Light microscopy

4.2 Light microscopy

4.2.1 Basic principles

The light microscope provides two-dimensional representation of structure over a total magnification range of roughly ×40 to ×1250. Interpretation of such images is a matter of skill and experience and needs to allow for the three-dimensional nature of features observed. The main components of a bench- type microscope are (1) an illumination system comprising a light source and variable apertures, (2) an objective lens and an ocular lens (eyepiece) mounted at the ends of a cylindrical body tube, and (3) a specimen stage (fixed or rotatable). Metallic specimens that are to be examined at high magnifi- cations are successively polished with 6, 1 and sometimes 0.25 µm diamond grit. Examination in the as-polished condition, which is generally advisable, will reveal structural features such as shrinkage or gas porosity, cracks and inclusions of foreign matter. Etching with an appropriate chemical reagent is used to reveal the arrangement and size of grains, phase morphology, compositional gradients (cor- ing), orientation-related etch pits and the effects of plastic deformation. Although actually only a few atomic diameters wide, grain boundaries are preferentially and grossly attacked by many etchants. In bright-field illumination, light is reflected back towards the objective from reflective surfaces, caus- ing them to appear bright. Dark-field illumination reverses this effect, causing grain boundaries to appear bright. The degree of chemical attack is sensitive to crystal orientation and an etched polycrys- talline aggregate will often display its grain structure clearly (Figure 4.2a). Preparation techniques for ceramics are essentially similar to those for metals and alloys. However, their porosity can cause two problems. First, there is a risk of entrapping diamond particles during polishing, making ultrasonic cleaning advisable. Second, it may be necessary to strengthen the structure by impregnating with liquid resin in vacuo, provided that pores are interconnected.

The objective, the most important and critical component in the optical train of the light microscope, is made up of a number of glass lenses and, sometimes, fluorite (CaF 2 ) lenses also. Lenses are subject to spherical and chromatic aberrations. Minimization and correction of these undesirable physical effects, greatly aided by modern computational techniques, is possible and objectives are classified according to the degree of correction, i.e. achromats, fluorites (semi-apochromats), apochromats. Lenses are usually coated in order to increase light transmission. As magnification is increased, the depth of field of the objective becomes smaller, typically falling from 250 µm at ×15 to 0.08 µm at ×1200, so that specimen flatness becomes more critical. The focal length and the working distance (separating its front lens from the specimen) of an objective differ. For instance, an f 2 mm objective may have a working distance of 0.15 mm.

Characterization and analysis 163

Microscope objective

AIR

OIL

Working distance

Specimen A Orientation A of grain (a)

(b)

Figure 4.2 (a) Reflection of light from etched specimen. (b) Use of oil to improve numerical aperture of objective.

Resolution, rather than magnification, is usually the prime concern of the skilled microscopist. It is the smallest separating distance (δ) that can be discerned between two lines in the image. The unaided eye, at the least distance of comfortable vision (about 250 mm), can resolve 0.1 mm. Confusingly, the resolution value for a lens with a so-called high resolving power is small. Resolution is determined by (1) the wavelength (λ) of the radiation and (2) the numerical aperture (NA) of the objective, and is expressed by the Abbe formula δ = λ/2NA.

The numerical aperture value, which is engraved upon the side of the objective, indicates the light-gathering power of the compound lens system and is obtained from the relation NA = n sin α, where n is the refractive index of the medium between the front lens face of the objective and the specimen and α is the semi-apex angle of the light cone defined by the most oblique rays collected by the lens. Numerical apertures range in typical value from 0.08 to 1.25. Despite focusing difficulties and the need for costly lenses, efforts have been made to use short-wavelength ultraviolet radiation: developments in electron microscopy have undermined the feasibility of this approach. Oil-immersion objectives enable the refractive index term to be increased (Figure 4.2b). Thus, by replacing air (n = 1) with a layer of cedar wood oil (n = 1.5) or monobromonaphthalene (n = 1.66), the number of rays of reflected light accepted by the front lens of the objective is increased, and resolution and contrast are improved. The range of wavelengths for visible light is approximately 400–700 nm; consequently, using the Abbe formula, it can readily be shown that the resolution limit of the light microscope is of the order of 200 nm. The ‘useful’ range of magnification is approximately 500–1000 NA. The lower end of the range can be tiring to the eyes; at the top end, oil-immersion objectives are useful.

