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Chapter 1
AN INTRODUCTION TO MICROSCOPY
Microscopy involves the study of objects that are too small to be examined by the unaided eye. In the SI (metric) system of units, the sizes of these objects are expressed in terms of sub-multiples of the meter, such as the micrometer (1 Pm = 10 -6^ m, also called a micron ) and also the nanometer (1 nm = 10 -9^ m). Older books use the Angstrom unit (1 Å = 10^ -10^ m), not an official SI unit but convenient for specifying the distance between atoms in a solid, which is generally in the range 2 3 Å.
To describe the wavelength of fast-moving electrons or their behavior inside an atom, we need even smaller units. Later in this book, we will make use of the picometer (1 pm = 10 -12^ m).
The diameters of several small objects of scientific or general interest are listed in Table 1-1, together with their approximate dimensions.
Table 1-1. Approximate sizes of some common objects and the smallest magnification M* required to distinguish them, according to Eq. (1.5).
Object Typical diameter D M* = 75Pm / D
Grain of sand 1 mm = 1000 μm None
Human hair 150 μm None
Red blood cell 10 μm 7.
Bacterium 1 μm 75
Virus 20 nm 4000
DNA molecule 2 nm 40,
Uranium atom 0.2 nm = 200 pm 400,
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1.1 Limitations of the Human Eye
Our concepts of the physical world are largely determined by what we see around us. For most of recorded history, this has meant observation using the human eye, which is sensitive to radiation within the visible region of the electromagnetic spectrum, meaning wavelengths in the range 300 – 700 nm. The eyeball contains a fluid whose refractive index ( n | 1.34) is substantially different from that of air ( n | 1). As a result, most of the refraction and focusing of the incoming light occurs at the eye’s curved front surface, the cornea ; see Fig. 1-1.
pupil (aperture)
iris (diaphragm)
cornea retina
n = 1.
u (>>f) v a f
(a)
(b)
(c)
'T
'T
f
'
'
' R
lens
D
'T
optic axis
d
d/
f/n
Figure 1-1. (a) A physicist’s conception of the human eye, showing two light rays focused to a single point on the retina. (b) Equivalent thin-lens ray diagram for a distant object, showing parallel light rays arriving from opposite ends (solid and dashed lines) of the object and forming an image (in air) at a distance f (the focal length) from the thin lens. (c) Ray diagram for a nearby object (object distance u = 25 cm, image distance v slightly less than f ).
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parallel beam of light strikes an opaque diaphragm containing a circular aperture whose radius subtends an angle D at the center of a white viewing screen. Light passing through the aperture illuminates the screen in the form of a circular pattern with diffuse edges (a disk of confusion ) whose diameter ' x exceeds that of the aperture. In fact, for an aperture of small diameter,
diffraction effects cause ' x actually to increase as the aperture size is
reduced, in accordance with the Rayleigh criterion:
' x | 0.6 O / sin D (1.1)
where O is the wavelength of the light being diffracted.
Equation (1.1) can be applied to the eye, with the aid of Fig. 1-1b, which shows an equivalent image formed in air at a distance f from a single focusing lens. For wavelengths in the middle of the visible region of the
spectrum, O | 500 nm and taking d | 4 mm and f | 2 cm, the geometry of
Fig. 1-1b gives tan D | ( d /2)/ f = 0.1 , which implies a small value of D and
allows use of the small-angle approximation: sin D | tan D. Equation (1.1)
then gives the diameter of the disk of confusion as ' x | (0.6)(500 nm)/0.1 = 3 Pm. Imperfect focusing (aberration) of the eye contributes a roughly equal amount of image blurring, which we therefore take as 3 Pm. In addition, the receptor cells of the retina have diameters in the range 2 Pm to 6 Pm (mean value | 4 Pm). Apparently, evolution has refined the eye up to the point where further improvements in its construction would lead to relatively little improvement in overall resolution, relative to the diffraction limit ' x imposed by the wave nature of light.
