MATERIALS CHARACTERIZATION Introduction to Microscopic and Spectroscopic Methods Yang Leng Hong Kong University of Science and Technology John. MATERIALS CHARACTERIZATION: INTRODUCTION TO MICROSCOPIC AND SPECTROSCOPIC METHODS BY YANG LENG PDF. Spend your time also for. Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Author(s). Prof. Yang Leng.

Materials Characterization Introduction To Microscopic And Spectroscopic Methods Pdf

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Download Citation on ResearchGate | Materials characterization: Introduction to microscopic and spectroscopic methods: Second edition | Now in its second. and spectroscopic methods, Materials characterization: introduction to microscopic by Y Leng Second edition. Singapore ; Hoboken, NJ: Wiley. Materials Characterization: Introduction to Microscopic and Spectroscopic Methods Now in its second edition, this continues to serve as an ideal textbook for.

Describe the connection issue. SearchWorks Catalog Stanford Libraries. Materials characterization [electronic resource]: Responsibility Yang Leng. Edition 2nd ed. Imprint Weinheim: Wiley-VCH, Physical description 1 online resource p. Online Available online. Wiley Online Library Full view. More options. Find it at other libraries via WorldCat Limited preview. After each polishing step, the surface should be cleaned in running water with cotton or tissue, followed by alcohol or hot air drying.

Alcohol provides fast drying of surfaces without staining. Electrolytic polishing is an alternative method of polishing metallic materials. A metal specimen serves as the anode in an electrochemical cell containing an appropriate electrolyte. The surface is smoothed and brightened by the anodic reaction in an electrochemical cell when the correct combination of bath temperature, voltage, current density and time are used.

The advantage of this method over conventional polishing is that there is no chance of plastic deformation during the polishing surface. Plastic deformation in the surface layer of specimens can be generated by compression and shear forces arising from conventional polishing methods. Plastic deformation from polishing may generate artifacts in microstructures of materials.

The aforementioned methods of specimen preparation, except microtomy, are regarded as an important part of metallography. For example, ceramic materials are brittle.

To avoid fracture they should be mounted and sectioned with a slow-speed diamond saw. Ceramic materials also should be carefully sectioned with a low-speed diamond saw. Composite materials may exhibit significant differences in mechanical properties between the reinforcement and matrix. These specimens require light pressure and copious cooling during grinding and polishing. Polymeric materials can be examined by either reflected or transmitted light microscopes.

For reflected light microscopy, specimen preparation is similar to that of metals. For transmitted light microscopy, a thin-section is required. Both surfaces of the thin- section should be ground and polished. This double-sided grinding and polishing can be done by mounting the specimen in epoxy, preparing one surface, mounting that polished surface on a glass slide, and finally grinding and polishing the other side.

Etching is a controlled corrosion process by electrolytic action between surface areas with differences in electrochemical potential.

Electrolytic activity results from local phys- ical or chemical heterogeneities which render some microstructural features anodic and others cathodic under specific etching conditions. During etching, chemicals etchants selectively dissolve areas of the specimen surface because of the differences in the electrochemical po- tential by electrolytic action between surface areas that exhibit differences.

Callister Jr. An Introduction, 7th ed.

Contribution of the National Institute of Standards and Technology. Also, grains are etched at different rates because of differences in grain orientation certain crystallographic planes are more subject to etching , resulting in crystal faceting.

Thus, the grains show different brightness. Etching a specimen that has a multi-phase microstructure will result in selective dissolution of the phases. Many chemical etchants are mixtures of acids with a solvent such as water. Acids ox- idize atoms of a specimen surface and change them to cations. Electrons released from atoms of specimen surfaces are combined with hydrogen to form hydrogen gas.

For more noble materials, etchants must contain oxidizers such as nitric acid, chromic acid, iron chloride and peroxides. Oxidizers release oxygen, which accepts electrons from atoms of the specimen surface. Table 3. Etching can simply be performed by immersion or swabbing. For immersion etching, the specimen is immersed in a suitable etchant solution for several seconds to several minutes, and then rinsed with running water.

The specimen should be gently agitated to eliminate adherent air bubbles during immersion. For swab etching, the polished surface of a specimen is wiped with a soft cotton swab saturated with etchant.

