Chemical microanalysis

5.4.5 Chemical microanalysis

5.4.5.1 Exploitation of characteristic X-rays Electron probe microanalysis (EPMA) of bulk sam-

ples is now a routine technique for obtaining rapid, accurate analysis of alloys. A small electron probe (³100 nm diameter) is used to generate X-rays from

a defined area of a polished specimen and the inten- sity of the various characteristic X-rays measured using

either wavelength-dispersive spectrometers (WDS) or energy-dispersive spectrometers (EDS). Typically the accuracy of the analysis is š0.1%. One of the lim- itations of EPMA of bulk samples is that the vol- ume of the sample which contributes to the X-ray signal is relatively independent of the size of the electron probe, because high-angle elastic scattering of electrons within the sample generates X-rays (see Figure 5.32). The consequence of this is that the spatial resolution of EPMA is no better than ¾2 µ m. In the last few years EDX detectors have been interfaced to transmission electron microscopes which are capable of operating with an electron probe as small as 2 nm. The combination of electron-transparent samples, in which high-angle elastic scattering is limited, and a small electron probe leads to a significant improvement in the potential spatial resolution of X-ray microanal- ysis. In addition, interfacing of energy loss spectrom- eters has enabled light elements to be detected and measured, so that electron microchemical analysis is now a powerful tool in the characterization of materi- als. With electron beam instrumentation it is required to measure (1) the wavelength or energies of emitted X-rays (WDX and EDX), (2) the energy losses of the fast electrons (EELS), and (3) the energies of emitted electrons (AES). Nowadays (1) and (2) can be carried out on the modern TEM using special detector systems, as shown schematically in Figure 5.33.

In a WDX spectrometer a crystal of known d- spacing is used which diffracts X-rays of a spe-

sary range of wavelengths, several crystals of different

d -spacings are used successively in a spectrometer. The range of wavelength is 0.1–2.5 nm and the corre-

The characterization of materials 151

weight sample, leads to a peak–background ratio of about 250. The crystal spectrometer normally uses a proportional counter to detect the X-rays, producing an electrical signal, by ionization of the gas in the counter, proportional to the X-ray energy, i.e. inversely proportional to the wavelength. The window of the counter needs to be thin and of low atomic number to minimize X-ray absorption. The output pulse from the counter is amplified and differentiated to produce a short pulse. The time constant of the electrical circuit is of the order of 1 µ s which leads to possible count

rates of at least 10 5 / s.

In recent years EDX detectors have replaced WDX detectors on transmission microscopes and are used together with WDX detectors on microprobes and on

Figure 5.32 Schematic diagram showing the generation of SEMs. A schematic diagram of a Si –Li detector is

electrons and X-rays within the specimen . shown in Figure 5.34. X-rays enter through the thin Be window and produce electron-hole pairs in the Si –Li. Each electron-hole pair requires 3.8 eV, at the operating temperature of the detector, and the number of pairs produced by a photon of energy E p is thus

3.8. The charge produced by a typical X-ray photon is ³10 16 C and this is amplified to give a shaped pulse, the height of which is then a measure of the

energy of the incident X-ray photon. The data are stored in a multi-channel analyser. Provided that the X-ray photons arrive with a sufficient time interval between them, the energy of each incident photon can

be measured and the output presented as an intensity versus energy display. The amplification and pulse shaping takes about 50 µ s and if a second pulse arrives before the preceding pulse is processed, both pulses are rejected. This results in significant dead time for count rates ½4000/s.

The number of electron-hole pairs generated by an X-ray of a given energy is subject to normal statisti- cal fluctuations and this, taken together with electronic noise, limits the energy resolution of a Si –Li detec- tor to about a few hundred eV, which worsens with increase in photon energy. The main advantage of

Figure 5.33 Schematic diagram of EDX and EELS in TEM . EDX detectors is that simultaneous collection of the whole range of X-rays is possible and the energy char- acteristics of all the elements >Z D 11 in the Periodic

lie between ³15 ° and 65 ° , is achieved by using crystals Table can be obtained in a matter of seconds. The main such as LiF, quartz, mica, etc. In a WDX spectrometer the specimen (which is the X-ray source), a bent crys- tal of radius 2r and the detector all lie on the focusing circle radius r and different wavelength X-rays are col- lected by the detector by setting the crystal at different

time-consuming since only one particular X-ray wave- length can be focused on to the detector at any one time.

The resolution of WDX spectrometers is controlled by the perfection of the crystal, which influences the range of wavelengths over which the Bragg condition is satisfied, and by the size of the entrance slit to the X-

Figure 5.34 Schematic diagram of Si–Li X-ray detector .

