Imaging of stacking faults

5.5.6 Imaging of stacking faults

Contrast at a stacking fault arises because such a

5.5.7 Application of dynamical theory

defect displaces the reflecting planes relative to each The kinematical theory, although very useful, has limi- other, above and below the fault plane, as illustrated in

tations. The equations are only valid when the crystal is

The characterization of materials 159

Figure 5.41 Schematic diagram showing (a) displacement of reflecting planes by a stacking fault and (b) the condition forg.R D n when the fault would be invisible.

oriented far from the exact Bragg condition, i.e. when s is large. The theory is also only strictly applicable for foils whose thickness is less than about half an

extinction distance ⊲ 1 2 g ⊳ and no account is taken of absorption. The dynamical theory has been developed to overcome these limitations.

The object of the dynamical theory is to take into account the interactions between the diffracted and transmitted waves. Again only two beams are consid- ered, i.e. the transmitted and one diffracted beam, and experimentally it is usual to orient the specimen in

a double-tilt stage so that only one strong diffracted beam is excited. The electron wave function is then

Figure 5.42 Computed intensity profiles about the foil considered to be made up of two plane waves –an inci-

dent or transmitted wave and a reflected or diffracted is the B.F. and the broken curve the D.F. image (from

Hirsch, Howie et al., 1965) .

wave ⊲

for different positions of the column in the crystal, rel- The two waves can be considered to propagate together

g 1 . r⊳

ative to the defect, then gives the bright and dark-field down a column through the crystal since the Bragg

images respectively. Figure 5.42 shows the bright- and

0 g dark-field intensity profiles from a stacking fault on an of the two waves are continually changing with depth

inclined plane, in full and broken lines, respectively. z in the column because of the reflection of electrons

A wide variety of defects have been computed, some from one wave to another. This is described by a pair

of which are summarized below: of coupled first-order differential equations linking the

1. Dislocations In elastically isotropic crystals, perfect

0 g . Displacement of an atom

screw dislocations show no contrast if the condition

g.b D 0 is satisfied. Similarly, an edge dislocation wave, as before, and the two differential equations

describing the dynamical equilibrium between incident will be invisible if g.b D 0 and if g.b ð u D 0

where u is a unit vector along the dislocation line and diffracted waves and b ð u describes the secondary displacements

0 associated with an edge dislocation normal to the

D g dz

g dislocation line and b. The computations also show that for mixed dislocations and edge dislocations

0 g s + g. for which g.b ð u<0.64 the contrast produced will

g dR

dz D g dz

be so weak as to render the dislocation virtually invisible. At higher values of g.b ð u some contrast

g is expected. In addition, when the crystal becomes because electrons are reflected from the transmitted

significantly anisotropic residual contrast can be

observed even for g.b D 0. wave amplitude, and contains the phase factor) and the

0 , the transmitted

The image of a dislocation lies to one side of reflection in the reverse direction.

the core, the side being determined by ⊲g.b⊳s. Thus These equations show that the effect of a displace-

the image of a dislocation loop lies totally outside ment R is to modify s locally, by an amount propor-

the core when (using the appropriate convention) tional to the derivative of the displacement, i.e. dR/dz,

⊲g.b⊳s is positive and inside when ⊲g.b⊳s is neg- which is the variation of displacement with depth z in

ative. Vacancy and interstitial loops can thus be the crystal. This was noted in the kinematical theory

distinguished by examining their size after chang- where dR/dz is equivalent to a local tilt of the lattice

0 j 2 g j 2 the sign of b.

160 Modern Physical Metallurgy and Materials Engineering

2. Partial dislocations Partials for which g.b D š 1 3 of the phase-factor ˛, such that when ˛ is positive (e.g. partial a/6[1 1 2] on ⊲1 1 1⊳ observed with 2 0 0

the first fringe is bright (corresponding to a higher reflection) will be invisible at both small and large

transmitted intensity) and vice versa on a positive deviations from the Bragg condition. Partials exam-

photographic print.

