Microstructural characterization of materials pdf free download

Valence electrons may be shared, not only with a nearest neighbour atom, but quite generally, throughout the solid. That is, the molecular orbitals of the electrons may not be localized to a specific pair of atoms. Electrons which are free to move throughout the solid are said to occupy a conduction band, and to be free electrons. The chemical bonding in such a solid is termed metallic bonding, and is characterized by a balance between two opposing forces: the coulombic attraction between the free electrons and the array of positively charged, metallic cations, and the repulsive forces between the closed shells of these cations.

The properties typical of the metallic bond are associated with the mobility of the free electrons especially the high thermal and electrical conductivity, and the optical reflectivity , and with the nondirectionality of this bond for example, mechanical plasticity or ductility.

In some cases, only small numbers of electrons may be present in the conduction band of a solid, either as a result of thermal excitation or due to the presence of impurities. Such materials are termed semiconductors, and they play a key role in the manufacture of electronic devices for the electronics industry.

If electrons are thermally excited to occupy a conduction band, then they leave behind vacant holes, which may also be mobile. Semiconductors in which the negatively charged electrons are the dominant electrical current carriers are termed n-type, while those in which the positively charged holes are responsible for the electronic properties are termed p-type.

If certain impurities are present in very low concentrations, then the electrons may not be free to move throughout the solid, and cannot confer electrical conductivity, but they will nevertheless occupy localized states. Many cation impurities in ceramics give rise to localized states that are easily excited and strongly absorb visible light.

They are then said to form colour centres. In precious and semi-precious jewels small quantities of cation impurities are dissolved in the single crystal jewel stone and impart the characteristic colour tones, for example, chromium in ruby. Such cation additions are also of major importance in the ceramics industry, and the effects may be either deleterious discoloration or advantageous a variety of attractive enamels and glazes, Figure 1.

Irradiation of transparent, The Concept of Microstructure 29 Figure 1. These colour centres may also nucleate localized crystallization. The illustration shows a glass jar from the time of the Roman Empire. Reproduced with permission of the Corning Museum of Glass. See colour plate section nonconducting solids creates large concentrations of point defects in the material. Such radiation damage is also often a cause of colour centres.

In addition to the three types of chemical bonding discussed above, many of the properties of engineering solids are determined by secondary, or van der Waals bonding, that is associated with molecular polarization forces. In its weakest form, the polarization force arises from the polarizability of an electron orbital. Rare gas atoms will liquefy and solidify at cryogenic temperatures as a consequence of the small reduction in potential energy achieved by polarization of an otherwise symmetrical electron orbital.

The ductility of the polymer, as well as its softening point and glass transition temperature, are determined by a combination of the molecular weight of the 30 Microstructural Characterization of Materials polymer chains and their polarizability.

This weak bonding is quite sufficient to ensure that engineering components manufactured from polymers are mechanically stable, and, under suitable circumstances, these high molecular weight polymers may partially crystallize. Stronger polarization forces exist when the molecular species has a lower symmetry and possesses a permanent dipole moment. A good example is carbon dioxide CO2 but similar molecular groupings are also often present in high performance engineering polymers.

Organic tissues are largely constructed from giant polar molecules with properties dictated by a combination of the molecular configuration and the position of the polar groups within the molecule. The strongest polarization forces are associated with a dipole moment due to hydrogen, namely the hydrogen bond. Hydrogen in its ionized form is a proton, with no electrons to screen the nucleus.

The ionic radius of hydrogen is therefore the smallest possible, and asymmetric molecular groupings which contain hydrogen can have very high dipole moments. These groups raise both the tensile strength and the softening point of the polymer. Single phase polycrystalline materials are made up of many small crystals or grains.

Each grain has identical atomic packing to that of its neighbours, although the neighbouring grains are not in the same relative crystal orientation. In polyphase materials all the grains of each individual phase have the same atomic packing, but this packing generally differs from that of the other phases present in the material.

