(For B.E. Mechanical Engineering Students) AIR WALK PUBLICATIONS (Near All India Radio) 80, Karneeshwarar Koil Street Mylapore, Chennai - 600 004. Ph.: 2466 1909, 94440 81904 Email: [email protected], [email protected]www.airwalkpublications.com METALLURGY AND MATERIALS ENGINEERING As per New Revised Syllabus of APJ Abdul Kalam Technological University Dr. S.Ramachandran, M.E., Ph.D., Dr. A. Anderson, M.E., Ph.D., Mr. N. Balaji, M.E., Sathyabama University Jeppiaar Nagar, Chennai - 600 119
As per New Revised Syllabus ofAPJ Abdul Kalam Technological University
Dr. S.Ramachandran, M.E., Ph.D.,
Dr. A. Anderson, M.E., Ph.D.,
Mr. N. Balaji, M.E.,
Sathyabama UniversityJeppiaar Nagar, Chennai - 600 119
and
First Edition: July 2016
ISBN : 978-93-84893-52-1
Price : Rs. 300/-ISBN:978-93-84893-52-1
SYLLABUS
ME210 METALLURGY AND MATERIALSENGINEERING
Chapter 1: IntroductionEarlier and present development of atomic structure; attributes
of ionization energy and conductivity, electronegativity and alloying;correlation of atomic radius to strength; electron configurations;electronic repulsionPrimary bonds: - characteristics of covalent, ionic and metallic bond:attributes of bond energy, cohesive force, density, directional andnon-directional and ductility.Properties based on atomic bonding:- attributes of deeper energywell and shallow energy well to melting temperature, coefficient ofthermal expansion - attributes of modulus of elasticity in metalcutting process –Secondary bonds:- classification- hydrogen bondand anomalous behavior of ice float on water, application- atomicmass unit and specific heat, application. (brief review only, noUniversity questions and internal assessment from these portions).
Crystallography:- Crystal, space lattice, unit cell- BCC, FCC,HCP structures - short and long range order – effects of crystallineand amorphous structure on mechanical properties.
Coordination number and radius ratio; theoretical density;simple problems - Polymorphism and allotropy.
Miller Indices: - crystal plane and direction (brief review) -Attributes of miller indices for slip system, brittleness of BCC, HCPand ductility of FCC - Modes of plastic deformation: - Slip andtwinning.
Schmid’s law, equation, critical resolved shear stress,correlation of slip system with plastic deformation in metals andapplications.
Syllabus S.1
Chapter 2: CrystalsMechanism of crystallization: Homogeneous and
heterogeneous nuclei formation, under cooling, dendritic growth, grainboundary irregularity.
Effects of grain size, grain size distribution, grain shape, grainorientation on dislocation/strength and creep resistance - Hall - Petchtheory, simple problems
Classification of crystal imperfections: - types ofdislocation – effect of point defects on mechanical properties - forestof dislocation, role of surface defects on crack initiation.
Burgers vector –dislocation source, significance of Frank - Readsource in metals deformation - Correlation of dislocation density withstrength and nano concept, applications.
Significance high and low angle grain boundaries on dislocation– driving force for grain growth and applications during heattreatment.
Polishing and etching to determine the microstructure andgrain size.
Fundamentals and crystal structure determination by X –raydiffraction, simple problems –SEM and TEM.
Diffusion in solids, Fick’s laws, mechanisms, applications ofdiffusion in mechanical engineering, simple problems.
Chapter 3: Phase Diagrams and Heat TreatmentPhase diagrams: - Limitations of pure metals and need of
alloying - classification of alloys, solid solutions, Hume Rothery‘s rule- equilibrium diagram of common types of binary systems: five types.
Coring - lever rule and Gibb‘s phase rule - Reactions: -monotectic, eutectic, eutectoid, peritectic, peritectoid.
Detailed discussion on Iron-Carbon equilibrium diagram withmicrostructure and properties changes in austenite, ledeburite, ferrite,cementite, special features of martensite transformation, bainite,spheroidite etc.
Heat treatment: - Definition and necessity – TTT for aeutectoid iron–carbon alloy, CCT diagram, applications - annealing,normalizing, hardening, spheroidizing.
Tempering:- austermpering, martempering and ausforming -Comparative study on ductility and strength with structure ofpearlite, bainite, spherodite, martensite, tempered martensite andausforming.
Hardenability, Jominy end quench test, applications- Surfacehardening methods:- no change in surface composition methods:-Flame, induction, laser and electron beam hardening processes-change in surface composition methods : carburizing and Nitriding;applications.
Chapter 4: Strengthening Mechanism Alloys Steels,Cast Iron and Non-ferrous Alloys
Types of Strengthening mechanisms: - work hardening,equation - precipitation strengthening and over ageing, dispersionhardening.
Cold working: Detailed discussion on strain hardening;recovery; re-rystallization, effect of stored energy; recrystallizationtemperature - hot working Bauschinger effect and attributes in metalforming.
Alloy steels:- Effects of alloying elements on steel: dislocationmovement, polymorphic transformation temperature, alpha and betastabilizers, formation and stability of carbides, grain growth,displacement of the eutectoid point, retardation of the transformationrates, improvement in corrosion resistance, mechanical properties
Nickel steels, Chromium steels etc. - Enhancement of steelproperties by adding alloying elements: - Molybdenum, Nickel,Chromium, Vanadium, Tungsten, Cobalt, Silicon, Copper and Lead.
High speed steels:- Mo and W types, effect of different alloyingelements in HSS
Syllabus S.3
Cast irons: Classifications; grey, white, malleable andspheroidal graphite cast iron etc, composition, icrostructure,properties and applications.
Principal Non ferrous Alloys: - Aluminum, Copper,Magnesium, Nickel, study of composition, properties, applications,reference shall be made to the phase diagrams whenever necessary.
Ways to improve fatigue life – effect of temperature on fatigue,thermal fatigue and its applications in metal cutting
Fracture: – Brittle and ductile fracture – Griffith theory ofbrittle fracture – Stress concentration, stress raiser – Effect of plasticdeformation on crack propagation. transgranular, intergranularfracture - Effect of impact loading on ductile material and itsapplication in forging, applications - Mechanism of fatigue failure.
Structural features of fatigue: - crack initiation, growth,propagation - Fracture toughness (definition only) – Ductile to brittletransition temperature (DBTT) in steels and structural changesduring DBTT, applications.
Mechanism of creep deformation - threshold for creep,prevention against creep - Super plasticity: need and applications
Composites:- Need of development of composites -geometricaland spatial Characteristics of particles – classification - fiber phase:- characteristics, classifications - matrix phase:- functions – only needand characteristics of PMC, MMC, and CMC – applications of
composites: aircraft applications, aerospace equipment and instrumentstructure, industrial applications of composites, marine applications,composites in the sporting goods industry, composite biomaterials.
Modern engineering materials: - only fundamentals, need,properties and applications of, intermetallics, maraging steel, superalloys, Titanium – introduction to nuclear materials, smart materialsand bio materials.
Ceramics:- coordination number and radius ratios- AX, AmXp,AmBmXp type structures – applications.