It is thus possible to distinguish between intrinsic and tial a/6[2 1 1] on ⊲1 1 1⊳ with 2 0 0 reflection) are

ined under conditions for which g.b D š 2 3 (i.e. par-

extrinsic faults and an example is shown in Figure 5.43 visible except at large deviations from the Bragg

for an intrinsic fault on ⊲1 1 1⊳. The foil orientation is condition. A partial dislocation lying above a simi-

[1 1 0] and the non-complementary nature of the first

fringe between B.F. and D.F. indicates the top of the ible for g.b D š 2 .

lar stacking fault is visible for g.b D š 1 3 and invis-

foil, marked T. Furthermore, from the B.F. images the

3. Stacking faults For stacking faults running from top first fringe is bright with 1 1 1, and dark with 1 1 1 and to bottom of the foil, the bright-field image is sym-

metrical about the centre, whereas the dark-field image is asymmetrical (see Figure 5.42). The top

5.5.8 Weak-beam microscopy

of the foil can thus be determined from the non- One of the limiting factors in the analysis of defects is complementary nature of the fringes by comparing

g / 3, bright- and dark-field images. Moreover, the inten-

i.e. typically >10.0 nm. It therefore follows that dis- sity of the first fringe is determined by the sign

locations closer together than about 20.0 nm are not

Bright field

Dark field

Bright field

Dark field

Figure 5.43 Bright-field and dark-field micrographs of an intrinsic stacking fault in a copper–aluminium alloy; the operating diffraction vectors are (a) 1 1 1 (b) 1 1 1 and (c) 1 1 1 (after Howie and Valdre, 1963; courtesy of Taylor and Francis) .

The characterization of materials 161

Figure 5.44 Symmetrical node in Fe–21Cr–14Ni stainless steel with D 18 š 4 mJ/m 2 , (a) B.F. with g D 111 (b) weak beam with g(5g) .

generally resolved. With normal imaging techniques, by repeated collisions with a ‘moderator’ of graphite the detail that can be observed is limited to a value

or heavy water until they are slow enough to produce about fifty to a hundred times greater than the reso-

further fission. If a collimator is inserted into the pile, lution of the microscope. This limitation can be over-

some of these slow neutrons 1 will emerge from it in come by application of the weak-beam technique in which crystals are imaged in dark-field using a very

of this neutron beam of energy E in electron-volts is large deviation parameter s. Under these conditions

the background intensity is very low so that weak in a pile is usually in the range 0–100 °

C, which cor- images are seen in very high contrast and the dis-

responds to a peak energy of several hundredths of location images are narrow, (³1.5 nm) as shown in

an electron-volt. The corresponding wavelength of the Figure 5.44. At the large value of s used in weak-beam,

neutron beam is about 0.15 nm and since this is very the transfer of energy from the direct to the diffracted

beam is very small, i.e. the crystal is a long way from similar to the wavelength of X-rays it is to be expected the Bragg condition and there is negligible diffraction.

that thermal neutrons will be diffracted by crystals. Moreover, it is only very near the core of the dis-

The properties of X-ray and neutron beams differ location that the crystal planes are sufficiently bent

in many respects. The distribution of energy among to cause the Bragg condition to be locally satisfied,

the neutrons in the beam approximately follows the

i.e. g.⊲dR/dz⊳ be large enough to satisfy the condi- Maxwellian curve appropriate to the equilibrium tem- tion [s C g.⊲dR/dz⊳] D 0. Therefore diffraction takes

perature and, consequently, there is nothing which cor- place from only a small volume near the centre of the

responds to characteristic radiation. The neutron beam dislocation, giving rise to narrow images. The abso-

is analogous to a beam of ‘white’ X-rays, and as a lute intensity of these images is, however, very small

result it has to be monochromatized before it can be even though the signal-to-background ratio is high and

used in neutron crystallography. Then, because only hence long exposures are necessary to record them.

about 1 in 10 3 of the neutrons in the originally weak collimated beam are reflected from the monochroma- tor, it is necessary to employ very wide beams several

5.6 Specialized bombardment

inches in cross-section to achieve a sufficiently high

techniques

counting rate on the boron trifluoride counter detec- tor (photographic detection is possible but not gen-

erally useful). In consequence, neutron spectrometers, The advent of nuclear reactors stimulated the applica-

5.6.1 Neutron diffraction

although similar in principle to X-ray diffractometers, tion of neutron diffraction to those problems of mate-

have to be constructed on a massive scale. rials science which could not be solved satisfactorily

by other diffraction techniques. In a conventional pile 1 These may be called ‘thermal’ neutrons because they are the fast neutrons produced by fission are slowed down

in thermal equilibrium with their surroundings.