In thermodynamic equilibrium, the grains of each phase also have a unique and fixed composition that depends on the temperature and composition of the material, and can usually be determined from the appropriate phase diagram. In general, the solid phases in engineering materials may be either crystalline or amorphous. Amorphous phases may form by several quite distinct routes: rapid cooling from the liquid phase, condensation from the gaseous phase, or as the result of a chemical reaction.

A good example of amorphous phases produced by chemical reaction are the highly protective oxide films formed on aluminium alloy and stainless steel components by surface reactions in air at room temperature. An analysis of the The Concept of Microstructure 31 angles between crystal facets permitted an exact description of the symmetry elements of a crystal, and led to speculation that crystal symmetry was a property of the bulk material. This was finally confirmed with the discovery, at the beginning of the twentieth century, that small, single crystals would strongly diffract X-rays at very specific, fixed angles, to give a sharp diffraction pattern that was characteristic of any crystal of the same material when it was oriented in the same relation to the incident X-ray beam, irrespective of the crystal size and shape.

The interpretation of these sharp X-ray diffraction maxima in terms of a completely ordered and regular atomic array of the chemical constituents of the crystal followed almost immediately, being pioneered by the father and son team of Lawrence and William Bragg. The concept of the crystal lattice was an integral part of this interpretation.

The atoms in a crystal were centred at discrete, essentially fixed distances from one another, and these interatomic separations constituted an array of lattice vectors that could be defined in terms of an elementary unit of volume, the unit cell for the crystal, that displayed all the symmetry elements characteristic of the bulk crystal.

This section introduces basic crystallography, and describes how a crystalline structure is interpreted and how crystallographic data can be retrieved from the literature. To understand the structure of crystals, it is convenient initially to ignore the positions of the atoms, and just concentrate on the periodicity, using a threedimensional periodic scaffold within which the atoms can be positioned. Such a scaffold is termed a crystal lattice, and is defined as a set of periodic points in space.

A single lattice cell the unit cell is a parallelepiped, and the unit cells can be packed periodically by integer displacements of the unit cell parameters. The unit cell parameters are the three coordinate lengths a, b, c determined by placing the origin of the coordinate system at a lattice point, and the three angles a, b, g subtended by the lattice cell axes Figure 1.

The various unit cells are generated from the different values of a, b, c and a, b, g. These crystal systems are, in order of increasing crystal symmetry: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic.

These seven crystal systems are each defined using primitive unit cells, in which each primitive cell only contains a single lattice point placed at the origin of the unit cell. However, more complicated point lattice symmetries are possible, each requiring that every lattice point should have identical surroundings. These permutations were first analysed by the French crystallographer Bravais in , who described the possible 14 point lattices the Bravais lattices , which are shown in Figure 1.

In real crystals each individual lattice point actually represents either a group of atoms or a single atom, and it is these atoms that are packed into the crystal. Various degrees of symmetry are possible in this periodic packing of the atoms and atom groups. For example, if a crystal is built of individual atoms located only at the lattice points Figure 1. The Concept of Microstructure 33 of a unit cell, then it will have the highest possible symmetry within that particular crystal system.

This symmetry will then be retained if there are symmetrical groups of atoms associated with each lattice point. However, the atomic groups around a lattice point might also pack with a lower symmetry, reducing the symmetry of the crystal, so that it belongs to a different symmetry group within the same crystal class. Combining the symmetries of the atom groups associated with a lattice point with that of the Bravais lattices leads to the definition of space groups, which provide criteria for filling the Bravais point lattices with atoms and groups of atoms in a periodic array.

It has been found that there are a total of different periodic space groups, and that the structure of a crystal can always be described by one or more of these space groups. This has been found to be the most convenient way to visualize any complex crystal structure. Let us examine the use of space groups to define a crystal structure using a simple example. Assume we wish to know the positions of all the atoms in a copper Cu crystal.

First we need a literature source which contains the crystallographic data. The principle data listed in the handbook for Cu appear in the format shown in Table 1. Following the name of the phase, a structure type is given. This is the name of a real material that serves as an example for this particular crystallographic structure, and in this example copper is its own structure type. Next the Pearson symbol and space group are listed, which refer to the type of lattice cell and the symmetry of the structure.