Light Microscopy 25 material such as platinum as the cathode in an electrochemical cell filled with electrolyte. The electrochemical reaction on the anode produces selective etching on the specimen surface. Since electrochemical etching is a chemical reaction, besides choosing a suitable etchant and electrolyte, temperature and time are the key parameters to avoiding under-etching and over- etching of specimens.

We may also use the method of tint etching to produce color contrast in microstructure. Tint etchants, usually acidic, are able to deposit a thin 40— nm film such as an oxide or sulfide on specimen surfaces.

Tint etching require a very high-quality polished surface for best results. Tint etching can also be done by heat tinting, a process by which a specimen is heated to a relatively low temperature in air.

As it warms, the polished surface is oxidized. The oxidation rate varies with the phase and chemical composition of the specimen. Thus, differences in the thickness of oxidation films on surfaces generate variations in color. Interference colors are obtained once the film reaches a certain thickness.

Effectiveness of heat tinting depends on the material of specimens: The light wave changes in either amplitude or phase when it interacts with an object as illustrated in Figure 1. The eye can only appreciate amplitude and wavelength differences in light waves, not their phase difference.

The most commonly used examination modes, bright-field and dark-field imaging, are based on contrast due to differences in wave amplitudes. The wave phase differences have to be converted to amplitude differences through special optical arrangements such as in the examination modes of phase contrast, polarized light and Nomarski contrast.

This section introduces commonly used modes of light microscopy for materials characterization. Dark-field imag- ing is also widely used to obtain an image with higher contrast than in bright-field.

Shaded areas indicate where the light is blocked.

In bright-field imaging, the specimen is evenly illuminated by a light source. Dark-field imaging requires that the specimen is illuminated by oblique light rays. There is a central stop in the light path to block the central portion of light rays from illuminating the specimen directly.

Thus, the angle of the light rays illuminating the specimen is so large that light from the specimen cannot enter the objective lens unless it are scattered by microscopic objects. The dark field in reflected illumination is also realized using a central stop in the light path Figure 1. The light rays in a ring shape will be further reflected in order to illuminate a specimen surface with an oblique angle.

Microscopic features such as grain boundaries and second phase particles appear self-luminous in the dark field image as shown in Figure 1. In the technique, a phase change due to light diffraction by an object is converted to an amplitude change. In addition to grain boundaries and oxide particles, annealing twins are revealed in the dark-field image. Constructive interference occurs when combining two same-wavelength waves that do not have a phase difference between them.

This optical arrangement creates completely destructive inter- ference when light is diffracted by an object in the specimen. A condenser annulus, an opaque black plate with a transparent ring, is placed in the front focal plane of the condenser lens. Thus, the specimen is illuminated by light beams emanating from a ring. The light beam that passes through a specimen without diffraction by an object the straight-through light beam will pass the ring of a phase plate placed at the back focal plane of the objective lens.

The phase plate is plate of glass with an etched ring of reduced thickness. The ring with Figure 1. Reproduced with permission from W. Light Microscopy 29 Figure 1.

Shading marks the paths of diffracted light. When the straight-through beam and diffracted beam recombine at the image plane, com- pletely destructive interference occurs. Thus, we expect a dark image of the object in phase contrast microscopy. Variation in phase retardation across the specimen produces variations in contrast. In reflected light microscopy, phase contrast can also be created with a condenser annulus and phase plate similar to those in transmitted light microscopy. Swayer, and D.

Optical anisotropy arises when materials transmit or reflect light with different velocities in different directions. Most materials exhibiting optical anisotropy have a non-cubic crystal structure. Light, as an electromagnetic wave, vibrates in all directions perpendicular to the direction of propagation.

If light waves pass through a polarizing filter, called a polarizer, the transmitted wave will vibrate in a single plane as illustrated in Figure 1. Such light is referred to as plane polarized light. When polarized light is transmitted or reflected by anisotropic material, the polarized light vibrates in a different plane from the incident plane.

Such polarization changes generate the contrast associated with anisotropic materials. For a transparent crystal, the optical anisotropy is called double refraction, or birefringence, because refractive indices are different in two perpendicular directions of the crystal.