To a reasonable approximation, these three different contributions to the retinal-image blurring can be combined in quadrature (by adding squares), treating them in a similar way to the statistical quantities involved in error
analysis. Using this procedure, the overall image blurring ' is given by:
( ') 2 = (3 Pm)^2 + (3 Pm)^2 + (4 Pm)^2 (1.2)
which leads to ' | 6 Pm as the blurring of the retinal image. This value
corresponds to an angular blurring for distant objects (see Fig. 1-1b) of
'T | ( ' / f ) | (6 Pm)/(2 cm) | 3 u 10 -4^ rad
| (1/60) degree = 1 minute of arc (1.3)
Distant objects (or details within objects) can be separately distinguished if they subtend angles larger than this. Accordingly, early astronomers were able to determine the positions of bright stars to within a few minutes of arc, using only a dark-adapted eye and simple pointing devices. To see greater detail in the night sky, such as the faint stars within a galaxy, required a telescope , which provided angular magnification.
An Introduction to Microscopy 5
Changing the shape of the lens in an adult eye alters its overall focal length by only about 10%, so the closest object distance for a focused image on the retina is u | 25 cm. At this distance, an angular resolution of 3 u 10 - rad corresponds (see Fig. 1c) to a lateral dimension of:
' R | ('T ) u | 0.075 mm = 75 Pm (1.4)
Because u | 25 cm is the smallest object distance for clear vision, ' R = 75 Pm can be taken as the diameter of the smallest object that can be resolved (distinguished from neighboring objects) by the unaided eye, known as its object resolution or the spatial resolution in the object plane.
Because there are many interesting objects below this size, including the examples in Table 1-1, an optical device with magnification factor M ( > 1) is needed to see them; in other words, a microscope.
To resolve a small object of diameter D , we need a magnification M* such that the magnified diameter ( M* D ) at the eye's object plane is greater or equal to the object resolution ' R (| 75 Pm) of the eye. In other words:
M * = (' R )/ D (1.5)
Values of this minimum magnification are given in the right-hand column of Table 1-1, for objects of various diameter D.
1.2 The Light-Optical Microscope
Light microscopes were developed in the early 1600’s, and some of the best observations were made by Anton van Leeuwenhoek, using tiny glass lenses placed very close to the object and to the eye; see Fig. 1-3. By the late 1600’s, this Dutch scientist had observed blood cells, bacteria, and structure within the cells of animal tissue, all revelations at the time. But this simple one-lens device had to be positioned very accurately, making observation ver ytiring in practice.
For routine use, it is more convenient to have a compound microscope , containing at least two lenses: an objective (placed close to the object to be magnified) and an eyepiece (placed fairly close to the eye ). By increasing its dimensions or by employing a larger number of lenses, the magnification M of a compound microscope can be increased indefinitely. However, a large value of M does not guarantee that objects of vanishingly small diameter D can be visualized; in addition to satisfying Eq. (1-5), we must ensure that aberrations and diffraction within the microscope are sufficiently low.
An Introduction to Microscopy 7
reflecting
specimen
transparent
specimen
objective
eyepiece
half-silvered
mirror
(a) (b)
Figure 1-4. Schematic diagrams of (a) a biological microscope, which images light transmitted through the specimen, and (b) a metallurgical microscope, which uses light (often from a built-in illumination source) reflected from the specimen surface.
individual components (organelles) within each biological cell. Because the light travels through the specimen, this instrument can also be called a transmission light microscope. It is used also by geologists, who are able to prepare rock specimens that are thin enough (below 0.1 Pm thickness) to be optically transparent.
The metallurgical microscope (Fig. 1-4b) is used for examining metals and other materials that cannot easily be made thin enough to be optically transparent. Here, the image is formed by light reflected from the surface of the specimen. Because perfectly smooth surfaces provide little or no contrast, the specimen is usually immersed for a few seconds in a chemical etch , a solution that preferentially attacks certain regions to leave an uneven surface whose reflectivity varies from one location to another. In this way,
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Figure 1-5. Light-microscope image of a polished and etched specimen of X70 pipeline steel, showing dark lines representing the grain boundaries between ferrite (bcc iron) crystallites. Courtesy of Dr. D. Ivey, University of Alberta.
the microscope reveals the microstructure of crystalline materials, such as the different phases present in a metal alloy. Most etches preferentially dissolve the regions between individual crystallites (grains) of the specimen, where the atoms are less closely packed, leaving a grain-boundary groove that is visible as a dark line, as in Fig. 1-5. The metallurgical microscope can therefore be used to determine the grain shape and grain size of metals and alloys.
