ASM Metals Handbook - Desk Edition (ASM_ 1998) Episode 14 ppsx

• Characterizing preferred crystallographic orientations by analysis of orientations of individual grains Spatial Resolution • Secondary electron imaging of surface topography: 10 nm •

Fig 4 Planes in three-dimensional crystals defined by their Miller indices Source: Ref 2

In simple crystal structures (e.g., cubic), planes with various combinations and permutations of the same indices have identical interplanar spacings These spacings are referred to as types of planes For example, in a cubic crystal (112), (121), (211), (-112), (-211), etc., all spacings are referred to as planes of the type {112}

A number of different types of information can be determined from XRD experiments The primary types of analyses and their uses are described in the following sections, along with information about the threshold sensitivity and precision, limitations, sample requirements, and capabilities of related techniques

References cited in this section

1 R Jenkins and R Snyder, Introduction to X-Ray Powder Diffractometry, John Wiley, 1996

2 C Barrett and T Massalski, Structure of Metals, McGraw-Hill, 1966

Identification of Compounds and Phases Using X-Ray Powder Diffraction

Typical Uses

X-ray powder diffraction is used to identify the crystalline phases present in a sample Examples of the types of questions that can be answered using x-ray powder diffraction include:

• Is a heat treated steel sample 100% martensite, or does it contain some retained austenite?

• What compounds are present in the corrosion product that formed when an aluminum alloy was exposed

to sea spray?

• What compounds are present in the scale formed on a ingot during high-temperature forging?

Solving these types of problems by x-ray powder diffraction is the most common use of XRD in metallurgy

Experimental Approach

In x-ray powder diffraction, an x-ray beam of a single known wavelength is used to determine the interplanar spacings of the planes in the sample The sample is typical polycrystalline, ideally containing a semi-infinite number of randomly oriented crystals Bragg's law dictates that each set of crystal planes will diffract at its own characteristic angle Once these angles at which diffraction occurs have been experimentally determined, the interplanar spacings corresponding to each of them can then be calculated by substituting these angles and the known wavelength of radiation used into Bragg's law The resulting set of interplanar spacings provides a "fingerprint" of the sample that can be compared to the

"interplanar spacing fingerprints" of over 100,000 known compounds, thus permitting identification of the compound(s) present in the sample

The results of a typical x-ray powder diffraction analysis are shown in Fig 5 The plot of diffracted intensity versus diffraction angle exhibits a number of peaks, each corresponding to a particular set of crystallographic planes and its

characteristic d-spacing The most important information is the angle at which diffraction occurs The relative intensities

of the peaks are determined by a number of factors beyond the scope of this article Suffice it to say that, for a sample made up of randomly oriented crystals of a given metal or compound, the relative intensities of the various diffraction peaks are predictable and reproducible within a few percent However, these intensities are of secondary importance in solving the powder diffraction pattern

Fig 5 X-ray powder pattern of Al2O3 Source: Ref 1

The pattern can also be summarized as a table of d-spacings (each corresponding to a angle) and corresponding intensities, typically expressed as a percentage of the most intense peak, as shown in Tables 1(a), 1(b), and 1(c)

Table 1(a) Identification of powder diffraction pattern from Al 2 O 3 using the Hanawalt search method

The diffracting angles and intensities (area under each peak) are measured from the unknown sample (in this example from the

diffractometer trace in Fig 5) d-spacings are then calculated for each diffraction peak using Bragg's law and the known wavelength

of radiation used (in this case, Cu K , = 1.54178 )

2 , degrees Intensity, 0 to 100 d, Miller indices

95.34 18 1.043 226

98.50 1 1.018 042

Table 1(b) Hanawalt search method

The d-spacings corresponding to the most intense peaks from the sample are then compared with a database of known compounds ordered by the d-spacings of their most intense peaks, resulting in a tentative identification of the sample A set of 25 compounds with

similar intense peaks is shown below Note that the 8 most intense peaks for Al2O3 correspond to intense peaks from the sample pattern given in Table 1(a)

Table 1(c) Hanawalt search method

A card containing all of the information for the tentatively identified compound is compared with the diffraction information from the sample The card for Al2O3 is shown below Note that all of the diffraction peaks in the sample pattern can be accounted for by Al2O3

If unidentified lines were present, it would indicate either that the tentative identification was incorrect, or that one or more additional compounds were present in the sample along with Al2O3 The information on the card enables identification of the Miller indices of the planes associated with each diffraction peak, shown in the last column of Table 1(b)

Historically, results such as those presented in Tables 1(a), 1(b), and 1(c) were compared with the d-spacing and intensity

fingerprints for 100,000 known compounds each tabulated on an index card and organized systematically by the

d-spacings of the several most intense peaks This search and match process is now greatly facilitated by computers that

contain all of the information on known compounds in an updatable database The search is based primarily of the

d-spacing information, rather than the intensities, because the assumption that the sample consists of randomly oriented crystals is frequently violated, thus altering the intensities

Samples Containing Multiple Phases or Compounds

Identification of metals and compounds by x-ray powder diffraction is relatively straightforward when the sample consists

of a single phase or compound When multiple phases or compounds are present, however, the task is more complex, as multiple "fingerprints" are superimposed on one another Fortunately, software is available to analyze and solve such complex patterns Solution of complex overlapping patterns can be simplified by providing additional information to the computer regarding what elements are, are not, and may be in the sample This information is typically obtained by x-ray fluorescence spectroscopy Once this elemental information has been input, the software searches only compounds that are consistent with it

Once the phases or compounds present in a multi-phase sample have been identified, the percentages of each phase or compound present can be deduced from the relative intensities of their diffraction peaks A common metallurgical example is the determination of the amount of retained austenite present in heat treated steels The most precise analyses are based on comparison of results from the unknown with those from a number of calibrated standards

Instrumentation

X-ray diffraction analyses have historically been conducted using two types of equipment: the Debye-Scherrer camera and the x-ray diffractometer The Debye-Scherrer camera is used for powdered samples (Fig 6) The camera is a light-tight hollow cylinder with a removable cover plate The powdered sample is placed in a hollow capillary tube at the center

of the camera A strip of photographic film is then placed around its inside perimeter, and the cover plate is applied The camera is then attached to an x-ray generating tube and the x-rays are directed onto the sample through a collimator The diffracted x-rays are recorded on the film, which is developed following 1 to 4 h of x-ray exposure (Fig 7) The angles

are measured from the film and converted to d-spacings Intensities are either estimated by eye or quantified using a

densitometer

Fig 6 Schematic of Debye-Scherrer powder method (a) Relationship of film to sample, incident beam, and

diffracted beams (b) Appearance of film when developed and laid flat Source: Ref 3

Fig 7 Debye-Scherrer films identifying phases in copper-zinc alloys of various compositions Source: Ref 2

The x-ray diffractometer avoids the use of film and is far better suited to automation The sample is flat, typically either a polished metal surface or a powder adhered to a flat glass slide The sample is exposed to the incident x-ray beam, and a counter is scanned over the desired range of angles (Fig 8) The result is a plot of diffracted intensity versus diffraction angle (Fig 5)

Fig 8 Schematic of x-ray diffractometer Typically, the x-ray tube remains stationary while the detector

mechanically scans a range of angles The sample also rotates with the detector such that diffraction is recorded from planes parallel to the sample surface

In recent years, position-sensitive wire detectors and solid state charge coupled device (CCD) detectors (in essence, a high resolution array of solid state light sensors) have permitted all of the diffracted signals to be collected simultaneously, thus overcoming the need to mechanically scan a detector scintillation counter over the range of diffraction angles This method of collection greatly increases the speed with which diffraction information can be obtained, and it provides a digital electronic format that is amenable to computer-assisted data reduction and analysis

Detection Threshold and Precision

• Threshold sensitivity: A phase or compound must typically represent 1 to 2% of the sample to be detected

• Precision of interplanar spacing and lattice parameter measurements: 0.3% relative in routine measurements; within 0.003% relative in experiments optimized for this purpose

• Precision of quantitative analyses of percentage of individual phases or compounds present in samples containing multiple compounds: 5 to 10% relative or 1 to 2% absolute, whichever is greater (presumes the use of calibrated standards)

Amount of Material Sampled

• Powdered samples: Entire sample

• Polished bulk materials: Typically 1 cm square area, sampling depth usually in the range 10 to 100

m (increases with decreasing average atomic number)

Limitations

• Noncrystalline samples produce no diffraction peaks

• Results represent average of many grains or crystals in the sample, not an individual particle Fine beams (down to 100 m diameter) can be used to characterize some individual particles