When a polarized light ray hits a birefringent crystal, the light ray is split into two polarized light waves ordinary wave and extraordinary wave vibrating in two planes perpendicular to each other. Because there are two refractive indices, the two split light rays travel at different velocities, and thus exhibit phase difference. The resultant polarized light is called elliptically polarized light because the projection of resultant vectors in a plane is elliptical.

Two plane-polarized light waves with a phase difference are generated by the materials. RI, refractive index. If the two polarized-light waves have another phase difference, the projection of resultant ray is a spiraling ellipse.

Differences in the resultant light can be detected by another polarizing filter called an ana- lyzer. Both polarizer and analyzer can only allow plane polarized light to be transmitted. The analyzer has a different orientation of polarization plane with respect to that of the polarizer. Anisotropic materials are readily identified by exposure to polarized light because their images can be observed with the polarizer and analyzer in the crossed position.

Such situa- tions are illustrated in Figure 1.

Polarized light can enhance the contrast of anisotropic materials, particularly when they are difficult to etch. It can also determine optical axis, demonstrate pleochroism showing different colors in different directions and examine the thickness of anisotropic coatings from its cross- sections. Polarized light revealed fine spherulite structures caused by crystallization.

An isotropic material either with cubic crystal structure or amorphous cannot change the plane orientation of polarizing light. When a polarized light wave leaves the material and passes through the analyzer in a crossed position, the light will be extinguished. The polarizer and analyzer are in a crossed position. Reproduced with per- mission from D. Reproduced from G.

Gendron, General Electric Co. Reproduced with permission from J. Scheirs, Compositional and Failure Analysis of Polymers: For example, if an isotropic transparent crystal is elastically deformed, it becomes optically anisotropic. A thick oxide film on isotropic metals also makes them sensitive to the direction of polarized light because of double reflection from surface irregularities in the film.

The images that DIC produces are deceptively three-dimensional with apparent shadows and a relief-like appearance. Nomarski microscopy also uses polarized light with the polarizer and the analyzer arranged as in the polarized light mode. In addition, double quartz prisms Wollaston prisms or DIC prisms are used to split polarized light and generate a phase difference. The working principles of Nomarski microscopy can be illustrated using the light path in a transmitted light microscope as illustrated in Figure 1.

The first DIC prism is placed behind the polarizer and in front of the condenser lens, and the second DIC prism is placed behind the objective lens and in front of the analyzer. The two beams created by the prism interfere coherently in the image plane and produce two slightly displaced images differing in phase, thus producing height contrast. The first DIC prism splits polarized light beam from the polarizer into two parallel beams traveling along different physical paths.

If a specimen does not generate a path difference between the two parallel beams as shown by two left- side beam pairs in Figure 1. Thus, the analyzer in the crossed position with a polarizer will block light transmission.

The first differential interference con- trast DIC prism not shown generates two parallel polarized beams illuminating the specimen.

The second DIC prism recombines two beams.

Materials Characterization : Introduction to Microscopic and Spectroscopic Methods

Elliptically polarized light is generated by the second DIC prism when phase difference between the two beams is induced by an object: The analyzer cannot block such light and a bright area will be visible. The optical arrangement of Nomarski microscopy in a reflected light microscope is similar to that of a transmitted light microscope, except that there is only one DIC prism serving both functions of splitting the incident beam and recombining reflected beams as illustrated in Figure 1.

Contrast enhancements are achieved in the Nomarski micrographs. The Nomarski image appears three-dimensional and illuminated by a low-angle light source. Reproduced with permission of Gonde Kiessler. Light Microscopy 37 the surface, particularly in transmitted light microscopy. The reason is that the phase differences generated in Nomarski microscopy may result from differences either in the optical path or in refractive index.

Fluores- cence is an optical phenomenon; it occurs when an object emits light of a given wavelength when excited by incident light. The incident light must have sufficient energy, that is, a shorter wavelength than that light emitting from the object, to excite fluorescence. While only a small number of materials exhibit this capability, certain types of materials can be stained with fluorescent dyes fluorchromes.

The fluorchromes can selectively dye certain constituents in materials, called fluorescent labeling. Fluorescent labeling is widely used for polymeric and biological samples.

