1.Introduction
Often materials are subject to forces (loads) when they are used. Mechanical engineers calculate those forces and material scientists how materials deform (elongate, compress, twist) or break as a function of applied load, time, temperature, and other conditions.
Materials scientists learn about these mechanical properties by testing materials. Results from the tests depend on the size and shape of material to be tested (specimen), how it is held, and the way of performing the test. That is why we use common procedures, or standards, which are published by the ASTM.
Concepts of Stress and Strain
To compare specimens of different sizes, the load is calculated per unit area, also called normalization to the area. Force divided by area is called stress. In tension and compression tests, the relevant area is that perpendicular to the force. In shear or torsion tests, the area is perpendicular to the axis of rotation.
s = F/A0 tensile or compressive stress
t = F/A0 shear stress
The unit is the Megapascal = 106 Newtons/m2.
There is a change in dimensions, or deformation elongation, DL as a result of a tensile or compressive stress. To enable comparison with specimens of different length, the elongation is also normalized, this time to the length L. This is called strain, e.
e = DL/L
The change in dimensions is the reason we use A0 to indicate the initial area since it changes during deformation. One could divide force by the actual area, this is called true stress (see Sec. 6.7).
For torsional or shear stresses, the deformation is the angle of twist, q (Fig. 6.1) and the shear strain is given by:
g = tg q
Stress—Strain Behavior
Elastic deformation. When the stress is removed, the material returns to the dimension it had before the load was applied. Valid for small strains (except the case of rubbers).
Deformation is reversible, non permanent
Plastic deformation. When the stress is removed, the material does not return to its previous dimension but there is a permanent, irreversible deformation.
In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's law:
s = E e
That is, E is the slope of the stress-strain curve. E is Young's modulus or modulus of elasticity. In some cases, the relationship is not linear so that E can be defined alternatively as the local slope:
E = ds/de
Shear stresses produce strains according to:
t = G g
where G is the shear modulus.
Elastic moduli measure the stiffness of the material. They are related to the second derivative of the interatomic potential, or the first derivative of the force vs. internuclear distance (Fig. 6.6). By examining these curves we can tell which material has a higher modulus. Due to thermal vibrations the elastic modulus decreases with temperature. E is large for ceramics (stronger ionic bond) and small for polymers (weak covalent bond). Since the interatomic distances depend on direction in the crystal, E depends on direction (i.e., it is anisotropic) for single crystals. For randomly oriented policrystals, E is isotropic. .
Anelasticity
Here the behavior is elastic but not the stress-strain curve is not immediately reversible. It takes a while for the strain to return to zero. The effect is normally small for metals but can be significant for polymers.
Elastic Properties of Materials
Materials subject to tension shrink laterally. Those subject to compression, bulge. The ratio of lateral and axial strains is called the Poisson's ratio n.
n = elateral/eaxial
The elastic modulus, shear modulus and Poisson's ratio are related by E = 2G(1+n)
Tensile Properties
Yield point. If the stress is too large, the strain deviates from being proportional to the stress. The point at which this happens is the yield point because there the material yields, deforming permanently (plastically).
Yield stress. Hooke's law is not valid beyond the yield point. The stress at the yield point is called yield stress, and is an important measure of the mechanical properties of materials. In practice, the yield stress is chosen as that causing a permanent strain of 0.002 (strain offset, Fig. 6.9.)
The yield stress measures the resistance to plastic deformation.
The reason for plastic deformation, in normal materials, is not that the atomic bond is stretched beyond repair, but the motion of dislocations, which involves breaking and reforming bonds.
Plastic deformation is caused by the motion of dislocations.
Tensile strength. When stress continues in the plastic regime, the stress-strain passes through a maximum, called the tensile strength (sTS) , and then falls as the material starts to develop a neck and it finally breaks at the fracture point (Fig. 6.10).
Note that it is called strength, not stress, but the units are the same, MPa.
For structural applications, the yield stress is usually a more important property than the tensile strength, since once the it is passed, the structure has deformed beyond acceptable limits.
Ductility. The ability to deform before braking. It is the opposite of brittleness. Ductility can be given either as percent maximum elongation emax or maximum area reduction.
%EL = emax x 100 %
%AR = (A0 - Af)/A0
These are measured after fracture (repositioning the two pieces back together).
Resilience. Capacity to absorb energy elastically. The energy per unit volume is the
area under the strain-stress curve in the elastic region.
Toughness. Ability to absorb energy up to fracture. The energy per unit volume is the total area under the strain-stress curve. It is measured by an impact test (Ch. 8)
True Stress and Strain
When one applies a constant tensile force the material will break after reaching the tensile strength. The material starts necking (the transverse area decreases) but the stress cannot increase beyond sTS. The ratio of the force to the initial area, what we normally do, is called the engineering stress. If the ratio is to the actual area (that changes with stress) one obtains the true stress.
Elastic Recovery During Plastic Deformation
If a material is taken beyond the yield point (it is deformed plastically) and the stress is then released, the material ends up with a permanent strain. If the stress is reapplied, the material again responds elastically at the beginning up to a new yield point that is higher than the original yield point (strain hardening, Ch. 7.10). The amount of elastic strain that it will take before reaching the yield point is called elastic strain recovery (Fig. 6. 16).
Compressive, Shear, and Torsional Deformation
Compressive and shear stresses give similar behavior to tensile stresses, but in the case of compressive stresses there is no maximum in the s-e curve, since no necking occurs.
Hardness
Hardness is the resistance to plastic deformation (e.g., a local dent or scratch). Thus, it is a measure of plastic deformation, as is the tensile strength, so they are well correlated. Historically, it was measured on an empirically scale, determined by the ability of a material to scratch another, diamond being the hardest and talc the softer. Now we use standard tests, where a ball, or point is pressed into a material and the size of the dent is measured. There are a few different hardness tests: Rockwell, Brinell, Vickers, etc. They are popular because they are easy and non-destructive (except for the small dent).
Variability of Material Properties
Tests do not produce exactly the same result because of variations in the test equipment, procedures, operator bias, specimen fabrication, etc. But, even if all those parameters are controlled within strict limits, a variation remains in the materials, due to uncontrolled variations during fabrication, non homogenous composition and structure, etc. The measured mechanical properties will show scatter, which is often distributed in a Gaussian curve (bell-shaped), that is characterized by the mean value and the standard deviation (width).
Design/Safety Factors
To take into account variability of properties, designers use, instead of an average value of, say, the tensile strength, the probability that the yield strength is above the minimum value tolerable. This leads to the use of a safety factor N > 1 (typ. 1.2 - 4). Thus, a working value for the tensile strength would be sW = sTS / N.
Not tested: true stress-true stain relationships, details of the different types of hardness tests, but should know that hardness for a given material correlates with tensile strength. Varia
Tuesday, January 29, 2008
Chapter-5: DIFUSSION
5.1 Introduction
Many important reactions and processes in materials occur by the motion of atoms in the solid (transport), which happens by diffusion.
Inhomogeneous materials can become homogeneous by diffusion, if the temperature is high enough (temperature is needed to overcome energy barriers to atomic motion.
5.2 Diffusion Mechanisms
Atom diffusion can occur by the motion of vacancies (vacancy diffusion) or impurities (impurity diffusion). The energy barrier is that due to nearby atoms which need to move to let the atoms go by. This is more easily achieved when the atoms vibrate strongly, that is, at high temperatures.
There is a difference between diffusion and net diffusion. In a homogeneous material, atoms also diffuse but this motion is hard to detect. This is because atoms move randomly and there will be an equal number of atoms moving in one direction than in another. In inhomogeneous materials, the effect of diffusion is readily seen by a change in concentration with time. In this case there is a net diffusion. Net diffusion occurs because, although all atoms are moving randomly, there are more atoms moving in regions where their concentration is higher.
5.3 Steady-State Diffusion
The flux of diffusing atoms, J, is expressed either in number of atoms per unit area and per unit time (e.g., atoms/m2-second) or in terms of mass flux (e.g., kg/m2-second).
Steady state diffusion means that J does not depend on time. In this case, Fick’s first law holds that the flux along direction x is:
J = – D dC/dx
Where dC/dx is the gradient of the concentration C, and D is the diffusion constant. The concentration gradient is often called the driving force in diffusion (but it is not a force in the mechanistic sense). The minus sign in the equation means that diffusion is down the concentration gradient.
5.4 Nonsteady-State Diffusion
This is the case when the diffusion flux depends on time, which means that a type of atoms accumulates in a region or that it is depleted from a region (which may cause them to accumulate in another region).
5.5 Factors That Influence Diffusion
As stated above, there is a barrier to diffusion created by neighboring atoms that need to move to let the diffusing atom pass. Thus, atomic vibrations created by temperature assist diffusion. Also, smaller atoms diffuse more readily than big ones, and diffusion is faster in open lattices or in open directions. Similar to the case of vacancy formation, the effect of temperature in diffusion is given by a Boltzmann factor: D = D0 × exp(–Qd/kT).
5.6 Other Diffusion Paths
Diffusion occurs more easily along surfaces, and voids in the material (short circuits like dislocations and grain boundaries) because less atoms need to move to let the diffusing atom pass. Short circuits are often unimportant because they constitute a negligible part of the total area of the material normal to the diffusion flux. .
Many important reactions and processes in materials occur by the motion of atoms in the solid (transport), which happens by diffusion.
Inhomogeneous materials can become homogeneous by diffusion, if the temperature is high enough (temperature is needed to overcome energy barriers to atomic motion.
5.2 Diffusion Mechanisms
Atom diffusion can occur by the motion of vacancies (vacancy diffusion) or impurities (impurity diffusion). The energy barrier is that due to nearby atoms which need to move to let the atoms go by. This is more easily achieved when the atoms vibrate strongly, that is, at high temperatures.
There is a difference between diffusion and net diffusion. In a homogeneous material, atoms also diffuse but this motion is hard to detect. This is because atoms move randomly and there will be an equal number of atoms moving in one direction than in another. In inhomogeneous materials, the effect of diffusion is readily seen by a change in concentration with time. In this case there is a net diffusion. Net diffusion occurs because, although all atoms are moving randomly, there are more atoms moving in regions where their concentration is higher.
5.3 Steady-State Diffusion
The flux of diffusing atoms, J, is expressed either in number of atoms per unit area and per unit time (e.g., atoms/m2-second) or in terms of mass flux (e.g., kg/m2-second).
Steady state diffusion means that J does not depend on time. In this case, Fick’s first law holds that the flux along direction x is:
J = – D dC/dx
Where dC/dx is the gradient of the concentration C, and D is the diffusion constant. The concentration gradient is often called the driving force in diffusion (but it is not a force in the mechanistic sense). The minus sign in the equation means that diffusion is down the concentration gradient.
5.4 Nonsteady-State Diffusion
This is the case when the diffusion flux depends on time, which means that a type of atoms accumulates in a region or that it is depleted from a region (which may cause them to accumulate in another region).