Syllabus S.5
Contents
1. Introduction
1.1 Introduction..................................................................... 1.21.1.1. Earlier and Present Development of atomic structure .............................................................. 1.2
1.2 Attributes of Ionization Energy and Conductivity.... 1.31.3 Electronegativity............................................................. 1.41.4 Alloying............................................................................ 1.41.5 Correlation of Atomic Radius to Strength ................. 1.41.6. Electron Configurations................................................ 1.51.7 Electronic Repulsion ...................................................... 1.61.8. Primary Bonds............................................................... 1.7
1.9. Bond Energy .................................................................. 1.111.10. Cohesive Force............................................................. 1.111.11. Density.......................................................................... 1.121.12. Directional and Non-directional Bonds .................... 1.121.13. Ductility ........................................................................ 1.121.14. Properties, Based on Atomic Bonding ..................... 1.131.15. Attributes of Modulus of Elasticity in Metal Cutting Process ........................................................... 1.161.16. Classification of Secondary Bonds............................ 1.16
1.16.1 Hydrogen Bond ................................................. 1.171.17. Anomalous Behaviour of Ice Float on Water ......... 1.181.18. Atomic Mass Unit (amu) ........................................... 1.181.19. Specific Heat................................................................ 1.191.20 Crystallography............................................................. 1.19
1.20.1. Structure ........................................................... 1.201.20.2 Crystal................................................................ 1.201.20.3. Space lattice ..................................................... 1.21
1.21. Unit Cell ...................................................................... 1.221.21.1. Lattice parameters ........................................... 1.231.21.2 Crystal systems ................................................. 1.251.21.3 Bravais lattices (Bravais crystal system) ...... 1.27
1.22 Metallic Crystal Structure .......................................... 1.281.22.1 Simple Cubic (SC)............................................ 1.281.22.2 Body Centered Cubic structure (BCC)........... 1.311.22.3 Face Centered Cubic Structure (FCC)........... 1.341.22.4 Hexagonal Close Packed (HCP) structure ..... 1.37
1.23. Short and Long Range Order ................................... 1.401.24. Coordination Number ................................................. 1.411.25. Radius Ratio ................................................................ 1.411.26. Theoretical Density ..................................................... 1.411.27. Polymorphism Or Allotropy....................................... 1.441.28. Miller Indices............................................................... 1.451.29 Crystallographic Direction and Planes ..................... 1.45
1.29.1. Steps for determining crystallographic direction indices .............................................. 1.451.29.2. Miller indexing of crystal plane. ................... 1.47
1.30. Attributes of Miller Indices Slip System. ............... 1.481.31. Brittleness of BCC, HCP and Ductility of FCC .... 1.501.32. Modes of Plastic Deformation ................................... 1.50
1.32.1. Deformation by Slip........................................ 1.511.32.2. Mechanism of Slip .......................................... 1.511.32.3. Deformation by Twinning............................... 1.521.32.4. Mechanism of twinning .................................. 1.53
2.5.1 ASTM grain size number.................................. 2.122.6 Effect of Point Defects On Mechanical Properties ... 2.122.7 Source of Dislocation ..................................................... 2.132.8 Cross Slip........................................................................ 2.132.9 Dislocation Climb ........................................................... 2.142.10 Jogs and Kinks ............................................................ 2.15
2.10.1 Super jogs.......................................................... 2.172.11 Forest of Dislocation.................................................... 2.182.12 Role of Surface Defects on Crack Initiation............ 2.192.13 Burgers Vector.............................................................. 2.192.14 Dislocation Source........................................................ 2.202.15 Frank and Read Source.............................................. 2.202.16 Correlation of Dislocation Density with Strength . 2.222.17 Mechanism of Crystallization..................................... 2.232.18 Effect of Grain Size, Grain Distribution, Grain Shape, Grain Orientation on Dislocation/strength and Creep Resistance. ............ 2.26
Contents C.3
2.19 Significance of High and Low Angle Grain Boundaries on Dislocation ....................................... 2.302.20 Driving Force for Grain Growth and Applications in Heat Treatment ..................................................... 2.312.21 Polishing and Etching to Determine the Microstructure and Grain Size ................................. 2.322.22 X-Ray Diffraction ......................................................... 2.342.23 Transmission Electron Microscope (TEM) .............. 2.412.24 Scanning Electron Microscope (SEM) ....................... 2.442.25 Diffusion in Solids ....................................................... 2.46
2.25.1 Steady - State diffusion................................... 2.472.25.2 Non-steady state diffusion ............................... 2.48
2.26 Diffusion Mechanism ................................................... 2.502.27 Applications of Diffusion............................................. 2.52
3. Phase Diagrams and Heat Treatment
3.1 Constitution of Alloys.................................................... 3.23.1.1 Limitations of pure metals................................ 3.33.1.2 Need of an alloy................................................. 3.3
3.2 Classification of Alloys .................................................. 3.43.2.1 Solid solution ...................................................... 3.43.2.2 Types of Solid Solution ..................................... 3.53.2.3 Solubility.............................................................. 3.9
3.5.1 Introduction ......................................................... 3.143.5.2 Importance, objective and Information of phase diagram ..................................................... 3.153.5.3 Classification of phase diagrams ..................... 3.16
3.5.4 Definition and Basic Concepts / Terminology in phase diagram ................................................ 3.163.5.5 Phase Diagram ................................................... 3.233.5.5.1 Construction of phase diagram ..................... 3.233.5.6 Phase diagram of pure substance.................... 3.25
3.6 Classification of Equilibrium Diagrams .................... 3.283.6.1 Binary Eutectic phase diagram........................ 3.283.6.1.1 Eutectic phase diagram of two metalscompletely soluble in liquid but completely insoluble in solid state. ................... 3.353.6.2 Peritectic Reaction (Binary Peritectic alloy system)......................................................... 3.373.6.3 Binary Monotectic system.................................. 3.403.6.4 Eutectoid Reactions ............................................ 3.413.6.5 Peritectoid reaction ............................................. 3.433.6.6 Phase diagram with intermediate phases andcompounds ..................................................................... 3.44
3.6.6.1 The SiO2 Al2O3 (Silica - Alumina) System 3.453.6.7 Ternary phase diagram ..................................... 3.47
Cu Ni System .................................................... 3.503.8.2 Interpretation of phase diagram ...................... 3.533.8.3 Lever Rule ........................................................... 3.563.8.4 Microstructure development in Isomorphous Alloys.................................................................... 3.573.8.5 Solid solution strengthening ............................. 3.603.8.6 Mechanical properties of Isomorphous alloys . 3.60
3.9 Iron - Carbon System ................................................... 3.62
Contents C.5
3.9.1 Introduction ......................................................... 3.623.9.2 Iron - Iron Carbide Equilibrium diagram ..... 3.623.9.2.1 Solid phases in Fe-Fe3C phase diagram ... 3.663.9.2.2 Invarient Reactions in Fe-Fe3C Phase diagram (Pertitectic, Eutectic and Eutectoid reactions in
Fe Fe3C phase diagram) .......................................... 3.693.9.2.3 Slow cooling of plain carbon steels(Hypoeutectoid steels and Hypereutectoid steels) ...... 3.723.9.2.4 Transformation in structure of cast iron..... 3.773.9.2.5 Micro-constituents of Iron carbon diagram . 3.79
3.10 Basics of Heat Treatment .......................................... 3.823.10.1 Definition of Heat treatment........................... 3.823.10.2 Objectives of Heat Treatment.......................... 3.83
3.11 ISothermal Transformation Diagrams (or) Time - Temperature - Transformation (TTT) Diagrams (or) S - Curves (or) C - Curves .............. 3.84
3.11.1 Bainite................................................................ 3.913.11.2 Spheroidite......................................................... 3.943.11.3 Transformation of Austenite upon continuouscooling ............................................................................ 3.963.11.4 Critical Cooling Rate ....................................... 3.98