Fluorescence microscopy can be performed by either transmitted or reflected illumination epi-illumination. Reflected light is more commonly used because it entails less loss of ex- cited fluorescence than transmitted light.

The dotted line indicates the path of excitation light, and the solid line indicates the path of fluorescent light. Reproduced with permission of Jingshen Wu.

A high pressure mercury or xenon light can be used for generating high intensity, short wavelength light. The light source should be ultravio- let, violet or blue, depending on the types of fluorchromes used in the specimen. A fluorescence filter set, arranged in a cube as shown in Figure 1. The exciter filter selectively transmits a band of short wavelengths for exciting a specific fluorchrome, while blocking other wavelengths.

The dichroic mirror reflects short wavelength light to objective lens and specimen, and also transmits returning fluorescent light toward the barrier filter. The barrier filter transmits excited fluorescent light only, by blocking other short wavelength light. Fluorescence labeling reveals the dispersed polymer particles in an asphalt matrix, which cannot be seen in the bright-field image. Image formation in a confocal microscope is significantly different from a con- ventional light microscope.

Compared with a conventional compound microscope, a modern confocal microscope has two distinctive features in its structure: Thus, the confocal microscope is often referred to as the confocal laser scan- ning microscope CLSM. The laser light provides a high-intensity beam to generate image signals from individual microscopic spots in the specimen. The scanning device moves the beam in a rectangular area of specimen to construct a 3D image on a computer.

The laser beam is focused as an intense spot on a certain focal plane of the specimen by a condenser lens, which is also serves as an objective lens to collect the reflected beam. A pinhole aperture is placed at a confocal plane in front of the light detector. The reflected beam from the focal plane in a specimen becomes a focused point at the confocal plane. The pinhole aperture blocks the reflected light from the out-of-focal plane from entering the detector.

Only the light signals Figure 1. Reproduced with permission from M.

Since the pinhole aperture can block a large amount of reflected light, high-intensity laser illumination is necessary to ensure that sufficient signals are received by the detector. The detector is commonly a photomultiplier tube PMT that converts light signals to electric signals for image processing in a computer.

To acquire an image of the focal plane, the plane has to be scanned in its two lateral directions x—y directions. To acquire a 3D image of a specimen, the plane images at different vertical positions should also be recorded. A scanning device moves the focal laser spot in the x—y directions on the plane in a regular pattern called a raster. After finishing one scanning plane, the focal spot is moved in the vertical direction to scan a next parallel plane.

Specimen scanning was used in early confocal microscopes. The specimen moves with respect to the focal spot and the optical arrangement is kept stationary as shown in Figure 1. The beam is always located at the optical axis in the microscope so that optical aberration is minimized. The main drawback of this method is the low scanning speed.

Laser scanning is realized by two scanning mirrors rotating along mutually perpendicular axes as shown in Figure 1. The scan mirror can move the focal spot in the specimen by sensitively changing the reflecting angle of mirror.

Changing the vertical position of the spot is still achieved by moving the specimen in the laser scanning method. The resolution of the confocal microscope is mainly determined by the size of focal spot of the laser beam. High spatial resolution about 0. Most confocal microscopes are the fluorescence type. The microscopic features under the specimen surface are effectively revealed when they are labeled with fluorescent dyes.

Therefore, the major use of confocal microscopy is confocal fluorescence microscopy in biology.

A three- dimensional 3D image is obtained by reconstructing a deck of plane images. The optical section sequence is from left to right and top to bottom. The bottom right image is obtained by 3D reconstruc- tion. The scale bar is 1 mm. Reproduced with permission from A. Clarke and C. A biological specimen, a Spathiphyllum pollen grain, was fluorescently labeled with acridine orange. In total, 80 sections of the pollen grain were imaged for 3D reconstruction.

The ver- tical distance between sections is 1. Although its major applications are in biology, confocal microscopy can also be used for examining the surface topography and internal structure of semi-transparent materials. Fig- ure 1. The particulates were fluorescently labeled and their locations in the polymer foam are revealed against the polymer foam surfaces.

Light Microscopy 43 Figure 1. The specimen is low density polyethylene LDPE containing fluores- cently labeled silica particles. The particle size and distribution in the polymer matrix can be clearly revealed by 3D confocal microscopy. Thus, confocal microscopy provides us a new dimension in light microscopy for materials characterization, even though its applications in materials science are not as broad as in biology.