5.5 Factors That Influence Diffusion
As stated above, there is a barrier to diffusion created by neighboring atoms that need to move to let the diffusing atom pass. Thus, atomic vibrations created by temperature assist diffusion. Also, smaller atoms diffuse more readily than big ones, and diffusion is faster in open lattices or in open directions. Similar to the case of vacancy formation, the effect of temperature in diffusion is given by a Boltzmann factor: D = D0 × exp(–Qd/kT).
5.6 Other Diffusion Paths
Diffusion occurs more easily along surfaces, and voids in the material (short circuits like dislocations and grain boundaries) because less atoms need to move to let the diffusing atom pass. Short circuits are often unimportant because they constitute a negligible part of the total area of the material normal to the diffusion flux. .
Chapter-4: IMPERFECTIONS
Imperfections in Solids
4.1 Introduction
Materials are often stronger when they have defects. The study of defects is divided according to their dimension:
0D (zero dimension) – point defects: vacancies and interstitials. Impurities.
1D – linear defects: dislocations (edge, screw, mixed)
2D – grain boundaries, surfaces.
3D – extended defects: pores, cracks.
Point Defects
4.2 Vacancies and Self-Interstitials
A vacancy is a lattice position that is vacant because the atom is missing. It is created when the solid is formed. There are other ways of making a vacancy, but they also occur naturally as a result of thermal vibrations.
An interstitial is an atom that occupies a place outside the normal lattice position. It may be the same type of atom as the others (self interstitial) or an impurity atom.
In the case of vacancies and interstitials, there is a change in the coordination of atoms around the defect. This means that the forces are not balanced in the same way as for other atoms in the solid, which results in lattice distortion around the defect.
The number of vacancies formed by thermal agitation follows the law:
NV = NA × exp(-QV/kT)
where NA is the total number of atoms in the solid, QV is the energy required to form a vacancy, k is Boltzmann constant, and T the temperature in Kelvin (note, not in oC or oF).
When QV is given in joules, k = 1.38 × 10-23 J/atom-K. When using eV as the unit of energy, k = 8.62 × 10-5 eV/atom-K.
Note that kT(300 K) = 0.025 eV (room temperature) is much smaller than typical vacancy formation energies. For instance, QV(Cu) = 0.9 eV/atom. This means that NV/NA at room temperature is exp(-36) = 2.3 × 10-16, an insignificant number. Thus, a high temperature is needed to have a high thermal concentration of vacancies. Even so, NV/NA is typically only about 0.0001 at the melting point.
stalline SiO2 (quartz) is still apparent in amorphous SiO2 (silica glass.)
4.3 Impurities in Solids
All real solids are impure. A very high purity material, say 99.9999% pure (called 6N – six nines) contains ~ 6 × 1016 impurities per cm3.
Impurities are often added to materials to improve the properties. For instance, carbon added in small amounts to iron makes steel, which is stronger than iron. Boron impurities added to silicon drastically change its electrical properties.
Solid solutions are made of a host, the solvent or matrix) which dissolves the solute (minor component). The ability to dissolve is called solubility. Solid solutions are:
homogeneous
maintain crystal structure
contain randomly dispersed impurities (substitutional or interstitial)
Factors for high solubility
Similar atomic size (to within 15%)
Similar crystal structure
Similar electronegativity (otherwise a compound is formed)
Similar valence
Composition can be expressed in weight percent, useful when making the solution, and in atomic percent, useful when trying to understand the material at the atomic level.
Miscellaneous Imperfections
4.4 Dislocations—Linear Defects
Dislocations are abrupt changes in the regular ordering of atoms, along a line (dislocation line) in the solid. They occur in high density and are very important in mechanical properties of material. They are characterized by the Burgers vector, found by doing a loop around the dislocation line and noticing the extra interatomic spacing needed to close the loop. The Burgers vector in metals points in a close packed direction.
Edge dislocations occur when an extra plane is inserted. The dislocation line is at the end of the plane. In an edge dislocation, the Burgers vector is perpendicular to the dislocation line.
Screw dislocations result when displacing planes relative to each other through shear. In this case, the Burgers vector is parallel to the dislocation line.
4.5 Interfacial Defects
The environment of an atom at a surface differs from that of an atom in the bulk, in that the number of neighbors (coordination) decreases. This introduces unbalanced forces which result in relaxation (the lattice spacing is decreased) or reconstruction (the crystal structure changes).
The density of atoms in the region including the grain boundary is smaller than the bulk value, since void space occurs in the interface.
Surfaces and interfaces are very reactive and it is usual that impurities segregate there. Since energy is required to form a surface, grains tend to grow in size at the expense of smaller grains to minimize energy. This occurs by diffusion, which is accelerated at high temperatures.
Twin boundaries: not covered
4.6 Bulk or Volume Defects
A typical volume defect is porosity, often introduced in the solid during processing. A common example is snow, which is highly porous ice.
4.7 Atomic Vibrations
Atomic vibrations occur, even at zero temperature (a quantum mechanical effect) and increase in amplitude with temperature. Vibrations displace transiently atoms from their regular lattice site, which destroys the perfect periodicity we discussed in Chapter 3.
4.1 Introduction
Materials are often stronger when they have defects. The study of defects is divided according to their dimension:
0D (zero dimension) – point defects: vacancies and interstitials. Impurities.
1D – linear defects: dislocations (edge, screw, mixed)
2D – grain boundaries, surfaces.
3D – extended defects: pores, cracks.
Point Defects
4.2 Vacancies and Self-Interstitials
A vacancy is a lattice position that is vacant because the atom is missing. It is created when the solid is formed. There are other ways of making a vacancy, but they also occur naturally as a result of thermal vibrations.
An interstitial is an atom that occupies a place outside the normal lattice position. It may be the same type of atom as the others (self interstitial) or an impurity atom.
In the case of vacancies and interstitials, there is a change in the coordination of atoms around the defect. This means that the forces are not balanced in the same way as for other atoms in the solid, which results in lattice distortion around the defect.
The number of vacancies formed by thermal agitation follows the law:
NV = NA × exp(-QV/kT)
where NA is the total number of atoms in the solid, QV is the energy required to form a vacancy, k is Boltzmann constant, and T the temperature in Kelvin (note, not in oC or oF).
When QV is given in joules, k = 1.38 × 10-23 J/atom-K. When using eV as the unit of energy, k = 8.62 × 10-5 eV/atom-K.
Note that kT(300 K) = 0.025 eV (room temperature) is much smaller than typical vacancy formation energies. For instance, QV(Cu) = 0.9 eV/atom. This means that NV/NA at room temperature is exp(-36) = 2.3 × 10-16, an insignificant number. Thus, a high temperature is needed to have a high thermal concentration of vacancies. Even so, NV/NA is typically only about 0.0001 at the melting point.
stalline SiO2 (quartz) is still apparent in amorphous SiO2 (silica glass.)
4.3 Impurities in Solids
All real solids are impure. A very high purity material, say 99.9999% pure (called 6N – six nines) contains ~ 6 × 1016 impurities per cm3.
Impurities are often added to materials to improve the properties. For instance, carbon added in small amounts to iron makes steel, which is stronger than iron. Boron impurities added to silicon drastically change its electrical properties.
Solid solutions are made of a host, the solvent or matrix) which dissolves the solute (minor component). The ability to dissolve is called solubility. Solid solutions are:
homogeneous
maintain crystal structure
contain randomly dispersed impurities (substitutional or interstitial)
Factors for high solubility
Similar atomic size (to within 15%)
Similar crystal structure
Similar electronegativity (otherwise a compound is formed)
Similar valence
Composition can be expressed in weight percent, useful when making the solution, and in atomic percent, useful when trying to understand the material at the atomic level.
Miscellaneous Imperfections
4.4 Dislocations—Linear Defects
Dislocations are abrupt changes in the regular ordering of atoms, along a line (dislocation line) in the solid. They occur in high density and are very important in mechanical properties of material. They are characterized by the Burgers vector, found by doing a loop around the dislocation line and noticing the extra interatomic spacing needed to close the loop. The Burgers vector in metals points in a close packed direction.
Edge dislocations occur when an extra plane is inserted. The dislocation line is at the end of the plane. In an edge dislocation, the Burgers vector is perpendicular to the dislocation line.
Screw dislocations result when displacing planes relative to each other through shear. In this case, the Burgers vector is parallel to the dislocation line.
4.5 Interfacial Defects
The environment of an atom at a surface differs from that of an atom in the bulk, in that the number of neighbors (coordination) decreases. This introduces unbalanced forces which result in relaxation (the lattice spacing is decreased) or reconstruction (the crystal structure changes).
The density of atoms in the region including the grain boundary is smaller than the bulk value, since void space occurs in the interface.
Surfaces and interfaces are very reactive and it is usual that impurities segregate there. Since energy is required to form a surface, grains tend to grow in size at the expense of smaller grains to minimize energy. This occurs by diffusion, which is accelerated at high temperatures.
Twin boundaries: not covered
4.6 Bulk or Volume Defects
A typical volume defect is porosity, often introduced in the solid during processing. A common example is snow, which is highly porous ice.
4.7 Atomic Vibrations
Atomic vibrations occur, even at zero temperature (a quantum mechanical effect) and increase in amplitude with temperature. Vibrations displace transiently atoms from their regular lattice site, which destroys the perfect periodicity we discussed in Chapter 3.
Chapter-3: STRUCTURE OF CRYSTALS
3.2 Fundamental Concepts
Atoms self-organize in crystals, most of the time. The crystalline lattice, is a periodic array of the atoms. When the solid is not crystalline, it is called amorphous. Examples of crystalline solids are metals, diamond and other precious stones, ice, graphite. Examples of amorphous solids are glass, amorphous carbon (a-C), amorphous Si, most plastics
To discuss crystalline structures it is useful to consider atoms as being hard spheres, with well-defined radii. In this scheme, the shortest distance between two like atoms is one diameter.
3.3 Unit Cells
The unit cell is the smallest structure that repeats itself by translation through the crystal. We construct these symmetrical units with the hard spheres. The most common types of unit cells are the faced-centered cubic (FCC), the body-centered cubic (FCC) and the hexagonal close-packed (HCP). Other types exist, particularly among minerals. The simple cube (SC) is often used for didactical purpose, no material has this structure.
3.4 Metallic Crystal Structures
Important properties of the unit cells are
· The type of atoms and their radii R.
· cell dimensions (side a in cubic cells, side of base a and height c in HCP) in terms of R.
· n, number of atoms per unit cell. For an atom that is shared with m adjacent unit cells, we only count a fraction of the atom, 1/m.
· CN, the coordination number, which is the number of closest neighbors to which an atom is bonded.
· APF, the atomic packing factor, which is the fraction of the volume of the cell actually occupied by the hard spheres. APF = Sum of atomic volumes/Volume of cell.
Unit Cell n CN a/R APF
SC 1 6 2 0.52
BCC 2 8 4Ö 3 0.68
FCC 4 12 2Ö 2 0.74
HCP 6 12 0.74
The closest packed direction in a BCC cell is along the diagonal of the cube; in a FCC cell is along the diagonal of a face of the cube.