3.23.1 The Jominy End quench test - Procedure .... 3.1443.24 Residual Stresses due to Hardening and Quench Cracks ............................................................ 3.1493.25 Case Hardening (or) Surface Hardening .................. 3.1513.26 Surface Hardening Methods [Without Change in Surface Composition] .................................................. 3.151
4.1 Types of Strengthening Mechanism ............................ 4.24.1.1 Work hardening (or) Strain hardening ........... 4.24.1.2 Precipitation strengthening treatment and overageing............................................................................. 4.34.1.3 Dispersion hardening ......................................... 4.7
4.2 Cold Working.................................................................. 4.84.2.1 Detailed Discussion on strain hardening........ 4.94.2.2 Recovery and recrystallisation .......................... 4.104.2.3 Effect of stored energy ....................................... 4.134.2.4 Recrystallization temperature ............................ 4.144.2.5 Grain growth....................................................... 4.15
4.3 Hot Working ................................................................... 4.154.3.1 Bauschiner effect and attributes in Metal forming ..................................................... 4.17
4.4 Alloy Steels ..................................................................... 4.194.4.1 Effect of alloying elements in steels ................ 4.19
4.15 Tool Steels..................................................................... 4.394.15.1. Plain Carbon Steels ........................................ 4.404.15.2. Low Alloy Tool Steels ..................................... 4.414.15.3. High Speed Steels (HSS) ............................... 4.414.15.4. High Chromium High Carbon Steels ........... 4.43
4.16 High Strength Low Alloy Steels (HSLA Steels) ..... 4.434.16.1 HSLA Classification ......................................... 4.444.16.2 Applications of HSLA ...................................... 4.44
4.17 Cast Iron ....................................................................... 4.454.17.1 Composition of cast iron ................................. 4.464.17.2 Effect of Composition Elements on cast irons 4.464.17.3 The influence of cooling rate on the properties of a cast iron.................................... 4.47
4.18 Classification of Cast Iron.......................................... 4.484.18.1. Grey cast iron .................................................. 4.484.18.2. White cast iron ................................................ 4.514.18.3. Malleable Cast Iron ........................................ 4.524.18.4 Spheroidal Graphite Cast Iron (Ductile iron (or) Nodular iron) ............................................. 4.554.18.5 Alloy Cast Iron ................................................. 4.60
4.19 Non Ferrous Metals..................................................... 4.66
Contents C.9
4.19.1 Important Features of Non Ferrous Metals.. 4.664.20 Copper and Copper Alloys.......................................... 4.67
5.4.2 High cycle fatigue............................................... 5.85.5 Fatigue Limit.................................................................. 5.95.6 Characteristics of Fatigue Failure............................... 5.10
5.6.1 Fatigue Strength ................................................. 5.105.6.2 Fatigue Life ......................................................... 5.10
5.7 Factors Affecting Fatigue Strength ............................. 5.105.8 Ways To Improve Fatigue Life.................................... 5.125.9 Effect of Temperature on Fatigue............................... 5.14
5.9.1 Low temperature fatigue.................................... 5.145.9.2 High temperature fatigue .................................. 5.14
5.10 Thermal Fatigue and its Application in Metal Cutting .............................................................. 5.15
5.10.1 Ways to prevent thermal fatigue .................... 5.155.11 Fracture and Types ..................................................... 5.15
5.11.1 Definition of fracture ....................................... 5.155.11.2 Steps in fracture............................................... 5.165.11.3 Types of fracture............................................... 5.165.11.4 Ductile fracture ................................................. 5.175.11.4.1 Mechanism of Ductile Fracture ................... 5.185.11.5 Brittle fracture .................................................. 5.205.11.6. Mechanism of Brittle Fracture (Griffith’s Theory) ............................................... 5.215.11.7 Brittle fracture Vs Ductile fracture................ 5.24
5.12 Stress Concentration and Stress Raisers ................. 5.265.13 Effect of Plastic Deformation on Crack Propagation 5.285.14 Fracture of Materials .................................................. 5.29
5.15 Effect of Impact Loading on Ductile Material and its Application in Forging ................................. 5.305.16 Mechanism of Fatigue Fracture ................................ 5.31
6.5 Mechanism of Creep Deformation ............................... 6.66.6 Prevention of Creep Fracture ...................................... 6.96.7 Parameters of Creep Behaviour .................................. 6.10
6.7.1 Creep - stress and temperature effects ............ 6.116.8 Threshold for Creep....................................................... 6.126.9 Superplasticity ................................................................ 6.136.10 Composites.................................................................... 6.13
6.10.1 Introduction ...................................................... 6.136.10.2 Need for the development of composites....... 6.156.10.3 Definition of composites .................................. 6.166.10.4 Classification of Composites........................... 6.166.10.5 Geometrical and Spatial characteristics ofparticles ......................................................................... 6.17
6.13.1 Aircraft .............................................................. 6.326.13.2 Marine ............................................................... 6.336.13.3 Chemical Industry ........................................... 6.336.13.4 Electrical & Electronics .................................. 6.346.13.5 Construction...................................................... 6.356.13.6 Sporting Goods................................................. 6.356.13.7 Automobiles....................................................... 6.366.13.8 Ordnance........................................................... 6.376.13.9 Agriculture and Fisheries ............................... 6.376.13.10 Mechanical industry ...................................... 6.376.13.11 Anti-corrosion equipment .............................. 6.376.13.12 Bio materials.................................................. 6.38
6.14 Intermetallics (or) Intermetallic Compound ............. 6.386.15 Maraging Steels (Ultra High Strength Steels)........ 6.396.16 Super Alloys and its Properties ................................ 6.416.17 Titanium and its Alloys.............................................. 6.416.18 Nuclear Materials ........................................................ 6.42
6.21.1 Introduction ....................................................... 6.446.21.2 Types of Ceramics ............................................ 6.456.21.3 Characteristics and Properties of Ceramics.. 6.45
Stabilized Zirconia) .......................................... 6.546.22.8 Some other engineering ceramics ................... 6.55
6.23 Classification of Ceramic Materials on the Basis of Applications.............................................................. 6.566.24 Coordination Number .................................................. 6.566.25 Radius Ratio ................................................................. 6.576.26 AX Crystal Structures................................................. 6.576.27 AX - Rock Salt Structure ........................................... 6.576.28 AX - Cesium Chloride Structure ............................... 6.586.29 AX - Zinc Blende Structure ....................................... 6.596.30 Am Xp - Crystal Structure .......................................... 6.596.31 Am Bm Xp - Crystal Structure .................................... 6.60
Earlier and present development of atomic structure;attributes of ionization energy and conductivity, electronegativityand alloying; correlation of atomic radius to strength; electronconfigurations; electronic repulsion (brief review only, noUniversity question from these portions)Primary bonds: – characteristics of covalent, ionic and metallicbond: attributes of bond energy, cohesive force, density, directionaland non–directional and ductility.properties based on atomic bonding: - attributes of deeperenergy well and shallow energy well to melting temperaturecoefficient of thermal expansion - attributes of modulus of elasticityin metal cutting process - Secondary bonds: classification -hydrogen bond and anomalous behavior of ice float on waterapplication - atomic mass unit and specific heat application.Crystallography: Crystal space lattice unit cell - BCC FCC HCPstructures - short and long range order - effects of crystalline andamorphous structure on mechanical properties.Coordination number and radius ratio; theoretical density; simpleproblems - Polymorphism and allotropy.Miller Indices: - crystal plane and direction (brief review) -attributes of miller indices for slip system brittleness of BCC HCPand ductility of FCC - Modes of plastic deformation: SliptwinningSchmid’s law, equation, critical resolved shear stress correlationof slip system with plastic deformation in metals and applications.