162 Modern Physical Metallurgy and Materials Engineering Neutron beams do, however, have advantages over

Table 5.4 Scattering amplitudes for X-rays and thermal

X-rays or electrons, and one of these is the extremely

neutrons

low absorption of thermal neutrons by most elements. Table 5.3 shows that even in the most highly absorbent

Scattering amplitudes elements (e.g. lithium, boron, cadmium and gadolin-

Element

At. no.

X-rays for Neutrons Ł ium) the mass absorption coefficients are only of the

ð10 same order as those for most elements for a comparable

X-ray wavelength, and for other elements the neutron absorption is very much less indeed. This penetrative

H 1 0.02 -0.4 property of the neutron beam presents a wide scope

3 0.28 Li 6 0.7 for neutron crystallography, since the whole body of a 7 Li

Li

-0.25 specimen may be examined and not merely its surface.

C 6 0.48 0.64 Problems concerned with preferred orientation, resid-

7 0.54 0.85 ual stresses, cavitation and structural defects are but

13 1.55 a few of the possible applications, some of which are 0.35

Al

22 2.68 -0.38 discussed more fully later.

Ti

Fe 26 3.27 Fe 56 1.0 Another difference concerns the intensity of scatter-

Fe 57 0.23 ing per atom, I a . For X-rays, where the scattering is by

27 3.42 0.28 electrons, the intensity I a increases with atomic num-

Co

29 3.75 0.76 ber and is proportional to the square of the atomic-form

Cu

30 3.92 0.59 factor. For neutrons, where the scattering is chiefly by

Zn

Ag 47 6.71 Ag 107 0.83 the nucleus, I a appears to be quite unpredictable. The

Ag 109 0.43 scattering power per atom varies not only apparently

79 12.37 0.75 at random from atom to atom, but also from isotope

Au

to isotope of the same atom. Moreover, the nuclear Ł The negative sign indicates that the scattered and incident component to the scattering does not decrease with

waves are in phase for certain isotopes and hence for certain

increasing angle, as it does with X-rays, because the elements. Usually the scattered wave from an atom is 180 nucleus which causes the scattering is about 10 out of phase with the incident wave. mm

in size compared with 10 mm, which is the size of the electron cloud that scatters X-rays. Table 5.4 gives

neutrons. This aspect is discussed later in relation to some of the scattering amplitudes for X-rays and ther-

the behaviour of ordered alloy phases. mal neutrons.

The major contribution to the scattering power arises The fundamental difference in the origin of scat-

from the nuclear component, but there is also an elec- tering between X-rays and neutrons affords a method

tronic (magnetic spin) component to the scattering. of studying structures, such as hydrides and carbides,

This arises from the interaction between the mag- which contain both heavy and light atoms. When X-

netic moment of the neutron and any resultant mag- rays are used, the weak intensity contributions of the

netic moment which the atom might possess. As a light atoms are swamped by those from the heavy

result, the neutron diffraction pattern from paramag- atoms, but when neutrons are used, the scattering

netic materials, where the atomic moments are ran- power of all atoms is roughly of the same order.

domly directed (see Chapter 6), shows a broad diffuse Similarly, structures made up of atoms whose atomic

background, due to incoherent (magnetic) scattering, numbers are nearly the same (e.g. iron and cobalt, or

superimposed on the sharp peaks which arise from copper and zinc), can be studied more easily by using

coherent (nuclear) scattering. In ferromagnetic metals the atomic moments are in parallel alignment through-

Table 5.3 X-ray and neutron mass absorption coefficients

out a domain, so that this cause of incoherent scattering is absent. In some materials (e.g. NiO or FeO) an

Element At. no. X-rays

Neutrons

alignment of the spins takes place, but in this case

D 0 .19 nm⊳

D 0 .18 nm⊳

the magnetization directions of neighbouring pairs of atoms in the structure are opposed and, in consequence,

Li

3 1.5 5.8 cancel each other out. For these materials, termed

B 5 5.8 38.4 anti-ferromagnetic, there is no net spontaneous mag-

C 6 10.7 0.002

netization and neutron diffraction is a necessary and

important tool for investigating their behaviour (see Cu

5.6.2 Synchrotron radiation studies

Au 79 390

0.29 Very large electrical machines known as synchrotron Pb

radiation sources (SRS) provide a unique source of

The characterization of materials 163

Figure 5.45 (a) Layout of SRS, Daresbury, and (b) wavelength spectrum of synchrotron radiation (after Barnes, 1990, pp. 708–715; by permission of the Institute of Metals) .

electromagnetic radiation for materials characterisa- are placed in independent experimental stations located tion. 1 Electrons from a hot cathode are accelerated

around the periphery of the ring chamber and irradi- in three stages by a linear accelerator (Linac), a

ated in order to produce spectroscopic, diffraction or booster synchrotron and an evacuated storage ring

imaging effects.