3.5 Density Computations
The density of a solid is that of the unit cell, obtained by dividing the mass of the atoms (n atoms x Matom) and dividing by Vc the volume of the cell (a3 in the case of a cube). If the mass of the atom is given in amu (A), then we have to divide it by the Avogadro number to get Matom. Thus, the formula for the density is:
3.6 Polymorphism and Allotropy
Some materials may exist in more than one crystal structure, this is called polymorphism. If the material is an elemental solid, it is called allotropy. An example of allotropy is carbon, which can exist as diamond, graphite, and amorphous carbon.
3.11 Close-Packed Crystal Structures
The FCC and HCP are related, and have the same APF. They are built by packing spheres on top of each other, in the hollow sites (Fig. 3.12 of book). The packing is alternate between two types of sites, ABABAB.. in the HCP structure, and alternates between three types of positions, ABCABC… in the FCC crystals.
Crystalline and Non-Crystalline Materials
3.12 Single Crystals
Crystals can be single crystals where the whole solid is one crystal. Then it has a regular geometric structure with flat faces.
3.13 Polycrystalline Materials
A solid can be composed of many crystalline grains, not aligned with each other. It is called polycrystalline. The grains can be more or less aligned with respect to each other. Where they meet is called a grain boundary.
3.14 Anisotropy
Different directions in the crystal have a different packing. For instance, atoms along the edge FCC crystals are more separated than along the face diagonal. This causes anisotropy in the properties of crystals; for instance, the deformation depends on the direction in which a stress is applied.
3.15 X-Ray Diffraction Determination of Crystalline Structure – not covered
3.16 Non-Crystalline Solids
In amorphous solids, there is no long-range order. But amorphous does not mean random, since the distance between atoms cannot be smaller than the size of the hard spheres. Also, in many cases there is some form of short-range order. For instance, the tetragonal order of cry
Atoms self-organize in crystals, most of the time. The crystalline lattice, is a periodic array of the atoms. When the solid is not crystalline, it is called amorphous. Examples of crystalline solids are metals, diamond and other precious stones, ice, graphite. Examples of amorphous solids are glass, amorphous carbon (a-C), amorphous Si, most plastics
To discuss crystalline structures it is useful to consider atoms as being hard spheres, with well-defined radii. In this scheme, the shortest distance between two like atoms is one diameter.
3.3 Unit Cells
The unit cell is the smallest structure that repeats itself by translation through the crystal. We construct these symmetrical units with the hard spheres. The most common types of unit cells are the faced-centered cubic (FCC), the body-centered cubic (FCC) and the hexagonal close-packed (HCP). Other types exist, particularly among minerals. The simple cube (SC) is often used for didactical purpose, no material has this structure.
3.4 Metallic Crystal Structures
Important properties of the unit cells are
· The type of atoms and their radii R.
· cell dimensions (side a in cubic cells, side of base a and height c in HCP) in terms of R.
· n, number of atoms per unit cell. For an atom that is shared with m adjacent unit cells, we only count a fraction of the atom, 1/m.
· CN, the coordination number, which is the number of closest neighbors to which an atom is bonded.
· APF, the atomic packing factor, which is the fraction of the volume of the cell actually occupied by the hard spheres. APF = Sum of atomic volumes/Volume of cell.
Unit Cell n CN a/R APF
SC 1 6 2 0.52
BCC 2 8 4Ö 3 0.68
FCC 4 12 2Ö 2 0.74
HCP 6 12 0.74
The closest packed direction in a BCC cell is along the diagonal of the cube; in a FCC cell is along the diagonal of a face of the cube.
3.5 Density Computations
The density of a solid is that of the unit cell, obtained by dividing the mass of the atoms (n atoms x Matom) and dividing by Vc the volume of the cell (a3 in the case of a cube). If the mass of the atom is given in amu (A), then we have to divide it by the Avogadro number to get Matom. Thus, the formula for the density is:
3.6 Polymorphism and Allotropy
Some materials may exist in more than one crystal structure, this is called polymorphism. If the material is an elemental solid, it is called allotropy. An example of allotropy is carbon, which can exist as diamond, graphite, and amorphous carbon.
3.11 Close-Packed Crystal Structures
The FCC and HCP are related, and have the same APF. They are built by packing spheres on top of each other, in the hollow sites (Fig. 3.12 of book). The packing is alternate between two types of sites, ABABAB.. in the HCP structure, and alternates between three types of positions, ABCABC… in the FCC crystals.
Crystalline and Non-Crystalline Materials
3.12 Single Crystals
Crystals can be single crystals where the whole solid is one crystal. Then it has a regular geometric structure with flat faces.
3.13 Polycrystalline Materials
A solid can be composed of many crystalline grains, not aligned with each other. It is called polycrystalline. The grains can be more or less aligned with respect to each other. Where they meet is called a grain boundary.
3.14 Anisotropy
Different directions in the crystal have a different packing. For instance, atoms along the edge FCC crystals are more separated than along the face diagonal. This causes anisotropy in the properties of crystals; for instance, the deformation depends on the direction in which a stress is applied.
3.15 X-Ray Diffraction Determination of Crystalline Structure – not covered
3.16 Non-Crystalline Solids
In amorphous solids, there is no long-range order. But amorphous does not mean random, since the distance between atoms cannot be smaller than the size of the hard spheres. Also, in many cases there is some form of short-range order. For instance, the tetragonal order of cry
Thursday, January 17, 2008
Chapter 2. ATOMIC STRUCTURE AND BONDING
2.2 Fundamental Concepts
Atoms are composed of electrons, protons, and neutrons. Electron and protons are negative and positive charges of the same magnitude, 1.6 × 10-19 Coulombs.
The mass of the electron is negligible with respect to those of the proton and the neutron, which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10-27 kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A the number of neutrons. Neutrons and protons have very similar masses, roughly equal to 1 amu. A neutral atom has the same number of electrons and protons, Z.
A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a mole is called the Avogadro number, Nav = 6.023 × 1023. Note that Nav = 1 gram/1 amu.
Calculating n, the number of atoms per cm3 in a piece of material of density d (g/cm3).
n = Nav × d / M
where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with a density d = 1.8 g/cm3, M =12, we get 6 × 1023 atoms/mol × 1.8 g/cm3 / 12 g/mol) = 9 × 1022 C/cm3.
For a molecular solid like ice, one uses the molecular mass, M(H2O) = 18. With a density of 1 g/cm3, one obtains n = 3.3 × 1022 H2O/cm3. Note that since the water molecule contains 3 atoms, this is equivalent to 9.9 × 1022 atoms/cm3.
Most solids have atomic densities around 6 × 1022 atoms/cm3. The cube root of that number gives the number of atoms per centimeter, about 39 million. The mean distance between atoms is the inverse of that, or 0.25 nm. This is an important number that gives the scale of atomic structures in solids.
2.3 Electrons in Atoms
The forces in the atom are repulsions between electrons and attraction between electrons and protons. The neutrons play no significant role. Thus, Z is what characterizes the atom.
The electrons form a cloud around the neutron, of radius of 0.05 – 2 nanometers. Electrons do not move in circular orbits, as in popular drawings, but in 'fuzzy' orbits. We cannot tell how it moves, but only say what is the probability of finding it at some distance from the nucleus. According to quantum mechanics, only certain orbits are allowed (thus, the idea of a mini planetary system is not correct). The orbits are identified by a principal quantum number n, which can be related to the size, n = 0 is the smallest; n = 1, 2 .. are larger. (They are "quantized" or discrete, being specified by integers). The angular momentum l is quantized, and so is the projection in a specific direction m. The structure of the atom is determined by the Pauli exclusion principle, only two electrons can be placed in an orbit with a given n, l, m – one for each spin. Table 2.1 in the textbook gives the number of electrons in each shell (given by n) and subshells (given by l).
2.4 The Periodic Table
Elements are categorized by placing them in the periodic table. Elements in a column share similar properties. The noble gases have closed shells, and so they do not gain or lose electrons near another atom. Alkalis can easily lose an electron and become a closed shell; halogens can easily gain one to form a negative ion, again with a closed shell. The propensity to form closed shells occurs in molecules, when they share electrons to close a molecular shell. Examples are H2, N2, and NaCl.
The ability to gain or lose electrons is termed electronegativity or electropositivity, an important factor in ionic bonds.
2.5 Bonding Forces and Energies
The Coulomb forces are simple: attractive between electrons and nuclei, repulsive between electrons and between nuclei. The force between atoms is given by a sum of all the individual forces, and the fact that the electrons are located outside the atom and the nucleus in the center.
When two atoms come very close, the force between them is always repulsive, because the electrons stay outside and the nuclei repel each other. Unless both atoms are ions of the same charge (e.g., both negative) the forces between atoms is always attractive at large internuclear distances r. Since the force is repulsive at small r, and attractive at small r, there is a distance at which the force is zero. This is the equilibrium distance at which the atoms prefer to stay.
The interaction energy is the potential energy between the atoms. It is negative if the atoms are bound and positive if they can move away from each other. The interaction energy is the integral of the force over the separation distance, so these two quantities are directly related. The interaction energy is a minimum at the equilibrium position. This value of the energy is called the bond energy, and is the energy needed to separate completely to infinity (the work that needs to be done to overcome the attractive force.) The strongest the bond energy, the hardest is to move the atoms, for instance the hardest it is to melt the solid, or to evaporate its atoms.
2.6 Primary Interatomic Bonds
Ionic Bonding
This is the bond when one of the atoms is negative (has an extra electron) and another is positive (has lost an electron). Then there is a strong, direct Coulomb attraction. An example is NaCl. In the molecule, there are more electrons around Cl, forming Cl- and less around Na, forming Na+. Ionic bonds are the strongest bonds. In real solids, ionic bonding is usually combined with covalent bonding. In this case, the fractional ionic bonding is defined as %ionic = 100 × [1 – exp(-0.25 (XA – XB)2], where XA and XB are the electronegativities of the two atoms, A and B, forming the molecule.
Covalent Bonding
In covalent bonding, electrons are shared between the molecules, to saturate the valency. The simplest example is the H2 molecule, where the electrons spend more time in between the nuclei than outside, thus producing bonding.
Metallic Bonding
In metals, the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place, in a similar way that the electrons in between the H atoms in the H2 molecule bind the protons.
2.7 Secondary Bonding (Van der Waals)
Fluctuating Induced Dipole Bonds
Since the electrons may be on one side of the atom or the other, a dipole is formed: the + nucleus at the center, and the electron outside. Since the electron moves, the dipole fluctuates. This fluctuation in atom A produces a fluctuating electric field that is felt by the electrons of an adjacent atom, B. Atom B then polarizes so that its outer electrons are on the side of the atom closest to the + side (or opposite to the – side) of the dipole in A. This bond is called van der Waals bonding.
Polar Molecule-Induced Dipole Bonds
A polar molecule like H2O (Hs are partially +, O is partially – ), will induce a dipole in a nearby atom, leading to bonding.
Permanent Dipole Bonds
This is the case of the hydrogen bond in ice. The H end of the molecule is positively charged and can bond to the negative side of another dipolar molecule, like the O side of the H2O dipole.
2.8 Molecules
If molecules formed a closed shell due to covalent bonding (like H2, N2) then the interaction between molecules is weak, of the van der Waals type. Thus, molecular solids usually have very low melting points
Atoms are composed of electrons, protons, and neutrons. Electron and protons are negative and positive charges of the same magnitude, 1.6 × 10-19 Coulombs.