1.1 INTRODUCTION
Atoms are basic units of matter and definingstructure of the element. An atom consists of a centralnucleus that is usually surrounded by one or moreelectrons. The central nucleus contains protons andneutrons.
1.1.1. Earlier and Present Development of atomicstructure
(i) The ideas and theories about atoms have beenaround for over 2000 years. In 440 B.C. democritusproposed tiny, indivisible particles in constant motion.However, aristotle did not accept the theory. Aristotlebelieved that matter can be divided infinitely withoutchanging its properties and he did many experiments usingthe scientific method. So more people believed him.
(ii) In 1803, John Dalton gave some basicassumptions (a) All matter consists of tiny particles calledatoms (b) Atoms are indestructible and unchangeable(c) one atom join with other atom, will make newsubstance. Most of the dalton’s theory was correct, but someof it was proven incorrect.
(iii) In 1897, J.J. Thomson discovered the electron.He used a cathode ray tube to conduct an experiment whichshowed that there are small particles inside atoms. Thisdiscovery identified an error in dalton’s atomic theory andhe included the presence of electron’s in atomic theory.
(iv) In 1909, Ernest Rutherford stated that, most ofthe atom’s mass is found in a region in the center callednucleus. He suggested that the nucleus contain a particlewith ve charge called protons. He calculated that nucleus
was 100000 times smaller the diameter of atom. Rutherfordmodel shows that the electrons travel in random patharound the nucleus.
(v) Niel bohr in the year 1913, suggested thatelectron travel around the nucleus in definite path.
(vi) Quantum mechanical model is based on quantumtheory. According to this theory, it is impossible to knowthe exact position and momentum of an electron at thesame time.
(vii) In 1926, Erwin shrodinger discovered thatelectrons donot move in orbits. He stated that electronmoves in waves and they have no exact location.
(viii) In 1932, chadwick discovered neutrons in thenucleus, which have no charge. Neutrons plays a major rolein the mass and radioactive properties of atoms.
(ix) The atomic theory has been further enhanced bythe concept that protons and neutrons are made of smallerunits called Quarks.
1.2 ATTRIBUTES OF IONIZATION ENERGY AND
CONDUCTIVITY
Ionization energy is the amount of energy required toremove an electron from an atom. This is also called asionization potential.
Ionization energy increase from left to right in theperiodic table and decrease from top to bottom. Noble gasespossess very high ionization energy because of the fullvalence shell.
Hg Hg e
Introduction 1.3
Conductivity is a measure of material’s ability toconduct an electric current.
1.3 ELECTRONEGATIVITY
Electronegativity is a measure of the ability of anatom in a molecule to attract electrons to itself.
Electronegativity increases from left to right anddecreases from top to bottom in the periodic table.
1.4 ALLOYING
Alloying is a process in which two or more metalelements are melted together in a definite proportion toform a specific material (or) alloy. Alloys are preferred oversingle element because of its superior properties such ascorrosion resistance, electrical resistance etc.
1.5 CORRELATION OF ATOMIC RADIUS TO STRENGTH
The strength of the bond depends on coulomb’s lawfor force acting between two charged particles where largeforce translates to a stronger bond. The equation is givenby,
F K q1 q2
r2
K constant
q1, q2 charges of ion
r distance between the ions.
Shorter the atomic radius, stronger the bond strength,whereas longer the atomic radius, weaker the bondstrength.
Generally atomic radius increases down the group anddecreases from left to right across a period.
1.6. ELECTRON CONFIGURATIONS
Electronic configuration describes the arrangement ofelectrons in space around the nucleus. Electronicconfiguration is important because it help us to predict thechemical behaviour of a element and also to predictwhether the elements will react or not.
Electronic configuration is generally given by fourquantum numbers. (i) Principal quantum number (ii)azimuthal quantum number (iii) Magnetic quantumnumber and (iv) Spin quantum number. The principal,quantum number n is used to refer the quantum shell to
which the electron belongs n 1, 2, 3. Azimuthal
quantum number l is used to determine the number ofenergy levels in the quantum shell. It is given by lowercase letters s, p, d, f and for every value of n, l can havea value from 0 to n 1. Magnetic quantum number mu
is used to describe the orientation in space of a particularorbital. [ml [l to l]]. Spin quantum number ms is
used to describe the orientation of electron in an atom ms
12
. Paulis exclusion principle states that no two
electron can have same set of four quantum numbers andthe electrons in the atom must have opposite spins in theirorbital.
The electrons in the outer most shell is called valenceelectrons and it is used in forming bonds with adjacentatoms. If there is no valence electrons, then the element is
Introduction 1.5
inert. For an example argon (18) has an electronic
configuration 1S2 2S2 2P6 3S2 3P6 and Neon (10) has
1S2 2S2 2P6. If the outer shells are completely filled, thenthe element is chemically stable. When the outer shell isincomplete, the element will tend to combine with anotherelement to form a stable structure. Example magnesium
1S2 2S2 2P6 3S1
1.7 ELECTRONIC REPULSION
The electronic repulsion is given by valence shellelectron pair repulsion (VSEPR) theory. This theory is usedto predict the shape of a molecule, based on theassumptions that all negatively charged valence electronsrepel each other. There are two types of electron pairssurround the central atom (i) bond pair (ii) lone pair.Bond pair is the active set of electrons and these electronpairs repel each other. Due to repulsion the electron pairsof central atom try to be as far as possible and arrangethemselves in a manner that the force of repulsion betweenthem is minimum. The force of repulsion between lone pairand bond pair is not same and the order of repulsion isgiven by
lone pair – lone pair > lone pair – bond pair >bond pair – bond pair
The shape of the molecule depends upon the no. of.electrons surrounding the central atom
Table (1.1) shows the geometry of the molecule andbond angle with respect to the number of electron pairs.
1.8. PRIMARY BONDS
Primary bonds are generally strong in nature. Thebond energy is higher than the secondary bond. They arebroadly classified into three types: (i) ionic bonds (ii)covalent bonds (iii) Metallic bonds.
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Introduction 1.7
1.8.1. Covalent Bond (or) Homo-Polar BondCovalent bond is formed between two (or) more atoms
by mutual sharing at electrons among themselves in orderto achieve stable structure
Fig (1.1) shows that, Nitrogen has 5 outermostelectron, and requires 3 electrons to complete the shell.Hydrogen has 1 electron in its outermost shell. To have thestable structure, nitrogen atom shares the electron withhydrogen to form a compound, ammonia NH3 [Pyramidal
Shape]
CharacteristicsCovalent bonds are directional. This is because the
shared pair of electrons remains in a definite space betweenthe two atoms.
High bond strength in covalent solids results in highmelting point, high strength and harness. Example Ammonia NH3, Methane CH4
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Fig:1.1.Covalent bond in the formation of amm onia
1.8.2. Ionic bondThe chemical bond formed between two ions with
opposite charges are called ionic bond. It is also called aselectrovalent bond. Example of ionic bond is Nacl.