References [1] Bradbury, S. Questions 1. A light ray passing through the center of a lens is not deviated; 2. A Light ray parallel with optic axis will pass through the rear focal point; and 3.

A ray passing through the front focal point will be refracted in a direction parallel to the axis. Sketch the light paths from object to image in a single lens system in following situations. The refractive index of vacuum is 1, and that of air can be treated as 1. Assume blue light is used in the microscope. The wavelength of electrons is 0. To avoid plastic deformation in the surface layer, what are the maximum compression forces that should be used for polishing the samples of annealed Al alloy and plain carbon steel, respectively?

If normal compression force cannot cause plastic deformation, what kind of loading on the samples more likely causes plastic deformation? What are the dif- ferences in their image quality? Diffraction methods can identify chemical compounds from their crystalline struc- ture, not from their compositions of chemical elements. It means that the different compounds or phases that have the same composition can be identified.

Diffraction methods include X-ray diffraction, electron diffraction and neutron diffraction. X-ray diffraction by crystals was dis- covered in , and since then it has been the most extensively studied and used technique for materials characterization. This chapter introduces X-ray diffraction methods. The theoretical background of diffraction discussed in this chapter is also applied to other types of diffrac- tion methods.

X-ray diffraction methods can be classified into two types: The spectroscopic technique known as the X-ray powder diffractometry, or sim- ply X-ray diffractometry, is the most widely used diffraction method and the main technique discussed in this chapter. Photographic techniques are not widely used as diffractometry in modern laboratories. One reason is that spectroscopic methods can replace most photographic methods. However, photographic methods are used to determine unknown crystal structures.

These methods will not be discussed in this chapter because they require extensive knowledge of crystallography. X-ray energy is characterized either by wavelength or photon energy. X-rays are produced by high-speed electrons accelerated by a high-voltage field colliding with a metal target.

Rapid deceleration of electrons on the target enables the kinetic energy of electrons to be converted to the energy of X-ray radiation. X-ray radiation from the anode is guided by the windows of the tube to produce an X-ray beam for diffraction.

To generate X-rays, we need a device called the X-ray tube. Figure 2. The high voltage maintained across these electrodes rapidly draws the electrons to the anode target. X-rays are produced at the point of impact on the target surface and radiated in all directions.

There are windows to guide X-rays out of the tube. Extensive cooling is necessary for the X-ray tube because most of the kinetic energy of electrons is converted into heat; less than one percent is transformed into X-rays.

These intensity maxima are the characteristic X-rays. X-ray diffraction methods commonly require a source with single-wavelength monochro- matic X-ray radiation. The monochromatic radiation must come from the characteristic X-rays that are generated by filtering out other radiations from the spectrum. The physical principles of characteristic X-ray generation are schematically illustrated in Figure 2.

When an incident electron has sufficient energy to excite an electron in the inner shell of an atom to a higher energy state, the vacancy left in the inner shell will be filled by an electron in an outer shell. As the electron falls to the inner shell, energy will be released by emitting an X-ray with a specific wavelength or photons with specific energy.

The probability of an L shell electron filling the K shell vacancy is much higher than that of an M shell electron. This phenomenon results from the subshell structure of the L shell as indicated by L1 and L2 and L3. For example, wavelengths generated by a copper target are approximately the following.

Table 2. Gen- erally, materials exhibit various abilities to absorb X-rays. The X-ray inten- sity I passing through an absorption layer with thickness x is expressed by the following equation.

It is independent of physical state of solid or liquid. The mass absorption coefficient generally decreases with decreasing wavelength of X-ray radiation.

For example, Figure 2. A jump-up point in the curve is called the absorption edge of the mass absorption coefficient. Reproduced with permission from R. Jenkins and R. The feature of absorption edge can be used for X-ray radiation filtering. The X-ray filtering mechanism is illustrated in Figure 2. X-ray diffraction methods are based on the phenomenon of wave interferences as introduced in Section 1. Two light waves with the same wavelength and traveling in the same direction can either reinforce or cancel each other, depending on their phase difference.