The mass of the electron is negligible with respect to those of the proton and the neutron, which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10-27 kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A the number of neutrons. Neutrons and protons have very similar masses, roughly equal to 1 amu. A neutral atom has the same number of electrons and protons, Z.
A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a mole is called the Avogadro number, Nav = 6.023 × 1023. Note that Nav = 1 gram/1 amu.
Calculating n, the number of atoms per cm3 in a piece of material of density d (g/cm3).
n = Nav × d / M
where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with a density d = 1.8 g/cm3, M =12, we get 6 × 1023 atoms/mol × 1.8 g/cm3 / 12 g/mol) = 9 × 1022 C/cm3.
For a molecular solid like ice, one uses the molecular mass, M(H2O) = 18. With a density of 1 g/cm3, one obtains n = 3.3 × 1022 H2O/cm3. Note that since the water molecule contains 3 atoms, this is equivalent to 9.9 × 1022 atoms/cm3.
Most solids have atomic densities around 6 × 1022 atoms/cm3. The cube root of that number gives the number of atoms per centimeter, about 39 million. The mean distance between atoms is the inverse of that, or 0.25 nm. This is an important number that gives the scale of atomic structures in solids.
2.3 Electrons in Atoms
The forces in the atom are repulsions between electrons and attraction between electrons and protons. The neutrons play no significant role. Thus, Z is what characterizes the atom.
The electrons form a cloud around the neutron, of radius of 0.05 – 2 nanometers. Electrons do not move in circular orbits, as in popular drawings, but in 'fuzzy' orbits. We cannot tell how it moves, but only say what is the probability of finding it at some distance from the nucleus. According to quantum mechanics, only certain orbits are allowed (thus, the idea of a mini planetary system is not correct). The orbits are identified by a principal quantum number n, which can be related to the size, n = 0 is the smallest; n = 1, 2 .. are larger. (They are "quantized" or discrete, being specified by integers). The angular momentum l is quantized, and so is the projection in a specific direction m. The structure of the atom is determined by the Pauli exclusion principle, only two electrons can be placed in an orbit with a given n, l, m – one for each spin. Table 2.1 in the textbook gives the number of electrons in each shell (given by n) and subshells (given by l).
2.4 The Periodic Table
Elements are categorized by placing them in the periodic table. Elements in a column share similar properties. The noble gases have closed shells, and so they do not gain or lose electrons near another atom. Alkalis can easily lose an electron and become a closed shell; halogens can easily gain one to form a negative ion, again with a closed shell. The propensity to form closed shells occurs in molecules, when they share electrons to close a molecular shell. Examples are H2, N2, and NaCl.
The ability to gain or lose electrons is termed electronegativity or electropositivity, an important factor in ionic bonds.
2.5 Bonding Forces and Energies
The Coulomb forces are simple: attractive between electrons and nuclei, repulsive between electrons and between nuclei. The force between atoms is given by a sum of all the individual forces, and the fact that the electrons are located outside the atom and the nucleus in the center.
When two atoms come very close, the force between them is always repulsive, because the electrons stay outside and the nuclei repel each other. Unless both atoms are ions of the same charge (e.g., both negative) the forces between atoms is always attractive at large internuclear distances r. Since the force is repulsive at small r, and attractive at small r, there is a distance at which the force is zero. This is the equilibrium distance at which the atoms prefer to stay.
The interaction energy is the potential energy between the atoms. It is negative if the atoms are bound and positive if they can move away from each other. The interaction energy is the integral of the force over the separation distance, so these two quantities are directly related. The interaction energy is a minimum at the equilibrium position. This value of the energy is called the bond energy, and is the energy needed to separate completely to infinity (the work that needs to be done to overcome the attractive force.) The strongest the bond energy, the hardest is to move the atoms, for instance the hardest it is to melt the solid, or to evaporate its atoms.
2.6 Primary Interatomic Bonds
Ionic Bonding
This is the bond when one of the atoms is negative (has an extra electron) and another is positive (has lost an electron). Then there is a strong, direct Coulomb attraction. An example is NaCl. In the molecule, there are more electrons around Cl, forming Cl- and less around Na, forming Na+. Ionic bonds are the strongest bonds. In real solids, ionic bonding is usually combined with covalent bonding. In this case, the fractional ionic bonding is defined as %ionic = 100 × [1 – exp(-0.25 (XA – XB)2], where XA and XB are the electronegativities of the two atoms, A and B, forming the molecule.
Covalent Bonding
In covalent bonding, electrons are shared between the molecules, to saturate the valency. The simplest example is the H2 molecule, where the electrons spend more time in between the nuclei than outside, thus producing bonding.
Metallic Bonding
In metals, the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place, in a similar way that the electrons in between the H atoms in the H2 molecule bind the protons.
2.7 Secondary Bonding (Van der Waals)
Fluctuating Induced Dipole Bonds
Since the electrons may be on one side of the atom or the other, a dipole is formed: the + nucleus at the center, and the electron outside. Since the electron moves, the dipole fluctuates. This fluctuation in atom A produces a fluctuating electric field that is felt by the electrons of an adjacent atom, B. Atom B then polarizes so that its outer electrons are on the side of the atom closest to the + side (or opposite to the – side) of the dipole in A. This bond is called van der Waals bonding.
Polar Molecule-Induced Dipole Bonds
A polar molecule like H2O (Hs are partially +, O is partially – ), will induce a dipole in a nearby atom, leading to bonding.
Permanent Dipole Bonds
This is the case of the hydrogen bond in ice. The H end of the molecule is positively charged and can bond to the negative side of another dipolar molecule, like the O side of the H2O dipole.
2.8 Molecules
If molecules formed a closed shell due to covalent bonding (like H2, N2) then the interaction between molecules is weak, of the van der Waals type. Thus, molecular solids usually have very low melting points
Saturday, January 12, 2008
Chapter-9: PHASE DIAGRAMS
9.1 Introduction
Definitions
Component: pure metal or compound (e.g., Cu, Zn in Cu-Zn alloy, sugar, water, in a syrup.)
Solvent: host or major component in solution.
Solute: dissolved, minor component in solution.
System: set of possible alloys from same component (e.g., iron-carbon system.)
Solubility Limit: Maximum solute concentration that can be dissolved at a given temperature.
Phase: part with homogeneous physical and chemical characteristics
9.2 Solubility Limit
Effect of temperature on solubility limit. Maximum content: saturation. Exceeding maximum content (like when cooling) leads to precipitation.
9.3 Phases
One-phase systems are homogeneous. Systems with two or more phases are heterogeneous, or mixtures. This is the case of most metallic alloys, but also happens in ceramics and polymers.
A two-component alloy is called binary. One with three components, ternary.
9.4 Microstructure
The properties of an alloy do not depend only on concentration of the phases but how they are arranged structurally at the microscopy level. Thus, the microstructure is specified by the number of phases, their proportions, and their arrangement in space.
A binary alloy may be
a. a single solid solution
b. two separated, essentially pure components.
c. two separated solid solutions.
d. a chemical compound, together with a solid solution.
The way to tell is to cut the material, polish it to a mirror finish, etch it a weak acid (components etch at a different rate) and observe the surface under a microscope.
9.5 Phase Equilibria
Equilibrium is the state of minimum energy. It is achieved given sufficient time. But the time to achieve equilibrium may be so long (the kinetics is so slow) that a state that is not at an energy minimum may have a long life and appear to be stable. This is called a metastable state.
A less strict, operational, definition of equilibrium is that of a system that does not change with time during observation.
Equilibrium Phase Diagrams
Give the relationship of composition of a solution as a function of temperatures and the quantities of phases in equilibrium. These diagrams do not indicate the dynamics when one phase transforms into another. Sometimes diagrams are given with pressure as one of the variables. In the phase diagrams we will discuss, pressure is assumed to be constant at one atmosphere.
9.6 Binary Isomorphous Systems
This very simple case is one complete liquid and solid solubility, an isomorphous system. The example is the Cu-Ni alloy of Fig. 9.2a. The complete solubility occurs because both Cu and Ni have the same crystal structure (FCC), near the same radii, electronegativity and valence.
The liquidus line separates the liquid phase from solid or solid + liquid phases. That is, the solution is liquid above the liquidus line.
The solidus line is that below which the solution is completely solid (does not contain a liquid phase.)
Interpretation of phase diagrams
Concentrations: Tie-line method
a. locate composition and temperature in diagram
b. In two phase region draw tie line or isotherm
c. note intersection with phase boundaries. Read compositions.
Fractions: lever rule
a. construct tie line (isotherm)
b. obtain ratios of line segments lengths.
Note: the fractions are inversely proportional to the length to the boundary for the particular phase. If the point in the diagram is close to the phase line, the fraction of that phase is large.
Development of microstructure in isomorphous alloys
a) Equilibrium cooling
Solidification in the solid + liquid phase occurs gradually upon cooling from the liquidus line. The composition of the solid and the liquid change gradually during cooling (as can be determined by the tie-line method.) Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line.
b) Non-equilibrium cooling
Solidification in the solid + liquid phase also occurs gradually. The composition of the liquid phase evolves by diffusion, following the equilibrium values that can be derived from the tie-line method. However, diffusion in the solid state is very slow. Hence, the new layers that solidify on top of the grains have the equilibrium composition at that temperature but once they are solid their composition does not change. This lead to the formation of layered (cored) grains (Fig. 9.14) and to the invalidity of the tie-line method to determine the composition of the solid phase (it still works for the liquid phase, where diffusion is fast.)
9.7 Binary Eutectic Systems
Interpretation: Obtain phases present, concentration of phases and their fraction (%).
Solvus line: limit of solubility
Eutectic or invariant point. Liquid and two solid phases exist in equilibrium at the eutectic composition and the eutectic temperature.
Note:
· the melting point of the eutectic alloy is lower than that of the components (eutectic = easy to melt in Greek).
· At most two phases can be in equilibrium within a phase field.
· Single-phase regions are separated by 2-phase regions.
Development of microstructure in eutectic alloys
Case of lead-tin alloys, figures 9.9–9.14. A layered, eutectic structure develops when cooling below the eutectic temperature. Alloys which are to the left of the eutectic concentration (hipoeutectic) or to the right (hypereutectic) form a proeutectic phase before reaching the eutectic temperature, while in the solid + liquid region. The eutectic structure then adds when the remaining liquid is solidified when cooling further. The eutectic microstructure is lamellar (layered) due to the reduced diffusion distances in the solid state.
To obtain the concentration of the eutectic microstructure in the final solid solution, one draws a vertical line at the eutectic concentration and applies the lever rule treating the eutectic as a separate phase
9.8 Equilibrium Diagrams Having Intermediate Phases or Compounds
A terminal phase or terminal solution is one that exists in the extremes of concentration (0 and 100%) of the phase diagram. One that exists in the middle, separated from the extremes, is called an intermediate phase or solid solution.
An important phase is the intermetallic compound, that has a precise chemical compositions. When using the lever rules, intermetallic compounds are treated like any other phase, except they appear not as a wide region but as a vertical line.