152 Modern Physical Metallurgy and Materials Engineering disadvantages are the relatively poor resolution, which

A to the number of atoms B, i.e. the concentrations of leads to a peak-background ratio of about 50, and the

A and B in an alloy, can be calculated using the com- limited count rate. The variation in efficiency of a Si –Li detector must

stoichiometric NiAl is shown in Figure 5.35 and the

be allowed for when quantifying X-ray analysis. At values of I Al K and I Ni K , obtained after stripping the back- ground, are given in Table 5.2 together with the final

in the Be window and at high energies (½20 kV), the analysis. The absolute accuracy of any X-ray analysis X-rays pass through the detector so that the decreasing

depends either on the accuracy and the constants Q, ω, cross-section for electron-hole pair generation results

etc. or on the standards used to calibrate the measured in a reduction in efficiency. The Si –Li detector thus

intensities.

has optimum detection efficiency between about 1 and If the foil is too thick then an absorption

20 kV. correction (A) may have to be made to the measured intensities, since in traversing a given path length

5.4.5.2 Electron microanalysis of thin foils to emerge from the surface of the specimen, the X- There are several simplifications which arise from the

rays of different energies will be absorbed differently. use of thin foils in microanalysis. The most important

This correction involves a knowledge of the specimen of these arises from the fact that the average energy

thickness which has to be determined by one of various loss which electrons suffer on passing through a thin

techniques but usually from CBDPs. Occasionally foil is only about 2%, and this small average loss

a fluorescence (F) correction is also needed since means that the ionization cross-section can be taken

element Z C 2. This ‘nostandards’ Z(AF) analysis can as a constant. Thus the number of characteristic X-

given an overall accuracy of ³2% and can be carried ray photons generated from a thin sample is given

out on-line with laboratory computers. simply by the product of the electron path length and

the appropriate cross-section Q, i.e. the probability of

5.4.6 Electron energy loss spectroscopy

ejecting the electron, and the fluorescent yield ω. The

(EELS)

intensity generated by element A is then given by

A disadvantage of EDX is that the X-rays from the

I A D iQωn light elements are absorbed in the detector window.

2 where Q is the cross-section per cm Windowless detectors can be used but have some for the particular disadvantages, such as the overlapping of spectrum ionization event, ω the fluorescent yield, n the number

lines, which have led to the development of EELS. of atoms in the excited volume, and i the current inci-

EELS is possible only on transmission specimens, dent on the specimen. Microanalysis is usually carried

and so electron spectrometers have been interfaced out under conditions where the current is unknown and

to TEMs to collect all the transmitted electrons lying interpretation of the analysis simply requires that the

within a cone of width ˛. The intensity of the various ratio of the X-ray intensities from the various elements

electrons, i.e. those transmitted without loss of energy

be obtained. For the simple case of a very thin speci- and those that have been inelastically scattered and lost men for which absorption and X-ray fluorescence can

energy, is then obtained by dispersing the electrons

be neglected, then the measured X-ray intensity from with a magnetic prism which separates spatially the element A is given by

electrons of different energies.

A typical EELS spectrum illustrated in Figure 5.36

I A /n A Q A ω A a A A shows three distinct regions. The zero loss peak is and for element B by

made up from those electrons which have (1) not been scattered by the specimen, (2) suffered photon

I B /n B Q B ω B a B B scattering (³1/40 eV) and (3) elastically scattered. The energy width of the zero loss peak is caused by the energy spread of the electron source (up to

the ionization cross-sections, the fluorescent yields, the ³2 eV for a thermionic W filament) and the energy fraction of the K line (or L and M) which is collected

resolution of the spectrometer (typically a few eV). and the detector efficiencies, respectively, for elements

The second region of the spectrum extends up to about

50 eV loss and is associated with plasmon excitations and B

A and B. Thus in the alloy made up of elements A

corresponding to electrons which have suffered one,

A two, or more plasmon interactions. Since the typical n B I a AB B mean free path for the generation of a plasmon is Q A ω A A A I B about 50 nm, many electrons suffer single-plasmon This equation forms the basis for X-ray microanaly-

B DK

losses and only in specimens which are too thick for

electron loss analysis will there be a significant third the factors needed to correct for atomic number differ-

sis of thin foils where the constant K AB contains all

plasmon peak. The relative size of the plasmon loss ences, and is known as the Z-correction. Thus from the

peak and the zero loss peak can also be used to measure measured intensities, the ratio of the number of atoms

the foil thickness. Thus the ratio of the probability of

The characterization of materials 153

Table 5.2 Relationships between measured intensities and composition for a NiAl alloy

Measured Cross-section

Figure 5.35 EDX spectrum from a stoichiometric Ni–Al specimen .