X-ray beams incident on a crystalline solid will be diffracted by the crystallographic planes as illustrated in Figure 2. Two in-phase incident waves, beam 1 and beam 2, are deflected by two crystal planes A and B. The deflected waves will not be in phase except when the following relationship is satisfied. Equation 2. Knowing the spacings of crystallographic planes by diffraction methods, we can determine the crystal structure of materials.

For example, the plane spacing of cubic crystal relates to the lattice parameter a by the following equation. Combining Equations 2. This should not be difficult for low-index planes of cubic systems. Reciprocal Lattice A crystallographic plane hkl is represented as a light spot of constructive interference when the Bragg conditions Equation 2.

Such diffraction spots of various crystallographic planes in a crystal form a three-dimensional array that is the reciprocal lattice of crystal. The reciprocal lattice is particularly useful for understanding a diffraction pattern of crystalline solids. A reciprocal lattice is in an imaginary reciprocal space that relates to the corresponding crystal lattice in real space. A direction in the crystal lattice is defined by a vector ruvw with unit vectors a, b and c in real space.

The indices of lattice points are those of the crystallographic plane which the points represent. X-ray Diffraction Methods 53 [] Diffraction planes Beam Diffraction pattern — — —— — — Figure 2.

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The reciprocal lat- tice plane is composed of diffraction spots from crystal planes hk0. The zone axis [] is perpendicular to the reciprocal lattice plane. The [] directions in real space are not perpendicular to the planes if [] are not perpendicular to [] and []; and r Crystal planes belonging to one crystal zone a group of crystallographic planes of which normal directions are perpendicular to one direction called the zone axis direction form one reciprocal lattice plane. The zone axis direction is perpendicular to that reciprocal lattice plane.

The reciprocal lattice plane is composed of the diffraction spots of crystallographic planes belonging to the [] zone. The conditions can also be graphically expressed by the Ewald sphere method using the concept of the reciprocal lattice. The center of the Ewald sphere is located at a crystal to be examined. The incident beam is represented by a line that passes through a crystal at the sphere center and targets the origin of the reciprocal lattice located on the surface of the sphere CO.

The diffraction beam is represented by line connect the sphere center and a lattice point of reciprocal lattice CB. The Bragg conditions are satisfied when a lattice point touches the Ewald sphere surface. The Bragg conditions for plane are satisfied when its reciprocal lattice point touches the surface of the Ewald sphere. This equivalence allows us to detect diffraction from crystallographic planes when the cor- responding reciprocal lattice points touch the Ewald sphere surface.

Formation of diffraction patterns from a single crystal can be well illustrated by the Ewald sphere as shown in Figure 2. Thus, the surface of the Ewald sphere is flat compared with the unit vectors of the reciprocal lattice for crystals. The relatively flat surface of the Ewald sphere touches a number of reciprocal lattice points, and these points form a diffraction pattern on the screen of a TEM as shown in the lower part of Figure 2.

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The Ewald sphere also predicts a ring type diffraction pattern in a polycrystalline material, which is considered as an aggregate of the crystals with all possible orientations in three- dimensional space. The short wavelength of electrons makes the Ewald sphere flat. Thus, the array of reciprocal lattice points in a reciprocal plane touches the sphere surface and generates a diffraction pattern on the TEM screen. The outer ring may be visible when the Ewald sphere surface touches the reciprocal plane above the original plane.

Rotation of a reciprocal lattice in all direc- tions reveals all possible crystallographic planes satisfying the Bragg conditions. The polycrystalline diffraction patterns shown at the right-hand side of Figure 2.

The Debye ring recorded by the Hull—Debye—Scherrer method results from randomly oriented crystals in the powder specimen, in which reciprocal lattice points of hkl touch the Ewald sphere surface in various directions to form individual rings.

It is equivalent to rotating a reciprocal lattice along an incident beam axis. Satisfying such conditions does not guarantee that we can detect or see diffraction from crystallographic planes because there is an issue of diffraction intensity.

Diffraction intensity may vary among planes even though the Bragg conditions are satisfied. This section does not extensively discuss diffraction intensity, but only introduces important factors affecting the intensity of the X-ray diffraction.