Sample Requirements

• Powders: 10 mg is typically enough

• Flat metal samples: Diffractometers can usually accommodate samples with lateral dimensions up to 5

cm and thicknesses up to 5 mm Ideally, the surface should be free of deformation in order to get sharp diffraction peaks Chemical or electropolishing can be used to remove the last vestiges of deformation in mechanically ground and/or polished samples

References cited in this section

1 R Jenkins and R Snyder, Introduction to X-Ray Powder Diffractometry, John Wiley, 1996

2 C Barrett and T Massalski, Structure of Metals, McGraw-Hill, 1966

3 Materials Characterization, Vol 10, ASM Handbook, ASM International, 1986, p 335

Measurement of Lattice Parameter Changes due to Alloying or Temperature

The addition of alloying elements, heating or cooling, and residual stresses cause slight changes in interplanar spacings, which cause slight shifts in the angles at which diffraction occurs XRD can be used to quantify these changes

Changes resulting from solid solution alloying can be determined using a diffractometer, as described earlier Similarly, temperature effects can be characterized using a diffractometer equipped with a furnace to heat the sample to the desired temperature

The systematic errors inherent in XRD measurements decrease with increasing diffraction angle As a result, lattice parameter measurements are typically based on information obtained at high diffraction angles The most precise lattice parameter measurements make use of curve-fitting procedures to extrapolate information to the limiting value of 90°

Precision

• 0.03% relative with moderate care

• 0.003% relative with the greatest care

Sample Requirements

• Identical to those indicated above for routine diffractometer examination

Measurement of Residual Stresses

X-ray residual stress measurement is substantially more complex, but its key principles are not difficult to understand Residual stresses are most often introduced during heat treating or welding and are caused by differential thermal contraction associated with temperature gradients in the material These stresses cause elastic strains in the material, which manifest themselves as slight departures from the material's normal (unstressed) lattice parameters or interplanar spacings XRD measurement of these changes in interplanar spacings, then, provides a direct measure of elastic strain, which can be used to calculate residual stress magnitude using the known elastic constants of the material

Because residual stresses must be calculated from small stress-induced changes in interplanar spacing, it is critical to know precisely the interplanar spacings in an unstressed sample of the material in question The planes that happen to be parallel to and very close to the free surface provide an internal calibration in this regard, because no stresses can be supported perpendicular to a free surface The problem then becomes one of comparing the interplanar spacings of planes parallel to the free surface with those inclined at various angles to the surface, and using the pertinent equations of elasticity to calculate from these differences the magnitudes of the stresses in various directions parallel to the surface From this, the principal in-plane stresses directions can be calculated

Instrumentation

Residual stresses are typically measured using an x-ray diffractometer equipped with a special specimen holder designed

to facilitate measurement of diffraction from planes inclined at various angles to the surface of the sample (General purpose diffractometers obtain diffraction information only from planes that are parallel to the sample surface See Fig 8.) Portable x-ray systems are also frequently used to make field stress measurements on structural components

Residual stresses vary with position in the component, so measurements are frequently made at numerous locations The spatial resolution of these measurements is defined by the diameter of the x-ray beam used The diameter is typically in the vicinity of 1 cm, but it can be as small as 30 m

Precision

• 5% relative or 5 MPa absolute, whichever is higher (in ideal laboratory conditions)

• Less precise information is obtained when portable x-ray equipment used for residual stress measurement of non-ideal structural components

Limitations

• Because XRD obtains information from the near-surface region of the sample, it only provides surface stress information and is not capable of measuring stresses in the interiors of components

Capabilities of Related Techniques

Neutron diffraction residual stress measurement is based on the same principles as XRD Because neutrons penetrate metals to far greater depths, it is possible to measure stresses in the interior or samples, rather than only surface stresses However, a neutron source is required, so such measurements cannot be made in the field

Characterization of Crystal Size and Defect Density from Peak Width and Shape

When Bragg's law was discussed earlier, it was noted that the angular range over which significant diffracted intensity is obtained depends on the number of adjacent planes from which diffracted beams are summed In the extreme case of only two adjacent planes, diffracted intensity would be maximum at the angles satisfying Bragg's law (where perfectly constructive interference occurs) However, it would vary continuously with diffraction angle, only being zero at the angles where perfectly destructive interference occurs, which would result in very broad diffraction peaks On the other hand, when the beams scattered by a semi-infinite number of adjacent planes are summed, constructive interference and significant diffracted intensity are only obtained at angles that exactly satisfy Bragg's law In this case, very narrow diffracted beams are obtained Intermediate between these extremes, the width of diffraction peaks increases with decreasing crystal size Peak broadening becomes significant as crystal size decreases below 0.5 m

Most cast or wrought metals have sufficiently large grain sizes to justify the assumption that summing occurs over a infinite number of adjacent planes, hence, narrow diffraction peaks are obtained Phases formed by low-temperature deposition processes and solid state transformations, however, frequently have much finer grains whose sizes can be estimated from the widths of their diffraction peaks (Fig 9)

semi-Fig 9 Effect of crystallite size on peak width Source: Ref 1

Crystal defects, such as dislocations and stacking faults, also interrupt the long-range periodicity of the crystal lattice, thus resulting in relaxation of the conditions for diffraction and broadening of diffraction peaks (Fig 10) Analysis of peak width and shape (the details of the intensity versus diffraction angle data) can be used to obtain information on the densities of such defects in the sample

Fig 10 Effect of dislocations introduced by cold working and removed by annealing on width of diffraction

peaks in brass Source: Ref 1

Peak width and shape measurements are typically made from the output of an x-ray diffractometer The results of such analyses are useful as semiquantitative indicators of crystallite size and defect density, but typically lack quantitative precision

Certain alloys exist as random solid solutions (atoms A and B randomly substituting for one another in identical lattice positions) at high temperature, but ordered compounds (atoms A and B arranged in specific nonrandom patterns) at lower temperature (Fig 11) Such ordering can give rise to additional diffracted beams, thus enabling ordering to be detected and characterized by XRD

Fig 11 Principles of diffraction from random and ordered solid solutions (a) Random solid solution: All planes

have equal numbers of A and B atoms, hence equal average scattering power, scattered beams from planes I and II are 180° out of phase and equal in amplitude, so net diffracted intensity is zero (b) Ordered compound: Adjacent planes are made up entirely of A and B atoms, so they have unequal scattering powers Scattered beams from planes I and II are 180° out of phase but unequal in amplitude, so net diffracted intensity is not zero (diffracted beam is obtained)

Because x-rays are scattered by their interactions with electrons, atoms of higher atomic number serve as more powerful scattering centers than those with lower atomic numbers Consider Fig 11, in which the filled circles represent A atoms

of low atomic number and low scattering power, whereas the open circles represent B atoms of high atomic number and higher scattering power

In a random solution (Fig 11a), successive planes I, II, III, etc will all have identical fractions of A and B atoms, so the amplitudes of the x-rays scattered from adjacent planes will be identical If, as shown in Fig 11(a), the beams scattered from adjacent planes are 180° out of phase with one another, perfect destructive interference will occur, and no diffracted beam will result

If ordering occurs so that successive planes have different fractions of A and B atoms, as shown in Fig 11(b), planes II and IV will have greater scattering power than planes I and III This increased scattering will result in different amplitudes for the beams scattered from adjacent planes Because their amplitudes are different, only partial destructive interference will occur between beams that are 180° out of phase with one another As a result, a diffracted beam will be observed The presence of extra "superlattice" lines in a diffraction pattern diffraction at angles where no diffraction occurs for the random solid solution is indicative of the solution becoming ordered (Fig 12) Studies of ordering are typically conducted using Debye-Scherrer cameras or diffractometers

Fig 12 Debye-Scherrer patterns for ordered and disordered Cu-25Au (at.%) (a) Ordered Cu3 Au compound obtained by slow cooling from 450 °C (840 °F); note extra "superlattice lines" not present in random disordered solid solution (b) Random solid solution obtained by quenching from 500 °C (930 °F) Source: Ref 4

Limitations

The intensities of these superlattice lines depends on the difference in atomic scattering power between the A and B atoms In cases where these atoms have greatly different atomic numbers, the amplitudes of the beams scattered from adjacent planes are markedly different, so interference is far from perfectly destructive and the superlattice lines are moderately intense In cases where the A and B atoms have nearly identical atomic numbers, however, the amplitudes of the beams scattered from adjacent planes are only slightly different So nearly perfectly destructive interference occurs, and the superlattice lines have such low intensities that they frequently cannot be detected