As we have seen, the resolution of a light-optical microscope is limited by diffraction. As indicated by Eq. (1.1), one possibility for improving
resolution (which means reducing ' x , and therefore ' and ' R ) is to decrease
the wavelength O of the radiation. The simplest option is to use an oil-
immersion objective lens: a drop of a transparent liquid (refractive index n ) is placed between the specimen and the objective so that the light being focused (and diffracted) has a reduced wavelength: O/ n. Using cedar oil ( n = 1.52) allows a 34% improvement in resolution.
Greater improvement in resolution comes from using ultraviolet (UV) radiation, meaning wavelengths in the range 100 – 300 nm. The light source
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Figure 1-7. Scanning transmission x-ray microscope (STXM) images of a clay-stabilized oil- water emulsion. By changing the photon energy, different components of the emulsion become bright or dark, and can be identified from their known x-ray absorption properties. From Neuhausler et al. (1999), courtesy of Springer-Verlag.
Unfortunately, such focusing devices are less efficient than the glass lenses used in light optics. Also, laboratory x-ray sources are relatively weak (x-ray diffraction patterns are often recorded over many minutes or hours). This situation prevented the practical realization of an x-ray microscope until the development of an intense radiation source: the synchrotron , in which electrons circulate at high speed in vacuum within a storage ring. Guided around a circular path by strong electromagnets, their centripetal acceleration results in the emission of bremsstrahlung x-rays. Devices called undulators and wobblers can also be inserted into the ring; an array of magnets causes additional deviation of the electron from a straight-line path and produces a strong bremsstrahlung effect, as in Fig. 1-6. Synchrotron x- ray sources are large and expensive (> $100M) but their radiation has a variety of uses; several dozen have been constructed throughout the world during the past 20 years.
An important feature of the x-ray microscope is that it can be used to study hydrated (wet or frozen) specimens such as biological tissue or water/oil emulsions, surrounded by air or a water-vapor environment during the microscopy. In this case, x-rays in the wavelength range 2.3 to 4.4 nm are used (photon energy between 285 and 543 eV), the so-called water window in which hydrated specimens appear relatively transparent. Contrast in the x-ray image arises because different regions of the specimen absorb the x-rays to differing extents, as illustrated in Fig. 1-7. The resolution of these images, determined largely by zone-plate focusing, is typically 30 nm.
In contrast, the specimen in an electron microscope is usually in a dry state, surrounded by a high vacuum. Unless the specimen is cooled well below room temperature or enclosed in a special “environmental cell,” any water quickly evaporates into the surroundings.
An Introduction to Microscopy 11
1.4 The Transmission Electron Microscope
Early in the 20th century, physicists discovered that material particles such as electrons possess a wavelike character. Inspired by Einstein’s photon description of electromagnetic radiation, Louis de Broglie proposed that their wavelength is given by
O = h / p = h/(mv) (1.5)
where h = 6.626 u 10 -34^ Js is the Planck constant; p , m , and v represent the momentum, mass, and speed of the electron. For electrons emitted into vacuum from a heated filament and accelerated through a potential
difference of 50 V, v | 4.2 u 10 6 m/s and O | 0.17 nm. Because this
wavelength is comparable to atomic dimensions, such “slow” electrons are strongly diffracted from the regular array of atoms at the surface of a crystal, as first observed by Davisson and Germer (1927).
Raising the accelerating potential to 50 kV, the wavelength shrinks to about 5 pm (0.005 nm) and such higher-energy electrons can penetrate distances of several microns (Pm) into a solid. If the solid is crystalline, the electrons are diffracted by atomic planes inside the material, as in the case of x-rays. It is therefore possible to form a transmission electron diffraction pattern from electrons that have passed through a thin specimen, as first demonstrated by G.P. Thomson (1927). Later it was realized that if these transmitted electrons could be focused, their very short wavelength would allow the specimen to be imaged with a spatial resolution much better than the light-optical microscope.
