Modern Physical Metallurgy and Materials Engineering

He was elected a Fellow of the Royal Society (1986), a Fellow of the Royal Academy of Engineering (1990) and appointed a Commander of the British Empire (CBE) in 1992. In 1986 he joined the School of Metallurgy and Materials. , University of Birmingham as a part-time lecturer and was involved in the board of the Federation of European Materials Societies (FEMS).

Preface

Chapter 1

The structure and bonding of atoms

The realm of materials science
The free atom

The four electron quantum numbers Rutherford conceived the atom to be a positively-

The Periodic Table
Interatomic bonding in materials

The principal quantum number is the most important quantum number as it is mainly responsible for determining the energy of the electron. Electrons with a principal quantum number n can occupy integral values of the orbital quantum number l between 0 and (n - 1).

Ill II lll llll Ill /I

Bonding and energy levels

The energies of the free electrons are spread over a range which increases as the atoms are brought together to form the metal. The energy gap between successive levels is not constant, but decreases as the energy of the levels increases.

Atomic arrangements in materials

The concept of ordering

In the second set in Figure 2.1b, the short-range order is noticeable, but the long-range order is apparently absent. From Figure 2.1 we can conclude that for such a substance the glassy state will have a lower bulk density.

Crystal lattices and structures

It is possible for certain substances to exist in either crystalline or vitreous forms (eg silica). In such cases it has been common to use a simpler orthogonal non-primitive lattice which will accommodate the atoms of the actual crystal structure, t.

Crystal directions and planes

With a stereographic representation of poles, the corresponding operation can be performed in the plane of the primitive circle using a transparent planar mesh, known as a Wulff mesh. Unique in cubic I. A less used alternative to the Wulff grid is the polar grid, where the N-S axis of the reference sphere is perpendicular to the equatorial projection plane.

1~11axis \

Selected crystal structures

Pure metals
Diamond and graphite
Coordination in ionic crystals
Silica
Alumina
Complex oxides

Thus, in the bcc structure shown in Figure 2.11c, the atom in the center of the cube is surrounded by eight equally spaced atoms, i.e. the structure of the mineral zinc mixture (c~-ZnS) shown in Figure 2.15 is often referred to as a prototype for other constructions.

Silicates

The SiO4 tetrahedron previously described in the discussion of silica (section 2.5.5) provides a highly effective key to the classification of the numerous silicate materials, natural and synthetic. In the latter case, an increased degree of corner sharing leads from structures in which isolated tetrahedra exist to those in which tetrahedra are arranged in pairs, chains, sheets, or frameworks (Table 2.4).

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Inorganic glasses

Network structures in glasses

There are certain limits on the amounts of the various substances that can be added. For example, up to 90% of the intermediate, lead oxide (PbO), can be added to silica glass.

Polymeric structures .1 Thermoplastics

Elastomers
Crystallinity in polymers

In the syndiotactic form, chlorine atoms are arranged symmetrically around and along the backbone of the molecule. For orthorhombic PE, the c-axes of lamellae are parallel to the length of the chain-extended molecules and are tangential to the spherulite (Figure 2.30).

Chapter 3

Structural phases

Crystallization from the melt

Plane-front and dendritic solidification at a cooled surface

Gentle stirring of the melt promotes this process, known as dendrite propagation, and can be used to produce a fine-grained and equiaxed structure (eg electromagnetic stirring of molten steel). The morphology of the interface, as well as the final grain structure of the casting, is then determined by thermal conditions at the solid/liquid interface.

SOLID LIQUID Gt

SOLID

LIQUID

Interface

Forms of cast structure
Gas porosity and segregation
Directional solidification
Production of metallic single crystals for research
Principles and applications of phase diagrams

The concept of a phase
The Phase Rule

However, in the absence of these influences, growth dominates over nucleation and the columnar region may extend to the center of the ingot (e.g. pure metal). A limited number of crystals can grow parallel to the main axis of the blade.

Freezing

Stability of phases

The free energy change accompanying the change represents the 'driving force' of the change and is given by the expression The way in which the absolute value of the free energy of a crystal varies with temperature is shown in Figure 3.9b, where H and - T S are plotted as a function of temperature.

Three-phase equilibria and reactions
Intermediate phases
Limitations of phase diagrams
S o m e key phase diagrams

The sharply defined minimum in the liquidus, the eutectic (easy-melting) point, is a typical feature of the reaction. Similarly, an ordinate can be constructed to pass through the minimum (or maximum) of the liquidus of a solid solution (Figure 3.38b).

The fl phase can be distributed evenly as particles throughout the a grains, in which case the mechanical properties of the material will be largely controlled by the ct phase. The structural properties and mechanical behavior of the industrial alloys known as brass can be understood from the copper-rich end of this diagram.

Gaseous 1

Ternary phase diagrams
AsSz = sapphirine MA = spinel

Principles of alloy theory
The mechanism of phase changes

The phases that form in the intermediate compositional regions of the equilibrium diagram can be (1) electrochemical or full-zone compounds, (2) size factor compounds, or (3) electron compounds. Such an arrangement provides large holes of the type shown in Figure 3.43b and these are best filled with the atomic ratio.