Capabilities of Related Techniques

Neutron diffraction can be used to detect and characterize ordering in cases of atoms of similar atomic number Neutron diffraction is based on the same principles as XRD, but scattering occurs based on nuclear interactions, rather that interactions with electrons As a result, neutron scattering power does not vary regularly with atomic number, and atoms with similar atomic number frequently have greatly different neutron scattering powers This provides for more intense neutron diffraction superlattice lines in ordered compounds involving atoms of similar atomic number

References cited in this section

1 R Jenkins and R Snyder, Introduction to X-Ray Powder Diffractometry, John Wiley, 1996

4 Taylor, X-Ray Metallography, John Wiley, 1961, p 444

Characterization of Preferred Orientations (or Textures)

As noted in the section "Identification of Compounds and Phases Using X-Ray Powder Diffraction," predictable and reproducible intensities are obtained for the diffracted beams corresponding to particular sets of planes in a given material, provided the sample consists of randomly oriented grains However, there are many causes of nonrandomness in grain orientation In bulk metals, preferred orientations are frequently caused by metal working operations, such as rolling, forging, or drawing Thin films deposited by methods, such as electroplating, plasma deposition, and chemical vapor deposition, also tend to grow in particular crystallographic directions The properties of materials exhibiting preferred orientations tend to be anisotropic For example, the forming behavior of sheet metal varies depending on the nature and degree of the preferred orientation produced by the previous rolling operations: the degree of working, the temperatures at which it was done, whether the sheet was unidirectionally rolled or cross rolled, etc XRD provides a means of characterizing such nonrandom orientations or textures

Instrumentation and Characterization

The simplest way to characterize nonrandom crystallographic orientation is to merely note the degree to which the diffracted intensities from different sets of planes parallel to the surface vary from what would be expected in an ideal sample containing no preferred orientation For example, a rolled plate in which the diffracted intensity from the {111} planes was 10 times that of a randomly oriented sample would be said to have a {111} texture, or a strong tendency to have the {111} planes aligned parallel to the surface

A more complete description of preferred orientation can be obtained by doing an x-ray diffractometer experiment in which the incident beam and the detector are set to measure diffraction from a preselected type of plane A specialized sample holder is used to rotate the sample through a wide range of orientations, and the diffracted intensity is measured as

a function of orientation relative to the prior rolling plane and direction The results are frequently presented in the form

of a topologic map on a hemispherical projection, termed a pole figure and shown in Fig 13 The "contour" lines denote the degree to which the plane of interest tends to be aligned in a particular orientation relative to the prior working axes Idealized orientations are often then associated with the preferred orientation

Fig 13 X-ray pole figure characterizing nonrandom distribution of {111} poles (plane normals) in sample from

rolled sheet Contours indicate pole densities of 1, 2, 3, 4, and 5 times those in a randomly oriented sample Numbers indicate local maxima Courtesy of Mike Eatough, Sandia National Laboratories

In recent years, the orientation distribution function (ODF) has been developed to more uniquely characterize the nature

of preferred orientations The ODF is geometrically equivalent to the combined information presented in pole figures corresponding to several different types of planes, but it is superior in that it provides a quantitative analytical description

of the probability of particular grain orientations

Determination of Single Crystal Orientations

The Laue Technique

The Laue technique employs an x-ray beam of continuously varying wavelength to determine the orientation of a single crystal sample of known crystal structure Referring to Fig 2, it can be seen that for a stationary single crystal sample in

which d-spacings and diffraction angles are fixed, the right hand side of Bragg's law has a single completely defined value

for each type of plane If an incident beam with a single x-ray wavelength is used, diffraction only occurs in the fortuitous case where this wavelength (or its multiple) happens to equal one of these values, making both sides of Bragg's law equal

In general, this is not the case, so typically no diffracted beams are obtained If the incident x-ray beam consists of a continuous range of wavelengths, however, diffraction can occur from each of the set of planes in the crystal (each set of planes "choosing" the wavelength that satisfies Bragg's law) The result is a set of diffracted beams whose arrangement is identical to what would result from a beam of light being reflected from the various types of plane in the crystal

Instrumentation

The most common experimental arrangement is the back-reflection Laue arrangements shown in Fig 14 The x-ray beam

is directed through a collimator onto the single crystal sample, and diffraction occurs from numerous crystal planes The sample is usually mounted on a goniometer that permits it to be rotated into the desired orientation based on the results of the Laue experiment Historically, the diffracted beams have been recorded on a flat piece of photographic film that is

developed following the experiment In recent years, CCD cameras have been replacing film, permitting electronic data collection and computer automated reduction of the diffraction information

Fig 14 Schematic showing back reflection Laue geometry

The symmetry of the resulting pattern is characteristic of the orientation of the crystal, as can be seen in Fig 15 Comparison of the angular relationships between different spots makes it possible to determine the Miller indices of the planes corresponding to each spot

Fig 15 Back reflection Laue photographs showing (a) low-index high symmetry orientation where the <001>

axis of the unit cell (in this case, cubic) is parallel to the beam (normal to the film) Note symmetry about 180° diffraction position at center of film (b) Higher index orientation (note lower symmetry) Courtesy of Mike Eatough, Sandia National Laboratories

Precision

• Routinely within 0.5 degrees

• Within 0.02 degrees under carefully controlled conditions

References

1 R Jenkins and R Snyder, Introduction to X-Ray Powder Diffractometry, John Wiley, 1996

2 C Barrett and T Massalski, Structure of Metals, McGraw-Hill, 1966

3 Materials Characterization, Vol 10, ASM Handbook, ASM International, 1986, p 335

4 Taylor, X-Ray Metallography, John Wiley, 1961, p 444

• Spatial resolution: Conventional light microscopes cannot resolve features smaller than 1 m

• Depth of field: Light microscopes cannot image rough surfaces samples must be flat in order to be in

focus

• Type of information provided: Light microscopes provide images and morphological information, but

they do not provide any direct chemical or crystallographic information about the microstructural features observed

During the past 50 years, however, several types of electron microscopy have been developed and refined to greatly extend our ability to resolve and characterize the morphologies of much smaller microstructural features, to image rough surfaces, and to obtain direct chemical and crystallographic information about microstructural features

This article reviews the three types of electron microscopies most commonly used in metallurgical studies: scanning electron microscopy, electron probe microanalysis, and transmission electron microscopy

Scanning Electron Microscopy (SEM)

• Imaging of rough surfaces

• Qualitative and semi-quantitative elemental analyses on microstructural features as small as 2 m

• Identifying crystalline compounds and determining crystallographic orientations of microstructural features as small as 1 m (recently developed capability not currently widely used, but likely to become so)

Typical Uses

• Characterizing fracture surface micro-appearance and determining the nature of the fracture process (dimple rupture, cleavage, fatigue, intergranular environmentally enhanced fracture, etc.)

• Quality assurance examination of microelectronic devices, interconnections, bonds, etc

• Detecting the onset of corrosion in small components and characterizing corrosion products

• Resolving fine microstructural features on polished and etched metallographic samples

• Performing qualitative and semi-quantitative elemental analyses on microstructural features, contaminant particles, etc

• Identifying microstructural phases and compounds by their crystal structures

• Characterizing preferred crystallographic orientations by analysis of orientations of individual grains

Spatial Resolution

• Secondary electron imaging of surface topography: 10 nm

• Backscattered electron imaging of atomic number contrast: 1 m

• X-ray characterization of elemental chemistry: 2 m using typical beam voltages of 20 kV (much better resolution, 100 nm, can be obtained using low voltage beams)

• Electron diffraction characterization of crystal structure and orientation: 1 m

Elemental Analysis Detection Threshold and Precision

• Threshold sensitivity for elemental analysis using EDS detector: 1%

• Precision of quantitative elemental analysis using EDS detector: 10% relative or 2% absolute, whichever is greater

Limitations

• Energy dispersive detectors used for chemical analysis have difficulty detecting and analyzing elements with atomic numbers less than 7 (nitrogen); older instruments with beryllium window detector cannot detect elements with atomic numbers lower than 11 (sodium)

Sample Requirements

• Sample size up to 5 cm can be accommodated by most SEMs, and SEMs equipped with large sample chambers can readily accommodate considerably larger samples, such as 15 and 20 cm silicon wafers from microelectronics production lines