Magnification is a subjective term; for instance, it varies with the distance of an image or object from the eye. Hence, microscopists sometimes indicate this difficulty by using the more readily defined term ‘scale of reproduction’, which is the lineal size ratio of an image (on a viewing screen or photomicrograph) to the original object. Thus, strictly speaking, a statement such as ×500 beneath a photomicrograph gives the scale of reproduction, not the magnification.

The ocular magnifies the image formed by the objective: the finally observed image is virtual. It can also correct for certain objective faults and, in photomicrography, be used to project a real image.

164 Physical Metallurgy and Advanced Materials

V max 3200

Total magnification

20 x10 16 x8 12.5 x6.3 x5 2.5/0.08

Figure 4.3 Range of ‘useful’ magnification in light microscope (from Optical Systems for the Microscope, 1967, p. 15; by courtesy of Carl Zeiss, Germany).

The ocular cannot improve the resolution of the system but, if inferior in quality, can worsen it. The most widely used magnifications for oculars are ×8 and ×12.5.

Two-dimensional features of a standard bench microscope, the mechanical tube length t m and optical tube length t o , are of special significance. The former is the fixed distance between the top of the body tube, on which the ocular rests, and the shoulder of the rotatable nosepiece into which several objectives are screwed. Objectives are designed for a certain t m value. A value of 160 mm is commonly used. (In Victorian times, it was 250 mm, giving a rather unwieldy instrument.)

The optical tube length t o is the distance between the front focal point of the ocular and the rear focal plane of the objective. Parfocalization, using matched parfocal objectives and oculars, enables the specimen to remain in focus when objectives are step-changed by rotating the nosepiece. With each change, t o changes but the image produced by the objective always forms in the fixed focal phase of the ocular. Thus, the distance between the specimen and the aerial image is kept constant. Some manufacturers base their sequences of objective and ocular magnifications upon preferred

numbers 1 rather than upon a decimal series. This device facilitates the selection of a basic set of lenses that is comprehensive and ‘useful’ (exempt from ‘empty’ magnification). For example, the Michel series of ×6.3, ×8, ×10, ×12.5, ×16, ×20, ×25, etc., a geometrical progression with a common ratio of approximately 1.25, provides a basis for magnification values for objectives and oculars. This rational approach is illustrated in Figure 4.3. Dashed lines represent oculars and thin solid lines represent objectives. The bold lines outline a box within which objective/ocular combinations give ‘useful’ magnifications. Thus, pairing of a ×12.5 ocular with a ×40 objective (NA = 0.65) gives

a ‘useful’ magnification of ×500.

1 The valuable concept of preferred numbers/sizes, currently described in document PD 6481 of the British Standards Institution, was devised by a French military engineer, Colonel Charles Renard (1847–1905). In 1879, during the

development of dirigible (steerable) balloons, he used a geometrical progression to classify cable diameters. A typical Renard series is 1.25, 1.6, 2.0, 2.5, 3.2, 4.0, 5.0, 6.4, 8.0, etc.

Characterization and analysis 165

Light source

Vertical reflector S

Figure 4.4 Schematic arrangement of microscope system for phase-contrast (a) and polarized light (b) microscopy.

4.2.2 Selected microscopical techniques

4.2.2.1 Phase-contrast microscopy

Phase-contrast microscopy is a technique that enables special surface features to be studied even when there is no color or reflectivity contrast. The light reflected from a small depression in a metallographic specimen will be retarded in phase by a fraction of a light wavelength relative to that reflected from the surrounding matrix and, whereas in ordinary microscopy a phase difference in the light collected by the objective will not contribute to contrast in the final image, in phase-contrast microscopy small differences in phases are transformed into differences in brightness which the eye can detect.