The focusing of electrons relies on the fact that, in addition to their wavelike character, they behave as negatively charged particles and are therefore deflected by electric or magnetic fields. This principle was used in cathode-ray tubes, TV display tubes, and computer screens. In fact, the first electron microscopes made use of technology already developed for radar applications of cathode-ray tubes. In a transmission electron microscope (TEM), electrons penetrate a thin specimen and are then imaged by appropriate lenses, in broad analogy with the biological light microscope (Fig. 1-4a).
Some of the first development work on electron lenses was done by Ernst Ruska in Berlin. By 1931 he had observed his first transmission image (magnification = 17 ) of a metal grid, using the two-lens microscope shown in Fig. 1-8. His electron lenses were short coils carrying a direct current, producing a magnetic field centered along the optic axis. By 1933, Ruska had added a third lens and obtained images of cotton fiber and aluminum foil with a resolution somewhat better than that of the light microscope.
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Figure 1-9. First commercial TEM from the Siemens Company, employing three magnetic lenses that were water-cooled and energized by batteries. The objective lens used a focal length down to 2.8 mm at 80 kV, giving an estimated resolution of 10 nm.
Although companies in the USA, Holland, UK, Germany, Japan, China, USSR, and Czechoslovakia have at one time manufactured transmission electron microscopes, competition has reduced their number to four: the Japanese Electron Optics Laboratory (JEOL) and Hitachi in Japan, Philips/FEI in Holland/USA, and Zeiss in Germany.
The further development of the TEM is illustrated by the two JEOL instruments shown in Fig. 1-10. Their model 100B (introduced around 1970) used both vacuum tubes and transistors for control of the lens currents and the high voltage (up to 100 kV) and gave a spatial resolution of 0.3 nm. Model 2010 (introduced 1990) employed integrated circuits and digital control; at 200 kV accelerating voltage, it provided a resolution of 0.2 nm.
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Figure 1-10. JEOL transmission electron microscopes: (a) model 100B and (b) model 2010.
The TEM has proved invaluable for examining the ultrastructure of metals. For example, crystalline defects known as dislocations were first predicted by theorists to account for the fact that metals deform under much lower forces than calculated for perfect crystalline array of atoms. They were first seen directly in TEM images of aluminum; one of M.J. Whelan’s original micrographs is reproduced in Fig. 1-11. Note the increase in resolution compared to the light-microscope image of Fig. 1-5; detail can now be seen within each metal crystallite. With a modern TEM (resolution | 0.2 nm), it is even possible to image individual atomic planes or columns of atoms, as we will discuss in Chapter 4.
Figure 1-11. TEM diffraction-contrast image ( M | 10,000) of polycrystalline aluminum. Individual crystallites (grains) show up with different brightness levels; low-angle boundaries and dislocations are visible as dark lines within each crystallite. Circular fringes (top-right) represent local changes in specimen thickness. Courtsey of M.J. Whelan, Oxford University.
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hydrated. But high-energy electrons are a form of ionizing radiation, similar to x-rays or gamma rays in their ability to ionize atoms and produce irreversible chemical changes. In fact, a focused beam of electrons represents a radiation flux comparable to that at the center of an exploding nuclear weapon. Not surprisingly, therefore, it was found that TEM observation kills living tissue in much less time than needed to record a high-resolution image.
Figure 1-13. A 3 MV HVEM constructed at the C.N.R.S. Laboratories in Toulouse and in operation by 1970. To focus the high-energy electrons, large-diameter lenses were required, and the TEM column became so high that long control rods were needed between the operator and the moving parts (for example, to provide specimen motion). Courtesy of G. Dupouy, personal communication.
An Introduction to Microscopy 17
1.5 The Scanning Electron Microscope
One limitation of the TEM is that, unless the specimen is made very thin, electrons are strongly scattered within the specimen, or even absorbed rather than transmitted. This constraint has provided the incentive to develop electron microscopes that are capable of examining relatively thick (so- called bulk ) specimens. In other words, there is need of an electron-beam instrument that is equivalent to the metallurgical light microscope but which offers the advantage of better spatial resolution.
