Introduction to Materials (PDF)

Introduction to Materials What is Material Science? Systematic and scientific study and usage of various materials is known as material science. Need for study Material Science In Designing, fabrication and smooth functioning of machines and structures. E.g.: - Design of...

Introduction to Materials What is Material Science? Systematic and scientific study and usage of various materials is known as material science. Need for study Material Science In Designing, fabrication and smooth functioning of machines and structures. E.g.: - Design of gears, Superstructure of a building, Oil refineries, IC chip. Selection of the material with optimum properties for given operating conditions. E.g.: - Strength and ductility. Deterioration of material properties. E.g.: -Exposure to high temperature and corrosion reduces material strength. Cost of the material and manufacturing cost. Classification of material science Material Science Mechanical Science of Engineering Engineering Behavior of Metals Metallurgy Materials Metals Materials in the study of material science are classified as that part of matter which is useful for an engineer in the practice of his profession. Usually materials refer to solids. The word science refers to physical science, in particular to physics and chemistry. The engineering usefulness of the matter is always kept in mind in material science. Therefore material science refers to interdisciplinary study of matter. Material Science is an applied science which studies correlations between the compositions, structures and properties of materials. It concerns itself with the nature and behaviour of all engineering materials. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 1 Metallurgy is the science and technology of metals. Metallurgy deals exclusively with the study of metals and alloys, their occurrences and behaviour. It is divided into two large groups: 1. Process or Extractive Metallurgy: The science of obtaining metals from ores, including mining, concentration, extraction and refining metals and alloys. 2. Physical Metallurgy: The science concerned with general relationship between the composition, structure and properties of metals & alloys as well as changes brought about by thermal, chemical and mechanical treatment. Materials which find application in engineering can be broadly classified into: (i) Metals and Alloys: These materials are characterized by their high thermal and electrical conductivity. They also possess good strength and ductility. They are usually opaque and may be polished to a high shine. Examples: Cast Irons, Steels, Aluminium, Silver, Gold, Brasses, Bronzes, etc. (ii) Ceramics and Glasses: Ceramics are compounds like certain metallic and non-metallic oxides, e.g., glass. These materials are hard and brittle. They are good insulators of electricity and heat. Examples: MgO, ZnO, SiC, Silica, Concrete, Cement, Rubber, etc. (iii) Polymers: These are organic compounds like plastics. They have low density and are good insulators of electricity. Examples: Plastics, Polyethylene, Poly Vinyl Chloride (PVC), Nylon, Cotton, Rubber, etc. Each of the above group of materials has their own set of properties. Some of the most important properties of engineering materials are: Mechanical Properties: Strength, hardness, ductility, malleability, toughness, resilience, creep, fatigue, etc. Physical properties: Shape, size, density, porosity, colour, etc. Chemical properties: Acidity, alkalinity, composition, corrosion resistance, atomic number, molecular weight, etc. Electrical properties: Electrical conductivity, resistivity, dielectric constant, dielectric strength, power factor, etc. Thermal properties: Specific heat, refractoriness, thermal conductivity, etc. Aesthetic properties: Feel, texture, appearance, shine, etc. Optical properties: Refractive index, absorptivity, etc. The above properties of materials guide us in selection of materials for specific applications. To give a few examples, an aircraft structure has to be built with materials having low density but high strength (i.e., high strength to weight Dept. of Aero & Auto Engg, M.I.T, Manipal Page 2 ratio); a steel melting furnace has been lined with refractory materials to withstand high temperatures; buildings and structures have to be built with materials having high compressive strength to withstand heavy loads; springs and machine beds are made of materials which are resilient in order to absorb shocks and vibrations; and so on. Decisions regarding engineering materials are an essential part of all branches of engineering practice. Hence, the right choice of the material for the given requirement, the proper use of that material and even the production of that new material are all the direct responsibility of the engineer. Criteria in selection of materials: Selection of engineering materials for engineering applications depends upon factors such as:  Properties in relation to the intended use  Availability of materials  Economy Properties in relation to the intended use: Before selecting a material for any particular use, it is necessary to assess the properties of the materials required to make it suitable for that purpose. Depending on the properties required an engineer will have to select any existing materials, or in special cases new materials will have to be developed. For example, mechanical strength is important if significant loads are to be supported; thermal conductivity is important if high temperatures are to be encountered, etc. Availability of materials: In many cases availability of the materials causes a problem. After studying property requirements an engineer may suggest a material which meets the requirement. But if the material is not easily available, then the engineer sometimes may even have to select a material having inferior properties roughly equal to the ideal one. Economy: Economy plays a vital role in selecting materials. A cheap material easy to fabricate and longer service life is always preferred. However, many a time, engineer will have to strike a compromise between material cost, fabrication cost and service life attainable. Science of Metals 1. Structure of Atoms- Electron structure of elements, modern periodic table. 