General uses of the technique include the examination of multi-phased alloys after light etching, the detection of the early stages of precipitation, and the study of cleavage faces, twins and other deformation characteristics. The optimum range of differences in surface level is about 20–50 nm, although under favorable conditions these limits may be extended. A schematic diagram of the basic arrangement for phase contrast in the metallurgical microscope is shown in Figure 4.4a. A hollow cone of light produced by an annulus A is reflected by the specimen and brought to an image in the back focal plane of the objective. A phase plate of suitable size should, strictly, be positioned in this plane but, for the ease of interchangeability of phase plates, the position Q in front of the eyepiece

E is often preferred. This phase plate has an annulus, formed either by etching or deposition, such that the light it transmits is either advanced or retarded by a quarter of a wavelength relative to the light transmitted by the rest of the plate and, because the light reflected from a surface feature is also advanced or retarded by approximately λ/4, the beam is either in phase or approximately λ/2 or π out of phase with that diffracted by the surface features of the specimen. Consequently, reinforcement or cancellation occurs, and the image intensity at any point depends on the phase difference produced at the corresponding point on the specimen surface, and this in turn depends upon the height of this point relative to the adjacent parts of the surface. When the light passing through the annulus is

166 Physical Metallurgy and Advanced Materials advanced in phase, positive phase contrast results and areas of the specimen which are proud of the

matrix appear bright and depressions dark; when the phase is retarded, negative contrast is produced and ‘pits’ appear bright and ‘hills’ dark.

4.2.2.2 Polarized-light microscopy

The basic arrangement for the use of polarized light is shown in Figure 4.4b. The only requirements of this technique are that the incident light on the specimen be plane polarized and that the reflected light be analyzed by a polarizing unit in a crossed relation with respect to the polarizer, i.e. the plane of polarization of the analyzer is perpendicular to that of the polarizer.

The application of the technique depends upon the fact that plane-polarized light striking the surface of an optically isotropic metal is reflected unchanged if it strikes at normal incidence. If the light is not at normal incidence the reflected beam may still be unchanged, but only if the angle of incidence is in, or at right angles to, the plane of polarization, otherwise it will be elliptically polarized. It follows that the unchanged reflected beam will be extinguished by an analyzer in the crossed position, whereas an elliptically polarized one cannot be fully extinguished by an analyzer in any position. When the specimen being examined is optically anisotropic, the light incident normally is reflected with a rotation of the plane of polarization and as elliptically polarized light; the amount of rotation and of elliptical polarization is a property of the metal and of the crystal orientation.

If correctly prepared, as-polished specimens of anisotropic metals will ‘respond’ to polarized light and a grain-contrast effect is observed under crossed polars as a variation of brightness with crystal orientation. Metals which have cubic structure, on the other hand, will appear uniformly dark under crossed polars, unless etched to invoke artificial anisotropy, by producing anisotropic surface films or well-defined pits. An etch pit will reflect the light at oblique incidence and elliptically polarized light will be produced. However, because such a beam cannot be fully extinguished by the analyzer in any position, it will produce a background illumination in the image which tends to mask the grain-contrast effect.

Clearly, one of the main uses of polarized light is to distinguish between areas of varying orientation, since these are revealed as differences of intensity under crossed polars. The technique is therefore very useful for studying the effects of deformation, particularly the production of preferred orientation, but information on cleavage faces, twin bands and sub-grain boundaries can also be obtained. If

a ‘sensitive tint’ plate is inserted between the vertical illuminator and the analyzer, each grain of

a sample may be identified by a characteristic color which changes as the specimen is rotated on the stage. This application is useful in the assessment of the degree of preferred orientation and in recrystallization studies. Other uses of polarized light include distinguishing and identifying phases in multi-phase alloys.

Near-perfect extinction occurs when the polars of a transmission microscope are crossed. If a thin section or slice of ceramic, mineral or rock is introduced and the stage slowly rotated, optically anisotropic crystals will produce polarization colors, developing maximum brilliance at 45 ◦ to any of the four symmetrical positions of extinction. The color of a crystal depends upon its birefringence, or capacity for double-refraction, and thickness. By standardizing the thickness of the section at 30–50 µm and using a Michel–Lévy color chart, it is possible to identify crystalline species. In

refractory materials, it is relatively easy to identify periclase (MgO), chromite (FeCrO 4 ), tridymite

(SiO 2 ) and zircon (ZrSiO 4 ) by their characteristic form and color.