Electrons can indeed be “reflected” (backscattered) from a bulk specimen, as in the original experiments of Davisson and Germer (1927). But another possibility is for the incoming ( primary ) electrons to supply energy to the atomic electrons that are present in a solid, which can then be released as secondary electrons. These electrons are emitted with a range of energies, making it more difficult to focus them into an image by electron lenses. However, there is an alternative mode of image formation that uses a scanning principle: primary electrons are focused into a small-diameter electron probe that is scanned across the specimen, making use of the fact that electrostatic or magnetic fields, applied at right angles to the beam, can be used to change its direction of travel. By scanning simultaneously in two perpendicular directions, a square or rectangular area of specimen (known as a raster ) can be covered and an image of this area can be formed by collecting secondary electrons from each point on the specimen.
The same raster-scan signals can be used to deflect the beam generated within a cathode-ray tube (CRT), in exact synchronism with the motion of the electron beam that is focused on the specimen. If the secondary-electron signal is amplified and applied to the electron gun of the CRT (to change the number of electrons reaching the CRT screen), the resulting brightness variation on the phosphor represents a secondary-electron image of the specimen. In raster scanning, the image is generated serially (point by point) rather than simultaneously, as in the TEM or light microscope. A similar principle is used in the production and reception of television signals.
A scanning electron microscope (SEM) based on secondary emission of electrons was developed at the RCA Laboratories in New Jersey, under wartime conditions. Some of the early prototypes employed a field-emission electron source (discussed in Chapter 3), whereas later models used a heated-filament source, the electrons being focused onto the specimen by electrostatic lenses. An early version of a FAX machine was employed for image recording; see Fig. 1-14. The spatial resolution was estimated to be 50 nm, nearly a factor of ten better than the light-optical microscope.
An Introduction to Microscopy 19
Figure 1-15. Hitachi-S5200 field-emission scanning electron microscope. This instrument can operate in SEM or STEM mode and provides an image resolution down to 1 nm.
1.6 Scanning Transmission Electron Microscope
It is possible to employ the fine-probe/scanning technique with a thin sample and record, instead of secondary electrons, the electrons that emerge (in a particular direction) from the opposite side of the specimen. The resulting is a scanning-transmission electron microscope (STEM). The first STEM was constructed by von Ardenne in 1938 by adding scanning coils to a TEM, and today many TEMs are equipped with scanning attachments, making them dual-mode ( TEM/STEM ) instruments.
In order to compete with a conventional TEM in terms of spatial resolution, the electrons must be focused into a probe of sub-nm dimensions. For this purpose, the hot-filament electron source that is often used in the SEM (and TEM) must be replaced by a field-emission source, in which electrons are released from a very sharp tungsten tip under the application of an intense electric field. This was the arrangement used by Crewe and co- workers in Chicago, who in 1965 constructed a dedicated STEM that operated only in scanning mode. The field-emission gun required ultra-high vacuum (UHV), meaning ambient pressures around 10-8^ Pa. After five years of development, this type of instrument produced the first-ever images of single atoms, visible as bright dots on a dark background (Fig. 1-16).
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Figure 1-16. Photograph of Chicago STEM and (bottom-left inset) image of mercury atoms on a thin-carbon support film. Courtesy of Dr. Albert Crewe (personal communication).
Atomic-scale resolution is also available in the conventional (fixed- beam) TEM. A crystalline specimen is oriented so that its atomic columns lie parallel to the incident-electron beam, and it is actually columns of atoms that are imaged; see Fig. 1-17. It was originally thought that such images might reveal structure within each atom, but such an interpretation is questionable. In fact, the internal structure of the atom can be deduced by analyzing the angular distribution of scattered charged particles (as first done for alpha particles by Ernest Rutherford) without the need to form a direct image.
Figure 1-17. Early atomic-resolution TEM image of a gold crystal (Hashimoto et al ., 1977), recorded at 65 nm defocus with the incident electrons parallel to the 001 axis. Courtesy Chairperson of the Publication Committee, The Physical Society of Japan, and the authors.
