1.1 Imaging Modes An accelerating voltage of around 200 kv is typical for a TEM[5]. The majority of the incident beam passes directly through a specially thinned electron transparent sample and is projected to the base of the column. An image is generated in a similar manner as in a transmission optical microscope. Electron rays scattered from a single point on the sample are focused by the objective lens to a single point on the phosphor screen. This one-to-one mapping generates an image in imaging mode. Now consider a set of rays scattered at the same angle with respect to the forward scattering direction (Figure 1). These rays will converge to a common point above the image. We refer to the plane where these points reside as the back focal plane. Every point projected on the back focal plane represents a set of rays scattered at the same angle (and rotation) with respect to the forward scattering direction. Hence, the image projected on the back focal plane is in fact a diffraction pattern. By the action of a set of projection lenses this image can be brought to the phosphor screen. The scattering geometry allows the user to select different parts of the beam by placing an aperture around a part of the beam at the back focal plane. If a small hole is placed, say, around the forward scattered beam (the point where the solid lines converge in Figure 1) an image will be generated by the forward scattered beam only. This is called bright-field imaging because bright areas of the image correspond to areas in the sample where relatively few electrons were absorbed or scattered. If, on the other hand, an aperture was placed around the point representing the scattered beam (dash-dot lines in Figure 1) an image would be generated only by rays scattered in that direction. If these rays satisfied the Bragg condition for a particular set of crystallographic planes, elements in the specimen properly oriented for this condition would appear bright against a dark background. This mode is known as dark-field imaging. It is tempting to say that the bright-field image and dark-field image are somehow inverses of each other. Areas appearing bright in a bright-field image generally appear dark in a dark-field image, 2

3 Figure 1: Classical ray diagram in a TEM following [7], showing both the forward scattered beam and Bragg-scattered beam for two arbitrary points in the sample. and vice versa. However, there is a subtler point. For a given sample and magnification, there is one single bright-field image, the one generated by the forward scattered beam. However, there are numerous dark-field images, each being generated by a different scattered beam. Areas in one dark-field image appearing bright may appear dark in another dark-field image of the sample if that region is not oriented for coherent scattering in that direction. It may be said, however, that the superposition of all possible dark-field images forms the inverse of the bright-field image. 1.2 Electromagnetic Lenses Electrons interact with electromagnetic fields according to the Lorentz force F = e(e + v B) (1) Electrostatic lenses operate by imposing an electric field E. This can be done by applying a voltage across physically separated plates. An oscilloscope operates by applying a time-varying voltage across parallel plates to cause an electron beam to scan across a fluorescent screen. The lenses in a TEM are radially symmetric solenoid electromagnets, imposing a magnetic field B (Figure 2). Ideally, the field has components in only the axial and radial directions. As an electron encounters the magnetic field, it is initially deflected in the tangential direction (mutually perpendicular both to the electron velocity and the field. It is the tangential velocity which enables the focusing action of the magnetic lens. The vector product v θ B z creates a force directed radially inward. The electron may be imagined as tracing the inside of a converging cone. When the electron crosses the mid-plane of the lens, the radial component of the field reverses in direction, which acts to slow the tangential velocity of the electron. By symmetry, the electron leaves the magnetic field with no tangential velocity, but having been deflected towards the center. The B field deviates most strongly from verticality far from the center. Therefore electrons that enter farthest from the axis are deflected most strongly inward. Parallel beams of electrons are 3

4 Figure 2: Schematic of the B field inside an electromagnetic lens. Magnetic flux lines flow from S to N. brought to a single focal point below (or inside, depending on focal length) the magnet. This non-trivial result indicates that electromagnets can be used to focus electron beams in a similar fashion as optical lenses. Thus microscopists speak of electron optics and recycle much of the terminology borrowed from optical microscopy. The tangential component of the trajectory causes the electron to trace out a spiral through the magnetic field. The resulting image will be rotated through some constant angle with respect to the incoming beam. This angle depends on the strength of the magnetic field, and hence on the magnification. Although attempts are made by modern microscopes to account for this rotation, care must be taken to calibrate the instrument. This is done by examining a sample which is easily indexed and comparing the relative rotation of the diffraction pattern and the magnified image. 2 Experimental Procedures Crystallites of molybdenum trioxide were used to determine the rotational correction. MoO 3 crystals were evaporated onto a lacy carbon substrate supported by a 200 µm copper mesh (purchased from Ted Pella Inc). The sample was investigated in a JEOL TM JEM 2011 Transmission Electron Microscope. Bright-field images of a particular crystallite were taken at 30k, 150k, and 400k magnification. A selected-area diffraction pattern was also taken to capture orientation information from the same crystallite. The diffraction pattern was indexed from knowledge of the crystal structure and lattice parameters[3]. The angle between the long edge of the crystallite and the image horizon was measured using ImageJ. The normal to this edge is known to be the [100] direction[2]. This angle was compared to the angle between the (100) reciprocal lattice direction and the image horizon. The relative angles were used to determine the relative mis-orientation of each magnified image. 3 Results 3.1 Indexing the Diffraction Pattern In order to determine relative rotation, a reference orientation must first be established from the diffraction pattern. MgO 3 is orthorhombic, with lattice parameters a =3.9628Å, b =13.855Å, and c =3.6964Å[3]. The rectilinear diffraction pattern (Figure 3) indicates that the crystallite is in a 4