(Figure 5.45a). As bunches of electrons travel around In the technique known as extended X-ray absorp- the periphery of the storage ring they attain ener-

tion fine-structure spectroscopy (EXAFS) attention is gies of up to 2 GeV and velocities approaching that

directed to the small discontinuities on the higher- of light. At these relativistic velocities, electron mass

energy flank beyond each vertical, characteristic ‘edge’ becomes 4000 times greater than the rest mass. Dipole

which appears in a plot of mass absorption ver- and quadrupole magnets constrain the bunches into

sus X-ray wavelength. These ‘finestructure’ (FS) fea- an approximately circular orbit and, by accelerating

tures derive from interference effects between electron them centripetally, cause electromagnetic radiation to

waves from excited atoms and waves back-scattered

be produced. The spectrum of this synchrotron radi- from surrounding atoms. Mathematical treatment ation is very wide, extending from short-wavelength

(using a Fourier transform) of the EXAFS spectra (‘hard’) X-rays to the infrared range (Figure 5.45b). A

yields a radial distribution plot of surrounding atomic wiggler magnet produces a strong (5 tesla) field and

density versus distance from the excited atom. By can extend the spectrum to even shorter wavelengths.

selecting the ‘edge’ for a particular type of atom/ion Compared with more orthodox sources of electromag-

and studying its fine structure, it is thus possible to netic radiation, the synchrotron offers the advantages

obtain information on its local environment and coor- of very high intensity, short wavelengths, precise col-

dination. This type of information is of great value limation of the beam and a smooth, continuous spec-

in structural studies of materials, such as glasses, trum. The high radiation intensity permits exposure

which only exhibit short-range order. For instance, the times that are often several orders of magnitude shorter

EXAFS technique has demonstrated that the network than those for comparable laboratory methods. The

structure of SiO 2 –Na 2 O–CaO glass is threaded by per- risk of beam damage to specimens by the flashes of

colation channels of modifier (sodium) cations. radiation is accordingly lessened. Specimens of met- als, ceramics, polymers, semiconductors, catalysts, etc.

5.6.3 Secondary ion mass spectrometry

(SIMS)

In 1980, the world’s first totally radiation-dedicated SRS came into operation at Daresbury, England. Electrons are

This important and rapidly-developing technique, ‘stored’ in the main ring for 10–20 h, traversing its 96 m

which enables material surfaces to be analysed with periphery more than 3 ð 10 6 times per second.

great chemical sensitivity and excellent resolution in

164 Modern Physical Metallurgy and Materials Engineering depth, is based upon the well-known phenomenon of

and provide ‘maps’ that show the lateral distribution sputtering. The target surface is bombarded with a

of elements at grain boundaries and precipitated focused beam of primary ions that has been accelerated

particles and hydrogen segregation in alloys. Imaging with a potential of 1–30 kV within a high-vacuum

SIMS has been applied to transverse sections through chamber (10 –10

torr). These ions generate a the complex scale layers which form when alloys series of collision cascades in a shallow surface layer,

are exposed to hot oxidizing gases (e.g. O 2 , CO 2 ). 0.5–5 nm deep, causing neutral atoms and, to a much

Its sensitivity is greater than that obtainable with smaller extent, secondary ions to be ejected (sputtered)

conventional EDX in SEM analysis and has provided from the specimen surface. Thus, a metallic oxide

a better understanding of growth mechanisms and the

special role of trace elements such as yttrium. M ,O , MO C and MO species. The secondary ions, which are thus either monatomic or clustered, positive

(MO) sample may act as a source of M, O, M C ,O C ,

or negative, are directed into a mass spectrometer

5.7 Thermal analysis

(analyser), wherein they are sorted and identified according to their mass/charge ratio. Exceptionally

5.7.1 General capabilities of thermal analysis

high elemental sensitivities, expressed in parts per Heating a material at a steady rate can produce chemi- million and even parts per billion, are achievable. All

cal changes, such as oxidation and degradation, and/or elements in the Periodic Table can be analysed and it

physical changes, such as the glass transition in poly- is possible to distinguish between individual isotopes.