9.9 Eutectoid and Peritectic Reactions
The eutectoid (eutectic-like) reaction is similar to the eutectic reaction but occurs from one solid phase to two new solid phases. It also shows as V on top of a horizontal line in the phase diagram. There are associated eutectoid temperature (or temperature), eutectoid phase, eutectoid and proeutectoid microstructures.
Solid Phase 1 à Solid Phase 2 + Solid Phase 3
The peritectic reaction also involves three solid in equilibrium, the transition is from a solid + liquid phase to a different solid phase when cooling. The inverse reaction occurs when heating.
Solid Phase 1 + liquid à Solid Phase 2
9.10 Congruent Phase Transformations
Another classification scheme. Congruent transformation is one where there is no change in composition, like allotropic transformations (e.g., a-Fe to g-Fe) or melting transitions in pure solids.
9.13 The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram
This is one of the most important alloys for structural applications. The diagram Fe—C is simplified at low carbon concentrations by assuming it is the Fe—Fe3C diagram. Concentrations are usually given in weight percent. The possible phases are:
· a-ferrite (BCC) Fe-C solution
· g-austenite (FCC) Fe-C solution
· d-ferrite (BCC) Fe-C solution
· liquid Fe-C solution
· Fe3C (iron carbide) or cementite. An intermetallic compound.
The maximum solubility of C in a- ferrite is 0.022 wt%. d-ferrite is only stable at high temperatures. It is not important in practice. Austenite has a maximum C concentration of 2.14 wt %. It is not stable below the eutectic temperature (727 C) unless cooled rapidly (Chapter 10). Cementite is in reality metastable, decomposing into a-Fe and C when heated for several years between 650 and 770 C.
For their role in mechanical properties of the alloy, it is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle
Thus, combining these two phases in solution an alloy can be obtained with intermediate properties. (Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.)
9.14 Development of Microstructures in Iron—Carbon Alloys
The eutectoid composition of austenite is 0.76 wt %. When it cools slowly it forms perlite, a lamellar or layered structure of two phases: a-ferrite and cementite (Fe3C).
Hypoeutectoid alloys contain proeutectoid ferrite plus the eutectoid perlite. Hypereutectoid alloys contain proeutectoid cementite plus perlite.
Since reactions below the eutectoid temperature are in the solid phase, the equilibrium is not achieved by usual cooling from austenite. The new microstructures that form are discussed in Ch. 10.
9.15 The Influence of Other Alloying Elements
As mentioned in section 7.9, alloying strengthens metals by hindering the motion of dislocations. Thus, the strength of Fe–C alloys increase with C content and also with the addition of other elements.
Definitions
Component: pure metal or compound (e.g., Cu, Zn in Cu-Zn alloy, sugar, water, in a syrup.)
Solvent: host or major component in solution.
Solute: dissolved, minor component in solution.
System: set of possible alloys from same component (e.g., iron-carbon system.)
Solubility Limit: Maximum solute concentration that can be dissolved at a given temperature.
Phase: part with homogeneous physical and chemical characteristics
9.2 Solubility Limit
Effect of temperature on solubility limit. Maximum content: saturation. Exceeding maximum content (like when cooling) leads to precipitation.
9.3 Phases
One-phase systems are homogeneous. Systems with two or more phases are heterogeneous, or mixtures. This is the case of most metallic alloys, but also happens in ceramics and polymers.
A two-component alloy is called binary. One with three components, ternary.
9.4 Microstructure
The properties of an alloy do not depend only on concentration of the phases but how they are arranged structurally at the microscopy level. Thus, the microstructure is specified by the number of phases, their proportions, and their arrangement in space.
A binary alloy may be
a. a single solid solution
b. two separated, essentially pure components.
c. two separated solid solutions.
d. a chemical compound, together with a solid solution.
The way to tell is to cut the material, polish it to a mirror finish, etch it a weak acid (components etch at a different rate) and observe the surface under a microscope.
9.5 Phase Equilibria
Equilibrium is the state of minimum energy. It is achieved given sufficient time. But the time to achieve equilibrium may be so long (the kinetics is so slow) that a state that is not at an energy minimum may have a long life and appear to be stable. This is called a metastable state.
A less strict, operational, definition of equilibrium is that of a system that does not change with time during observation.
Equilibrium Phase Diagrams
Give the relationship of composition of a solution as a function of temperatures and the quantities of phases in equilibrium. These diagrams do not indicate the dynamics when one phase transforms into another. Sometimes diagrams are given with pressure as one of the variables. In the phase diagrams we will discuss, pressure is assumed to be constant at one atmosphere.
9.6 Binary Isomorphous Systems
This very simple case is one complete liquid and solid solubility, an isomorphous system. The example is the Cu-Ni alloy of Fig. 9.2a. The complete solubility occurs because both Cu and Ni have the same crystal structure (FCC), near the same radii, electronegativity and valence.
The liquidus line separates the liquid phase from solid or solid + liquid phases. That is, the solution is liquid above the liquidus line.
The solidus line is that below which the solution is completely solid (does not contain a liquid phase.)
Interpretation of phase diagrams
Concentrations: Tie-line method
a. locate composition and temperature in diagram
b. In two phase region draw tie line or isotherm
c. note intersection with phase boundaries. Read compositions.
Fractions: lever rule
a. construct tie line (isotherm)
b. obtain ratios of line segments lengths.
Note: the fractions are inversely proportional to the length to the boundary for the particular phase. If the point in the diagram is close to the phase line, the fraction of that phase is large.
Development of microstructure in isomorphous alloys
a) Equilibrium cooling
Solidification in the solid + liquid phase occurs gradually upon cooling from the liquidus line. The composition of the solid and the liquid change gradually during cooling (as can be determined by the tie-line method.) Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line.
b) Non-equilibrium cooling
Solidification in the solid + liquid phase also occurs gradually. The composition of the liquid phase evolves by diffusion, following the equilibrium values that can be derived from the tie-line method. However, diffusion in the solid state is very slow. Hence, the new layers that solidify on top of the grains have the equilibrium composition at that temperature but once they are solid their composition does not change. This lead to the formation of layered (cored) grains (Fig. 9.14) and to the invalidity of the tie-line method to determine the composition of the solid phase (it still works for the liquid phase, where diffusion is fast.)
9.7 Binary Eutectic Systems
Interpretation: Obtain phases present, concentration of phases and their fraction (%).
Solvus line: limit of solubility
Eutectic or invariant point. Liquid and two solid phases exist in equilibrium at the eutectic composition and the eutectic temperature.
Note:
· the melting point of the eutectic alloy is lower than that of the components (eutectic = easy to melt in Greek).
· At most two phases can be in equilibrium within a phase field.
· Single-phase regions are separated by 2-phase regions.
Development of microstructure in eutectic alloys
Case of lead-tin alloys, figures 9.9–9.14. A layered, eutectic structure develops when cooling below the eutectic temperature. Alloys which are to the left of the eutectic concentration (hipoeutectic) or to the right (hypereutectic) form a proeutectic phase before reaching the eutectic temperature, while in the solid + liquid region. The eutectic structure then adds when the remaining liquid is solidified when cooling further. The eutectic microstructure is lamellar (layered) due to the reduced diffusion distances in the solid state.
To obtain the concentration of the eutectic microstructure in the final solid solution, one draws a vertical line at the eutectic concentration and applies the lever rule treating the eutectic as a separate phase
9.8 Equilibrium Diagrams Having Intermediate Phases or Compounds
A terminal phase or terminal solution is one that exists in the extremes of concentration (0 and 100%) of the phase diagram. One that exists in the middle, separated from the extremes, is called an intermediate phase or solid solution.
An important phase is the intermetallic compound, that has a precise chemical compositions. When using the lever rules, intermetallic compounds are treated like any other phase, except they appear not as a wide region but as a vertical line.
9.9 Eutectoid and Peritectic Reactions
The eutectoid (eutectic-like) reaction is similar to the eutectic reaction but occurs from one solid phase to two new solid phases. It also shows as V on top of a horizontal line in the phase diagram. There are associated eutectoid temperature (or temperature), eutectoid phase, eutectoid and proeutectoid microstructures.
Solid Phase 1 à Solid Phase 2 + Solid Phase 3
The peritectic reaction also involves three solid in equilibrium, the transition is from a solid + liquid phase to a different solid phase when cooling. The inverse reaction occurs when heating.
Solid Phase 1 + liquid à Solid Phase 2
9.10 Congruent Phase Transformations
Another classification scheme. Congruent transformation is one where there is no change in composition, like allotropic transformations (e.g., a-Fe to g-Fe) or melting transitions in pure solids.
9.13 The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram
This is one of the most important alloys for structural applications. The diagram Fe—C is simplified at low carbon concentrations by assuming it is the Fe—Fe3C diagram. Concentrations are usually given in weight percent. The possible phases are:
· a-ferrite (BCC) Fe-C solution
· g-austenite (FCC) Fe-C solution
· d-ferrite (BCC) Fe-C solution
· liquid Fe-C solution
· Fe3C (iron carbide) or cementite. An intermetallic compound.
The maximum solubility of C in a- ferrite is 0.022 wt%. d-ferrite is only stable at high temperatures. It is not important in practice. Austenite has a maximum C concentration of 2.14 wt %. It is not stable below the eutectic temperature (727 C) unless cooled rapidly (Chapter 10). Cementite is in reality metastable, decomposing into a-Fe and C when heated for several years between 650 and 770 C.
For their role in mechanical properties of the alloy, it is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle
Thus, combining these two phases in solution an alloy can be obtained with intermediate properties. (Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.)
9.14 Development of Microstructures in Iron—Carbon Alloys
The eutectoid composition of austenite is 0.76 wt %. When it cools slowly it forms perlite, a lamellar or layered structure of two phases: a-ferrite and cementite (Fe3C).
Hypoeutectoid alloys contain proeutectoid ferrite plus the eutectoid perlite. Hypereutectoid alloys contain proeutectoid cementite plus perlite.
Since reactions below the eutectoid temperature are in the solid phase, the equilibrium is not achieved by usual cooling from austenite. The new microstructures that form are discussed in Ch. 10.
9.15 The Influence of Other Alloying Elements
As mentioned in section 7.9, alloying strengthens metals by hindering the motion of dislocations. Thus, the strength of Fe–C alloys increase with C content and also with the addition of other elements.
Chapter 2. ATOMIC STRUCTURE AND BONDING
2.2 Fundamental Concepts
Atoms are composed of electrons, protons, and neutrons. Electron and protons are negative and positive charges of the same magnitude, 1.6 × 10-19 Coulombs.
The mass of the electron is negligible with respect to those of the proton and the neutron, which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10-27 kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A the number of neutrons. Neutrons and protons have very similar masses, roughly equal to 1 amu. A neutral atom has the same number of electrons and protons, Z.
A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a mole is called the Avogadro number, Nav = 6.023 × 1023. Note that Nav = 1 gram/1 amu.
Calculating n, the number of atoms per cm3 in a piece of material of density d (g/cm3).
n = Nav × d / M
where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with a density d = 1.8 g/cm3, M =12, we get 6 × 1023 atoms/mol × 1.8 g/cm3 / 12 g/mol) = 9 × 1022 C/cm3.