2. Crystal Structure- Crystal & metallic structure of metals, atom arrangements. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 3  3. Bonds in Solid-bonds between atoms and molecules. Bond strength. 4. Electron Theory of Metals-Different models and their study in applications of study of conductors, insulators, semi-conductors. Study of super conductors Mechanical Behaviour of metals 1. Mechanical Properties of Metal: Stress and strain, Tensile properties, Hardness, Brittle, Ductile, Malleable properties 2. Mechanical Tests of Metals 3. Deformation of Metals 4. Fracture of Metals- Fracture and NDT techniques Engineering Metallurgy 1. Iron-Carbon Alloy System-Structure of iron & steel, Iron-carbon diagram, transformation of alloys and steel under various condition 2. Heat treatment– Objective and process of heat treatment 3. Corrosion of metals- corrosion prevention, life enhancement improving outward appearance of metals. Engineering Material 1. Ferrous and Non- ferrous materials 2. Organic materials- rubber plastics etc 3. Composite materials 4. Semi-conductor and transistor 5. Insulating materials 6. Magnetic materials Types of materials 1. Crystalline i. E.g.:-Iron, Copper, Aluminum 2. Amorphous or Non crystalline i. E.g.: - Wood, paper, plastics, glass What is Crystals? “Small body having a regular polyhedral form, bounded by smooth surfaces, acquired under the action of intermolecular forces.” Crystals are also known as grains. Single Crystals 1. Periodic arrangement of atoms 2. Repeated throughout the structure without interruption 3. All unit cells have same orientation 4. Not found in nature 5. Produced artificially by controlling environment 6. Used in modern technologies- IC’s, Sugar, Salt, diamond etc Dept. of Aero & Auto Engg, M.I.T, Manipal Page 4 Polycrystalline Solids 1. Solid is composed of many small crystals or grains, 2. Mismatch between regions where grains meet. 3. These regions are called grain boundaries. 4. The grains have different crystallographic orientation. Types of solids: The principal forms of solids are (1) Crystalline solids & (2) Amorphous solids. Solids in which the arrangement of atoms in three dimensions is regular and repetitive are known as crystalline solids. Solids in which the arrangement of atoms in three dimensions is not regular and not repetitive and the pattern breaks at different planes are known as non-crystalline or amorphous solids.A comparison between the features of crystalline & amorphous solids: Crystalline solids Amorphous solids The basic structural unit is a The basic structural unit is a molecule. crystal/grain. Number of crystals come together to Chains of molecules come together to form a crystalline solid. form an amorphous solid. Each crystal contains number of Chains of molecules are random repetitive blocks called unit cells within the solid and occur in no which are neatly arranged in a particular order. They are irregular and symmetrical order. lack symmetry. Density of crystalline solid is generally Density of amorphous solid is high. generally high. They have a stable structure. Their structure is unstable. These melt at a definite melting These melt over a range of temperature. temperature. e.g. metals, alloys, NaCl and many e.g. glass, polymer, elastomer, etc. oxides Dept. of Aero & Auto Engg, M.I.T, Manipal Page 5 Although all materials can be classified as crystalline or amorphous there are certain materials which can occur as both. For example, Silicate can occur as crystalline solid (quartz) or as a non-crystalline solid (silicate glass). It is also true that many materials exist as combinations of both crystalline and amorphous solids. They have short range order and are termed as aggregates. Space lattice and lattice points: A space lattice may be defined as an Unit cell Lattice points infinite array of points in three dimensions in which every point has surroundings or environment identical to that of every point in the array. In case of a crystalline solid, it is the three dimensional network of imaginary lines connecting the atoms. The points of intersection of these lines are lattice points about which the atoms or ions making the solid are located. Space lattice, unit cell & lattice points Unit Cell The unit cell is the smallest structural unit or building block that can describe the crystal structure. Repetition of the unit cell generates the entire crystal. Parameters of unit cell Types of Crystal system 1. Cubic crystal system 2. Tetragonal crystal system Dept. of Aero & Auto Engg, M.I.T, Manipal Page 6  3. Hexagonal crystal system 4. Orthorhombic crystal system 5. Rhombohedral crystal system 6. Monoclinic crystal system 7. Triclinic crystal system Summary of crystal systems Si No Crystal System Axial Lengths Interaxial angles (α,β,γ) (a,b,c) 1 Cubic a=b=c α=β=γ=90 2 Tetragonal a=b≠c α=β=γ=90 3 Hexagonal a=b≠c α=β=90,γ=120 4 Orthorhombic a≠b≠c α=β=γ=90 5 Rhombohedral a=b=c α=β=γ≠90 6 Monoclinic a≠b≠c α=β=90,γ≠90 7 Triclinic a≠b≠c α≠β≠γ≠90 Body centered cubic structure (BCC): In BCC lattice, atoms are located at the eight corners of the cubic cell and one atom at the geometric center of the volume of the cube. Thus a total of 9 atoms are present. If the atoms are represented as spheres, the center atom touches each corner atom, but these corner atoms do not touch each other. BCC unit cell Each corner atom is shared by eight adjacent