Figure 5.36 Schematic energy-loss spectrum, showing the zero-loss and plasmon regions together with the characteristic ionization edge, energy E nl and intensity I nl .

154 Modern Physical Metallurgy and Materials Engineering

exciting a plasmon loss, P 1 , to not exciting a plasmon,

obviously an important method for studying oxidation,

P 0 , is given by P 1 / P 0 D t/L, where t is the thickness,

catalysis and other surface chemical reactions, but has L the mean free path for plasmon excitation, and P 1 also been used successfully to determine the chem-

and P 0 are given by the relative intensities of the istry of fractured interfaces and grain boundaries (e.g. zero loss and the first plasmon peak. If the second

temper embrittlement of steels). plasmon peak is a significant fraction of the first peak

The basic instrumentation involves a focusable elec- this indicates that the specimen will be too thick for

tron gun, an electron analyser and a sample support accurate microanalysis.

and manipulation system, all in an ultra-high-vacuum The third region is made up of a continuous back-

environment to minimize adsorption of gases onto the ground on which the characteristic ionization losses

surface during analysis. Two types of analyser are in are superimposed. Qualitative elemental analysis can

use, a cylindrical mirror analyser (CMA) and a hemi-

be carried out simply by measuring the energy of the spherical analyser (HSA), both of which are of the edges and comparing them with tabulated energies.

energy-dispersive type as for EELS, with the differ- The actual shape of the edge can also help to define

ence that the electron energies are much lower, and the chemical state of the element. Quantitative analysis

electrostatic rather than magnetic ‘lenses’ are used to requires the measurement of the ratios of the intensities

separate out the electrons of different energies. of the electrons from elements A and B which have

In the normal distribution the Auger electron peaks suffered ionization losses. In principle, this allows the

appear small on a large and often sloping background,

which gives problems in detecting weak peaks since to be obtained simply from the appropriate ionization

ratio of the number of A atoms, N A , and B atoms, N B ,

amplification enlarges the background slope as well cross-sections, Q K . Thus the number of A atoms will

as the peak. It is therefore customary to differentiate

be given by the spectrum so that the Auger peaks are emphasized N

D ⊲1/Q A ⊳ [I A K /I 0 ] as doublet peaks with a positive and negative displace-

A ment against a nearly flat background. This is achieved and the number of B atoms by a similar expression, so

by electronic differentiation by applying a small a.c. that

signal of a particular frequency in the detected signal. N A /N B DI A Q B B A K Chemical analysis through the outer surface layers can K I K Q K be carried out by depth profiling with an argon ion gun.

where I A K is the measured intensity of the K edge for

element A, similarly for I B K and I 0 is the measured

5.5 Observation of defects

intensity of the zero loss peak. This expression is

similar to the thin foil EDX equation.

5.5.1 Etch pitting

To obtain I K the background has to be removed so that only loss electrons remain. Because of the

Since dislocations are regions of high energy, their presence of other edges there is a maximum energy

presence can be revealed by the use of an etchant range over which I K can be measured which is

which chemically attacks such sites preferentially. This about 50–100 eV. The value of Q K must therefore be

method has been applied successfully in studying replaced by Q K ⊲⊳ which is a partial cross-section cal-

metals, alloys and compounds, and there are many culated for atomic transition within an energy range 

fine examples in existence of etch-pit patterns show- of the ionization threshold. Furthermore, only the loss

ing small-angle boundaries and pile-ups. Figure 5.37a electrons arising from an angular range of scatter ˛ at

shows an etch-pit pattern from an array of piled-up dis- the specimen are collected by the spectrometer so that

locations in a zinc crystal. The dislocations are much

a double partial cross-section Q⊲, ˛⊳ is appropriate. closer together at the head of the pile-up, and an anal- Thus analysis of a binary alloy is carried out using the

ysis of the array, made by Gilman, shows that their equation

spacing is in reasonable agreement with the theory of Eshelby, Frank and Nabarro, who have shown that the

