Itransm'"ed\
5.4.5 Chemical microanalysis
5.4.5.1 E x p l o i t a t i o n o f characteristic X - r a y s Electron probe microanalysis (EPMA) of bulk sam- ples is now a routine technique for obtaining rapid, accurate analysis of alloys. A small electron probe (~,100 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 :k0.1%. 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 -~2 jam. 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 rim.
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- cific wavelength, ~., at an angle 0, given by the Bragg equation, n)~ - 2d sin0. Different wavelengths are selected by changing 0 and thus to cover the neces- 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- sponding d-spacing for practicable values of 0, which
The characterization of materials 151
specimen x
_ ,
"~Auger electrons secondary
electrons
backscattered electrons
characteristic
continuum X-rays ~ X-rays
Figure 5.32 Schematic diagram showing the generation of electrons and X-rays within the specimen.
electron ~ MCA and
source EDX ~ computer
f . -
specimen ",~
microscope
column
screen71 o
~
~ EELS differentmagnetic 9 ~ _ / energies spectrometer~~.~~ i ~ MCA computer and
electron
detector
Figure 5.33 Schematic diagram of EDX and EELS in TEM.
lie between ~ 15 ~ and 65 ~ is achieved by using crystals 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 angles, 0. The operation of the spectrometer is very 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- ray detector; taking the resolution (A~.) to "-~ 0.001 nm
then ,k/AZ is about 300 which, for a medium atomic 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 ItS which leads to possible count rates of at least 105/s.
In recent years EDX detectors have replaced WDX detectors on transmission microscopes and are used together with WDX detectors on microprobes and on SEMs. A schematic diagram of a S i - L i detector is 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 Ep is thus Ep/3.8. The charge produced by a typical X-ray photon is ~-~,10-16 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 ~ts 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 > 4000/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 S i - L i detec- tor to about a few hundred eV, which worsens with increase in photon energy. The main advantage of 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 -- 11 in the Periodic Table can be obtained in a matter of seconds. The main
.rays
Be j
~, detector
T
1 i . . .
liquid ~,.~
N2 "-
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 leads to a peak-background ratio of about 50, and the limited count rate.
The variation in efficiency of a S i - L i detector must be allowed for when quantifying X-ray analysis. At low energies (< 1 kV) the X-rays are mostly absorbed in the Be window and at high energies (>20 kV), the X-rays pass through the detector so that the decreasing cross-section for electron-hole pair generation results in a reduction in efficiency. The S i - L i detector thus has optimum detection efficiency between about 1 and 20 kV.
5.4.5.2 Electron microanalysis of thin foils There are several simplifications which arise from the use of thin foils in microanalysis. The most important of these arises from the fact that the average energy loss which electrons suffer on passing through a thin foil is only about 2%, and this small average loss means that the ionization cross-section can be taken as a constant. Thus the number of characteristic X- ray photons generated from a thin sample is given simply by the product of the electron path length and the appropriate cross-section Q, i.e. the probability of ejecting the electron, and the fluorescent yield o9. The intensity generated by element A is then given by
Ia = iQo9n
where Q is the cross-section per cm 2 for the particular ionization event, o9 the fluorescent yield, n the number of atoms in the excited volume, and i the current inci- dent on the specimen. Microanalysis is usually carried out under conditions where the current is unknown and interpretation of the analysis simply requires that the ratio of the X-ray intensities from the various elements be obtained. For the simple case of a very thin speci- men for which absorption and X-ray fluorescence can be neglected, then the measured X-ray intensity from element A is given by
[A Of. nAQAogAaArIA and for element B by
la oc nBQBOgBaBrlB
where n, Q, 09, a and ~ represent the number of atoms, the ionization cross-sections, the fluorescent yields, the fraction of the K line (or L and M) which is collected and the detector efficiencies, respectively, for elements A and B. Thus in the alloy made up of elements A and B
llA IAQBOgBaBrlB IA
tX : g A B - -
nB IBQAogAaArlA IB
This equation forms the basis for X-ray microanaly- sis of thin foils where the constant K AB contains all the factors needed to correct for atomic number differ- ences, and is known as the Z-correction. Thus from the measured intensities, the ratio of the number of atoms
A to the number of atoms B, i.e. the concentrations of A and B in an alloy, can be calculated using the com- puted values for Q, w, o, etc. A simple spectrum for stoichiometric NiA1 is shown in Figure 5.35 and the values of I~ l and IN i, obtained after stripping the back- ground, are given in Table 5.2 together with the final analysis. The absolute accuracy of any X-ray analysis depends either on the accuracy and the constants Q, w, etc. or on the standards used to calibrate the measured intensities.
If the foil is too thick then an absorption correction (A) may have to be made to the measured intensities, since in traversing a given path length to emerge from the surface of the specimen, the X- rays of different energies will be absorbed differently.