Fig (1.2) shows that the sodium (Na) has 1 excesselectron in its outermost shell and chlorine (Cl) has 7electrons. When sodium and chlorine placed together, dueto strong electrostatic attraction, the sodium transfer theoutermost electron to chlorine and form the compoundsodium chloride (Nacl).
Example: Nacl, NaBr, KBr, MgO.
Characteristics of Ionic Bond(i) Ionic bonds are non-directional because an ion has
the same attraction from all directions for an ion ofopposite charge.
(ii) Ionic bonds results in the formation of a3-Dimensional structure called an ionic lattice.
(iii) They bound with strong force of attraction thus havehigh melting and boiling point.
1.8.3. Metallic BondingThis type of chemical bond is formed between atoms
in a metallic element. The metallic atom gives up, all theirvalence electrons and become positive ion cores. These
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Fig:1 .2.Electron transfer in Nacl form ation
Introduction 1.9
electrons form an electron cloud, which moves freely insidethe cloud, and gets bond to the several positive ion cores,thus forming a metallic bond. Refer fig (1.3)
Characteristics of Metallic Bond(i) Metallic bond is the characteristics of the elements
having small number of valence electron, Which areloosely held. So that they can easily be released tothe common pool (cloud)
(ii) Metallic bonds is non-specific, non-directional, andacting equally strong in all directions which leadsto highly co-ordinate close-packed structuresaccounting for the unique plastic properties ofmetals and for their ability to form alloys.
(iii) The opaque, lustre of metal is due to the reflectionof light by free electrons.
The amount of energy required to break a bond (or)molecule into its component atoms are called bond energy.
Attributes of Bond Energy1. Magnitude of the bond energy depends on the size
of atoms forming the bond.
2. Bond energy decreases with increase in the numberof lone pairs on the bonded atom. This is due torepulsion of lone pairs of electrons of the two bondedatoms.
C CNo lone
pair
N NOne lone
pair
O OTwo lone
pair
3. Triple bond in a diatomic molecule has greater bondenergy than double bond and double bond hasgreater than single bond between same atoms.
C C C C C Cdecreasing bond energy
1.10. COHESIVE FORCE
Cohesive force is the intermolecular attractive forcebetween the molecule of the same type. During rainfall,water has strong cohesion which pulls its moleculestogether, forming droplets. This force tends to unitemolecules of a liquid, gathering them into relatively largeclusters.
Example: Rain falls in droplets rather than a fine mist
Introduction 1.11
1.11. DENSITY
Density is defined as mass of material per unit
volume. Unit: kg/m3
Density mass
volume
The Temperature changes do not significantly affectthe density of material, although materials do expand onheating but the change in size is very small.
1.12. DIRECTIONAL AND NON-DIRECTIONAL BONDS
Non-directional, bonds occur in metals, as the valenceelectrons are attracted to the nuclei of neighboring atomsbut not in a particular direction.
Example: Ionic bond and metallic bond.
Directional bond, are those where the positive ions arestrongly attracted to the negative ions in the particulardirection
Example: Covalent bond.
1.13. DUCTILITY
The ability of a material to undergo plasticdeformation without fracture is called as ductility. Theductility is determined by tension test using two commonmeasurements
Attributes of deeper and shallower energy wellto melting temperature, coefficient of thermalexpansion
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Introduction 1.13
Physical properties are predicted based on interatomicforces that bind the atoms together. Consider theinteraction of two isolated atoms as they are getting closerfrom an infinite separation. At large distance interactionsare negligible but interactions grow up as they approacheach other. The forces are of two types, attractive forceFA and repulsive force FR and magnitude of each is
function of interatomic distance. The orgin of the attractivepart, depends on the particular type of bonding. Therepulsion between atoms, when they brought to each otheris related to pauli’s exclusion principle.
The net force F is sum of both attractive andrepulsive components. When FA and FR balance (or) become
equal, there is no net force [i.e FA FR 0]
Mathematically, Energy (E) and Force (F) is relatedas
E Fdr
At equilibrium spacing r0, net force is zero and net
energy corresponds to minimum energy E0. The minimum
energy E0 is the binding energy required to separate two
atoms from their equilibrium to an infinite distance apart.Refer Fig 1.4.
The energy E0, shape and depth of the curve defines
various properties like melting point, elastic modulus andthermal expansion coefficient. The curve indicates thestrength of the bond based on the depth of the potentialwell. The more deep the well, the more stable is themolecule.
Increase in depth of the potential well, increases themelting temperature.
Fig 1.5 (a) shows the potential energy curve whichis deeper and narrow. Thus the materials which have deepand narrow curve results in high melting temperature.
Fig 1.5 (b) shows the potential energy curve whichis shallow and broad. Thus the materials which haveshallow and broad curve results in low meltingtemperature.
The mean interatomic distance increase is less withdeeper energy well than that in shallower energy well asshown in [Fig 1.5 (a) and 1.5 (b)]. Greater the bondingenergy, the deeper and more narrow the potential energycurve and thus the increase in interatomic distance withrise in temperature is low. In the case of deeper energywell the curve is deep and narrow which results in lowthermal expansion coefficient and in shallower energy wellthe curve is shallow (not deep and narrow) so it has highthermal expansion co-efficient.
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Introduction 1.15
1.15. ATTRIBUTES OF MODULUS OF ELASTICITY IN
METAL CUTTING PROCESS
The ratio of stress to the corresponding strain isconstant, within the elastic limit. This constant ratio iscalled young’s modulus (or) modulus of elasticity.
E StressStrain
The modulus of elasticity is the measure of stiffnessof the material. When the value of E is small it indicatesthe material is flexible and if the value is large, it indicate,the stiffeness and rigidity of the material. In the metalcutting process, modulus of elasticity of the cutting toolsand holder affect the material rigidity.
1.16. CLASSIFICATION OF SECONDARY BONDS
Secondary BondsSecondary bonds are weaker than the primary bonds.
1.16.1 Hydrogen Bond(i) Hydrogen bond is a special type of dipole bond that
occurs between the molecules in which one end ishydrogen atom.
(ii) The one electron belonging to the hydrogen atom isfairly loosely held and if the adjacent atom in themolecule is strongly electro negative (Oxygen, Fluorine),then this tendency can produce a strong permanentdipole results in bonding.
(iii) The peculiar property of water is because ofhydrogen bonding. In water molecules, the oxygenmolecule binds electron from both hydrogen atomsmore tightly than thehydrogen.
(iv) Hydrogen bonds arestronger thanVanderwaal’s bondbut weaker thancovalent and ionicbond.
(v) The strength ofhydrogen bond is inthe range10 50 kJ/mol
The above Fig 1.6 shows the hydrogen bondingformation in the water molecule.
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Introduction 1.17
1.17. ANOMALOUS BEHAVIOUR OF ICE FLOAT ON
WATER
(i) Most substances in their solid state have moredensity than their liquid state. But water has apeculiar behaviour than those substances.
(ii) Generally all liquids contract on cooling. Water alsocontracts on cooling till 4 C but on cooling below
4 C upto 0 C, water expands
(iii) So ice, the solid state of water has less density thanwater, which making the ice to float on water.[normally ice is 9% less dense than water]
(iv) This is because of hydrogen bonding in the watermolecule. The above mentioned effects are theanomalous behaviour of water.