• No preparation is typically required for clean metal samples

• Nonconductive samples or samples with marginally conductive surface regions must be coated with a thin layer of conductive material A thin gold-palladium layer is typically sputtered onto samples intended for imaging only, whereas a thin carbon layer is typically vacuum evaporated onto samples where x-ray microanalysis will be performed

y-axis electromagnetic beam scanning coils The raster rate can be varied by the operator one complete pass over the area

of interest can take as little as s (typically used for lower resolution screening of various areas on the surface), or as long as 20 s (typically used for higher resolution photographing of an area of interest) Several types of detectors are used

to monitor the various signals emitted from each spot on the sample as the beam impinges on it The outputs of these detectors are electronically processed and used to modulate the intensity of the spots on a cathode ray tube (CRT) whose scan is synchronized with that of the electron beam's raster on the sample surface The result is a television-type image of the portion of the sample surface being scanned by the beam Portions of the surface that produce strong response signals appear bright on the CRT, while portions that produce weak response signals appear dark

Fig 1 Schematic of a scanning electron microscope (a) Electron beam produced and focused to a fine spot on

sample surface Scanning coils enable the position of the beam to be rastered across a selected portion of the sample surface Signals produced by the sample at the point where the beam impinges include secondary electrons, backscattered electrons, and characteristic x-rays (b) Detected signals are collected, amplified, and used to modulate the intensity of a cathode ray tube, whose raster is synchronized with that of the beam

The images viewed on the CRT have historically been recorded photographically, but in recent years are increasingly being recorded electronically Such electronic recording facilitates electronic image enhancement, quantification of the sizes and shapes of features appearing on the images, electronic transmission of images to other locations, and electronic incorporation of images into reports

As can be seen from the above description, the SEM really is not a microscope in the classical sense it has no lenses that magnify the image The sole purpose of the magnetic lenses is to focus the beam to a very small spot on the sample surface The magnification of the image is defined by area on the sample surface over which the electron beam is rastered and the size of the CRT screen on which the image is displayed Magnification is increased simply by decreasing the area over which the beam is rastered, or decreased by increasing the area over which the beam is rastered

Several types of signals can typically be detected and used to generate images on the CRT The images corresponding to these different signals reveal different types of information The three primary types of signals and images, secondary electrons, backscattered electrons, and x-rays, are described in the following paragraphs

Beam-Sample Interactions. When the incident electron beam impinges on the surface, it penetrates a short distance into the sample, interacting with the atoms in the sample as it penetrates Typical penetration distances range from one to several micrometers depending on the atomic numbers of the elements in the sample (greater penetration depths for low atomic number elements, lesser depths for high atomic number elements) and the incident beam accelerating voltage (greater penetration for higher accelerating voltages) The beam spreads out as it penetrates, typically resulting in a pear-shaped interaction volume (Fig 2)

Fig 2 Monte Carlo simulations of the interaction volume of a 20 keV primary electron beam in an iron sample

(a) Electron trajectories (b) Sites of K-shell ionizations and production of characteristic x-rays Source: Ref 1

Two important types of interactions occur between the incident electrons and the sample's atoms, resulting in the three primary signals (Fig 3) Some of the incident electrons interact with the electrons associated with the atoms of the sample, "knocking them out" of the conduction band and other orbitals, and generating secondary electrons The atoms from which electrons have been removed are now in "excited states" and "relax" as electrons from higher energy levels fill the vacated sites Each of these relaxation events is accompanied by the release of energy equal to the difference in energies between the two atomic energy levels involved Transitions involving inner shell electrons often result in the generation of energy levels involved Transitions involving inner shell electrons often result in the generation of x-ray photons This is identical to the atomic process described in the section on x-ray fluorescence spectroscopy in the article

"Bulk Elemental Analysis." As in x-ray fluorescence spectroscopy, the energies of these x-rays can be compared to the known characteristic energies of each element, enabling the atoms in the sample to be chemically identified, as illustrated

in Fig 3 of that same article Each incident electron typically interacts with tens to hundreds of atoms before its energy is eventually expended Each time an incident electron interacts with an atom in this way, its path is deflected somewhat This accounts for the spreading of the beam as it enters the sample and the pear-shaped interaction volume, as illustrated

in Fig 2 of the article "Bulk Elemental Analysis." Other incident electrons interact with the much heavier nuclei of the atoms in the sample These electrons typically "bounce back," as would a ping pong ball striking a bowling ball For obvious reasons, these are termed backscattered electrons

Fig 3 Interaction of the primary electron beam with atoms in the sample resulting in backscattered primary

electrons, secondary electrons, and characteristic x-rays

Secondary Electron Imaging of Surface Topography. Secondary electron images provide information on the topography of the same a "picture" of the portion of the sample surface over which the beam is being rastered The secondary electrons generated in the sample have relatively low energies, on the order of a few electron volts (eV) As a result, only the secondary electrons produced close to the sample surface (within 10 nm) are able to escape from the sample Secondary electrons produced deeper in the interaction volume interact with other atoms, dissipate their energies, and are absorbed before reaching the surface (Fig 4) The secondary electrons emitted from the sample are attracted to the secondary electron detector by a positive bias of several hundred volts Because the secondary electrons have kinetic energies of only a few electron volts, their paths are easily influenced by this bias, and a high percentage of them enter the detector and are counted

Fig 4 Regions in the interaction volume from which various signals escape SE, secondary electrons; BSE

backscattered electrons

The number of secondary electrons exiting the sample is controlled mostly by the local geometry of the surface at the point where in incident beam impinges on it As can be seen in Fig 5, when the beam impinges on a rough sample at the top of a sharp peak, a great deal of the interaction volume is within 10 nm of a free surface, hence a very large number

of secondary electrons exit the sample and are collected by the detector The resulting intense signal results in a bright spot on the CRT Conversely, when the incident beam impinges at the bottom of a deep valley, very little of the interaction volume is within 10 nm of a free surface, hence a very few secondary electrons exit the sample, resulting in

a dark spot on the CRT For inclined surfaces, the number of escaping secondary electrons increases with increasing angle

of inclination (Fig 5)

Fig 5 Effect of local surface geometry on secondary electron signal strength Cross section of rough surface

illustrating that strongest secondary electron signals originate from tops of sharp peaks, strength of secondary electron signal decreases with increasing angle between the primary beam and the sample surface, and weakest secondary electron signals originate from deep holes

The net result is that, in secondary electron images, sharp peaks appear brightest, highly inclined edges appear somewhat less bright, portions of the surface perpendicular to the beam appear darker, and the bottoms of deep recesses appear darkest This is very similar to the pattern of contrast that results when inclined visible light impinges on a macroscopically rough surface Our brains are accustomed to "processing" images with this type of contrast, and correctly interpret secondary electron images as topography or pictures of the sample's surface

These principles of secondary electron contrast are apparent in the SEM photograph or a dimpled fracture surface, shown

in Fig 6 The surface consists of cup-shaped dimples, each corresponding to a microscopic failure event, and sharp ridges where adjacent failure events joined The secondary electron image reveals the ridges as bright, the inclined dimple walls

as less bright, and the perpendicular dimple bottoms are darker

Fig 6 Secondary electron image of dimples on ductile fracture surface Source: Ref 2

Because secondary electrons are collected from only the top 10 nm of the sample where very little beam spreading has occurred, each digital examination point on the sample surface can be quite small and still be distinct from neighboring examination points As a result, it is possible to resolve adjacent surface features with dimensions of 10 nm by secondary electron imaging or less under special conditions State of the art instruments with field emission electron guns have 1 nm secondary electron imaging resolution Furthermore, the primary requirement for a sharp image is that the incident beam be focused to sharp spot on each digital examination point at which it impinges on the surface Because the cone angle of the focused beam can be made quite small, it is possible to satisfy this requirement simultaneously for both peaks and valleys on relatively rough surfaces This provides outstanding depth of field, which is the ability to focus simultaneously on both the highs and lows of rough surfaces

In addition to imaging naturally rough surfaces, such as metal fractures, secondary electron imaging can also be used to examine the surfaces of polished and etched metallographic samples The fact that secondary electron imaging can resolve features 100 times smaller than can be resolved by light microscopy enables SEMs to use higher magnifications

to characterize fine microstructural features that cannot be resolved by light microscopy (Fig 7)

Fig 7 Secondary electron image of polished and etched sample of Fe-0.8%C showing details of pearlite (A and

B) growing into austenite (transformation interrupted by quenching) Source: Ref 3