mers, conversions/inversions in ceramics and phase Studies of the self-diffusion of oxygen and nitrogen

changes in metals. Thermal analysis is used to comple- have been hindered because these light elements have

ment X-ray diffraction analysis, optical and electron no isotopes that can be used as radioactive tracers.

microscopy during the development of new materi-

als and in production control. Sometimes it is used method for determining self-diffusion coefficients. The

SIMS based on the stable isotope 18 O provides a rapid

to define the temperature and energy change associated physical process whereby ions are ejected is difficult

with a structural change; at other times it is used quali- to express in rigorous theoretical terms, consequently

tatively to provide a characteristic ‘fingerprint’ trace of SIMS is usually semiquantitative, with dependence

a particular material. The various techniques of thermal upon calibration with standard samples of known

analysis measure one or more physical properties of a composition. SIMS is a valuable complement to other

sample as a function of temperature. Figure 5.46 illus- methods of surface analysis.

trates three basic methods of thermal analysis, namely The available range of beam diameter is 1 µ m to thermogravimetric analysis (TGA), differential thermal

several millimetres. Although various types of ion

analysis (DTA) and differential scanning calorimetry

(DSC). Respectively, they measure change in mass positively-charged beams are a common choice. How-

O 2 C , 16 O , Cs , etc.)

beam are available (e.g. Ar , 32 C

(TGA) and energy flow (DTA, DSC). They can apply ever, if the sample is insulating, positive charge tends

programmed heating and cooling, but usually operate to accumulate in the bombarded region, changing the

with a slowly rising temperature. The sample chamber effective value of the beam voltage and degrading the

may contain air, oxygen, nitrogen, argon, etc. or be quality of signals. One partial remedy, applicable at

evacuated. A sample of a few tens of milligrams will low beam voltages, is to ‘flood’ the ion-bombarded area

often suffice.

with a high-intensity electron beam. In some variants Recently-developed methods have extended the of SIMS laser beams are used instead of ion beams.

range of thermal analysis and other aspects of Of the large and growing variety of methods

behaviour can now be studied. For instance, covered by the term SIMS, the dynamic, static

using dynamic mechanical thermal analysis (DMTA), and imaging modes are especially useful. Materials

mechanical as well as structural information can be being investigated include metals, ceramics, polymers,

obtained on the viscoelastic response of a polymeric catalysts, semiconductors and composites. Dynamic

sample to tensile, bend or shear stresses during heating. SIMS, which uses a relatively high beam current, is an

important method for determining the distribution and very low concentration of dopants in semiconductors.

5.7.2 Thermogravimetric analysis

The beam scans a raster, 100–500 µ m in size, and In a thermobalance the mass of a sample is contin- slowly erodes the surface of the sample. Secondary

uously determined and recorded while the sample is ions from the central region of the crater are analysed

being slowly heated (Figure 5.46a). Temperatures up to produce a precise depth profile of concentration.

C are available. It has been applied Static SIMS uses a much smaller beam current and the

to at least 1000 °

to the decomposition of rubbers (Figure 5.47a), kinetic final spectra tend to be more informative, providing

studies of metallic oxidation, glass transitions and soft- chemical data on the top few atomic layers of the

ening in polymers. Equilibrium is not attained within sample surface. Little surface damage occurs and the

the sample and the method is insensitive to the more method has been applied to polymers. The imaging

subtle solid-state changes. When changes overlap, it version of SIMS has a resolution comparable to SEM

can be helpful to plot the first derivative, υm/υt, of

The characterization of materials 165

Figure 5.46 Basic methods of thermal analysis. (a) Thermogravimetric analysis (TGA). (b) differential thermal analysis (DTA) and (c) differential scanning calorimetry (DSC) .

the graphical trace in a procedure known as derivative material. Ideally, the specific heat capacities of S and thermogravimetric analysis (DTGA).