5 [100], [010] or [001] zone-axis orientation. The two orthogonal reciprocal lattice directions are very close in magnitude, and must therefore correspond to the (100) and (001) directions. The spacings along each reciprocal lattice direction are readily measured in ImageJ, leading to the conclusion that the smaller spacings along the 2 o clock direction correspond to the (100) reciprocal direction. Other spots are visible which do not line up with the primary pattern. However, these are easily distinguished by their low intensity. It is likely that the beam captured information from nearby crystallites in addition to the crystal of interest. Figure 3: Electron Diffraction pattern in the (010) zone-axis orientation 3.2 Crystal Orientation MoO 3 is known to condense into long prismatic crystallites, with the [010] and [100] directions normal to the long axis[2]. Furthermore, from knowledge of the diffraction pattern, the [010] direction points normal to the surface of the lacy carbon substrate. This orientation allows for an easy measurement between the indexed diffraction pattern and the long edge of the crystallite. 3.3 Relative Rotation For the levels of magnification examined the rotational correction of the microscope is quite good; within a few degrees at the worst. Magnified images are shown superimposed over the diffraction pattern in Figure 4. The rotational misalignment for 30k, 150k, and 400k was +0.1, -0.5, and 1.9 respectively in the clockwise direction. Rotation-free imaging is certainly a bold claim, and despite excellent control, the JEM 2011 falls just short of this goal (Figure 5). 5

6 (a) Relative rotation: +0.1 (b) Relative rotation: -0.5 (c) Relative rotation: +1.9 Figure 4: Images at three different magnifications with the diffraction pattern superimposed, illustrating a very small but noticable angular mismatch 4 Discussion Although they will not be considered in this study, there exist certain thresholds above which the image rotation suffers an extreme disturbance of These discontinuities may be difficult or impractical to remove due to the complexity of the lens configuration employed. Even with the presence of these discontinuities, image rotation is a systematic effect. It affects every area of the image equally and does not reduce the power of the microscope. 4.1 Digital Microscopy Rotation correction is not an insurmountable technical problem. The principle difficulty in the JEM 2011 is that the manufacturer decided to correct for rotation physically, i.e. by correcting the paths of the electron beam by the use of additional electromagnets. This enables rotation correction on the phosphorescent viewing screen. If the viewing screen was removed entirely and the operator interfaced with a computer screen exclusively, the correction could be done in software. Programmatic correction could be made extremely accurate by the use of correctional algorithms 6

7 2 Relative Rotation under Magnification 1.5 Rotation Angle [ ] Magnification ( 1000) Figure 5: Image rotation vs. magnification, revealing no clear trend in deviations or fuzzy logic tables taking into account several different parameters, such as lens current and beam voltage. This method would require considerably simpler equipment. 4.2 Balancing Act Rotation is not the greatest of the microscopists concerns. Although cylindrical symmetry of the electromagnetic lens is required to enforce electron focus, it can be shown[6] that perfect symmetry necessarily introduces a spherical aberration. The term refers to optics, in which a convex lens with a spherical profile causes rays entering the lens far from the axis to be bent too aggressively. A spherical profile is not the ideal shape for an optical lens, however it is generally a much easier to shape to manufacture than more complicated profiles. Much to our dismay, it turns out that asymmetry of the electron lens introduces another problem. A lens with astigmatism brings electron rays on different planes into focus at different points. Given the already short depth of field of the TEM, astigmatism sharply reduces the resolving power of the optics. Although all of these problems can be mitigated through meticulous calibration, they cannot be eliminated. Often, correcting one problem means introducing another problem in another codependent subsystem. 5 Conclusions It is very easy to answer many of these fundamental biological questions; you just look at the thing! - Richard Feynman, There s Plenty of Room at the Bottom Electron microscopy has become, in many ways as it was imagined, a revolutionary technology which has changed the way that we do science. It finds its way into new fields yearly, with applications in physics, chemistry, materials science, geology, and biology. Many of the problems put 7

8 forward by Richard Feynman in his 1959 talk[4] on the emerging field of nanotechnology have been solved or are being advanced at a surprising rate[8]. Amongst the multitude of new challenges put forwarded by electron optics, image rotation is relatively easy to correct if one is cognizant of its effects. By its very nature, rotation is a source of systematic error. It does not reduce resolution or coherence of the image because it affects every electron in the same manner. It is likely that in several years, electron microscopes will no longer have analog interfaces and manual rotation calibration will be a thing of the past. References [1] B.D. Cullity, Elements of X-Ray Diffraction. Addison-Wesley, Massachusetts, 2nd Edition, (1978) [2] S. Nakahara and A.G. Cullis, Simple method for determining the absolute sense of image rotation in a transmission electron microscope, Ultramicroscopy 45 (1992) [3] Collaboration: Authors and editors of the volumes III/17G-41D: MoO3: phase diagram, crystal structure, lattice parameters, interatomic distances. Madelung, O., Rossler, U., Schulz, M. (ed.). SpringerMaterials - The Landolt-Bornstein Database ( DOI: / [4] R. Feynman There s Plenty of Room at the Bottom, Lecture, American Physical Society, Enginering and Science, Cal Tech (1959) [5] B. Fultz and J.M. Howe, Transmission Electron Microscopy and Diffractometry of Materials, Springer New York, 2nd Edition, (2001) [6] L. Jacob and J.R. Shah, Trajectories in the Symmetrical Electron Lens Journ. Appl. Phys. 24, 10 (1953) [7] J.M. Rodenburg, Learn to use TEM, Diffraction Mode, Oct 21 (2004), [8] Second TEAM Workshop, Materials Research in an Aberration-Free Environment, July 18-19, 2002 Lawrence Berkeley National Laboratory, 8