For a molecular solid like ice, one uses the molecular mass, M(H2O) = 18. With a density of 1 g/cm3, one obtains n = 3.3 × 1022 H2O/cm3. Note that since the water molecule contains 3 atoms, this is equivalent to 9.9 × 1022 atoms/cm3.
Most solids have atomic densities around 6 × 1022 atoms/cm3. The cube root of that number gives the number of atoms per centimeter, about 39 million. The mean distance between atoms is the inverse of that, or 0.25 nm. This is an important number that gives the scale of atomic structures in solids.
2.3 Electrons in Atoms
The forces in the atom are repulsions between electrons and attraction between electrons and protons. The neutrons play no significant role. Thus, Z is what characterizes the atom.
The electrons form a cloud around the neutron, of radius of 0.05 – 2 nanometers. Electrons do not move in circular orbits, as in popular drawings, but in 'fuzzy' orbits. We cannot tell how it moves, but only say what is the probability of finding it at some distance from the nucleus. According to quantum mechanics, only certain orbits are allowed (thus, the idea of a mini planetary system is not correct). The orbits are identified by a principal quantum number n, which can be related to the size, n = 0 is the smallest; n = 1, 2 .. are larger. (They are "quantized" or discrete, being specified by integers). The angular momentum l is quantized, and so is the projection in a specific direction m. The structure of the atom is determined by the Pauli exclusion principle, only two electrons can be placed in an orbit with a given n, l, m – one for each spin. Table 2.1 in the textbook gives the number of electrons in each shell (given by n) and subshells (given by l).
2.4 The Periodic Table
Elements are categorized by placing them in the periodic table. Elements in a column share similar properties. The noble gases have closed shells, and so they do not gain or lose electrons near another atom. Alkalis can easily lose an electron and become a closed shell; halogens can easily gain one to form a negative ion, again with a closed shell. The propensity to form closed shells occurs in molecules, when they share electrons to close a molecular shell. Examples are H2, N2, and NaCl.
The ability to gain or lose electrons is termed electronegativity or electropositivity, an important factor in ionic bonds.
2.5 Bonding Forces and Energies
The Coulomb forces are simple: attractive between electrons and nuclei, repulsive between electrons and between nuclei. The force between atoms is given by a sum of all the individual forces, and the fact that the electrons are located outside the atom and the nucleus in the center.
When two atoms come very close, the force between them is always repulsive, because the electrons stay outside and the nuclei repel each other. Unless both atoms are ions of the same charge (e.g., both negative) the forces between atoms is always attractive at large internuclear distances r. Since the force is repulsive at small r, and attractive at small r, there is a distance at which the force is zero. This is the equilibrium distance at which the atoms prefer to stay.
The interaction energy is the potential energy between the atoms. It is negative if the atoms are bound and positive if they can move away from each other. The interaction energy is the integral of the force over the separation distance, so these two quantities are directly related. The interaction energy is a minimum at the equilibrium position. This value of the energy is called the bond energy, and is the energy needed to separate completely to infinity (the work that needs to be done to overcome the attractive force.) The strongest the bond energy, the hardest is to move the atoms, for instance the hardest it is to melt the solid, or to evaporate its atoms.
2.6 Primary Interatomic Bonds
Ionic Bonding
This is the bond when one of the atoms is negative (has an extra electron) and another is positive (has lost an electron). Then there is a strong, direct Coulomb attraction. An example is NaCl. In the molecule, there are more electrons around Cl, forming Cl- and less around Na, forming Na+. Ionic bonds are the strongest bonds. In real solids, ionic bonding is usually combined with covalent bonding. In this case, the fractional ionic bonding is defined as %ionic = 100 × [1 – exp(-0.25 (XA – XB)2], where XA and XB are the electronegativities of the two atoms, A and B, forming the molecule.
Covalent Bonding
In covalent bonding, electrons are shared between the molecules, to saturate the valency. The simplest example is the H2 molecule, where the electrons spend more time in between the nuclei than outside, thus producing bonding.
Metallic Bonding
In metals, the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place, in a similar way that the electrons in between the H atoms in the H2 molecule bind the protons.
2.7 Secondary Bonding (Van der Waals)
Fluctuating Induced Dipole Bonds
Since the electrons may be on one side of the atom or the other, a dipole is formed: the + nucleus at the center, and the electron outside. Since the electron moves, the dipole fluctuates. This fluctuation in atom A produces a fluctuating electric field that is felt by the electrons of an adjacent atom, B. Atom B then polarizes so that its outer electrons are on the side of the atom closest to the + side (or opposite to the – side) of the dipole in A. This bond is called van der Waals bonding.
Polar Molecule-Induced Dipole Bonds
A polar molecule like H2O (Hs are partially +, O is partially – ), will induce a dipole in a nearby atom, leading to bonding.
Permanent Dipole Bonds
This is the case of the hydrogen bond in ice. The H end of the molecule is positively charged and can bond to the negative side of another dipolar molecule, like the O side of the H2O dipole.
2.8 Molecules
If molecules formed a closed shell due to covalent bonding (like H2, N2) then the interaction between molecules is weak, of the van der Waals type. Thus, molecular solids usually have very low melting points
Atoms are composed of electrons, protons, and neutrons. Electron and protons are negative and positive charges of the same magnitude, 1.6 × 10-19 Coulombs.
The mass of the electron is negligible with respect to those of the proton and the neutron, which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10-27 kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A the number of neutrons. Neutrons and protons have very similar masses, roughly equal to 1 amu. A neutral atom has the same number of electrons and protons, Z.
A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a mole is called the Avogadro number, Nav = 6.023 × 1023. Note that Nav = 1 gram/1 amu.
Calculating n, the number of atoms per cm3 in a piece of material of density d (g/cm3).
n = Nav × d / M
where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with a density d = 1.8 g/cm3, M =12, we get 6 × 1023 atoms/mol × 1.8 g/cm3 / 12 g/mol) = 9 × 1022 C/cm3.
For a molecular solid like ice, one uses the molecular mass, M(H2O) = 18. With a density of 1 g/cm3, one obtains n = 3.3 × 1022 H2O/cm3. Note that since the water molecule contains 3 atoms, this is equivalent to 9.9 × 1022 atoms/cm3.
Most solids have atomic densities around 6 × 1022 atoms/cm3. The cube root of that number gives the number of atoms per centimeter, about 39 million. The mean distance between atoms is the inverse of that, or 0.25 nm. This is an important number that gives the scale of atomic structures in solids.
2.3 Electrons in Atoms
The forces in the atom are repulsions between electrons and attraction between electrons and protons. The neutrons play no significant role. Thus, Z is what characterizes the atom.
The electrons form a cloud around the neutron, of radius of 0.05 – 2 nanometers. Electrons do not move in circular orbits, as in popular drawings, but in 'fuzzy' orbits. We cannot tell how it moves, but only say what is the probability of finding it at some distance from the nucleus. According to quantum mechanics, only certain orbits are allowed (thus, the idea of a mini planetary system is not correct). The orbits are identified by a principal quantum number n, which can be related to the size, n = 0 is the smallest; n = 1, 2 .. are larger. (They are "quantized" or discrete, being specified by integers). The angular momentum l is quantized, and so is the projection in a specific direction m. The structure of the atom is determined by the Pauli exclusion principle, only two electrons can be placed in an orbit with a given n, l, m – one for each spin. Table 2.1 in the textbook gives the number of electrons in each shell (given by n) and subshells (given by l).
2.4 The Periodic Table
Elements are categorized by placing them in the periodic table. Elements in a column share similar properties. The noble gases have closed shells, and so they do not gain or lose electrons near another atom. Alkalis can easily lose an electron and become a closed shell; halogens can easily gain one to form a negative ion, again with a closed shell. The propensity to form closed shells occurs in molecules, when they share electrons to close a molecular shell. Examples are H2, N2, and NaCl.
The ability to gain or lose electrons is termed electronegativity or electropositivity, an important factor in ionic bonds.
2.5 Bonding Forces and Energies
The Coulomb forces are simple: attractive between electrons and nuclei, repulsive between electrons and between nuclei. The force between atoms is given by a sum of all the individual forces, and the fact that the electrons are located outside the atom and the nucleus in the center.
When two atoms come very close, the force between them is always repulsive, because the electrons stay outside and the nuclei repel each other. Unless both atoms are ions of the same charge (e.g., both negative) the forces between atoms is always attractive at large internuclear distances r. Since the force is repulsive at small r, and attractive at small r, there is a distance at which the force is zero. This is the equilibrium distance at which the atoms prefer to stay.
The interaction energy is the potential energy between the atoms. It is negative if the atoms are bound and positive if they can move away from each other. The interaction energy is the integral of the force over the separation distance, so these two quantities are directly related. The interaction energy is a minimum at the equilibrium position. This value of the energy is called the bond energy, and is the energy needed to separate completely to infinity (the work that needs to be done to overcome the attractive force.) The strongest the bond energy, the hardest is to move the atoms, for instance the hardest it is to melt the solid, or to evaporate its atoms.
2.6 Primary Interatomic Bonds
Ionic Bonding
This is the bond when one of the atoms is negative (has an extra electron) and another is positive (has lost an electron). Then there is a strong, direct Coulomb attraction. An example is NaCl. In the molecule, there are more electrons around Cl, forming Cl- and less around Na, forming Na+. Ionic bonds are the strongest bonds. In real solids, ionic bonding is usually combined with covalent bonding. In this case, the fractional ionic bonding is defined as %ionic = 100 × [1 – exp(-0.25 (XA – XB)2], where XA and XB are the electronegativities of the two atoms, A and B, forming the molecule.
Covalent Bonding
In covalent bonding, electrons are shared between the molecules, to saturate the valency. The simplest example is the H2 molecule, where the electrons spend more time in between the nuclei than outside, thus producing bonding.
Metallic Bonding
In metals, the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place, in a similar way that the electrons in between the H atoms in the H2 molecule bind the protons.
2.7 Secondary Bonding (Van der Waals)
Fluctuating Induced Dipole Bonds
Since the electrons may be on one side of the atom or the other, a dipole is formed: the + nucleus at the center, and the electron outside. Since the electron moves, the dipole fluctuates. This fluctuation in atom A produces a fluctuating electric field that is felt by the electrons of an adjacent atom, B. Atom B then polarizes so that its outer electrons are on the side of the atom closest to the + side (or opposite to the – side) of the dipole in A. This bond is called van der Waals bonding.
Polar Molecule-Induced Dipole Bonds
A polar molecule like H2O (Hs are partially +, O is partially – ), will induce a dipole in a nearby atom, leading to bonding.
Permanent Dipole Bonds
This is the case of the hydrogen bond in ice. The H end of the molecule is positively charged and can bond to the negative side of another dipolar molecule, like the O side of the H2O dipole.