N A Q B ⊲, ˛⊳I A ⊲, ˛⊳

number of dislocations n that can be packed into a N B Q A K ⊲, ˛⊳I K B ⊲, ˛⊳

applied stress. The main disadvantage of the technique Values of Q⊲, ˛⊳ may be calculated from data in the

literature for the specific value of ionization edge, , ˛ is its inability to reveal networks or other arrangements and incident accelerating voltage, but give an analysis

in the interior of the crystal, although some informa- accurate to only about 5%; a greater accuracy might

tion can be obtained by taking sections through the

be possible if standards are used. crystal. Its use is also limited to materials with low dislocation contents ⊲<10 4 mm ⊳ because of the lim- ited resolution. In recent years it has been successfully

used to determine the velocity v of dislocations as a Auger electrons originate from a surface layer a few

5.4.7 Auger electron spectroscopy (AES)

function of temperature and stress by measuring the atoms thick and therefore AES is a technique for study-

distance travelled by a dislocation after the application ing the composition of the surface of a solid. It is

of a stress for a known time (see Chapter 7).

The characterization of materials 155

(a)

50 µ Figure 5.37 Direct observation of dislocations. (a) Pile-up in a zinc single crystal (after Gilman, 1956, p. 1000).

(b)

(b) Frank-Read source in silicon (after Dash, 1957; courtesy of John Wiley and Sons) .

The technique of dislocation decoration has the It is well-known that there is a tendency for solute

5.5.2 Dislocation decoration

advantage of revealing internal dislocation networks but, when used to study the effect of cold-work on the

atoms to segregate to grain boundaries and, since these dislocation arrangement, suffers the disadvantage of may be considered as made up of dislocations, it is

requiring some high-temperature heat-treatment dur- clear that particular arrangements of dislocations and

ing which the dislocation configuration may become sub-boundaries can be revealed by preferential precip-

modified.

itation. Most of the studies in metals have been carried out on aluminium–copper alloys, to reveal the dislo-

5.5.3 Dislocation strain contrast in TEM

cations at the surface, but recently several decoration The most notable advance in the direct observation of techniques have been devised to reveal internal struc-

dislocations in materials has been made by the applica- tures. The original experiments were made by Hedges

tion of transmission techniques to thin specimens. The and Mitchell in which they made visible the disloca-

technique has been used widely because the disloca- tions in AgBr crystals with photographic silver. After

tion arrangements inside the specimen can be studied.

a critical annealing treatment and exposure to light, the It is possible, therefore, to investigate the effects of colloidal silver separates along dislocation lines. The

plastic deformation, irradiation, heat-treatment, etc. on technique has since been extended to other halides, and

the dislocation distribution and to record the move- to silicon where the decoration is produced by diffus-

ment of dislocations by taking cine-films of the images ing copper into the crystal at 900 °

on the fluorescent screen of the electron microscope. the crystal to room temperature, the copper precipi-

C so that on cooling

One disadvantage of the technique is that the materi- tates. When the silicon crystal is examined optically,

als have to be thinned before examination and, because using infrared illumination, the dislocation-free areas

the surface-to-volume ratio of the resultant specimen transmit the infrared radiation, but the dislocations dec-

is high, it is possible that some rearrangement of dis- orated with copper are opaque. A fine example of

locations may occur.

dislocations observed using this technique is shown

A theory of image contrast has been developed in Figure 5.37b.

which agrees well with experimental observations. The

156 Modern Physical Metallurgy and Materials Engineering basic idea is that the presence of a defect in the lattice

g 0 D 1, is then causes displacements of the atoms from their position

in the perfect crystal and these lead to phase changes t

in the electron waves scattered by the atoms so that the amplitude diffracted by a crystal is altered. The image seen in the microscope represents the electron

and since r.s is small and g.r is an integer this reduces intensity distribution at the lower surface of the speci-

to

men. This intensity distribution has been calculated by

a dynamical theory (see Section 5.5.7) which considers

the coupling between the diffracted and direct beams 0 but it is possible to obtain an explanation of many

observed contrast effects using a simpler (kinematical)

theory in which the interactions between the transmit- ted and scattered waves are neglected. Thus if an elec-

where z is taken along the column. The intensity from

0 .r⊳

such a column is

where k 0 j j 2 2 2 2 2 dent on an atom at position r there will be an elastically

g DI g g ]⊲sin

1 .r⊳ with a phase difference from which it is evident that the diffracted intensity

oscillates with depth z in the crystal with a periodicity diffracted wave. If the crystal is not oriented exactly