X-ray diffraction by a crystal arises from X-ray scattering by individual atoms in the crystal. The diffraction intensity relies on collective scattering by all the atoms in the crystal. In an atom, the X-ray is scattered by electrons, not nuclei of atom. An electron scatters the incident X-ray beam to all directions in space.

The X-ray intensity of electron scattering can be calculated by the following equation. The last term in the equation shows the angular effect on intensity, called the polarization factor.

The incident X-ray is unpolarized, but the scattering process polarizes it. The total scattering intensity of an atom at a certain scattering angle, however, is less than the simple sum of intensities of all electrons in the atom. There is destructive interference between electrons due to their location differences around a nucleus, as illustrated in Figure 2.

The intensity from a Cu atom does not equal 29 times that of a single electron in Equation 2. The atomic scattering factor f is used to quantify the scattering intensity of an atom. Structure Extinction The most important aspect of intensity calculations is the structure extinction. This term refers to interference between scattering atoms in a unit cell of a crystal. If there is more than one atom in a unit cell for example, a face-centered cubic lattice has four atoms in a unit cell , intensity from certain crystallographic planes can become extinct due to interference between atoms on different planes.

When the Bragg conditions are satisfied for plane diffraction, and thus, the path difference ABC equals one wavelength, diffraction from the plane of the base-centered crystal Figure 2. This means that no diffraction from the plane in a body-centered crystal can be detected. Note that diffraction of plane in a body- centered crystal can be detected at another angle that it makes DEF equal to one wavelength.

The structure extinction of intensity can be calculated by the structure factor F. Suppose that there are N atoms per unit cell, and the location of atom n is known as un , vn , wn and its atomic structure factor is fn.

The structure factor for hkl plane Fhkl can be calculated. We can calculate the diffraction intensity of and using Equation 2. Practically, we do not have to calculate the structure extinction using Equation 2.

Their structure extinction rules are given in Table 2. From the lowest Miller indices, the planes are given as following. For a unit cell with more than one type of atom, the calcuation based on Equation 2. We need to know the exact values of f for each type of atom in order to calculate F. Often, reduction of diffraction intensity for certain planes, but not total extinction, is seen in crystals containing mulitple chemical elements.

The XRD instrument is called an X-ray diffractometer. In the diffractometer, an X-ray beam of a single wavelength is used to examine polycrystalline specimens.

By continuously changing the incident angle of the X-ray beam, a spectrum of diffraction intensity versus the angle between incident and diffraction beam is recorded. Diffractometry enables us to identify the crystal structure and quality by analyzing then comparing the spectrum with a database containing over 60, diffraction spectra of known crystalline substances. The X-ray radiation generated by an X-ray tube passes through special slits which collimate the X-ray beam. These Soller slits are commonly used in the diffractometer.

They are made from a set of closely spaced thin metal plates parallel to the figure plane of Figure 2. A divergent X-ray beam passing through the slits strikes the specimen. The specimen is usually in the form of a flat plate that is supported by specimen table not shown in Figure 2.

X-rays are diffracted by the specimen and form a convergent beam at receiving slits before they enter a detector. Skip to Main Content. Materials Characterization: Yang Leng. First published: Print ISBN: About this book Now in its second edition, this continues to serve as an ideal textbook for introductory courses on materials characterization, based on the author's experience in teaching advanced undergraduate and postgraduate university students.

The new edition retains the successful didactical concept of introductions at the beginning of chapters, exercise questions and an online solution manual. The first part covers commonly used methods for microstructure analysis, including light microscopy, X-ray diffraction, transmission and scanning electron microscopy, as well as scanning probe microscopy. The second part of the book is concerned with techniques for chemical analysis and introduces X-ray energy dispersive spectroscopy, fluorescence X-ray spectroscopy and such popular surface analysis techniques as photoelectron and secondary ion mass spectroscopy.

This section concludes with the two most important vibrational spectroscopies infra-red and Raman and the increasingly important thermal analysis.Constructive interference occurs when combining two same-wavelength waves that do not have a phase difference between them.

The first part covers commonly used methods for microstructure analysis, including light microscopy, X-ray diffraction, transmission and scanning electron microscopy, as well as scanning probe microscopy. The analyzer cannot block such light and a bright area will be visible. Diffraction intensity may vary among planes even though the Bragg conditions are satisfied.

Includes bibliographical references and index.