(v) Example: Rivers and lakes freezes from the top tobottom, thus allowing the aquatics to survive at thebottom even which the surface is frozen.
1.18. ATOMIC MASS UNIT (AMU)
Atomic mass unit is defined to be 1/12th of the massof an atom of carbon - 12. One AMU is approximately equal
to 1.66 10 24 grams
1 AMU 1
NA
NA avagardo’s number 6.023 1024
The mass of an atom in AMU is equal to the sum ofnumber of protons and neutrons in the nucleus.
AMU is used to express the relative mass and alsoto differentiate various isotope of elements.
1.19. SPECIFIC HEAT
Specific heat is defined as amount at heat requiredto raise the temperature of one gram of substance by onedegree celsius.
unit J/g C
Application(i) Substance having low specific heat capacity are
useful in making cooking instruments such as fryingpan, pot, etc because they can quickly heated upwhen small amount of heat is supplied.
(ii) Sensitive thermometers also made from thematerials with small heat capacity
(iii) Heat storage instruments are made from thesubstance with high specific heat capacity.
1.20 CRYSTALLOGRAPHY
1.20.1 IntroductionMost of the inorganic solids we encounter in our daily
life are crystalline. The name crystal comes from the Greekword “krystallos” which means clear ice. The physicalstructure of solid materials of engineering importancedepends mainly on the arrangements of the atoms, ions ormolecules that make up the solid and the bonding forcesbetween them. The physical properties like ductility,malleability, conductivity, insulation ability , magnetic,toughness, hardness etc., are closely related to the structureof the solids. For this, knowledge of crystallography is veryimportant. Crystallography is a branch of science in
Introduction 1.19
which internal structure of crystal, their properties,external or internal symmetries of crystal are studied alongwith the study of geometric form and other physicalproperties by using X-ray, electron beams and neutronbeams, etc.
Solid materials are classified according to theregularity with which atoms are arranged with respect toone another and are classified as crystalline or noncrystalline (Amorphous) materials or solids.
Crystalline solids: If the atoms of a solid are arrangedin a pattern that repeats itself in three dimensions, theyform a solid that has Long Range Order (LRO) and arereferred as crystalline solid. Examples are metals, alloys,some ceramic materials etc. A crystalline material may beeither in the form of single crystal or an aggregate of manycrystals known as poly crystalline.
Non crystalline (or) Amorphous solidsMaterials or solids whose atoms and ions are not
arranged in a long range, periodic and repeatable manner,possess only Short Range Order (SRO) and exist only inimmediate neighbourhood of an atom or a molecule arecalled Non crystalline (or) Amorphous solids. Examples aremost polymers, ceramics, glasses and some metals.
1.20.1. StructureThe arrangement and disposition of atoms within a
crystal is called structure.
1.20.2 CrystalThe systematic geometric pattern arrangement of
1.20.3. Space latticeIt is a periodic arrangement of points arranged in
regular manner and having repeat distances a
, b and c
in
three directions called fundamental lattice vectors. If atomsare placed at these lattice positions, we obtain a crystallinesolid. Refer Fig 1.7.
The repeating unit assembly (atom, molecule, ion orradical) located at each lattice point is called the basis ormotif. Every basis is identical in composition, arrangementand orientation.
So a crystal structure has two specifications
1. Lattice
2. Basis or Motif
Lattice Basis = Crystal structure
So a lattice is completely characterized by six
parameters, three distance a
, b
, c and 3 angles , ,
(crystallographic axes and links axial angles) as shown inFig. 1.8
+
Lattice Basis Crystal structure
Fig. 1.7. Space lattice.
Introduction 1.21
In the context of crystal structure lattice means athree-dimensional array of points coordinating with atomposition (or sphere centres).
1.21. UNIT CELL
A unit cell is the minimum area cell in two dimensionand minimum volume cell in three dimension by repetitionof which, whole crystalline solid may be generated.
Unit cells for most crystal structures areparallelopipeds or prisms having three sets of parallel faces.
X
Z
Ya
c
b
Fig. 1.8. Lattice Parameters of a unit cell.
Z
X
Y
Latticepoints
Lattice points
U nit cell
Fig. 1.9. Lattice structure, space lattice, lattice points and unit cell.
A unit cell is the basic structural unit or building block ofthe crystal structure and defines the crystal structure byvirtue of its geometry and atom positions. Fig. 1.9 showslattice structure, space lattice, lattice points and a unit cell.
Structure The arrangement and disposition of atomswithin a crystal is called structure.
Crystal The systematic geometric pattern arrangement ofatoms and molecules in a solid is called crystal.
1.21.1. Lattice parameters
If a unit cell is so chosen that it contains latticepoints only at its corners, it is called primitive unit cell orsimple unit cell.
A primitive unit cell contains only one lattice pointbecause each point at eight corners is shared with adjacent8 unit cells. The edge length of the unit cell, called a latticeconstant or a lattice parameter, is a lattice translation ina given direction.
(b)(a)Fig.1.10 (A)For the face centered cubic crystal structure: (a) a hard sphere unit cell representation,(b) a reduced - sphere unit cell,
Introduction 1.23
Examples of primitive unit cells are Monoclinic,Triclinic, Simple cubic.
The unit cells which contains more than one latticepoint are called non primitive cells. Examples are Bodycentered and Face centered cubic cells.
Miller indicesMiller indice is a system of notation for designating
crystallographic planes and directions of crystals.
Atomic Packing Factor (APF)APF is the ratio of the volume of the atoms per unit
cell to the total volume occupied by the unit cell.
Coordination numberCoordination number is the number of nearest atoms
directly surrounding a given atom in a crystal i.e., nearestneighbors to an atom in a crystal.
(a) a (b)
Fig 1.10 (B)For the body- centered cubic crystal structure: (a) a hard sphere unit cell representation,(b) a reduced - sphere unit cell
1.21.2 Crystal systemsCrystal system is a scheme by which crystal
structures are classified according to unit cell geometry.This geometry is specified in terms of relationship betweencrystallographic axes a, b, c and interaxial angles , , .These are seven different crystal systems and their latticeparameter relationships and figures showing unit cellgeometrices are shown in table 1.2.
The cubic system has the greatest degree ofsymmetry. Examples are Body Centred Cubic (BCC) andFace Centered Cubic (FCC). Triclinic system is leastsymmetric. Example: Hexagonal Closed Pack (HCP).
1.21.3 Bravais lattices (Bravais crystal system)
There are seven types of crystals depending upontheir axial ratios a, b, c and interaxial angles , , .Bravais showed that there are only fourteen possibledifferent networks of lattice points (space lattices). Thecrystals and corresponding bravais lattices with theircharacteristics are summarized as below table 1.3.
(a) P- type (b) C- type
(c) I- type (d) F- type
Fig. 1.11 Lattice Type.
ab
c
Introduction 1.27
Table 1.3
S.No.
Crystalclass
Interceptson axes
Interaxial anglesBravaislattice
Examples
1. Cubic a b c 90 P, I, FNaCl,CaF2
2. Tetragonal a b c 90 P, I NiSO4
3. Orthorhombic a b c 90P, I, C,
FKNO3,BaSO4
4. Monoclinic a b c 90 P, CNa2 SO3,
FeSO4
5. Triclinic a b c PCuSO4,K2Cr2O7
6. Hexagonal a b c 90, 120 P SiO2, AgI7. Trigonal a b c 90 P CaSO4
1.22 METALLIC CRYSTAL STRUCTURE
There are many different types of crystal structures,some of which are quite complicated. Most of the metalscrystallize in one of the following space lattice structures.