Here, the Pearson symbol, cF4, means a cubic c face-centred lattice F with four atoms per unit cell that is, one atom for each lattice point, in this case. Finally the Wyckoff generating sites are given. These are the sites of specific atoms within the crystal structure, upon which the space group symmetry operators act.

The last term, the occupancy, indicates the probability that a site is occupied by a particular atom species. In the case of Cu, all the sites neglecting vacancy point defects are occupied by Cu, so the occupancy is 1. How do we generate the crystal structure?

These can be found in the International Tables For Table 1. Hahn, ed. An example is given in Figure 1. The data in the tables provide all the symmetry operators for any specific space group.

In order to generate atomic positions from the generating site data listed for Cu, we add the x, y, z values of the generating site to the values listed in the tables. Returning to our example, Cu has a generating site of type 4a with x,y,z equal to 0,0,0. In the tables, the Wyckoff generating site for 4a has an operator of 0,0,0. This is our first atom site. Now we activate the general operators which are also listed. There are therefore four Cu atoms in our unit cell, as shown schematically in Figure 1.

In a crystal, two or more lattice directions may be geometrically equivalent, and it is sometimes useful to distinguish a family of crystal directions. For example, in a cubic crystal the x-axis is defined by the direction [] in square brackets , but the y and z directions, [] and [] are, by symmetry, geometrically equivalent.

Angular brackets are used as a shorthand for the family of hi directions. Note that all directions which are parallel in the crystal lattice are considered equivalent, regardless of their point of origin, and are denoted by the same direction indices [uvw]. Since the direction indices define the shortest repeat distance in the lattice along the line of the vector, they cannot possess a common factor. It follows that the direction indices [] and [] should be written [] and [], respectively.

Finally, the direction indices all have the dimension of length, the unit of length being defined by the dimensions of the unit cell. Crystal planes are described in terms of the reciprocal of the intercepts of the plane with the axes of a coordinate system that is defined by the unit cell Figure 1. All planes which are parallel in the lattice are described by the same indices, irrespective of the intercepts they make with the coordinate axes although different values of n will be required to clear the fractions.

Reversing the sign of all three Miller indices does not define a new plane. While the letters [uvw], with square brackets, are used to define a set of parallel direction indices, the letters hkl , with round brackets, are used to define the Miller indices of a parallel set of lattice planes.

Note that the dimensions of the Miller indices are those of inverse length, and that the units are the inverse dimensions of the unit cell. Unlike the direction indices, Miller indices having a common factor do have a specific meaning: they refer to fractional values of the interplanar spacing in the unit cell.

Thus the indices are divisible by 2, and correspond to planes which are parallel to, but have just half the spacing of the planes. In cubic crystals, but only in cubic crystals, any set of direction indices is always normal to the crystal planes having the same set of Miller indices. That is, the [] direction in a crystal of cubic symmetry is normal to the plane. This is not generally true in less symmetric crystals, even though it may be true for some symmetry directions.

If a number of crystallographically distinct crystal planes intersect along a common direction [uvw], then that shared direction is said to be the zone axis of these planes, and the planes are said to lie on a common zone.

There is a simple way of finding out whether or not a particular plane hkl lies on a given zone [uvw]. This is true for all crystal symmetries. It is a great convenience to be able to plot the prominent crystal planes and directions in a crystal on a two-dimensional projection, similar to the projections familiar to us from geographical mapping.

By far the most useful of these is the stereographic projection. In the stereographic projection the crystal is imagined to be positioned at the centre of a sphere, the projection sphere, and the crystal directions and normals to the prominent crystal planes are projected from the centre of this sphere the centre of the crystal to intersect its surface Figure 1.

Straight lines are then drawn from the south pole of the projection sphere, through the points of intersection of these crystallographic directions and crystal plane normals with the sphere surface, until the lines intersect a plane placed tangential to the sphere at its north pole. All points around the equator of the sphere now project onto the tangent plane as a circle of radius equal to the diameter of the projection sphere.