cubes whereas, the atom at the center cannot be shared by adjacent cubes. Hence, the contribution of each corner atom per unit cell is 1/8th (one-eighth) and contribution of each body centered atom per unit cell is 1 (one). Therefore, the effective number of atoms per unit cell may be calculated as follows: Dept. of Aero & Auto Engg, M.I.T, Manipal Page 7  Contribution of 8 corner atoms/unit cell = 8 × 1/8 =1 Contribution of 1 body centred atom/unit cell =1×1 =1  Effective no. of atoms/unit cell of BCC is 2 atoms Examples of metals that crystallize as BCC crystal structure are: Cr, -Fe, -Fe, Mo, Ve, Na, Li, Ba, W, -brass, etc. Face cantered cubic structure (FCC): This structure is also sometimes known as Cubic Close Packed (CCP) structure. In FCC lattice, atoms are located at the eight corners of the cubic cell and six atoms are located at the face centers of six faces of the cubic cell. But, none of the atoms are located at the body center of the cubic cell. If the FCC unit cell atoms are represented as spheres, each face centered atom touches its adjacent corner atoms. The eight corner atoms do not touch each other. Each corner atom is shared by eight adjacent cubes. Hence, the contribution of each corner atom per unit cell is 1/8 th (one-eighth). Each face centered atom is shared by two adjacent cubic cells. Hence, the contribution of each face centered atom per unit cell is ½ (half). Therefore, the effective number of atoms per unit cell may be calculated as follows: Contribution of 8 corner atoms/unit cell = 8 × 1/8 =1 Contribution of 6 face centered atom/unit cell = 6 × 1/2 =3  Effective no. of atoms/unit cell of FCC is 4 atoms This indicates that FCC structure is more densely packed than BCC structure. Examples of metals that crystallize as FCC crystal structure are: Al, Ni, Cu, Au, Ag, Pb, Pt, -Fe, -Sn, -brass etc. Hexagonal close packed (HCP) structure OR Close packed hexagonal (CPH) structure: In HCP structure, the basic unit cell is a hexagonal prism. One atom is present at each corner of the hexagonal prism, i.e., 12 corner atoms. At the center of each hexagonal basal plane a face centered atom is present, i.e., 2 face centered atoms. In addition to these, there are 3 atoms lying inside the hexagonal unit cell, in the form of an equilateral triangle mid way between the two basal Dept. of Aero & Auto Engg, M.I.T, Manipal Page 8 planes. If the basal planes are divided into six equilateral triangles, the three additional atoms are nested in the centre of alternate equilateral triangle. Thus, a total of 17 atoms are present. Each face centered atoms of the basal planes touch the adjacent corner atoms. All the 3 atoms at the center of the hexagonal unit cell touch the face centered atoms of the two basal planes but they do not touch all the corner atoms. The parallel repetition of this hexagonal unit cell along three perpendicular directions will not built up the entire lattice. The true unit cell of the hexagonal lattice is the portion PQRSKLMN as shown in fig. he hexagonal prism therefore contains two whole true unit cells and two halves of the true unit cells. Each corner atom of the basal plane is shared by six neighbouring hexagonal unit cells (3 below the corner atom + 3 above the corner atom). Therefore, the contribution of each corner atom per hexagonal unit cell is 1/6th atom. Each face centered atom of the basal plane is shared by two hexagonal unit cells (1 below the face centered atom + 1 above the face centered atom). Therefore, the contribution of each face centered atom of the basal plane per hexagonal unit cell is 1/2 atom. The three internal atoms contribute totally three atoms per hexagonal unit cell. Therefore, the effective number of atoms per unit cell may be calculated as follows: Contribution of 12 corner atoms/unit cell = 12 × 1/6 = 2 Contribution of 2 face centered atom/unit cell = 2 × 1/2 =1 Contribution of 3 internal atoms/unit cell =3×1 =3  Effective no. of atoms/unit cell of HCP is 6 atoms This indicates that HCP structure is more densely packed than BCC structure. Examples of metals that crystallize as HCP crystal structure are: Mg, Zn, Be, Co, graphite, etc. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 9  Q R S P C A c B a M L a K N HCP unit cell To find Atomic packing factor It is defined as the percentage amount of volume inside a unit cell that has been occupied by the effective number of atoms of that unit cell. Volume of effective number of atoms per unit cell APF= ∗ 100 Volume of the unit cell 𝑁∗𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑝ℎ𝑒𝑟𝑖𝑐𝑎𝑙 𝑎𝑡𝑜𝑚 APF= ∗ 100 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 N- Effective number of atoms per unit cell r- Radius of spherical atom V- Volume of the unit cell Atomic packing factor (APF) or Packing efficiency (): It is defined as the percentage amount of volume inside a unit cell that has been occupied by the effective number of atoms of that unit cell. It is given by the percentage ratio of total volume of the effective number of atoms per unit cell to the volume of the unit cell. Volume of Effective number of atoms per unit cell APF or   100 Volume of the unit cell N  Volume of a spherical atom  100 Volume of the unit cell  4 r 3  N     3  100 V Dept. of Aero & Auto Engg, M.I.T, Manipal Page 10 where, N = Effective number of atoms per unit cell r = Radius of the spherical atom V = Volume of the unit cell The APF gives a measure of the closeness of packing (or density of packing) of atoms inside the unit cell. Atomic packing factor for FCC unit cell: The relationship between the lattice constant ‘a’ and the atomic radius ‘r’ can be r found by considering the atomic r arrangement on one face of a FCC unit cell a r as shown in fig 2.10. r a2 + a2 = (4r)2 2a2 = 16r2 a  a  2 2 r   4r 2 Fig 2.10 Atomic arrangement on a face of the FCC unit