(i) Simple Cubic structure (SC)
(ii) Body Centered Cubic structure (BCC)
(iii) Face Centered Cubic structure (FCC)
(iv) Hexagonal Close Packed structure (HCP)
1.22.1 Simple Cubic (SC)In simple cubic, the lattice
points are situated only at thecorners of the unit cells. Eachcell has eight corners and eightcell meets at each corner.
(a) Effective number of atoms per unit cellEffective number of
atoms per unit cell is theproduct of the number ofatoms per lattice points andthe number of lattice pointsper unit cell.
For SC, there are eightcorners of the cube and ateach corner there is an atom.Each corner atom is stored byeight adjoining cubes, therefore the share of cube
18
8 1 atom/unit cell (Fig.1.12.(b)). Also has 1 lattice
point per unit cell.
(b) Coordination numberIn SC, each lattice
points has six nearestneighbours at a distance of‘a’. Therefore, thecoordination number of SCis 6. There is one atom ateach of the eight cornersof the cube. Any cornerhas four nearest neighbouratom in the same planeand two nearest neighbors,one exactly above and theother exactly below in a vertical plane.
Coordination Number of SC = 4 2 6
Fig. 1.12(b). Isolated unit cell m odel of simple cubic cell.
12
3
4
6A
Fig. 1.12(c). Nearest Neighbours in a SC cell
Introduction 1.29
If ‘a’ is the side of the unit cell, then the distancebetween the nearest neighbors will be equal to ‘a’.
(c) Atomic radiusAtomic radius is defined as the
half of the distance between thecentres of two neighboring atomsassuming that the atoms arespherical in shape and are in contactin a crystal.
Refer Fig. 1.12.(d). One atomis there at each of the corner of acube. If a is the lattice parameter (length of the cube edge)and r is the atomic radius, then we have
a 2r (or) atomic radius r a2
(d) Atomic Packing Factor (APF)Atomic Packing Factor (APF) is defined as “The ratio
of the volume of the atoms per unit cell to the volume ofthe unit cell”. It is the packing of atoms in a unit cell ofthe crystal structure of a material.
(e) Void spaceVacant space left unutilized in a unit cell is called as
void space and is often expressed in percentage.
For general void space 1 APF 100
For simple cubic, void space 1 0.52 100 48%
1.22.2 Body Centered Cubic structure (BCC)In a BCC structure, a unit cell has one atom in the
centre of cube and one atom each at all the corners. Thecorner atoms is shared by other adjoining body centredcubes (Fig. 1.13).
The various properties of BCC are given here.
(a) Effective Number of atomsIn general, the average number of atoms per unit cell
Neffective
Nc
8
Nf
2
Ni
1
where Nc Total No. of corner atoms in unit cell
Nf Total No. of face atoms in unit cell
Ni Inside or centre atom in unit cell
(a) a (b)
Fig.1.13 Body-Centered Cubic crystal structure:(a) a hard sphere unit cell representation,(b) a reduced - sphere unit cell
Introduction 1.31
For BCC Neffective 88
02
11
1 1 2 Atoms/unit
cell
(b) Coordination NumberFor any corner atoms of unit cell, the atom is
surrounded by eight unit cells having eight body centeredatoms, hence the coordination number is 8. Similarly thecentre atom of each unit cell is surrounded by eight equidistant neighbors, hence the coordination number of BCCis 8.
(a) Effective number of atoms per unit cellFor F.C.C, we have
Neff Nc
8
Nf
2
Ni
1
88
62
1 3 4 atoms
Effective Atoms for FCC is 4
(b) Coordination numberFor any corner atom of the unit cell, the nearest are
the face centered atoms and there will be 4 face centeredatoms of the surrounding unit cells in its own place, 4 facecentered atoms below this plane and 4 face centered atomsabove this place.
Hence the coordination number for FCC is 4 4 4 12
(c) Atomic radiusConsider Fig. 1.15
From the le ABG we have AG2 AB2 BG2
r 2r r2 a2 a2
16r2 2a2
a
a
Fig. 1.14. (c) FCC cubic lattice.
Introduction 1.35
so r 2a2
16
a 24
Atomic radius r a 2
4
(d) Atomic Packing Factor (APF)In FCC, Number of atoms per unit cell is 4 and
(f) Examples: Metals possessing FCC structure are Cu,Al, Pb, Ni, Co, etc.
1.22.4 Hexagonal Close Packed (HCP) structure
C
B
a
aH G
F
K E
Basal plane
(c) H.C.P
Fig. 1.16. H.C.P
(d) One of the 3 rhom buses taken from hexagon
AE
K
B D
A �
D
c
a (b) The sharing of atoms by the unit cell.
(a) a reduced - sphere unit cell
H exagonal Close - Packed crystal structure
Fig.1.16
Introduction 1.37
A HCP structure consists of 12 atoms, one at eachcorner of the hexagaonal prism, one atom each at the centreof the hexagonal faces and one atom at the centre of theline connecting the perpendiculars of three rhombuses,namely DFFG, BDGH and BKED as shown in the Fig.1.16 (a) & (c) which combine and form a hexagonal closedpacked structure.
A HCP unit cell requires two parameters Edge of unitcell ‘a’ and the distance between the two hexagonal basalplanes ‘c’. The axial ratio c/a varies from 1.58 for berylliumto 1.88 for cadmium.
(a) Effective number of atoms per unit cell
For HCP Neff Nc
6
Nf
2
Ni
1
Neff 126
22
31
6 atoms/unit cell
The effective number of atoms per unit cell is 6and like FCC, each atom of HCP is in contact with 12nearest neighbors.
(b) Coordination numberIn a HCP each atom has 3 adjacent atoms of top
layer, 3 adjacent atoms in bottom layer and is surroundedby six neighboring atoms in the middle layer. All these 12atoms are in contact with the atom being considered. Hencethe coordination number of HCP is 12.
(c) Atomic radiusIn HCP, one atom exists along the edge of the
hexagon so the nearest distance between two neighbors isa 2r.
(d) Atomic Packing Factor (APF)Refer Fig. 1.16 we have
Area of le DGH 1/2 Base altitude
1/2 a a sin 60 . . . DHG HGD 60
Total area BHGFEK 6 1/2 a2 sin 60 3a2 sin 60
Volume of HCP unit cell Area height 3a2 sin 60 c
...(i)
Atomic radius r a/2
Atomic packing factor (APF)
Volume of atom per unit cell
Volume of unit cell
(APF) 6 4/3 r3
3a2 sin 60 c
a3c sin 60
Assuming c/a ratio of HCP = 1.633 we have
APF
3 1.633 0.866 0.74
(e) Void space
Void space 1 APF 100 1 0.74 26%
(f) ExamplesHCP is found in the following metals zinc, cadmium,
beryllium, magnesium, etc.
Introduction 1.39
Table 1.4 Properties of some crystal structures
Sl.No.
PropertiesSimpleCubeS.C
Bodycentred
cubeB.C.C.
Facecentred
cubeF.C.C.
Closepacked
hexagonal H.C.P.