2.8 Molecules
If molecules formed a closed shell due to covalent bonding (like H2, N2) then the interaction between molecules is weak, of the van der Waals type. Thus, molecular solids usually have very low melting points
Chapter 1. INRODUCTION
1 .1 Historical Perspective
Materials are so important in the development of civilization that we associate Ages with them. In the origin of human life on Earth, the Stone Age, people used only natural materials, like stone, clay, skins, and wood. When people found copper and how to make it harder by alloying, the Bronze Age started about 3000 BC. The use of iron and steel, a stronger material that gave advantage in wars started at about 1200 BC. The next big step was the discovery of a cheap process to make steel around 1850, which enabled the railroads and the building of the modern infrastructure of the industrial world.
1.2 Materials Science and Engineering
Understanding of how materials behave like they do, and why they differ in properties was only possible with the atomistic understanding allowed by quantum mechanics, that first explained atoms and then solids starting in the 1930s. The combination of physics, chemistry, and the focus on the relationship between the properties of a material and its microstructure is the domain of Materials Science. The development of this science allowed designing materials and provided a knowledge base for the engineering applications (Materials Engineering).
Structure:
· At the atomic level: arrangement of atoms in different ways. (Gives different properties for graphite than diamond both forms of carbon.)
· At the microscopic level: arrangement of small grains of material that can be identified by microscopy. (Gives different optical properties to transparent vs. frosted glass.)
Properties are the way the material responds to the environment. For instance, the mechanical, electrical and magnetic properties are the responses to mechanical, electrical and magnetic forces, respectively. Other important properties are thermal (transmission of heat, heat capacity), optical (absorption, transmission and scattering of light), and the chemical stability in contact with the environment (like corrosion resistance).
Processing of materials is the application of heat (heat treatment), mechanical forces, etc. to affect their microstructure and, therefore, their properties.
1.3 Why Study Materials Science and Engineering?
· To be able to select a material for a given use based on considerations of cost and performance.
· To understand the limits of materials and the change of their properties with use.
· To be able to create a new material that will have some desirable properties.
All engineering disciplines need to know about materials. Even the most "immaterial", like software or system engineering depend on the development of new materials, which in turn alter the economics, like software-hardware trade-offs. Increasing applications of system engineering are in materials manufacturing (industrial engineering) and complex environmental systems.
1.4 Classification of Materials
Like many other things, materials are classified in groups, so that our brain can handle the complexity. One could classify them according to structure, or properties, or use. The one that we will use is according to the way the atoms are bound together:
Metals: valence electrons are detached from atoms, and spread in an 'electron sea' that "glues" the ions together. Metals are usually strong, conduct electricity and heat well and are opaque to light (shiny if polished). Examples: aluminum, steel, brass, gold.
Semiconductors: the bonding is covalent (electrons are shared between atoms). Their electrical properties depend extremely strongly on minute proportions of contaminants. They are opaque to visible light but transparent to the infrared. Examples: Si, Ge, GaAs.
Ceramics: atoms behave mostly like either positive or negative ions, and are bound by Coulomb forces between them. They are usually combinations of metals or semiconductors with oxygen, nitrogen or carbon (oxides, nitrides, and carbides). Examples: glass, porcelain, many minerals.
Polymers: are bound by covalent forces and also by weak van der Waals forces, and usually based on H, C and other non-metallic elements. They decompose at moderate temperatures (100 – 400 C), and are lightweight. Other properties vary greatly. Examples: plastics (nylon, Teflon, polyester) and rubber.
Other categories are not based on bonding. A particular microstructure identifies composites, made of different materials in intimate contact (example: fiberglass, concrete, wood) to achieve specific properties. Biomaterials can be any type of material that is biocompatible and used, for instance, to replace human body parts.
1.5 Advanced Materials
Materials used in "High-Tec" applications, usually designed for maximum performance, and normally expensive. Examples are titanium alloys for supersonic airplanes, magnetic alloys for computer disks, special ceramics for the heat shield of the space shuttle, etc.
1.6 Modern Material's Needs
· Engine efficiency increases at high temperatures: requires high temperature structural materials
· Use of nuclear energy requires solving problem with residues, or advances in nuclear waste processing.
· Hypersonic flight requires materials that are light, strong and resist high temperatures.
· Optical communications require optical fibers that absorb light negligibly.
· Civil construction – materials for unbreakable windows.
· Structures: materials that are strong like metals and resist corrosion like plastics.
Materials are so important in the development of civilization that we associate Ages with them. In the origin of human life on Earth, the Stone Age, people used only natural materials, like stone, clay, skins, and wood. When people found copper and how to make it harder by alloying, the Bronze Age started about 3000 BC. The use of iron and steel, a stronger material that gave advantage in wars started at about 1200 BC. The next big step was the discovery of a cheap process to make steel around 1850, which enabled the railroads and the building of the modern infrastructure of the industrial world.
1.2 Materials Science and Engineering
Understanding of how materials behave like they do, and why they differ in properties was only possible with the atomistic understanding allowed by quantum mechanics, that first explained atoms and then solids starting in the 1930s. The combination of physics, chemistry, and the focus on the relationship between the properties of a material and its microstructure is the domain of Materials Science. The development of this science allowed designing materials and provided a knowledge base for the engineering applications (Materials Engineering).
Structure:
· At the atomic level: arrangement of atoms in different ways. (Gives different properties for graphite than diamond both forms of carbon.)
· At the microscopic level: arrangement of small grains of material that can be identified by microscopy. (Gives different optical properties to transparent vs. frosted glass.)
Properties are the way the material responds to the environment. For instance, the mechanical, electrical and magnetic properties are the responses to mechanical, electrical and magnetic forces, respectively. Other important properties are thermal (transmission of heat, heat capacity), optical (absorption, transmission and scattering of light), and the chemical stability in contact with the environment (like corrosion resistance).
Processing of materials is the application of heat (heat treatment), mechanical forces, etc. to affect their microstructure and, therefore, their properties.
1.3 Why Study Materials Science and Engineering?
· To be able to select a material for a given use based on considerations of cost and performance.
· To understand the limits of materials and the change of their properties with use.
· To be able to create a new material that will have some desirable properties.
All engineering disciplines need to know about materials. Even the most "immaterial", like software or system engineering depend on the development of new materials, which in turn alter the economics, like software-hardware trade-offs. Increasing applications of system engineering are in materials manufacturing (industrial engineering) and complex environmental systems.
1.4 Classification of Materials
Like many other things, materials are classified in groups, so that our brain can handle the complexity. One could classify them according to structure, or properties, or use. The one that we will use is according to the way the atoms are bound together:
Metals: valence electrons are detached from atoms, and spread in an 'electron sea' that "glues" the ions together. Metals are usually strong, conduct electricity and heat well and are opaque to light (shiny if polished). Examples: aluminum, steel, brass, gold.
Semiconductors: the bonding is covalent (electrons are shared between atoms). Their electrical properties depend extremely strongly on minute proportions of contaminants. They are opaque to visible light but transparent to the infrared. Examples: Si, Ge, GaAs.
Ceramics: atoms behave mostly like either positive or negative ions, and are bound by Coulomb forces between them. They are usually combinations of metals or semiconductors with oxygen, nitrogen or carbon (oxides, nitrides, and carbides). Examples: glass, porcelain, many minerals.
Polymers: are bound by covalent forces and also by weak van der Waals forces, and usually based on H, C and other non-metallic elements. They decompose at moderate temperatures (100 – 400 C), and are lightweight. Other properties vary greatly. Examples: plastics (nylon, Teflon, polyester) and rubber.
Other categories are not based on bonding. A particular microstructure identifies composites, made of different materials in intimate contact (example: fiberglass, concrete, wood) to achieve specific properties. Biomaterials can be any type of material that is biocompatible and used, for instance, to replace human body parts.
1.5 Advanced Materials
Materials used in "High-Tec" applications, usually designed for maximum performance, and normally expensive. Examples are titanium alloys for supersonic airplanes, magnetic alloys for computer disks, special ceramics for the heat shield of the space shuttle, etc.
1.6 Modern Material's Needs
· Engine efficiency increases at high temperatures: requires high temperature structural materials
· Use of nuclear energy requires solving problem with residues, or advances in nuclear waste processing.
· Hypersonic flight requires materials that are light, strong and resist high temperatures.
· Optical communications require optical fibers that absorb light negligibly.
· Civil construction – materials for unbreakable windows.
· Structures: materials that are strong like metals and resist corrosion like plastics.
Syllabus of Material Science
MATERIAL SCIENCE AND ENGINEERING
Group A
Introduction to materials . Metal and alloys, ceramics, polymers and semi conducting materials-introduction and application as engineering materials.
Defects in solids . Point, line and surface defects. Diffusion in solids.
Phase diagrams . Mono-component and binary systems, non-equilibrium system, phase diagram and. application in crystalline and non-crystalline solids.
Mechanical properties . Tensile strength, yield strength, elastic and viscoelastic properties, creep, stress relaxation and impact. Fracture behaviour. Ductile fracture, Griffith theory, effect of heat treatment and temperature on properties of metals.
Deformation of metals. Elastic and plastic deformation, slip, twin, dislocation theory, critical resolved shear stress, deformation in polycrystalline materials; season cracking, Bachinger's effect, strengthening mechanics; work hardening recovery, crystallization and grain growth, cold and hot working. .
Group B
Heat treatment . Iron-carbon system. Annealing, normalising, hardening,. critical cooling rate, hardenability, age hardening, surface hardening, tempering.
Thermal properties . High temperature materials; materials for cryogenic application, thermally insulating materials. (Specific heat, thermal conductivity, thermal expansion).
Ceramic materials and polymers . Silicon structures, polymerism . in glass, electrical properties of ceramic phases, rocks, building stones, refractories.
Polymerisation mechanism , structural properties of polymer, thermoplastics, thermosets, elastomer, resins, composites, particles and fibre reinforced composite. Composite material including nano material.
Electronic properties . Magnetism, diamagnetism, paramagnetism, ferromagnetism, magnetic energy, zone theory of solids, zones in conductors and insulators.
Group A
Introduction to materials . Metal and alloys, ceramics, polymers and semi conducting materials-introduction and application as engineering materials.
Defects in solids . Point, line and surface defects. Diffusion in solids.
Phase diagrams . Mono-component and binary systems, non-equilibrium system, phase diagram and. application in crystalline and non-crystalline solids.
Mechanical properties . Tensile strength, yield strength, elastic and viscoelastic properties, creep, stress relaxation and impact. Fracture behaviour. Ductile fracture, Griffith theory, effect of heat treatment and temperature on properties of metals.
Deformation of metals. Elastic and plastic deformation, slip, twin, dislocation theory, critical resolved shear stress, deformation in polycrystalline materials; season cracking, Bachinger's effect, strengthening mechanics; work hardening recovery, crystallization and grain growth, cold and hot working. .
Group B
Heat treatment . Iron-carbon system. Annealing, normalising, hardening,. critical cooling rate, hardenability, age hardening, surface hardening, tempering.
Thermal properties . High temperature materials; materials for cryogenic application, thermally insulating materials. (Specific heat, thermal conductivity, thermal expansion).
Ceramic materials and polymers . Silicon structures, polymerism . in glass, electrical properties of ceramic phases, rocks, building stones, refractories.
Polymerisation mechanism , structural properties of polymer, thermoplastics, thermosets, elastomer, resins, composites, particles and fibre reinforced composite. Composite material including nano material.