All points on the projection sphere that lie in the northern hemisphere will project within this circle, which is termed the stereogram. Points lying in the southern hemisphere will project outside the circle of the stereogram, but by reversing the direction of projection from the north pole to a plane tangential to the south pole we can also represent points lying in the southern hemisphere but using an open circle in order to distinguish the southern hemisphere points.

This avoids having to plot any points outside the area of the stereogram. Any such two-dimensional plot of the crystal plane normals and crystal directions constitutes a stereographic projection. It is conventional to choose a prominent symmetry plane usually one face of the unit cell for the plane of these stereographic projections. The Concept of Microstructure 39 Figure 1. The plane contains the [] and [] directions, while the [] zone contains the normals to the and planes. However, as noted above, the crystal directions for this very low symmetry crystal do not coincide with the plane normals having the same indices.

A stereogram stereographic projection for a cubic crystal, with the plane of the projection parallel to a cube plane is shown in Figure 1. Plane normals and crystal directions with the same indices now coincide, as do the plots of crystal planes and the corresponding zones. The high symmetry of the cubic system divides the stereogram into 24 geometrically equivalent unit spherical triangles that are projected onto the stereogram from the surface of the projection sphere we ignore the southern hemisphere, since reversing the sign of a plane normal does not change the crystal plane.

The angular unit cell parameters, a, b and g, that define the angles between the axes of the unit cell, are also marked on the stereogram. Note that the normals to the faces of the unit cell do not coincide with the axes of the unit cell.

The zones defined by coplanar directions and plane normals pass through the centre of the projection sphere by definition and intercept this sphere along circles which have the diameter of the projection sphere. These circles then project onto the stereogram as traces of larger circles, termed great circles, whose maximum curvature is equal to that of the stereogram. The minimum curvature of a great circle is zero that is, it projects as a straight line , and so straight lines on the stereogram correspond to planes whose traces pass through the centre of the stereographic projection.

The bounding edges of any unit spherical triangle that defines the symmetry elements of a crystal are always great circles. Another property of the stereographic projection is that the cone of directions that make a fixed angle to any given crystallographic direction or crystal plane normal also projects as a circle on the plane of the stereogram. Such circles are termed small circles but beware, The Concept of Microstructure 41 Figure 1. The projection consists of 24 unit spherical triangles bounded by great circles.

Each triangle contains all the symmetry elements of the crystal. It follows that the angular scale of a stereographic projection is strongly distorted, as can be seen from a standard Wulff net Figure 1. This Wulff net scale is identical to the angular scale commonly used to map the surface of the globe. Finally, some spherical triangles, defined by the intersection of three great circles, have geometrical properties which are very useful in applied crystallography. The sum of the angles at the intersections that form the corners of the spherical triangle always exceeds 2p, while the sides of the spherical triangles, on a stereographic projection also define angles.

If more than one of the six angular elements of a spherical triangle is a right angle, then at least four elements of the triangle are right angles and if only two of the angles are given, then all the remaining four angles can be derived. Compare the unit triangle for the triclinic unit cell shown in Figure 1. Hexagonal crystals present a special problem, since the usual Miller indices and direction indices do not reflect the hexagonal symmetry of the crystal.

It is common practice to introduce an additional, redundant axis into the basal plane of the hexagonal unit cell. Note that the generating pole of the small circle is not at the centre of the projected circle on the stereogram. A basal plane stereogram for a hexagonal crystal zinc is given in Figure 1. Families of crystal planes in a hexagonal lattice have similar indices in the four Miller index notation. Summary The term microstructure is taken to mean those features of a material, not visible to the eye, that can be revealed by examining a selected sample with a suitable probe.

Microstructural information includes the identification of the phases present crystalline or glassy , The Concept of Microstructure 43 Figure 1. The two commonest forms of probe used to characterize microstructure are electromagnetic radiation and energetic electrons. In the case of electromagnetic radiation, the optical microscope and the X-ray diffractometer are the two most important tools.