R should be similar. DTA is generally regarded as a semi-quantitative or qualitative method. It has been used in studies of devitrification in oxide glasses and

the glass transition in polymers. Figure 5.47b shows DTA 1 reveals changes during the heating of a sample

5.7.3 Differential thermal analysis

a comparison of the thermal response of high-alumina which involve evolution or absorption of energy. As

cement (HAC) and Portland cement. The amount of an shown diagrammatically in Figure 5.46b, a sample S

undesirable weakening phase can be derived from the and a chemically and thermally inert reference material

relative lengths of the ordinates X and Y in the HAC R (sintered alumina or precipitated silica) are mounted

trace.

in a recessed heating block and slowly heated. The thermocouples in S and R are connected in opposi-

5.7.4 Differential scanning calorimetry

tion; their temperature difference T is amplified and In this method, unlike DTA, the sample and reference plotted against temperature. Peak area on this trace is a

body have separate resistive heaters (Figure 5.46c). function of the change in enthalpy ⊲H⊳ as well as the

When a difference in temperature develops between mass and thermal characteristics of the sample S. Small

sample S and reference R, an automatic control loop samples can be used to give sharper, narrower peaks,

heats the cooler of the two until the difference is provided that they are fully representative of the source

eliminated. The electrical power needed to accomplish this equalizer is plotted against temperature. An

1 Usually accredited to H. Le Chatelier (1887): improved endothermic change signifies that an enthalpy increase version and forerunner of modern DTA used by

has occurred in S; accordingly, its peak is plotted W. C. Roberts-Austen (1899) in metallurgical studies of

upwards (unlike DTA traces). Differences in thermal alloys.

conductivity and specific heat capacity have no effect

166 Modern Physical Metallurgy and Materials Engineering

Figure 5.47 Examples of thermal analysis (a) TGA curve for decomposition of rubber, showing decomposition of oil and polymer in N 2 up to 600 ° C and oxidation of carbon black in air above 600 ° C (Hill and Nicholas, 1989), (b) DTA curve for high-alumina cement and Portland cement (Hill and Nicholas, 1989) and (c) DTA curve for a quenched glassy polymer (Hay, 1982) .

and peak areas can be expressed as energy per unit Barrett, C. S. and Massalski, T. B. (1980). Structure and mass. DSC has proved particularly valuable in polymer

Metals and Alloys . McGraw-Hill, New York. research, often being used in combination with other

Cullity, B. D. (1978). Elements of X-ray Diffraction . techniques, such as evolved gas analysis (EGA). DSC

Addison-Wesley, Reading, MA. has been used in studies of the curing characteristics Dehoff, R. T. and Rhines, F. N. (eds) (1968). Quantitative Microscopy . McGraw-Hill, New York. of rubbers and thermoset resins, transitions in

Gifkins, R. C. (1970). Optical Microscopy of Metals, Pitman, liquid crystals and isothermal crystallization rates

Melbourne.

in thermoplastics. Figure 5.47c is a trace obtained Hay, J. N. (1982). Thermal methods of analysis of polymers. for a quenched amorphous polymer. DSC has also

In Analysis of Polymer Systems, edited by L. S. Bark and been used in studies of the exothermic behaviour of

N. S. Allen, Chap. 6. Applied Science, London. cold-worked metals as they release ‘stored energy’

Hill, M. and Nicholas, P. (1989). Thermal analysis in during annealing, energy absorption during eutectic materials development. Metals and Materials, November, 639–642, Institute of Materials.

melting of alloys, precipitation in aluminium-based Jones, I. P. (1992). Chemical Microanalysis using Electron alloys, relaxation transformations in metallic glasses

Beams . Institute of Materials, London. and drying/firing transitions in clay minerals.

Loretto, M. H. (1984). Electron Beam Analysis of Materials. Chapman and Hall, London. Loretto, M. H. and Smallman, R. E. (1975). Defect Analysis in Electron Microscopy . Chapman and Hall, London.

Further reading

Modin, H. and Modin, S. (1973). Metallurgical Microscopy.

Butterworths, London.

Barnes, P. (1990). Synchrotron radiation for materials sci- Patzelt, W. J. (1974). Polarised Light Microscopy: Princi- ence research. Metals and Materials, November, 708–715,

ples, Instruments, Applications , Ernst Leitz Wetzlar GmbH, Institute of Materials.

Lahn-Wetzlar.

The characterization of materials 167 Pickering, F. B. (1976). The Basis of Quantitative Metal-

Vickerman, J. C., Brown, A. and Reed, N. M. (eds) (1990). lography , Inst. of Metallurgical Technicians Monograph

Secondary Ion Mass Spectrometry: Principles and Appli- No. 1.

cations . Clarendon Press, Oxford. Richardson, J. H. (1971). Optical Microscopy for the Materi-

Wendlandt, W. W. (1986). Thermal Analysis. 3rd edn. Wiley, als Sciences . Marcell Dekker, New York.

New York.