This correction involves a knowledge of the specimen thickness which has to be determined by one of various techniques but usually from CBDPs. Occasionally a fluorescence (F) correction is also needed since element Z + 2. This 'nostandards' Z(AF) analysis can given an overall accuracy of ~ 2 % and can be carried out on-line with laboratory computers.
5 . 4 . 6 E l e c t r o n e n e r g y loss s p e c t r o s c o p y ( E E L S )
A disadvantage of EDX is that the X-rays from the light elements are absorbed in the detector window.
Windowless detectors can be used but have some disadvantages, such as the overlapping of spectrum lines, which have led to the development of EELS.
EELS is possible only on transmission specimens, and so electron spectrometers have been interfaced to TEMs to collect all the transmitted electrons lying within a cone of width a. The intensity of the various electrons, i.e. those transmitted without loss of energy and those that have been inelastically scattered and lost energy, is then obtained by dispersing the electrons with a magnetic prism which separates spatially the electrons of different energies.
A typical EELS spectrum illustrated in Figure 5.36 shows three distinct regions. The zero loss peak is made up from those electrons which have (1)not been scattered by the specimen, (2)suffered photon scattering ( ~ 1 / 4 0 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
~ 2 eV for a thermionic W filament) and the energy resolution of the spectrometer (typically a few eV).
The second region of the spectrum extends up to about 50 eV loss and is associated with plasmon excitations corresponding to electrons which have suffered one, two, or more plasmon interactions. Since the typical mean free path for the generation of a plasmon is about 50 nm, many electrons suffer single-plasmon losses and only in specimens which are too thick for electron loss analysis will there be a significant third plasmon peak. The relative size of the plasmon loss peak and the zero loss peak can also be used to measure 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 NiA! alloy
Measured Cross-section Fluorescent Detector Analysis
intensities Q, yield efficiency at. %
(10 -24 cm 2 ) to r I
NiKa 16 250 297 0.392 0.985 50.6
AIKa 7 981 2935 0.026 0.725 49.4
2 4 6 8
keV Figure 5.35 EDX spectrum from a stoichiometric N i - A l specimen.
I
AIKo!1 spectrum from stoichometric ]1NI Ka AI-Ni specimen
Ni Kg
FS 6163
>
i -
IO(~'A)
A
. ~ zero - loss
(a,A)
peak
/ /
,,..
, I Enl
i i i ii
0 energy loss
Figure 5.36 Schematic energy-loss spectrum, showing the zero-loss and plasmon regions together with the characteristic ionization edge, energy En/ and intensity In/.
154 Modern Physical Metallurgy and Materials Engineering exciting a plasmon loss, Pi, to not exciting a plasmon, P0, is given by Pl/P0 = t/L, where t is the thickness, L the mean free path for plasmon excitation, and P i and P0 are given by the relative intensities of the zero loss and the first plasmon peak. If the second plasmon peak is a significant fraction of the first peak this indicates that the specimen will be too thick for accurate microanalysis.
The third region is made up of a continuous back- ground on which the characteristic ionization losses are superimposed. Qualitative elemental analysis can be carried out simply by measuring the energy of the edges and comparing them with tabulated energies.
The actual shape of the edge can also help to define the chemical state of the element. Quantitative analysis requires the measurement of the ratios of the intensities of the electrons from elements A and B which have suffered ionization losses. In principle, this allows the ratio of the number of A atoms, NA, and B atoms, NB, to be obtained simply from the appropriate ionization cross-sections, QK. Thus the number of A atoms will be given by
NA = (1/Q'~)[l~/lo]
and the number of B atoms by a similar expression, so that
B B A
NA/NB -- I ~ Q K / I K Q K
where I~ is the measured intensity of the K edge for element A, similarly for I~ and I0 is the measured intensity of the zero loss peak. This expression is similar to the thin foil EDX equation.
To obtain IK the background has to be removed so that only loss electrons remain. Because of the presence of other edges there is a maximum energy range over which IK can be measured which is about 5 0 - 1 0 0 eV. The value of QK must therefore be replaced by QK (A) which is a partial cross-section cal- culated for atomic transition within an energy range A of the ionization threshold. Furthermore, only the loss electrons arising from an angular range of scatter a at the specimen are collected by the spectrometer so that a double partial cross-section Q(A, ct) is appropriate.
Thus analysis of a binary alloy is carried out using the equation
NA Q~,(A, o~)I~(A, or)
NB Q'~(A, ot)l~(A, et)
Values of Q(A, c~) may be calculated from data in the literature for the specific value of ionization edge, A, oe and incident accelerating voltage, but give an analysis accurate to only about 5%; a greater accuracy might be possible if standards are used.