Electronic properties . Magnetism, diamagnetism, paramagnetism, ferromagnetism, magnetic energy, zone theory of solids, zones in conductors and insulators.
Wednesday, January 9, 2008
SECTION 'B' EXAMINATION ( CODE 4 )
CHEMICAL ENGINEERING (Branch Code 4)
Compulsory Subjects
IC 402 Engineering Management
CH 403 Chemical Reaction Engineering
CH 404 Transport Phenomena
CH 405 Chemical Engineering Thermodynamics
CH 406 Chemical Process Principles
CH 407 Chemical Engineering Equipment Design
Optional Subjects (Any three from any one Group)
Group I Transfer Process
CH 411 Mass Transfer Operations
CH 412 Heat Transfer Operations
CH 413 Mechanical Operations
CH 414 Fluid Mechanics
CH 415 Instrumentation and Control
Group II Process Technology
CH 421 Fuels and Combustion
CH 422 Biochemical Engineering
CH 423 Mechanical Operations
CH 424 Chemical Process Technology
CH 425 Instrumentation and Control
Group III Process Industries
CH 431 Polymer Materials and Technology
CH 432 Petrochemical Engineering
CH 433 Industrial Pollution and Control
CH 434 Fertilizer Technology
CH 435 Instrumentation and Control
CIVIL ENGINEERING (Branch Code 05)
Compulsory Subjects
IC 402 Engineering Management
CV 403 Civil Engineering Materials and Construction Practices
CV 404 Geo-technical and Foundation Engineering
CV 405 Water Resources Systems
CV 406 Principles of Geo-informatics
CV 407 Analysis and Design of Structures
Optional Subjects (Any three from any one Group)
Group I Structural Engineering
CV 411 Advanced Structural Analysis
CV 412 Design of RCC and Pre-stressed Concrete Structures
CV 413 Design of Steel Structures
CV 414 Structural Dynamics
CV 415 Seismic Design of Structures
Group II Environmental Engineering
CV 421 Principles of Environmental Engineering
CV 422 Environmental Engineering — Processes and Management
CV 423 Air Pollution and Its Control
CV 424 Design of Water and Wastewater Treatment Systems
CV 425 Waste Management and Environmental Impact Assessment
Group III Infrastructure and Urban Development
CV 431 Transportation Engineering
CV 432 Traffic and Transportation Systems
CV 433 Town Planning and Urban Development
CV 434 Design of Water and Wastewater Treatment Systems
CV 435 Construction Management Systems
COMPUTER SCIENCE AND ENGINEERING (Branch Code 06)
Compulsory Subjects
IC 402 Engineering Management
CP 403 Data Structures
CP 404 Programming Languages
CP 405 Pulse and Digital Circuits
CP 406 Computer Architecture
CP 407 Systems Analysis and Design
Optional Subjects (Any three from any one Group)
Group I Computer Applications
CP 411 Graph Theory and Combinatorics
CP 412 Computer Networks
CP 413 Operating Systems
CP 414 Artificial Intelligence
CP 415 Database Management Systems
Group II Hardware Engineering
CP 421 Parallel Processing
CP 422 Computer Networks
CP 423 Operating Systems
CP 424 Computer Graphics
CP 425 Micro-processors and Micro-controllers
Group III Information Technology
CP 431 Pattern Recognition and Image Processing
CP 432 Theory of Computation
CP 433 Operating Systems
CP 434 Computer Graphics
CP 435 Software Engineering
ELECTRICAL ENGINEERING (Branch Code 07)
Compulsory Subjects
IC 402 Engineering Management
EL 403 Power Systems
EL 404 Circuit and Field Theory
EL 405 Electrical Machines
EL 406 Measurements and Control
EL 407 Design of Electrical Systems
Optional Subjects (Any three from any one Group)
Group I Power Systems
EL 411 Energy Systems
EL 412 Power Electronics
EL 413 High Voltage Engineering and Power Apparatus
EL 414 Power System Performance
EL 415 Micro-processors and Micro-controllers
Group II Electrical Machines and Drives
EL 421 Advanced Aspects of Electrical Machines
EL 422 Power Electronics
EL 423 Electrical Drives
EL 424 Electrical Power Utilization
EL 425 Micro-processors and Micro-controllers
Group III Control and Instrumentation
EL 431 Control Theory
EL 432 Power Electronics
EL 433 Process Control Systems
EL 434 Instrumentation Systems
EL 435 Micro-processors and Micro-controllers
ELECTRONICS AND COMMUNICATION ENGINEERING (Branch Code 08)
Compulsory Subjects
IC 402 Engineering Management
EC 403 Communication Engineering
EC 404 Circuit Theory and Control
EC 405 Micro-processors and Micro-controllers
EC 406 Electronic Circuits
EC 407 Design of Electronic Devices and Circuits
Optional Subjects (Any three from any one Group)
Group I Telecommunication Engineering
EC 411 Broadcast and Television Engineering
EC 412 Radar and Antenna Engineering
EC 413 Microwave Engineering
EC 414 Optical and Satellite Communication
EC 415 Computer Networks and Communication
Group II Integrated Circuits & Systems Engineering
EC 421 Digital Hardware Design
EC 422 Pulse and Digital Circuits
EC 423 IC Design Techniques
EC 424 Solid State Physics and Semiconductor Devices
EC 425 Software Engineering
Group III Control and Instrumentation
EC 431 Sensors and Transducers
EC 432 Industrial Instrumentation and Computer Control
EC 433 Biomedical Electronics
EC 434 Signal Processing
EC 435 Control Systems
CHEMICAL ENGINEERING (Branch Code 4)
Compulsory Subjects
IC 402 Engineering Management
CH 403 Chemical Reaction Engineering
CH 404 Transport Phenomena
CH 405 Chemical Engineering Thermodynamics
CH 406 Chemical Process Principles
CH 407 Chemical Engineering Equipment Design
Optional Subjects (Any three from any one Group)
Group I Transfer Process
CH 411 Mass Transfer Operations
CH 412 Heat Transfer Operations
CH 413 Mechanical Operations
CH 414 Fluid Mechanics
CH 415 Instrumentation and Control
Group II Process Technology
CH 421 Fuels and Combustion
CH 422 Biochemical Engineering
CH 423 Mechanical Operations
CH 424 Chemical Process Technology
CH 425 Instrumentation and Control
Group III Process Industries
CH 431 Polymer Materials and Technology
CH 432 Petrochemical Engineering
CH 433 Industrial Pollution and Control
CH 434 Fertilizer Technology
CH 435 Instrumentation and Control
CIVIL ENGINEERING (Branch Code 05)
Compulsory Subjects
IC 402 Engineering Management
CV 403 Civil Engineering Materials and Construction Practices
CV 404 Geo-technical and Foundation Engineering
CV 405 Water Resources Systems
CV 406 Principles of Geo-informatics
CV 407 Analysis and Design of Structures
Optional Subjects (Any three from any one Group)
Group I Structural Engineering
CV 411 Advanced Structural Analysis
CV 412 Design of RCC and Pre-stressed Concrete Structures
CV 413 Design of Steel Structures
CV 414 Structural Dynamics
CV 415 Seismic Design of Structures
Group II Environmental Engineering
CV 421 Principles of Environmental Engineering
CV 422 Environmental Engineering — Processes and Management
CV 423 Air Pollution and Its Control
CV 424 Design of Water and Wastewater Treatment Systems
CV 425 Waste Management and Environmental Impact Assessment
Group III Infrastructure and Urban Development
CV 431 Transportation Engineering
CV 432 Traffic and Transportation Systems
CV 433 Town Planning and Urban Development
CV 434 Design of Water and Wastewater Treatment Systems
CV 435 Construction Management Systems
COMPUTER SCIENCE AND ENGINEERING (Branch Code 06)
Compulsory Subjects
IC 402 Engineering Management
CP 403 Data Structures
CP 404 Programming Languages
CP 405 Pulse and Digital Circuits
CP 406 Computer Architecture
CP 407 Systems Analysis and Design
Optional Subjects (Any three from any one Group)
Group I Computer Applications
CP 411 Graph Theory and Combinatorics
CP 412 Computer Networks
CP 413 Operating Systems
CP 414 Artificial Intelligence
CP 415 Database Management Systems
Group II Hardware Engineering
CP 421 Parallel Processing
CP 422 Computer Networks
CP 423 Operating Systems
CP 424 Computer Graphics
CP 425 Micro-processors and Micro-controllers
Group III Information Technology
CP 431 Pattern Recognition and Image Processing
CP 432 Theory of Computation
CP 433 Operating Systems
CP 434 Computer Graphics
CP 435 Software Engineering
ELECTRICAL ENGINEERING (Branch Code 07)
Compulsory Subjects
IC 402 Engineering Management
EL 403 Power Systems
EL 404 Circuit and Field Theory
EL 405 Electrical Machines
EL 406 Measurements and Control
EL 407 Design of Electrical Systems
Optional Subjects (Any three from any one Group)
Group I Power Systems
EL 411 Energy Systems
EL 412 Power Electronics
EL 413 High Voltage Engineering and Power Apparatus
EL 414 Power System Performance
EL 415 Micro-processors and Micro-controllers
Group II Electrical Machines and Drives
EL 421 Advanced Aspects of Electrical Machines
EL 422 Power Electronics
EL 423 Electrical Drives
EL 424 Electrical Power Utilization
EL 425 Micro-processors and Micro-controllers
Group III Control and Instrumentation
EL 431 Control Theory
EL 432 Power Electronics
EL 433 Process Control Systems
EL 434 Instrumentation Systems
EL 435 Micro-processors and Micro-controllers
ELECTRONICS AND COMMUNICATION ENGINEERING (Branch Code 08)
Compulsory Subjects
IC 402 Engineering Management
EC 403 Communication Engineering
EC 404 Circuit Theory and Control
EC 405 Micro-processors and Micro-controllers
EC 406 Electronic Circuits
EC 407 Design of Electronic Devices and Circuits
Optional Subjects (Any three from any one Group)
Group I Telecommunication Engineering
EC 411 Broadcast and Television Engineering
EC 412 Radar and Antenna Engineering
EC 413 Microwave Engineering
EC 414 Optical and Satellite Communication
EC 415 Computer Networks and Communication
Group II Integrated Circuits & Systems Engineering
EC 421 Digital Hardware Design
EC 422 Pulse and Digital Circuits
EC 423 IC Design Techniques
EC 424 Solid State Physics and Semiconductor Devices
EC 425 Software Engineering
Group III Control and Instrumentation
EC 431 Sensors and Transducers
EC 432 Industrial Instrumentation and Computer Control
EC 433 Biomedical Electronics
EC 434 Signal Processing
EC 435 Control Systems
syllabus of section A
SECTION 'A' EXAMINATION ( DIPLOMA SCHEME )
AD 301 Fundamentals of Design and Manufacturing
AD 302 Material Science and Engineering
AD 303 Computing and Informatics
AD 304 Society and Environment
AD 301 Fundamentals of Design and Manufacturing
AD 302 Material Science and Engineering
AD 303 Computing and Informatics
AD 304 Society and Environment
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