cell Effective number of atoms, NFCC = 4 per unit cell  4 r 3  N FCC     FCC   3  100 V  4 r 3  N FCC      3  100 a3  4 r 3  4   3  100  16 r  2 2 100 3  3  4r  3 64 r 3    2   74.04% Dept. of Aero & Auto Engg, M.I.T, Manipal Page 11 Atomic packing factor for BCC unit cell: The relationship between the lattice constant ‘a’ and the atomic radius ‘r’ can be Z found by considering the r atomic arrangement on one solid diagonal of a BCC r a unit cell as shown in fig 2.11. Triangle XPQ is right- r Y angled at P. r a X a2 + a2 = (XY)2 P 2a2 = (XY)2 a Triangle XYZ is right- Fig 2.11 Atomic arrangement on a solid diagonal of the BCC unit cell angled at Y with hypotenuse XZ = 4r (XY)2 + (YZ)2 = (XZ)2 i.e., 2a2 + a2 = (4r)2 4r a 3a2 = 16r2  3 Effective number of atoms, NBCC = 2 per unit cell  4 r 3  N BCC     BCC   3   100 V  4 r 3  N BCC      3   100 a3  4 r 3  2   3   100  8 r  3 3  100 3  3  4r  3 64 r 3    3  68.02% Dept. of Aero & Auto Engg, M.I.T, Manipal Page 12 Atomic packing factor for HCP unit cell: The volume of the hexagonal unit cell, R V = Area of the hexagonal basal plane × height The hexagonal basal plane can be divided into six a h equilateral triangles as shown in fig 2.12. Then, area of the hexagonal basal plane = 6 × area of triangle P a Q PQR Fig. 2.12 Area of HCP basal plane a 3 Altitude of the triangle PQR, h = tan 60o × a/2 = 2 a 3 a2 3 Area of triangle PQR = ½ × a × h = ½ × a × 2 = 4 a2 3 3 3a 2 Area of the hexagonal basal plane = 6 × 4 = 2 Volume of the hexagonal unit cell, V = Area of the hexagonal basal plane × height 8 ca  1.633a Height of HCP unit cell, 3 3 3a 2 8 a  V = 2 × 3 = 3 2a 3 It may be observed that, a = 2r Dept. of Aero & Auto Engg, M.I.T, Manipal Page 13   4 r 3  N HCP     HCP   3  100 V  4 r 3  N HCP      3  100 3 2a 3  4 r 3  6   3  24 r 3 1   100   100 3 2  (2r )3 3 24 2r 3  74.05% Crystallographic Planes and Directions – Miller Indices: Miller indices were introduced in 1839 by the British mineralogist William Hallowes Miller. The method was also historically known as the Millerian system, and the indices as Millerian, although this is now rare. It is necessary to be able to define planes and directions within crystalline solids. A labeling system that uses combinations of 3 integers or “indices” to define crystallographic directions and planes is used. This system is known as the Miller System. It has some similarities with conventional vector systems especially for simple cubic systems. For more complex crystal structures (such as found in geology and magnetic/electronic devices) then the Miller system becomes very useful indeed. Crystallographic Directions: A crystallographic direction is basically a vector between two points in the crystal. Any direction can be defined by following a simple procedure. Step 1: Position the vector so that it is in convenient position within your chosen coordinate system. It is convenient to position the vector so as to pass through the origin of the coordinate system. Any vector may be translated throughout the crystal lattice by moving parallel to itself. Step 2: Find the projection of the vector onto each of the three axes in terms of the unit cell dimensions. The projection on the axes are nothing but the ‘steps’ to be moved parallel to X, Y & Z axes starting from the origin (start point) of the vector to reach its end point. These projections on the three axes are expressed in terms of the unit cell dimensions. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 14 Step 3: To get the Miller Index we express the vector as a set of whole numbers (by multiplying or dividing throughout by a common number), and enclose in square brackets [uvw]. Notation of crystallographic directions: There are certain conventions used when expressing Crystallographic directions using the Miller system. Directions are enclosed in square brackets. Negative directions are represented by putting a bar above the appropriate integer, e.g. is the opposite direction to. The choice of negative directions is arbitrary but it is essential to be consistent. Example problem on Miller indices for crystallographic direction: Find the Miller indices for the vector shown in the unit cell shown in fig. 2.13 where, a=b=c. Fig. 2.13 Example problem on direction indices Step 1: The given vector is passing through the origin of the coordinate system. Step 2: Take the intercepts of the vector on the X, Y & Z axes. Intercept on X Intercept on Y Intercept on Z axis axis axis a/2 b 0 Step 3: Since a=b=c, the intercepts will be: ½, 1 & 0. Multiplying throughout by 2 and enclosing within square brackets we get, to be the direction indices of the given vector. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 15 A few more examples to determine the directional indices are shown in the fig. 2.14. Fig. 2.14 Examples of some crystallographic directions Families of Equivalent Directions: Due to the symmetry of crystal structures the spacing and arrangement of atoms may be the same in several directions. These are known as equivalent directions. A group of equivalent directions is known as a family of directions. Families of directions are written in angular brackets. These families of directions will become important when we consider slip directions. For example consider the FCC unit cell. The arrangement of atoms lying diagonally across a face is always the same. So, all the directions running diagonally across a face are equivalent. You could list each direction in turn and see they all have a similar form. = , , , , , = , , , , , Crystallographic Planes: Crystallographic planes can be represented in a similar way to crystallographic directions by using three indices. As when finding a direction you must ensure Dept. of Aero & Auto Engg, M.I.T, Manipal Page 16 the plane is in a convenient position in your co-ordinate system. You