As birefringence occurs within the crystal, each incident ray forms ordinary and extraordinary rays which are polarized in different planes and travel through the crystal at different velocities. On leaving the analyzer, these out-of-phase ‘fast’ and ‘slow’ rays combine to produce the polarization color. This color is complementary to color cancelled by interference and follows Newton’s sequence: yellow, orange, red, violet, blue, green. More delicate, higher-order colors are produced as the phase difference between the emergent rays increases. Anisotropic crystals are either uniaxial or biaxial,

Characterization and analysis 167 having one or two optic axes, respectively, along which birefringence does not occur. (Optic axes do

not necessarily correspond with crystallographic axes.) It is therefore possible for quartz (uniaxial) and mica (biaxial) crystals to appear black because of their orientation in the slice. Uniaxial (tetragonal and hexagonal systems) can be distinguished from biaxial crystals (orthorhombic, triclinic and monoclinic systems) by introducing a Bertrand lens into the light train of the microscope to give a convergent beam, rotating the stage and comparing their interference figures: uniaxial crystals give a moving ‘ring and brush’ pattern, biaxial crystals give two static ‘eyes’. Cubic crystals are isotropic, being highly symmetrical. Glassy phases are isotropic and also appear black between crossed polars; however, glass containing residual stresses from rapid cooling produces fringe patterns and polarization colors. The stress-anisotropic properties of plastics are utilized in photoelastic analyses of transparent models of engineering structures or components made from standard sheets of constant thickness and stress- optic coefficient (e.g. clear Bakelite, epoxy resin). The fringe patterns produced by monochromatic light and crossed polars in a polariscope reveal the magnitude and direction of the principal stresses that are developed when typical working loads are applied.

4.2.2.3 Hot-stage microscopy

The ability to observe and photograph phase transformations and structural changes in metals, ceram- ics and polymers at high magnifications while being heated holds an obvious attraction. Various designs of microfurnace cell are available for mounting in light microscope systems.

For studies at moderate temperatures, such as spherulite formation in a cooling melt of polypropy- lene, the sample can be placed on a glass slide, heated in a stage fitment and viewed through crossed polars with transmitted light. For metals, which have an increasing tendency to vaporize as the tem- perature is raised, the polished sample is enclosed in a resistance-heated microfurnace and viewed by reflected light through an optically worked window of fused silica. The chamber can be either evacuated (10 −6 torr) or slowly purged with inert gas (argon). The latter must be dry and oxygen free. A Pt:Pt–10Rh thermocouple is inserted in the specimen. The furnace should have a low thermal inertia and be capable of heating or cooling the specimen at controlled rates; temperatures of up to 1800 ◦

C are possible in some designs. The presence of a window, and possibly cooling devices, drastically reduces the available working distance for the objective lens, particularly when a large numerical aperture or high magnification are desired. One common solution is to use a Burch- type reflecting objective with an internal mirror system, which gives a useful working distance of 13–14 mm. The type of stage unit described has been used for studies of grain growth in austen- ite and the formation of bainite and martensite in steels, allotropic transformations, and sintering mechanisms in powder compacts.

When polished polycrystalline material is heated, individual grains tend to reduce their volume as

a result of surface tension and grain boundaries appear as black lines, an effect referred to as thermal etching or grooving. If a grain boundary migrates, as in the grain growth stage of annealing, ghost images of former grooves act as useful markers. As the melting point is approached, there is often a noticeable tendency for grain boundary regions to fuse before the bulk grains; this liquation effect is due to the presence of impurities and the atomic misfit across the grain boundary surface. When interpreting the visible results of hot-stage microscopy, it is important to bear in mind that surface effects do not necessarily reflect what is happening within the bulk material beneath the surface. The technique can produce artefacts; the choice between evacuation and gas purging can be crucial. For instance, heating in vacuo can favor decarburization and grain coarsening in steel specimens.

The classic method for studying high-temperature phases and their equilibria in oxide systems was based upon rapid quenching (e.g. silicates). This indirect method is slow and does not always preserve the high-temperature phase(s). A direct microscopical technique uses the U-shaped notch of a thermocouple hot junction as the support for a small non-metallic sample. In the original

168 Physical Metallurgy and Advanced Materials design, 2 the junction was alternately connected by high-speed relay at a frequency of 50 Hz to a

power circuit and a temperature-measuring circuit. The sample could be heated to temperatures of up to 2150 ◦

C and it was possible to observe crystallization from a melt directly through crossed polars. Although unsuitable for metals and highly volatile materials, the technique has been applied to glasses, slags, refractories, Portland cements, etc., providing information on phase changes, devitrification, sintering shrinkage, grain growth and the ‘wetting’ of solids by melts.