Backscattered Electron Imaging and Atomic Number Contrast. Backscattered electron images, on the other hand, provide contrast based on differences in average atomic number of different portions of the sample Because backscattered electrons result from direct collision of light incident electrons with the heavy nuclei of atoms in the sample, it is not surprising that the strength of the backscattered electron signal increases with increasing nuclear mass, that is, with increasing atomic number Backscattered electrons exit the sample with kinetic energies similar to those for the incident electrons (thousands of electron volts), so their paths are essentially unaffected by the few hundred volt bias

of the secondary electron detector Backscattered electrons are typically collected by solid state annular detectors placed above the sample to maximize the number of electrons that can be collected in a line-of-sight fashion Backscattered electron images display portions of the sample surface with relatively high average atomic number as bright; portions of the sample surface with lower average atomic number appear darker (Fig 8)

Fig 8 Backscattered electron image showing atomic number contrast in as-cast Cu-Al-Mg alloy Brightest areas

represent phases containing the greatest concentration of high atomic number copper Darker areas represent phases of progressively lower average atomic number Courtesy of Joe Michael, Sandia National Laboratories

Because backscattered electrons have higher kinetic energies than secondary electrons, they can escape from far deeper in the interaction volume Because the beam diverges as it penetrates in the sample, backscattered electron image spatial resolution is not as good as that of secondary electron images Backscattered electron resolution is typically 1 m, similar to that of light microscopy This resolution can be improved to 100 nm by using low voltage beams Excellent depth of field is retained with backscattered electron imaging, for the same reason discussed for secondary electron imaging

X-Ray Detection and Elemental Microanalysis. X-rays provide information on which elements are present in small portions of the sample The atomic principles by which the characteristic x-rays are generated are identical to those discussed in the section on x-ray fluorescence spectroscopy in the article "Bulk Elemental Analysis," except that excitation is provided by the incident electron beam, rather than an incident x-ray beam In effect, then, the scanning electron microscope provides a mini-x-ray spectrometer with a very fine incident beam that can be used to probe the chemistries of very small operator-selected portions of the sample

Many scanning electron microscopes are equipped with an energy dispersive x-ray detector The operation and characteristics of EDS detectors are described in the section on x-ray fluorescence spectroscopy in the article "Bulk Elemental Analysis." This detector and the associated electronics provide a histogram of the x-ray energies emitted from the sample As with bulk x-ray spectroscopy, the characteristic x-ray energies observed tell which elements are present, and the relative intensities of the various characteristic x-ray peaks provide information on the relative concentrations of the elements present, as illustrated in Fig 3 of that same article

X-ray spectra can be collected either from an area on the surface defined by the beam's x-y raster, or from an individual

point by stopping the raster and adjusting the scan coils to move the beam to the desired location on the sample surface In either case, x-rays are typically collected for tens to hundreds of seconds, and the x-ray histogram displayed on a second CRT, rather than the CRT used for imaging The results of most analyses are displayed as secondary electron images with x-ray spectra corresponding to particular features of interest (Fig 9)

Fig 9 Backscattered electron image of 82%Au-15.5%Ni-1.75%V-0.75%Mo active braze alloy joined to

Mo-Al 2 O 3 cermet Accompanying x-ray spectrum obtained from area 1 shows the phase forming at the interface to

be rich in nickel and vanadium Courtesy of Bonnie McKenzie, Sandia National Laboratories

If desired, a single x-ray energy can be selected corresponding to an element of interest, the instrument returned to the scanning mode, and an image generated in which the brightness is modulated by the concentration of this element at each point on the raster The resulting x-ray maps can provide exceptionally useful information on how various elements are distributed in the sample, particularly when taken in conjunction with secondary electron or backscattered electron images However, because energy dispersive x-ray detectors are characterized by a moderate level of background noise, the x-ray maps they generate are not as high in quality as ones generated when the x-rays are analyzed using wavelength dispersive crystal spectrometers (See Fig 4-6 in the section "X-Ray Fluorescence Spectroscopy" of the article "Bulk Elemental Analysis" for discussion of the strengths and weaknesses of these different types of x-ray detectors.) Scanning electron microscopes are occasionally equipped with a wavelength dispersive detector to facilitate x-ray mapping, but more often such mapping is done using an electron probe microanalyzer, as will be described in the next section

Characteristic ray escape the sample from the entire interaction volume (Fig 4) As a result, the spatial resolution for ray microanalysis is on the order of several micrometers It is a common misconception that SEMs can perform chemical analyses with the same resolution as secondary electron imaging While surface features as small as 10 nm can be

x-"seen" by secondary electron imaging, chemical analyses of such features really provide elemental information on not only the feature itself, but the entire several micrometer volume surrounding it

As with bulk x-ray fluorescence spectroscopy, only elements with atomic numbers of 7 or greater can be readily detected and analyzed Elements with lower atomic numbers produce very few x-rays, and the x-rays produced have very low energies and are easily absorbed Older instruments equipped with beryllium window detectors are limited to elements with atomic numbers of 11 or higher because the low energy x-rays produced by lower atomic number elements are mostly absorbed in the detector window More modern ultrathin window detectors enable detection of elements down

to atomic number 5 Lower atomic number elements must be detected by other means, as will be described in the section on Auger electron microscopy

Diffracted Beams and Crystallographic Microanalysis. Recent developments have also made it possible to collect and analyze crystallographic information from features observed in the SEM The divergent beam of characteristic x-rays generated as the incident electron beam penetrates the sample can also be diffracted from the portion of the sample

in the immediate vicinity of the beam interaction zone The resulting diffraction pattern, termed a Kossel pattern, is particularly useful for measuring interplanar spacings with high precision The precise interplanar spacing information can, in turn, be used to measure residual stresses in individual grains The divergent beam of backscattered electrons also has a wave character and can similarly diffract from the planes in the surrounding grain The resulting electron diffraction pattern, termed a Kikuchi pattern, is analogous to the x-ray Kossel pattern, but is made up of straight lines that are easier

to index These Kikuchi patterns can be used to identify crystalline phases (similar to x-ray powder diffraction but based

on a different diffraction geometry), as well as to determine orientation distribution functions in a grain-by-grain fashion These Kossel and Kikuchi patterns can be readily solved and interpreted by computer methods An example of a Kikuchi pattern and its computer assisted solution are shown in Figure 10 Most SEMs are not yet equipped to perform these types

of crystallographic analyses, but it is likely that these powerful capabilities will become more commonly available

Fig 10 Kikuchi pattern identification of sigma phase in stainless steel following exposure to elevated

temperature (a) Backscattered electron image Arrow indicates the dark sigma phase identified by the Kikuchi patterns (b) Backscattered electron Kikuchi pattern (c) Computer solution of Kikuchi pattern Courtesy of Joe Michael, Sandia National Laboratories

Voltage Contrast and Analysis of Microelectronic Devices. Additional types of specialized imaging can also be done with scanning electron microscopes Several types are particularly useful in examining and analyzing active microelectronic devices For example, because secondary electrons escape from the sample with kinetic energies of only a few electron volts, the strength of the secondary electron signal will vary substantially with the voltages presenting various parts of an operating electrical device For the simplest case of a DC device in which potential differences of a few volts exist, more secondary electrons will be emitted from negatively biased portions, and fewer from positively biased portions In the secondary electron image, then, the negatively biased portions will appear bright and the positively biased portions will appear dark In the more complex case of microelectronic circuit operating at high frequency, strobe-like "pictures" of the circuit's operation can be obtained by rapid "blanking" of the incident beam synchronously with the device, such that each "picture point" on the secondary electron image corresponds to the same "phase" in the circuit's operation A series of such "strobe images" can be taken corresponding to successive phases in the circuit's operation, showing the potentials of different conduction lines and circuit elements at each phase, which provides a powerful tool for troubleshooting microelectronic circuits

Capabilities of Related Techniques:

Electron probe microanalysis is very similar to SEM, but usually equipped with several crystal spectrometers for wavelength dispersive x-ray analysis This provides greatly improved capabilities for quantitative microanalysis, x-ray mapping, and characterizing elemental profiles in the vicinities of interfaces Flat polished samples are required in order

to take full advantage of quantification capabilities

Transmission electron microscopy provides markedly better spatial resolution for imaging and x-ray microanalysis, and provides for crystallographic analysis by electron diffraction Crystallographic analysis methods are more highly developed than those for SEM Sample preparation is tedious, and only very small portions of the sample can be viewed

Scanning Auger Microscopy can perform microanalyses on low atomic number elements down to lithium (atomic number 3) Analyses originate from very near surface region (first few atomic layers), so sample surfaces must be atomically clean or results will be representative of surface contaminants rather than the underlying sample