then need to follow these steps: Step 1: Position the plane so that it is in convenient position within your chosen coordinate system. It is convenient to position the plane so that it will not pass through the origin of the coordinate system. If the plane is passing through the origin, shift the origin to the adjacent unit cell or consider an identical plane in the adjacent unit cell. Any plane may be translated throughout the crystal lattice by moving parallel to itself. Step 2: Find the points of intersection of the plane and the axes in terms of the unit cell dimensions. If a plane is parallel to an axis its intercept is considered infinite. Step 3: Take the reciprocals of the intercepts. Step 4: Convert to smallest possible whole numbers (by multiplying or dividing throughout by a common number) and enclose the indices in round brackets (parenthesis). Notation of crystallographic planes: There are certain conventions used when expressing Crystallographic planes using the Miller system. Planes are enclosed in round brackets (parenthesis). Negative directions are represented by putting a bar above the appropriate integer, e.g. (111) is the plane opposite to the plane (111). The choice of negative planes is arbitrary but it is essential to be consistent. Example problem on Miller indices for crystallographic plane: Find the Miller indices for the plane shown in fig. 2.15(a) where, a=b=c. (a) Example problem on plane indices (b) Example problem on plane indices Dept. of Aero & Auto Engg, M.I.T, Manipal Page 17 Step 1: The given plane passes through the origin. Hence, the origin is shifted to the adjacent unit cell as shown in fig. 2.15(b). Step 2: Find the intercepts of the plane with the X, Y & Z axes: Intercept on X Intercept on Y Intercept on Z axis axis axis  -b c/2  -1 1/2 Step 3: Take the reciprocals of the intercepts we get: 0, -1 & 2 Step 4: Enclose the indices in round brackets (parenthesis) we get (012) to be Miller indices of the given plane. A few more examples of the Miller indices for some planes are shown in fig. 2.16. Examples of some crystallographic planes Dept. of Aero & Auto Engg, M.I.T, Manipal Page 18 Families of Equivalent planes: Due to the symmetry of crystal structures the spacing and arrangement of atoms may be the same in several planes. These are known as equivalent planes, and a group of equivalent planes are known as a family of planes. Families of planes are written in curly brackets. For example think about a FCC crystal structure. The arrangement of atoms on each face is the same, so the planes describing each face are equivalent. In this case they are all part of the {001} family of planes. {001} = (001), (010), (100), (001) , (010) , (100) Close-packed planes are tightly packed planes of atoms. They are very important in understanding the behaviour of dislocations, which you will learn about in the next chapter. In FCC unit cells the {111} planes are all close packed. {111} = (111), (111) , (111) , (111) , (111) , (111) In BCC unit cells there are no fully close-packed planes, although there are close packed directions on the {110} planes. Relationship between crystallographic planes & directions: Conventionally, a plane in analytical geometry is expressed by a vector normal to the plane under consideration. It may be observed from figure 2.15, that the miller indices for a plane and a vector normal to it are same. For example, the miller indices for a plane perpendicular to X axis is (100) and the direction indices of a vector normal to it is. Similarly, the miller indices for a plane perpendicular to Z axis is (001) and the direction indices of a vector normal to it is. In general, if (uvw) is the miller indices of a plane, then the direction indices of a vector normal to it is [uvw]. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 19  Comparison of crystallographic planes and directions Crystal Imperfections An ideal crystal is a perfect crystal in which each atom has identical surroundings. Real crystals are not perfect. A real crystal always has a large number of imperfections in the lattice. Since real crystals are of finite size, they have a surface to their boundary. At the boundary, atomic bonds terminate and hence the surface itself is an imperfection. One can reduce crystal defects considerably, but can never eliminate them entirely. Crystals defects are known as crystal imperfections. Types of defects: 1. Point Imperfections/ Zero dimensional defects 2. Line or Linear Imperfections/ One Dimensional Defects 3. Surface or Plane Imperfections (or Two Dimensional Defects) 4. Volume Imperfections (Three Dimensional Defects) 1. Point imperfections A point imperfections present in a crystal if a regular atom in the crystal lattice is absent or an extra atom (an impurity atom or an atom from the same crystal) is present in the regular crystal lattice structure Point defects exist during the original crystallization itself. These defects may be formed due to:  Irradiation with high energy particles Dept. of Aero & Auto Engg, M.I.T, Manipal Page 20   Plastic deformation process  Quenching  By increasing the temperature, that increases the amplitude of vibration of atoms. Point defects cause local distortion of the crystal lattice.Schottky & Frankel point defects influence certain physical properties of metals ( Like electrical conductivity, magnetic properties) as well as phase transformation in metals and alloys. 1) Vacancy Defect – lattice points at which atoms are absent. 2) Interstitial Defect – presence of extra atom in between regular lattice points. 