4.2.2.4 Microhardness testing

The measurement of hardness with a microscope attachment, comprising a diamond indenter and means for applying small loads, dates back more than 50 years. Initially used for small components (watch gears, thin wire, foils), microhardness testing was extended to research studies of individual phases, orientation effects in single crystals, diffusion gradients, ageing phenomena, etc. in metal- lic and ceramic materials. Nowadays, testing at temperatures up to 1000 ◦

C is possible. In Europe, the pyramidal Vickers-type (interfacial angle 136 ◦ ) indenter, which produces a square impression, is generally favored. Its counterpart in general engineering employs test loads of 5–100 kgf: in microhardness testing, typical test loads are in the range 1–100 gf (1 gf = 1 pond = 1 p = 9.81 mN).

A rhombic-based Knoop indenter of American origin has been recommended for brittle and/or anisotropic material (e.g. carbides, oxides, glass) and for thin foils and coatings where a shallow depth of impression is desired. The kite-shaped Knoop impression is elongated, with a 7:1 axial ratio.

Microhardness tests need to be very carefully controlled and replicated, using as large a load as possible. The surface of the specimen should be strain-free (e.g. electropolished), plane and perpendicular to the indenter axis. The indenter is lowered slowly at a rate of <1 mm min −1 under vibration-free conditions, eventually deforming the test surface in a manner analogous to steady-state creep. This condition is achieved within 15 s, a test period commonly used.

The equations for Vickers hardness (H V ) and Knoop hardness (H K ) take the following forms:

H V = 1854.4(P/d 2 ) kgf mm −2 (4.1)

H K = 14228(P/d 2 ) kgf mm −2 (4.2) In these equations, which have the dimensions of stress, load P and diagonal length d are measured

in gf and µm, respectively. The first equation is based upon the surface area of the impression; the second is based upon its projected area and the length of the long diagonal.

The main potential difficulty concerns the possible dependence of microhardness values (H m ) upon test load. As the test load is reduced below a certain threshold, the measured microhardness value may tend to decrease or increase, depending upon the material. In these circumstances, when measuring absolute hardness rather than relative hardness, it is useful to consider the material’s behavior in terms of the Meyer equation, which relates indenting force P to the diagonal length of the Vickers-type impression produced, d, as follows:

P = kd n . (4.3) The Meyer exponent n expresses the strain-hardening characteristics of the material as it deforms

plastically during the test; it increases in value with the degree of strain hardening. For simple compar- isons of relative microhardness, hardness values at a fixed load can be compared without allowance for

2 Developed by W. Gutt and co-workers at the Building Research Station, Watford.

Characterization and analysis 169

(kgf mm

Test load

Indentation diagonal d(␮m)

Figure 4.5 Meyer line for material with load-independent hardness (by courtesy of Carl Zeiss, Germany).

load dependence. On the other hand, if absolute values of hardness are required from low-load tests, it is advisable to determine the Meyer line for the particular material over a comparatively small load range by plotting P values against the corresponding d values, using log–log graph paper. (Extrapo- lations beyond the chosen load range are unwise because the profile of the Meyer line may change.) Figure 4.5 shows the Meyer line, slope n, for a material giving load-dependent microhardness values.

The slope n is less than 2, which is usual. The H m curve has a negative slope and microhardness values increase as the load increases. One way of reporting load-dependent microhardness results is to state three hardness numbers in terms of a standard set of three diagonal d-values, as shown in Figure 4.5.

The approximate values for the set shown are H 5 µm = 160, H 10 µm = 140, H

20 µm = 120. When the anisotropy ratio for elastic moduli is high, microhardness values can vary greatly from grain to grain in polycrystalline material.

Combination of the Vickers equation with the Meyer equation gives the following expression:

H V n = constant × d −2 . (4.4) Accordingly, if n = 2, which is true for the conventional Vickers macrohardness test, the gradient of

the H m line becomes zero and hardness values are conveniently load independent.