Chapter 4

Defects in solids

Point defects

Point defects in metals

Then the free energy, G, or strictly F of a crystal with n defects, relative to the free energy of the perfect crystal, is. The equilibrium number of vacancies increases rapidly with increasing temperature, due to the exponential form of the expression, and for most metals has a value of about 10 -4 near the melting point.

Vacancies are destroyed at the edge of the extra half-plane of atoms from the dislocation, as shown in Figure 4.4a and 4.4b. Below a certain temperature, the migration of vacancies will be too slow to maintain equilibrium, and at lower temperatures there will be a concentration of vacancies above the equilibrium number.

Point defects in non-metallic crystals Point defects in non-metallic, particularly ionic, struc-
Irradiation of solids
Concept of a dislocation
Edge and screw dislocations
The Burgers vector
Mechanisms of slip and climb

This variation in the orientation of the line with respect to the Burgers vector gives rise to a difference in the structure of the dislocation. In contrast, when the line of dislocations is parallel to the slip direction, the dislocation line is known as a screw dislocation.

Cross plane p-,,v sli Zl~im~ry p plane

Dislocations in ionic structures
Grain boundaries
Extended dislocations and stacking faults in close-packed crystals
Volume defects

Void formation and annealing
Irradiation and voiding
Voiding and fracture

Defect behaviour in some real materials

Dislocation vector diagrams and the Thompson tetrahedron
Dislocations and stacking faults in fcc s t r u c t u r e s
Dislocations and stacking faults in cph structures

Twelve perfect dislocations of the type ~ ( 1 1 2 3 ) 1

In (b), the notation [1 1 O) is used instead of the usual notation [1 1 O] to indicate the meaning of the vector direction. The energy of the system of stair-rod dislocations in the final configuration is proportional.

Moreover, because the Burgers vectors of the partial dislocations are parallel, it is not possible to separate the partial dislocations by an applied stress unless one of them is anchored by some obstacle in the crystal. When the dislocation line is along the [1 1 1] direction, it can dissociate in any of the three.

Dislocations and stacking faults in ordered structures

However, it is generally recognized that the stacking fault energy is very high in bcc metals, so dissociation must be limited. The symmetric configuration can be unstable, and the equilibrium configuration is a partial dislocation at the intersection of two {1 1 2} planes and the other two are equidistant, one in each of the other two.

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Dislocations and stacking faults in ceramics
Defects in crystalline polymers
Defects in glasses
Stability of defects .1 Dislocation loops

Voids
Nuclear irradiation effects .1 B e h a v i o u r of point defects and

Chapter 5

In the case of smaller aluminum cations, further dissociation of each of the similar half-particles is required. Conversely, the elimination of the interstitial plane will cause the material to grow.

The characterization of materials

Light microscopy

Basic principles
Selected microscopical techniques

The length of the optical tube to is the distance between the front focal point of the eyepiece and the rear focal plane of the objective. Changes arise with every change, but the image produced by the objective always forms in the fixed focal phase of the eyepiece.

Iri.~ A Light B

A schematic diagram of the basic arrangement for phase contrast in the metallurgical microscope is shown in Figure 5.4a. 4, the beam is either in phase or approximately ~./2 or Jr out of phase with it being bent by the surface features of the sample.

The light reflected from a small indentation in a metallographic sample will be delayed in phase by a fraction of a light wavelength compared to that reflected from the surrounding matrix, whereas in general General applications of the technique include investigation of multiphase alloys after light etching, detection of the early stages of precipitation,.

X-ray diffraction analysis

Production and absorption of X-rays The use of diffraction methods is of great importance

The characteristic radiation is produced when the accelerated electrons have enough energy to eject one of the inner electrons (for example, in the level) from its shell. The vacant Is level is then occupied by one of the other electrons from a higher energy level and during the transition an emission of X radiation occurs.

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The radiation emitted, as shown in Figure 5.8a, can be separated into two components, a continuous spectrum spread over a wide range of wavelengths and a superimposed line spectrum characteristic of the metal being bombarded. The energy of the 'white' radiation, as the continuous spectrum is called, increases as the atomic number of the target and approximately as the square of the applied voltage, while the characteristic radiation is only generated when a certain critical voltage is exceeded.

1 K. absorptton

Diffraction of X-rays by crystals

Yet a third application of the powder method as an inspection technique is the detection of a preferred orientation of the grains in a polycrystalline aggregate. The intensity diffracted at the various angles is automatically recorded on a diagram of the form shown in Figure 5.13c, and this can be quickly analyzed for the appropriate 0 and d values.

Typical interpretative procedures for diffraction patterns

The technique is often used in routine chemical analysis, as accurate intensity measurements allow the quantitative assessment of various elements in a sample. The square of the amplitude of the resultant wave, F, then gives the intensity, which can be calculated using the value of f and the atomic coordinates of each atom in the unit cell.

The origin of the scattering can be attributed to the differences in electron density between the heterogeneous regions and the surrounding matrix. The construction of part of the reciprocal lattice of a face-centered cubic crystal lattice is shown in Figure 5.17.