3) Substitutional/Impurity-replacement of regular atom by a substitutional or impurity (foreign) atom. 4) Ionic Defects- presence or absence of ions causing electrical/magnetic disturbances i) Schottky defect ii) Frankel defect Vacancy Defect: Vacancies are formed by atoms leaving their regular positions at the lattice points and jumping to the surface of the crystal or occupying the evacuated place of an atom at the crystal surface or, less frequently, by atoms jumping into an interstitial position. Absence of atoms Vacancy Defect Thermal vacancies – Usually, some atoms in the crystals will have their kinetic energies greater than the mean kinetic energy value of other atoms which is characteristic of temperature. Such atoms, located nearer to the surface of the crystal, jump to the surface of the crystal. Their places may be occupied by other atoms, farther from the surface, whose lattice points are freed. This is how thermal vacancies are created. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 21 Thermal vacancies are formed at the free surfaces of crystals, grain boundaries, blow holes and cracks. The number of thermal vacancies at temperatures nearer to the melting point may reach one percent of the total number of atoms in the crystals. A crystal which is in thermodynamic equilibrium at a given temperature, has an equilibrium concentration of thermal defects and a definite distribution of them according to size. The number of vacancies at equilibrium of a given temperature can be determined from the equation:  E    n d  Ne  KT  where, nd = The number of defects N = Total number of atomic sites /m3 E = Energy of activation necessary to form the defect K = Boltzmann constant T = Absolute temperature On cooling, the vacancy concentration is lowered by diffusion of vacancies to grain boundaries or dislocations. (B) Interstitial Defect: Interstitial defects are Presence of extra atom formed by jumping of an atom into an interstitial position of a regular crystal lattice. This defect may also be created due to the insertion of atoms of foreign material in the regular crystal lattice of a crystal. Interstitial Defect In the closely packed lattices, typical of most metals, the energy required to form interstitial atoms is several times greater than that required to form thermal vacancies. For this reason, the interstitial atoms are rare in metals and thermal vacancies are the main point defects in such metals. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 22 Schottky’s Defect: Cations Anions A vacancy created due to the absence of a pair of ions (cation & anion) in an ionic crystal is called Missing Cation Missing Anion as Schottky’s Defect. The vacancy of the missing pair of ions maintains electrical neutrality in the crystal. Schotty’s Defect in an ionic crystal Frenkel’s Defect: Cations Anions A Frenkel’s defect is formed when an ion is Initial position of displaced Displaced Cation displaced from its regular location to an interstitial location. Usually, the cations being Cation the smaller sized ions, are the ones which are displaced to the interstitial position. The electrical neutrality of the crystal is not effected due to the presence of this defect. Frenkel’s Defect in an ionic crystal Substitutional/ Impurity atom (C) Substitutional/Impurity defect: If a foreign atom substitutes a parent atom in the regular lattice structure, such a defect is called as substitutional defect. Substitutional/Impurity Effects of points defects:  Point defects cause local distortion of the crystal lattice.  Displacement (relaxation) around a vacancy occurs only in the first two layers of neighbouring atoms, and is only a fraction of the inter atomic distance.  The displacement of the neighbouring atoms around an interstitial atom in close packed lattices is considerably greater than that around a vacancy.  Schottky and Frenkel point defects influence certain physical properties of metals (like electrical conductivity, magnetic properties, etc.) as well as phase transformations in metals and alloys. (2) Linear Imperfections or Line Defects or Dislocations: Dept. of Aero & Auto Engg, M.I.T, Manipal Page 23 The Line/Linear defects in crystalline solids that result from lattice distortion centered about a line is called dislocation. A dislocation can be considered as a localized linear distortion of the atomic arrangement caused by the displacement of one group of atoms from an adjacent group. These dislocations are naturally occurring during the crystal formation itself. Dislocations play an important role in the mechanical behaviour of materials. Dislocations are of two types: (A) Edge Dislocation (B) Screw Dislocation Edge Dislocation: An edge dislocation in its cross section is essentially a localized distortion of the crystal lattice due to the presence of an extra half plane of atoms. Extra half plane of atoms  (a) Cross sectional view of an Edge Dislocation Line Edge Dislocation (b) 3D view of an Edge Dislocation From the figure, we can see that above the edge dislocation line, an extra half plane of atoms is present. The length of the half plane of atoms (along the edge dislocation line) may extend over several interatomic distances. Above the line of dislocation the atoms of the crystal are closer together, below they are farther apart. A dislocation produces compressive stress below the dislocation and tensile stress above it. According to convention, a dislocation is said to be positive if the extra half plane is in the upper part of the crystal and is denoted by the symbol ‘’ (inverted T). It is said to be negative, if it is in the lower part of the crystal and is denoted by a symbol ‘T’. The difference between positive and negative dislocations is purely arbitrary. A turning a crystal up-side-down, a positive dislocation is converted into a negative one and vice-versa. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 24 Screw Dislocation: It is also the localized distortion of the crystal lattice such that the atomic planes are bent into a helical surface about a central distortion line. If we go around the centre of distortion so produced, we move parallel to the line of distortion by one inter Screw Dislocation Line atomic distance. It is similar 3D view of a Screw Dislocation to a screw moving forward or backward by a distance equal to its pitch when turned through 360 o. This centre line of distortion is known as ‘Screw Dislocation Line’. Difference b/t edge dislocation and screw dislocations Edge dislocation Screw dislocation 1. An edge dislocation is a A screw dislocation is also a line defect line defect where there is a formed when a part of the crystal displaces discontinuity in a line of angularly over the remaining part. atoms. 2. Atomic bonds around Atomic bonds around a dislocation line dislocation line undergo undergo shear distortion. tensile & compressive stresses. 3. Force required to form Force required will be more edge dislocation is less. 4. Travel faster under load. Will travel slowly under load. 3. Surface imperfections a) Grain Boundaries b) Tilt boundaries c) Twin boundaries d) Stacking Faults Dept. of Aero & Auto Engg, M.I.T, Manipal Page 25 a) Grain boundaries They are those regions which separate crystal of different orientations. It is formed when two adjoining growing crystals meet at their surfaces. b) Tilt boundaries It is a type of low angle grain boundary where the orientation difference between two neighboring crystals is less than 100. c) Twin boundaries This is another type of surface imperfections where the atomic arrangement on one side of the twin boundary is a mirror reflection of the arrangement on the other side. This are formed generally during annealing or mechanical working of metals. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 26 d) Stacking faults They are surface imperfections created by an error in the stacking sequence of atomic planes in the crystals. 4. Volume Defects Volume defects are those defects like cracks foreign inclusions etc. which are three dimensional and are much larger than other types of imperfections. These are normally introduced into solids during processing and fabrication techniques and have a considerable effect on the properties of materials. Fig: Shows the photographic view of various defects seen in the crystal lattice structure of a metal Define diffusion “Diffusion refers to the net flux of any species, such as ions, atoms, electrons, holes, and molecules”. The magnitude of this flux depends on initial concentration gradient and temperature. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 27 There are three types of diffusion mechanisms, 1. Atomic diffusion by vacancy migration. 2. Atomic diffusion by interstitially migration 3. Diffusion by interchange of atoms. Factors affecting diffusion 1. Temperature 2. Crystal Structure 3. Atomic packing factor 4. Grain boundaries 5. Grain size 6. Atomic size 7. Concentration gradient Various Properties of materials 1. Physical Properties: - shape, size, color, specific gravity, porosity, structure, finish etc. 2. Mechanical Properties: - elasticity, plasticity, ductility, brittleness, hardness, toughness, stiffness, resilience, creep, endurance, strength etc. 3. Technological Properties: - malleability, machinability, weldability, formability or workability, castability etc 4. Thermal Properties: - Specific heat, thermal conductivity, thermal expansion, latent heat, thermal stresses, thermal shock etc. 5. Electrical Properties: - conductivity, resistivity, relative capacity, dielectric strength etc. 6. Chemical Properties:- atomic weight, equivalent weight, molecular weight atomic number, acidity, alkalinity, chemical composition, corrosion, etc. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 28  Stress strain Diagram Characteristic Behaviour Property Units Strength Strong, weak Ultimate strength MPa Elastic strength Elastic then plastic Yield strength MPa Stiffness Flexible, rigid Modulus of MPa elasticity Ductility Draws, forms easily % Elongation, Dimensionless % Area reduction Hardness Resists surface indentation Brinell No. MPa Corrosion resistance Resists chemicals, Galvanic series Activity oxidation number Fatigue resistance Endures many load cycles Endurance limit MPa Conductivity Conducts, Insulates Thermal (Btu/hr) (heat, electric) conductivity Electrical conductivity Creep resistance Time dependent stretching Creep strength MPa Impact resistance Shock, impact loads Charpy energy N-m Dept. of Aero & Auto Engg, M.I.T, Manipal Page 29 Density (mass) Heavy, light Mass density N/m3 Density (weight) Weight density Temperature Softens, or melts easily Melting point degrees C, F tolerance Types of deformation 1. Elastic deformation 2. Plastic deformation 1. Elastic deformation When material retains its original shape and size even after subjecting load. 2. Plastic deformation The term plastic deformation may be defined as the process of permanent deformation which exists in a metal even after the removal of the stress. It is due to this property that the metals are subjected to various operations like rolling, forging, drawing, spinning etc. The plastic deformation in crystalline materials occurs at temperatures lower than 0.4 Tm. There are two basic modes of plastic deformation 1. Slip or gliding 2. Twinning The slip mode is common in many crystals at ambient and elevated temperatures. At low temperatures the mode of deformation changes over to twinning in a number of cases. Difference b/t Elastic deformation and plastic deformation Si No Elastic Deformation Plastic Deformation 1 It is a deformation, which It is a permanent deformation which appears and disappears with the exists even after the removal of stress application and removal of stress 2 The elastic deformation is the The plastic deformation takes place beginning of the progress of after the elastic deformation has deformation stopped Dept. of