References cited in this section

1 J Goldstein et al., Scanning Electron Microscopy and Microanalysis, 2nd ed., Plenum, 1992, p 85

2 B Gabriel, SEM: A User's Manual for Materials Science, American Society for Metals, 1985, p 110

3 Materials Characterization, Vol 10, ASM Handbook, ASM International, 1986

Electron Probe Microanalysis (EPMA)

Capabilities and Typical Uses

The electron probe microanalyzer (frequently termed the electron microprobe) is essentially a scanning electron microscope that has been optimized to perform high quality elemental microanalyses Historically, the two instruments were developed separately and for different purposes, but as they evolved they became increasingly similar While most SEMs are primarily imaging instruments to which rapid elemental microanalysis capabilities have been added, electron microprobes are primarily quantitative microanalyzers that are capable of imaging the areas being analyzed Electron microprobes are used primarily for the following:

• Quantitative microanalyses of microstructural features

• Quantitative elemental profiling of compositional gradients (similar to Fig 22b, but with 1 m spatial resolution)

• X-ray mapping to show how elements of interest are concentrated or depleted in different micro-areas or microstructural features (Fig 11)

Fig 11 Electron microprobe elemental map showing distributions of elements in stranded wire soldered to a

terminal pin (a) Backscattered electron image (b-h) Elemental maps showing locations and concentrations of iron, nickel, copper, silver, tin, gold, and lead, respectively Source: Ref 3

Operating Principles and Instrumentation

The electron microprobe and scanning electron microscope operate on identical principles The key differences are that electron microprobes are typically equipped with several crystal spectrometers to facilitate wavelength dispersive x-ray analysis Qualitative analysis is typically performed using an energy dispersive x-ray analysis Qualitative analysis is typically performed using an energy dispersive x-ray detector, but subsequent quantitative analyses are done using the wavelength dispersive crystal spectrometers (WDS) As described in the section on x-ray fluorescence spectroscopy in the article "Bulk Elemental Analysis" and illustrated in Fig 4-6, wavelength dispersive x-ray analysis has several advantages over energy dispersive analysis:

• Much better signal-to-noise ratio, which facilitates qualitative analysis and the generation of much higher quality x-ray maps

• Better separation of x-rays with similar energies (or wavelengths), which enables elements that are difficult to distinguish with EDS detectors, such as molybdenum and sulfur, to be unequivocally identified and quantified

• Better detection of low atomic number elements that produce small numbers of low energy x-rays Electron microprobes can identify and semi-quantify elements with atomic numbers in the 4 to 7 range, which are more difficult to detect and analyze with EDS systems

Other key factors to be considered include:

• Electron microprobes have high and very stable beam currents to maximize x-ray counting statistics and minimize variations in x-ray generation rate associated with instrumental fluctuations

• Electron microprobes have precisely controlled automated specimen stages to facilitate large numbers of composition measurements to be made in an automated computer controlled fashion

• Electron microprobes are equipped with sophisticated computer hardware and software to facilitate data reduction and quantitative plotting and mapping of results

Spatial Resolution

• Backscattered electron imaging of atomic number contrast: 1 m

• X-ray characterization of elemental chemistry: 2 m, sampling depth 2 m

Elemental Analysis Detection Threshold and Precision

• Threshold sensitivity for elemental analysis using WDS detector: 0.01%

• Precision of quantitative elemental analysis using WDS detector: 0.5% relative or 0.02% absolute, whichever is greater

• Nonconductive samples or samples with marginally conductive surface regions must be coated with a thin layer of conductive material, typically carbon

Capabilities of Related Techniques

X-Ray fluorescence spectroscopy (XRF) provides bulk elemental analysis X-ray fluorescence spectroscopy instruments equipped with fine beam and x-y scanning capabilities provide elemental mapping on much larger samples but with much poorer spatial resolution

Transmission electron microscopy (TEM) provides markedly better spatial resolution for x-ray microanalysis but

at the expense of poorer counting statistics uncertainty TEM sample preparation is tedious, and only very small portions

of the sample can be viewed

Scanning Auger microscopy (SAM) can perform microanalyses on low atomic number elements down to lithium (atomic number 3), but analyses are less quantitative Analyses originate from very near surface region (first few atomic layers), so sample surfaces must be atomically clean or results will be representative of surface contaminants rather than the underlying sample

Reference cited in this section

3 Materials Characterization, Vol 10, ASM Handbook, ASM International, 1986

Transmission Electron Microscopy (TEM)

Terminology

Transmission electron microcopy (TEM) has been used since the 1950s to obtain very high resolution images of microstructures As TEMs were enhanced to include features such as digitally scanned point beams and energy dispersive x-ray detectors for chemical microanalysis, alternative names, such as scanning transmission electron microscopy (STEM) and analytical electron microscopy (AEM), were coined and became commonly used This section incorporates all of these under the general title transmission electron microscopy

• Qualitative and semi-qualitative elemental analyses with spatial resolution approaching 10 nm, roughly

100 times better than SEMs or electron microprobes

• Identifying crystalline compounds and determining crystallographic orientations of microstructural features as small as 30 nm

Typical Uses

The combination of capabilities described above make the TEM a very powerful tool for high resolution microstructural characterization Typical uses include:

• Characterizing dislocation arrangements resulting from deformation and annealing

• Identifying and characterizing the morphologies, elemental compositions, and crystallographic aspects

of very fine microstructural features, e.g., strengthening precipitates produced during age hardening

• Determining orientation relationships between parent and product phases, matrix and twins, etc

• Characterizing compositional gradients over very short distances, e.g., diffusion profiles associated with phase transformations

• Determining phase diagrams by characterization of microstructural phase equilibria

Spatial resolution

• Imaging: 0.2 nm

• X-ray characterization of elemental chemistry: 10 nm

• Electron diffraction characterization of crystal structure and orientation: 30 nm

Elemental Analysis Detection Threshold and Precision

• Threshold sensitivity: 1%

• Precision of quantitative elemental analyses: 10% relative or 2% absolute, whichever is greater

Limitations

• Sample preparation is tedious, and only small portions of the sample can be analyzed

• Elemental chemical analysis cannot be readily done for elements with atomic numbers less than 7, and counting statistics are not as good as with EPMA

• Only very small portions of the sample can be analyzed, so it is crucial to ensure that the microstructure characterized is representative of the bulk material

Operating Principles

Instrumentation. A simplified schematic of a TEM is shown in Fig 12 The top portion of the column is similar to

that of an SEM Electrons are produced and are accelerated down the column by a voltage differential in the electron gun typically in the range of 100,000 to 400,000 V) The column must be kept under vacuum while the microscope is operating As the beam passes down the microscope column, it is focused by variable strength electromagnetic condenser lenses These condenser lenses can either focus the beam to a fine spot on the sample or flood a much larger portion of the sample with a parallel beam of electrons

Fig 12 Schematic of transmission electron microscope, shown operating in the conventional parallel beam

mode The beam can also be focused to a small spot and rastered over the sample Courtesy of Tom Headley, Sandia National Laboratories

Sample Preparation. The sample typically consists of a 3 mm diameter disk of material that has been specially prepared so that a portion of it is thin enough to permit the electron beam to penetrate completely through it The maximum permissible thickness varies with the elements making up the sample (high atomic number elements are less transmissive) and the beam accelerating voltage (higher accelerating voltages enhance beam penetration), but it is typically in the range of one hundred to several hundred nanometers Samples are thinned by a variety of methods including mechanical cutting and grinding (used in the preliminary steps of sample preparation), electrolytic polishing (commonly used for final thinning of metals), and ion milling (used with both metals and insulating materials) It is crucial that any damaged layer introduced during preliminary mechanical preparation be fully removed during subsequent electropolishing or ion milling Typically these preparation steps are done in a way that produces an hourglass cross section in the disk, as shown in Figure 13 Final thinning is continued until a hole first forms near center of the disk, then the electropolishing or ion milling processes are immediately halted The thin tapered portions of material adjacent to the hole are frequently thin enough to be electron transparent If electropolishing or ion milling are continued too long, the thin electron transparent sections adjacent to the hole will be removed and the remaining material will likely be too thick

to be penetrated by the electron beam

Fig 13 Steps in TEM specimen preparations (a) A disk with an 3 mm diameter and 0.1 to 0.3 mm thick is

cut from the bulk sample (b) The disc is thinned preferentially at its center (typically by fine mechanical grinding, chemical, or electrochemical methods), producing an hourglass profile (c) Final thinning (typically by electrochemical or ion beam methods) is continued until a hole forms The very thin material around the hole is usually thin enough to be penetrated by the TEM electron beam

As the preceding description implies, TEM sample preparation is a tedious and time consuming process Even when the sample preparation process is successful, only a very small portion of the sample is electron transparent and amenable to characterization Because the results of TEM analyses represent information obtained from very small amounts of material, it is exceedingly important to ensure that the material being characterized is representative of the bulk material Hence, TEM should usually be done in conjunction with other types of analysis, such as metallography, x-ray diffraction, and scanning electron microscopy, which readily characterize much larger amounts of material, albeit with lower resolution Transmission electron microscopy is an exceptionally powerful method for characterizing microstructural details, but it is important to balance this detailed look at the "leaves" with a good overview of the "forest."