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The optical arrangement is similar to that of the glass lenses in a projection-type light microscope, although it is customary to use several stages of magnification in the electron microscope. This facility compensates for the fact that it is difficult to move the large magnetic lenses in the evacuated column of the electron microscope in an analogous manner to the glass lenses in a light microscope.

A shift can be seen in the electron microscope because it locally changes the orientation of the crystal, thereby changing the diffraction intensity. The g indices of the crystal planes (hkl) which are located at the Bragg angle can be obtained from SAD.

Chemical microanalysis

Thus, the number of characteristic X-ray photons generated by a thin sample is simply given by the product of the electron path length and the appropriate cross section Q, i.e., the relative magnitude of the plasmon loss peak and the zero loss peak might as well be. used to measure sheet thickness.

Auger electron spectroscopy (AES)

The actual shape of the rim can also help determine the chemical state of the element. Due to the presence of other edges, the maximum energy range in which IK can be measured is about eV.

Observation of defects .1 Etch pitting

Dislocation decoration
Contrast from crystals
Imaging of dislocations
Imaging of stacking faults
Application of dynamical theory
W e a k - b e a m microscopy

Comparing the two images in (a) and (b) shows that the effect of tilting the sample, thereby changing the reflective plane, is to make the long helix B in (a) disappear in (b). This was noted in the kinematic theory, where d R / d z corresponds to a local tilt of the lattice planes.

Specialized bombardment techniques

Neutron diffraction
Secondary ion mass spectrometry ( S I M S )

For X-rays, where the scattering is by electrons, the intensity la increases with the atomic number and is proportional to the square of the atomic form factor. Secondary ions from the central region of the crater are analyzed to produce an accurate depth profile of the concentration.

Thermal analysis

General capabilities of thermal analysis
Thermogravimetric analysis
Differential thermal analysis
Differential scanning calorimetry In this method, unlike DTA, the sample and reference

The beam scans a grid with a size of 100-500 µm and slowly erodes the surface of the sample. DSC has been used in studies of the curing properties of rubbers and thermosetting resins, transitions in liquid crystals, and isothermal crystallization rates in thermoplastic materials.

Chapter 6

The physical properties of materials

Introduction
Density
Thermal properties .1 Thermal expansion

Specific heat capacity
Free energy of transformation

Diffusion .1 Diffusion laws

M e c h a n i s m s of diffusion
Factors affecting diffusion

Anelasticity and internal friction
Ordering in alloys

Long-range and short-range order

The specific heat of a metal is almost entirely due to the vibrational motion of the ions. According to quantum theory, the average energy of a normal mode of the crystal.

With decreasing temperature and thus thermal agitation, these regions of order become wider, until at Tc they begin to bond together and the alloy consists of an interlaced network of small ordered regions. It is clear that changes in the degree of order will depend on atomic migration, so the rate of approach to the equilibrium configuration will be governed by an exponential factor of the usual form, i.e.

At high temperatures well above Tc, there are more than the arbitrary number of AB atom pairs, and as the temperature decreases, small nuclei of order continually form and disperse in an otherwise disordered matrix. Below Tc, these domains absorb each other (cf. grain growth) as a result of antiphase domain boundary mobility until long-range order is established.

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Detection of ordering

178 Modern Physical Metallurgy and Materials Engineering at a critical temperature Tc it becomes zero; the general shape of the curve is shown in figure 6.12. However, because the change in lattice arrangement takes place over a temperature range, the specific heat versus temperature curve will be of the form shown in Figure 6.4b.

Electrical properties

Electrical conductivity

Semiconductors

In such intrinsic semiconductors, as we call them, the current carriers are electrons in the conduction band and holes in the valence band in equal numbers. A pentavalent impurity that donates conduction electrons without creating holes in the valence band is called a donor.

Conduction band

In this case, silicon becomes a p-type semiconductor, as the movement of electrons in one direction of the zone is accompanied by the movement of 'holes' in the other, and consequently they act as if they were positive carriers. If an impurity exists in an otherwise intrinsic semiconductor, the number of electrons in the conduction band becomes greater than the number of holes in the valence band, and therefore the electrons are the majority carriers and the holes are the minority carriers.

Donor level

On the other hand, the addition of lower valence elements than silicon, such as aluminum, removes electrons from the filled zones, leaving 'holes' in the valence band structure. The spare electrons of the impurity atoms are bound near the impurity atoms in energy levels known as the donor levels which are close to the conduction band.

Valency band 1 Valency band

The result of modern physical metallurgy and materials science is that silicon becomes an n-type semiconductor, because conduction occurs through negative carriers.

Acceptor level

Holes Electrons

Emitter

Holes

Reverse

Magnetic properties

Diamagnetism and paramagnetism
Ferromagnetism

Each electron acts like a small magnet and can take on two orientations in a magnetic field, along the field or in the other opposite direction, depending on the direction of the electron spin. Accordingly, the energy of the electron is decreased or increased, which can be easily represented by the band theory.