1 k 0 ⊳ when k 1 is the wave vector of the

equal to 1/s. The maximum wavelength of this oscil- at the Bragg angle the reciprocal lattice point will be

lation is known as the extinction 1 g since the either inside or outside the reflecting sphere and the

diffracted intensity is essentially extinguished at such positions in the crystal. This sinusoidal variation of

reciprocal lattice vector of the lattice plane giving rise intensity gives rise to fringes in the electron-optical to reflection and s is the vector indicating the devia-

image of boundaries and defects inclined to the foil tion of the reciprocal lattice point from the reflection

surface, e.g. a stacking fault on an inclined plane is sphere (see Figure 5.39). To obtain the total scattered

generally visible on an electron micrograph as a set amplitude from a crystal it is necessary to sum all the

of parallel fringes running parallel to the intersec- scattered amplitudes from all the atoms in the crys-

tion of the fault plane with the plane of the foil (see tal, i.e. take account of all the different path lengths

Figure 5.43).

for rays scattered by different atoms. Since most of In an imperfect crystal, atoms are displaced from the intensity is concentrated near the reciprocal lattice

their true lattice positions. Consequently, if an atom point it is only necessary to calculate the amplitude

at r n is displaced by a vector R, the amplitude of diffracted by a column of crystal in the direction of

the wave diffracted by the atom is multiplied by the diffracted by a column of crystal in the direction of the diffracted beam and not the whole crystal, as

shown in Figure 5.38. The amplitude of the diffracted the Bragg angle and F the structure factor.

g on the bottom surface of the crystal. The dislocation is at a depth y and a distance x from the column. (b) Variation of intensity with depth in a crystal .

The characterization of materials 157

less and hence the dislocation will appear as a line since ⊲k 1 k 0 ⊳DgCs the resultant amplitude is

1 k 0 ⊳.R ]. Then,

in dark contrast. It follows that the image of the

dislocation will lie slightly to one or other side of

g D g ⊳ the dislocation core, depending on the sign of (g.b)s.

0 This is shown in Figure 5.39 for the case where the crystal is oriented in such a way that the incident beam

If we neglect s.R which is small in comparison with makes an angle greater than the Bragg angle with

g .R, and g.r which gives an integer, then in terms of the reflecting planes, i.e. s > 0. The image occurs on the column approximation

that side of the dislocation where the lattice rotation

brings the crystal into the Bragg position, i.e. rotates

g D g ⊳ the reciprocal lattice point onto the reflection sphere.

0 Clearly, if the diffracting conditions change, i.e. g or The amplitude, and hence the intensity, therefore s change sign, then the image will be displaced to the

may differ from that scattered by a perfect crystal, other side of the dislocation core. The phase angle introduced by a lattice defect is

finite or not, and image contrast is obtained when zero when g.R D 0, and hence there is no contrast, i.e. g.R 6D 0. the defect is invisible when this condition is satisfied.

is the angle between g and R, then g.R D 0 when the

displacement vector R is normal to g, i.e. parallel to the In general, crystals observed in the microscope appear

5.5.4 Contrast from crystals

reflecting plane producing the image. If we think of the light because of the good transmission of electrons. In

lattice planes which reflect the electrons as mirrors, it is detail, however, the foils are usually slightly buckled

easy to understand that no contrast results when g.R D so that the orientation of the crystal relative to the

0, because the displacement vector R merely moves the electron beam varies from place to place, and if one

reflecting planes parallel to themselves without altering part of the crystal is oriented at the Bragg angle, strong

the intensity scattered from them. Only displacements diffraction occurs. Such a local area of the crystal

which have a component perpendicular to the reflecting then appears dark under bright-field illuminations, and

plane, i.e. tilting the planes, will produce contrast. is known as a bend or extinction contour. If the

A screw dislocation only produces atomic displace- specimen is tilted while under observation, the angular

ments in the direction of its Burgers vector, and hence conditions for strong Bragg diffraction are altered, and

because R D b such a dislocation will be completely the extinction contours, which appear as thick dark

‘invisible’ when b lies in the reflecting plane producing bands, can be made to move across the specimen. To

the image. A pure edge dislocation, however, pro- interpret micrographs correctly, it is essential to know

duces some minor atomic displacements perpendicular the correct sense of both g and s. The g-vector is the

to b, as discussed in Chapter 4, and the displacements line joining the origin of the diffraction pattern to the

give rise to a slight curvature of the lattice planes. An strong diffraction spot and it is essential that its sense is

edge dislocation is therefore not completely invisible correct with respect to the micrograph, i.e. to allow for

when b lies in the reflecting planes, but usually shows any image inversion or rotation by the electron optics.

some evidence of faint residual contrast. In general, The sign of s can be determined from the position of

the Kikuchi lines with respect to the diffraction spots, as discussed in Section 5.4.1.