Beam-Sample Interactions. Once a sample with adequate electron transparency has been inserted into the microscope, a wealth of crystallographic, morphological, and chemical information can be obtained from it As the incident electron beam penetrates a crystalline sample a variety of diffraction and excitation events occur These provide:

• Identification of phases and compounds based on interplanar spacing fingerprints obtained from electron diffraction patterns (equivalent to x-ray powder diffraction, but on very small preselected microstructural features)

• Determination of crystallographic orientations from single-crystal electron diffraction patterns (equivalent to x-ray Laue orientation determination, but on very small grains, precipitates, or other microstructural features)

• Imaging of microstructural features (similar to metallography, but with 1000 times better resolution, and based on a diffraction contrast, rather than reflected light contrast)

• Elemental analysis (qualitative and quantitative) based on characteristic x-ray emission (equivalent to elemental analysis in the SEM or EPMA, but with 10 to 100 times better spatial resolution)

Electron Diffraction. Because the electron beam has a wave character, it can be diffracted by the planes in the crystal

in cases where Bragg's law is satisfied, essentially as was described in the previous article on "X-Ray Diffraction for Bulk Structural Analysis" and illustrated in Fig 2 in that article If such diffraction occurs from a large number of fine randomly oriented crystals in the sample, this results in a series of axisymmetric cones, each cone corresponding to a specific interplanar spacing and the associated diffraction angle that satisfies Bragg's law These cones intersect the viewing screen as circular rings, and can be recorded either on the underlying film or CCD detector as rings The radius of each ring can be measured and used to calculate the diffraction angle and corresponding interplanar spacing The set of interplanar spacings can then be used to identify the crystalline phases or compound(s) making up the sample, exactly as was described in the article "X-Ray Diffraction for Bulk Structural Analysis." An example of this is shown in Figure 14

Fig 14 Electron diffraction ring pattern obtained from numerous grains in a polycrystalline aluminum sample

Starting with the innermost ring, the rings correspond to {111}, {200}, {220}, {311}, and {222} planes Source: Ref 3

Alternatively, if the electron beam impinges on a single grain or crystal, an electron diffraction pattern consisting of a series of spots is obtained This pattern is similar to a single crystal x-ray Laue pattern The symmetry and angular relationships between the spots enable the crystallographic orientation of the grain to be determined Figure 15 shows an example of orientation determination from a single crystal electron diffraction pattern In cases of related orientations, such as epitaxial nucleation of one phase on another, or the formation of oriented precipitates with a parent phase, the orientation relationships between the phases can be determined from these electron diffraction patterns

Fig 15 Electron diffraction spot pattern from a single grain in a polycrystalline aluminum sample The spots are

indexed in the accompanying computer-generated drawing Source: Ref 3

Imaging of Microstructural Features. Electron diffraction also provides the primary source of image contrast in metals and other crystalline materials Consider a relatively broad incident beam that impinges uniformly across several grains in a thin sample (Fig 16) Electron beams in the range of 100,000 to 400,000 V have much shorter wavelengths than x-rays, which makes typical diffraction angles quite small As a result, nearly all grains diffract to some extent Some grains are oriented in ways that particular planes satisfy Bragg's law precisely These grains diffract strongly Other grains are oriented in ways that none of their planes satisfy Bragg's law precisely, but some planes are within a small fraction of

a degree, hence they diffract to a limited extent

Fig 16 Development of TEM image contrast due to differential diffraction Grains that are poorly oriented for

diffraction transmit a higher percentage of the beam and appear bright in the image; those ideally oriented for diffraction transmit a lower percentage of the beam and appear dark in the image

The degree to which diffraction occurs varies the extent to which the incident beam is directly transmitted through the sample from grain to grain Grains least oriented for diffraction directly transmit much of the incident beam and diffract only a small amount of it Other grains are ideally oriented for diffraction and directly transmit much less of the incident beam and diffract much of it The directly transmitted beam, then, it not uniform in intensity across its diameter but carries intensity variations corresponding to the grains through which it passed and their differing level of diffraction When the directly transmitted beam is imaged, magnified, and projected onto the viewing screen, this provides light and dark contrast in the image Grains that transmitted a high percentage of the incident beam appear bright, and those that diffracted more of the incident beam appear dark Figure 17 shows an example of this type of grain contrast

Fig 17 Transmission electron microscopy grain orientation contrast in a sample of fine-grained polycrystalline

silicon Courtesy of Tom Headley, Sandia National Laboratories

In addition to contrast arising from grain-to-grain orientation differences, any crystalline defects that result in local variations in diffraction also produce light and dark contrast in the image As a result, defects such as dislocations and stacking faults can be imaged by the TEM Figure 18 shows an example of dislocations in aluminum imaged by TEM

Fig 18 Transmission electron microscopy imaging of dislocations in aluminum Source: Ref 3

In addition to the bright field images obtained from the directly transmitted beam, dark field images can also be obtained from any of the diffracted beams These images are particularly useful in cases where two or more superimposed diffraction patterns are obtained corresponding to adjacent features in the sample Dark field imaging makes it possible to determine which diffraction spots correspond to each feature, thus facilitating the determination of crystallographic characteristics such as orientation relationships and habit planes An example of a dark field image obtained from multiple defraction spots is provided in Fig 19

Fig 19 Transmission electron microscopy dark field image of same area as in Fig 17 Dark field image was

obtained by imaging numerous diffraction spots, so most areas that strongly diffracted and appeared dark in Fig 17 now appear bright Areas that diffracted weakly and appeared bright in Fig 17 now appear dark Courtesy of Tom Headley, Sandia National Laboratories

Direct imaging of particular crystal planes can be accomplished using a combination of the directly transmitted beam and one or more diffracted beams This enables high-resolution characterization of individual lattice planes and defects, as illustrated in Fig 20

Fig 20 High-resolution TEM lattice image of zinc oxide formed by combining transmitted and (002) diffracted

beams The interplanar spacing is 0.26 nm A grain boundary, inclined to the incident beam, is visible in the upper portion of the micrograph Source: Ref 3

Excitation and characteristic x-ray production also occurs as the incident electron beam interacts with the atoms in the sample As in the SEM and EPMA, this provides the equivalent of a x-ray fluorescence spectrometer that can probe the chemistries of very small operator-selected portions of the sample The energies and intensities of these characteristic x-rays are typically detected and analyzed using an EDS system, enabling qualitative identification of the elements present

in the sample and quantitative determination of their relative concentrations, respectively It the TEM, however, the thinness of the sample significantly reduces the size of the interaction volume, as shown in Fig 21 This occurrence limits the degree to which electron beam spreading occurs in the sample, and provides the ability to perform chemical analyses with significantly better spatial resolution than in the SEM or EPMA This resolution permits chemical characterization of features as small as 10 nm and determination of chemical gradients over submicrometer distances, as shown in Fig 22 Because the interaction volume is much smaller than in bulk samples, however, much smaller numbers of x-ray photons are produced This results in poorer counting statistics, so quantitative analyses obtained by TEM typically have larger degrees of uncertainty than those obtained by EPMA

Fig 21 X-ray generation volume in thin TEM samples Note that the thin sample results in reduced spreading of

the incident electron beam, thus reducing the diameter of the x-ray generation region and providing better spatial resolution for elemental microanalysis than is possible with typical thick SEM or EPMA samples

Fig 22 Copper concentration profile measured by TEM adjacent to the grain boundary in an aged Al-4.7%Cu

alloy (a) Transmission electron microscopy image showing large CuAl2 precipitates along boundary at left and right sides Dark spots near the center correspond to probe positions during x-ray microanalysis (b) Composition profile across the grain boundary Source: Ref 3