The optical microscope uses radiation in the visible range of wavelengths 0. There is a simple trigonometrical relationship linking all six angles see text. The electron microscope uses a wide range of electron beam energies to probe the microstructure of a specimen. The interaction of a probe beam with the sample may be either elastic or inelastic. Elastic interaction involves the scattering of the beam without loss of energy, and is the basis of diffraction analysis, either using X-rays or high energy electrons.

Inelastic interactions may Figure 1. The Concept of Microstructure 45 result in contrast in an image formed from elastically scattered radiation as when one phase absorbs light while another reflects or transmits the light. Inelastic interactions can also be responsible for the generation of a secondary signal. In the scanning electron microscope the primary, high-energy electron beam generates low energy, secondary electrons that are collected from a scanned raster to form the image.

Inelastic scattering and energy adsorption is also the basis of many microanalytical techniques for the determination of local chemical composition. Both the energy lost by the primary beam and that generated in the secondary signal may be characteristic of the atomic number of the chemical elements present in the sample beneath the probe.

The energy dependence of this signal the energy spectrum provides information that identifies the chemical constituents that are present, while the intensity of the signal can be related to the chemical composition. Many engineering properties of materials are sensitive to the microstructure, which in turn depends on the processing conditions. That is, the microstructure is affected by the processing route, while the structure-sensitive properties of a material not just the mechanical properties are, in their turn, determined by the microstructure.

This includes the microstructural features noted above grains and particles as well as various defects in the microstructure, for example porosity, microcracks and unwanted inclusions phases associated with contamination. The ability of any experimental technique to distinguish closely-spaced features is termed the resolution of the method and is usually limited by the wavelength of the probe radiation, the characteristics of the probe interaction with the specimen and the nature of the image-forming system.

In general, the shorter the wavelength and the wider the acceptance angle of the imaging system for the signal, then the better will be the resolution. On the other hand, the wavelength associated with energetic electrons is very much less than the interplanar spacings in crystals, so that the transmission electron microscope is potentially able to resolve the crystal lattice itself. The resolution of the scanning electron microscope is usually limited by inelastic scattering events that occur in the sample.

This resolution is of the order of a few nanometres for secondary electrons, but only of the order of 1 mm for the characteristic X-rays emitted by the different chemical species Some microscopic methods of materials characterization are capable of resolving individual atoms, in the sense that the images observed reflect a physical effect associated with these atoms. Scanning probe microscopy includes scanning tunnelling and atomic force microscopy, both of which can probe the nanostructure on the atomic scale.

Many microstructural features may be quantitatively described by microstructural parameters. Two important examples are the volume fraction of a second phase and the grain or particle size, both of which usually have a major effect on mechanical properties.

Background Citations. Methods Citations. Results Citations. Citation Type. Has PDF. Publication Type. More Filters. X-ray … Expand. Acknowledgements 1. Introduction 1. View 1 excerpt, cites background. View 1 excerpt. Transmission and scanning analytical electron microscopy: Equipment and methods of nanodiagnostics and nanometrology.

In this review we focus attention on the main methodological approaches for determining and visualizing nanostructural states that can be found in compacted bulk, film, or powder materials. Schroder, Dieter K. Brazel, Christopher S. Microstructural characterization is usually achieved by allowing some form of probe to interact with a carefully prepared specimen.

File Name: microstructural characterization of materials pdf free download. Microstructural Characterization of Materials. Microstructural Characterization of Materials: An Assessment. Microstructural Characterization of Materials, 2nd Edition.

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Thermodynamics and statistical physics books free download. To browse Academia. Log in with Facebook Log in with Google. Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up. Download Free PDF. Microstructural characterization of materials Wayne Kaplan. A short summary of this paper.

Download Download PDF. Translate PDF. Kaplan Microstructural characterization is usually achieved by allowing some form of probe to interact with a carefully prepared specimen. The most commonly used probes are visible light, X-ray radiation, a high- energy electron beam, or a sharp, flexible needle. These four types of probe form the basis for optical microscopy, X-ray diffraction, electron microscopy, and scanning probe microscopy.