Aero & Auto Engg, M.I.T, Manipal Page 30  3 It takes place over a short range It takes place over a wide range of of stress-strain curve stress-strain curve 4 In elastic deformation, the In plastic deformation, the strain strain reaches its maximum occurs simultaneously with the value after the stress has application of stress reached its maximum value Slip The term slip may be defined as a shear deformation which moves the atoms through many inter atomic distances relative to their initial positions. The slip occurs most readily in specific directions on certain crystallographic planes. Generally, the slip plane is the plane of greatest atomic density and the slip direction is the closest-packed direction within the slip plane. Planes of greatest atomic density are also the most widely spaced planes in the crystal structure The resistance to slip is generally less for these planes than for any other set of planes. The slip plane together with the slip direction is called the slip system. Several slip systems may exist for a particular crystal structure. Number of slip systems in F.C.C metals are 12 in B.C.C metals 48 and H.C.P metals only 3.Certain metals show additional slip systems with increased temperature. Slip direction remains the same while the slip plane changes with the temperature. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 31  Twinning The term twinning may be defined as the plastic deformation which takes place along two planes due to a set of forces applied on a given metal piece. Twinning process, the movement of atoms is only a fraction of inter-atomic distance. The twinning occurs due to the growth and movement of dislocations in the crystal lattice. Difference b/t Slip and twinning Sl Slip Twinning No 1 In this process, the deformation takes In this process, the deformation place due to the sliding of atomic planes takes place due to orientation of over the others. However, the one part of the crystal with respect orientation of the crystal above and to the other. The twinned portion below the slip plane is the same after is the mirror image of the original deformation as before. lattice. 2 In this process, the atomic movements In this process, the atomic are over large distances. movements are over a fraction of atomic spacing 3 It requires lower stress for atomic It requires higher stress for atomic movements. movements Dept. of Aero & Auto Engg, M.I.T, Manipal Page 32 4 It occurs on widely spaced planes. It occurs on every atomic plane involved in the deformation within the twinned region of the crystal Slip v/s Twinning 1. Amount of movement In slip atoms move a whole number of interatomic spacing, while in twinning atoms move fractional amount. 2. Microscopic appearance: Slip appears as thin lines and twinning as broad lines or bands. 3. Lattice orientation: In slip there a little change in lattice orientation and steps are visible only on the surface which can be removed by polishing. In twinning there is different lattice orientation and polishing will not remove the steps. Mechanism of strengthening the metals Types of Strengthening a) Strengthening by grain size reduction b) Solid-solution strengthening c) Strain hardening 1) Strengthening by grain size reduction Adjacent grains normally have different crystallographic orientations and, of course, a common grain boundary. During plastic deformation, slip or dislocation motion must take place across this common boundary.A fine- grained materials is harder and stronger than one that is coarse grained, since the former has a greater total grain boundary area to dislocation motion. It Dept. of Aero & Auto Engg, M.I.T, Manipal Page 33 should also be mentioned that grain size reduction improves not only strength, but also the toughness of many alloys. 2) Solid-solution strengthening Another technique to strengthen and harden metals is alloying with impurity atoms that go into either substitutional or interstitial solid solution.Alloys are stronger than pure metals because impurity atoms that go into solid solution ordinarily impose strains on the surrounding host atoms.Resistance to slip is greater when impurity atoms are present. 3) Strain hardening It is the phenomenon whereby a ductile metal becomes harder and stronger as it is plastically deformed below recrystallization temperature. Sometimes it is also called work hardening. Most metals strain hardens at room temperature. Recovery, Recrystallization and Grain growth Inducing plastic deformation to a polycrystalline metal specimen at temperatures that are lower than its melting point produces micro structural and property changes that include 1. Change in grain shape 2. Work hardening 3. An increase in dislocation density. A fraction of the energy expended in deforming the material is stored in the material as strain energy, which would change its properties like electrical, corrosion resistance, etc. These can be revert back to stage where no strain was applied. Recovery During recovery, some of the stored internal strain energy is relieved by virtue of strain dislocation motion; as a result of enhanced atomic diffusion at elevated temperatures, number of dislocation are reduced. Some physical properties like electrical & thermal conductivities are recovered. Recrystallization: Dept. of Aero & Auto Engg, M.I.T, Manipal Page 34 Even after recovery the grains are still in high strain energy state, recrystallization is the formation of a new set of strain-free and equaled grains. After recrystallization some mechanical properties are restored like ductility. Grain growth: After recrystallization, the strain free grain tends to grow if the metal specimen is left at elevated temperatures. Consequently, small grains are mixed with large grains and form a single big grain. Dept. of Aero & Auto Engg, M.I.T, Manipal Page 35