The exceptional utility of TEM is based on its ability to obtain imaging, chemistry, and crystallographic information in combination with one another, and with very high spatial resolution (on very small microstructural features) Figure 23 provides a typical example of how these capabilities can be combined to understand microstructural phenomena in great detail However, these strengths are seriously offset by the difficulty of specimen preparation and the fact that not only very small amounts of material are examined Scanning electron microscopy and EPMA require much simpler sample preparation and can readily locate and characterize specific areas of interest in larger samples, including failed engineering components Until recently, SEM and EPMA were capable only of combined imaging and chemical characterization but not crystallographic characterization As new methods for SEM crystallographic characterization are developed, however, these instruments will become increasingly powerful Transmission electron microscopy will remain exceptionally useful for analyses that require very high resolution, but it is likely that SEM and EPMA will be used increasingly for a broader range of application that do not require submicron spatial resolution

Fig 23 Combined TEM imaging, electron diffraction identification, and elemental microanalysis of P, , and

intermetallic phases of alloy 22 weld metal Source: Ref 3

Capabilities of Related Techniques

X-ray diffraction (XRD) provides faster and more precise crystallographic information, but averaged over bulk sample rather than corresponding to individual microstructural features

Scanning Electron Microscopy (SEM). Sample preparation is much simpler Scanning electron microscopy can characterize much larger samples and selected areas of interest Imaging resolution is not as good as TEM Spatial resolution for chemical analysis and crystallographic analysis is not as good as TEM Scanning electron microscopy techniques for crystallographic analysis are not as mature as those for TEM

Electron Probe Microanalysis (EPMA). Sample preparation is much simpler Electron probe microanalysis can characterize much larger samples and selected areas of interest Spatial resolution for chemical analysis is not as good as TEM, but counting statistics are much better, providing higher quality quantitative analyses

Reference cited in this section

3 Materials Characterization, Vol 10, ASM Handbook, ASM International, 1986

References

1 J Goldstein et al., Scanning Electron Microscopy and Microanalysis, 2nd ed., Plenum, 1992, p 85

2 B Gabriel, SEM: A User's Manual for Materials Science, American Society for Metals, 1985, p 110

3 Materials Characterization, Vol 10, ASM Handbook, ASM International, 1986

Scanning Auger Microprobe (SAM)

Capabilities

The scanning Auger microprobe is basically a scanning electron microscope (SEM) with two additional features:

• An Auger electron detector replaces an x-ray detector The Auger detector is used to measure the energies of Auger electrons emitted from the sample These characteristic energies enable identification

of the elements present in the first few atomic layers of the surface The concentrations of each element present can also be determined from the number of electrons detected at each characteristic energy All elements except hydrogen and helium can be identified and analyzed in this way

• An in situ ion milling capability provides for gradual removal of surface layers, thereby permitting depth profiling of elemental compositions within about 1 m of the surface

Typical Uses

These capabilities make the SAM well suited for the following types of applications:

• Identification and mapping of light elements (atomic numbers 3 to 9) that are difficult to detect using SEM or electron probe microanalysis (EPMA)

• Elemental characterization of surface contaminants

• Depth profiling of elemental compositions within 1 m of the surface (this is particularly widely used

in microelectronics applications)

Spatial Resolution

• Secondary electron imaging of surface topography: 10 nm (same as SEM)

• Auger electron characterization of elemental chemistry: 10 to 20 nm; sampling depth: 1 nm

Elemental Analysis Detection Threshold and Precision

• Threshold sensitivity: 0.5%

• Precision of quantitative analyses: 10% relative or 0.5% absolute, whichever is greater

Limitations

• Cannot detect hydrogen or helium

• Quantitative analyses are typically lower in quality than those of EPMA

Fig 1 Schematic of a scanning Auger microprobe

Physical Basis. Auger electrons are emitted as the excited atoms relax In a sense, they are the compliments of the characteristic x-rays that are used for chemical characterization in x-ray fluorescence (XRF), SEM, EPMA, and transmission electron microscopy (TEM) When atoms become excited by electrons being ejected from their inner shells, electrons from higher energy shells fill these vacated sites This process always results in the release of energy equal to the energy difference between the donor and acceptor levels For more information, see the section "X-Ray Fluorescence Spectroscopy" in the article "Bulk Elemental Analysis" in this Handbook However, emission of characteristic x-rays is only one of the mechanisms by which this energy can be released Another common mechanism is by the release of an Auger electron

An Auger electron is an electron from one of the outer shells that is ejected from the atom with kinetic energy equal to the energy released by the relaxation event minus the energy required to remove the Auger electron from its orbit (Fig 2) Because both energies associated with the relaxation events and the binding energies of the outer shell electrons provide characteristic "fingerprints" for each element, so do their differences, the energies of Auger electrons Hence, the energies

of Auger electrons can also be detected and used to identify which elements are in the portion of the sample being excited

by the incident electron beam These characteristic Auger electrons typically have energies of tens to thousands of electron volts

Fig 2 Comparison of production of x-rays and Auger electrons Source: Ref 1

The tendency for excited atoms to relax by Auger electron production versus x-ray photon emission increases with decreasing atomic number Elements with atomic numbers less than 7 produce few characteristic x-rays but many Auger electrons (except for hydrogen and helium) As a result, SAM is commonly used for microstructural detection and quantification of such elements Higher atomic number elements, however, produce more x-rays, so these elements are typically detected and quantified using SEM or EPMA Although when analysis of the first few atomic layers is desired, SAM provides elemental analyses corresponding to this very near surface region

While Auger electrons are generated throughout the beam-sample interaction volume, most of these dissipate some or all

of their characteristic energies by interacting with the electrons belonging to other atoms in the sample The only Auger electrons that escape the sample with their original characteristic energies are those generated within a few atom layers of the sample's surface If the energies of all emitted electrons are detected and analyzed, then a graph similar to Fig 3 is obtained The lowest energy range is dominated by secondary electrons, the highest energy range is dominated by backscattered electrons, and the mid-energy range is dominated by Auger electrons, nearly all of which have had their characteristic energies reduced by interactions with the sample But if Fig 3 is examined closely, small signals can be found at particular energies These represent the characteristic energies of the "undisturbed" Auger electrons that were generated by atoms at the surface or within a few atomic distances below the surface

Fig 3 Electron energy distribution from silver sample Differentiated signal most clearly reveals the peak

corresponding to Auger electrons that were produced very near the surface and exited the sample prior to interacting with other atoms Source: Ref 2

Electron Collection and Energy Measurement. The energies of the emitted electrons are usually measured using a cylindrical "mirror" that has a variable negative potential applied to it, as shown in Fig 1 As electrons enter the inlet aperture and pass though the analyzer chamber, the negative bias on the wall of the chamber repels them and causes them

to travel in curved paths The curvature of this path varies inversely with the kinetic energy of each electron; the paths of electrons with low kinetic energy are more easily deflected than those paths of electrons with high kinetic energy This information provides a means of measuring the energy distribution of the electrons emitted from the sample An electron detector is mounted near the exit aperture of the cylindrical mirror, and the negative bias applied to the mirror is gradually increased The numbers of electrons entering the detector is counted as a function of mirror bias This information enables the energy distribution of the electrons to be plotted

The portion of the signal corresponding to the "undisturbed" Auger electrons is very small compared with the signal resulting from backscattered and Auger electrons whose energies have been reduced by interactions within the sample

This situation is typically overcome by differentiating the signal and plotting dN/dE versus E, as shown in Fig 3 Because

the Auger electrons typically originate in the outer electron shells, their energies are somewhat affected by bonding between atoms These small energy shifts, which can frequently be discriminated by the energy analyzer, provide the ability to determine some information about the elements to which the atoms of interest are bonded

Scanning Auger microprobe results are often presented as secondary electron images with accompanying Auger electron spectra identifying the elements present in particular features of interest Low atomic number elements that cannot be detected by SEM and EPMA are readily detected in Auger spectra Figure 4 provides an example of the use of Auger electrons to detect low atomic number elements with high spatial resolution

Fig 4 Scanning Auger identification of elements, including some of low atomic number, present in several

phases in a copper-beryllium alloy (a) Secondary electron image showing inclusions (b-e) Auger spectra obtained from the indicated microstructural features (b) The long rod-shaped precipitate (point 1) is a beryllium sulfide (c) The small round precipitate (point 2) is a titanium carbide (d) The small irregular precipitate (point 3) is also a titanium carbide (e) The large blocky angular precipitate (point 4) is a beryllium carbide Source: Ref 2

Alternatively, the detector can be set to the energy associated with a particular element or compound of interest and the electron beam rastered over the surface, resulting in a map indicating the areas of high concentration of this material (Fig 5)