(i) Unit cellvolume
a3 a3 a3 3 32
a2c
(ii) No. ofatoms perunit cell
1 2 4 6
(iii) Co-ordinationnumber
6 8 12 12
(iv) Nearestneighbourdistance
(2r)
a 3 a2
a2
a
(v) Packingfactor
0.52 0.68 0.74 0.74
(vi) Examples Polonium IronBarium
Chromium
AluminiumCopperLeadGold
ZincMagnesium
1.23. SHORT AND LONG RANGE ORDER
(i) Orderliness is the arrangement of atom andmolecules in solids and liquids.
(ii) Orderliness over distance comparable to theinteratomic distance is called short range order.Whereas orderliness repeated over infinitely greatdistance is called long range order.
Coordination number is the number of nearest atomsdirectly surrounding a given atom in a crystal i.e., nearestneighbors to an atom in a crystal.
1.25. RADIUS RATIO
Radius ratio is defined as ionic radius of the smallerion divided by the ionic radius of the larger ion. Ionic radiusgenerally increase with co-ordination number.
Radius ratio r2
r1
Table 1.5
CoordinationNumber
Radius Ratio Geometry
2 0.155 Linear
3 0.155 0.225 Triangular Planar
4 0.225 0.414 Tetrahedral
6 0.414 0.732 Octahedral
8 0.732 1.00 cubic
Table 1.5 shows the relationship between coordinationnumber and radius ratio
1.26. THEORETICAL DENSITY
The study of the crystal structure in a metallic solidis used for the calculation of theoretical density by thebelow mentioned formula
NcA
VcNa
Introduction 1.41
Where Nc no. of. atoms in unit cell
A atomic weight
Vc Volume of unit cell
NA Avagardo’s number.
Problems on Theoretical density1.1. Iron has BCC structure, an atomic radius of 0.124 nmand an atomic weight of 55.85g/mol. compute the theoreticaldensity and compare it with the experimental density.
Experimental density 7.87g/cm3
Solution:
Nc A
Vc NA
For BCC structure, Nc 2 atoms/unit cell
Volume of unit cell 4R 3
3
4 0.124 10 7
3
3
2.34 10 23 cm
2 55.85
2.34 10 23 6.022 10 23
7.90 g/cm3
1.2. NaCl crystal is FCC lattice. Calculate its theoretical
density if the edge of the cube is 5.62 10 10 m long and
( Na ions occupies the centre of the edges and centreof cube )
Effective number of Cl 8 18
6 12
4
( Cl ion occupies the corners and centre of faces ofthe cube )
Effective number of NaCl 4
Nc A
Vc NA
4 58.5 10 3
6.022 1023 5.62 10 10
2.19 103kg/m3
Problem on Radius Ratio
1.3. Show that the minimum cation - to - anion radius ratiofor the co-ordination number 3 is 0.155.
g/mol
kgg
mol 1 m3
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Introduction 1.43
Solution:For the coordination number 3, small cation is
surrounded by three anions to form an equilateral triangle
AP
rA; AO
rA rC
By using side length ratio AP
/AO
is a function of the
angle as AP
AO cos
30, because line AO
bisects the 60 angle BAC
AP
AO
rA
rA rC
cos 30 32
using cation-anion radius ratio, rC
rA
1 3/2
3/2
0.155
1.27. POLYMORPHISM OR ALLOTROPY
Two or more crystals having identical atomiccompositions but different arrangements orstructure are called polymorphous.
The ability of a single substance to exist in morethan one physical form is known as polymorphismor allotropy.
For example carbon exists in three forms namelydiamond, graphite and fullerence. Thetransformation in phases/structure may bereversible or irreversible and the reversible
transformation is known as enantiotropy (Eg.) Iron Fe, Fe, Fe, Fe others are cobalt,manganese, etc.
1.28. MILLER INDICES
(i) Miller indices are used to specify directions andplanes
(ii) There directions and planes could be in lattice orcrystals.
(iii) The no. of indices will match with the dimension ofthe lattice Example In 1D there is 1 index and in2D these is 2 indices etc.
1.29 CRYSTALLOGRAPHIC DIRECTION AND PLANES
A crystallographic direction is defined as a linebetween two points or a vector. For cubic crystals thecrystallographic direction indices are the vector componentsof the direction resolved along each of the coordinate axesand reduced to the smallest integers.
1.29.1. Steps for determining crystallographicdirection indices
1. Draw a direction vector (line) from an origin whichis usually a corner of the cube until it emerges fromthe cube surface.
2. The length of the vector on each of the three axesis determined and these are measured in terms ofthe unit cell dimensions a, b, c.
3. Divide or multiply these numbers by a commonfactor to convert them into smallest integers. Theseare direction indices.
Introduction 1.45
4. The direction indices are enclosed in square bracketswith no commas.
Fig 1.17 shows the various direction indices with ina unit cell
O
S
R X
Z
Y
T[111]
[100]
[110]
Fig. 1.17 (a) [100],[110] and [111] directions within a unit cell.
1.29.2. Miller indexing of crystal plane.Planes passing through lattice points are called lattice
planes. A crystalline solid has many planes in it and it isvery difficult to write their geometric equations. So, millerdevised a scheme for indexing planes by integer. The stepsinvolved are
Choose 3 prominent axis along 3 probabledirection of crystal and find out the intercept ofgiven plane with these fundamental axis in termof fundamental lattice vectors.
Take the reciprocals of these number so obtained.
Reduce these numbers to the smallest threeintegers having same ratio.
Enclose the result in parenthesis hE kE l
These indices are known as “Miller Indices”. HenceMiller indices are the three smallest possible integers whichhave the same ratios as the reciprocals of the intercepts ofthe plane concerned on the three axes: h k l is called theMiller indices for the plane.
Example: To find Miller indice of planes havingintercepts 4, 1, 2
Step 1: The terms a, b, c are 4, 1, 2
Step 2:Taking reciprocals we have
14
, 11
, 12
Step 3: Integer in same ratio: take LCM of 4, 1, 24 and
multiply we get 44
, 41
, 42
1, 4, 2
Step 4: So Miller indices are (1, 4, 2)
Introduction 1.47
1.30. ATTRIBUTES OF MILLER INDICES SLIP SYSTEM.
A zero miller indices indicates that the plane isparallel to that corresponding crystal axis e.g. ( 13 0 ) means plane is parallel to Z axis and ( 0 01 ) means plane is parallel to X and Y axis. Fig.
1.18 shows the miller indices for (6 2 3), (0 01), (1 1 2), (0 1 0), 0 1
0, (0 1 1), (1 1 1)
A negative miller indices shows that the planeh
k l cuts the x axis on the negative side of the
origin eg 1
0 0
Miller indices represent a family of parallel planes(2 0 0) and (1 0 0) are parallel planes as shownin Fig. 1.19
Bracket { } are used to represent all sets of afamily of planes example { 100 } represents100, 010, 001, 1
00, 01
0, 001
Y
XO
Z
(100) Y
XO
Z
(110)
Y
X
Z
(111)
Fig. 1.19. M iller Indies.
Z
X
Y (222)
Introduction 1.49
When the integers used in miller indices containmore than one digit the indices must be separatedby commas for clarity for eg, (5, 12, 10).
1.31. BRITTLENESS OF BCC, HCP AND DUCTILITY OF FCC
The metals which have BCC structure (Iron,molybdenum, tungsten, Chromium etc) are brittle at alltemperatures. Yield strength [ stress at which the materialbegin to deform plastically] is strongly dependent ontemperature. At low temperature BCC metals have highyield strength which results in plastic flow stress (that ishigher than fracture stress) and hence the brittle fractureis more likely to happen. This holds good for low and hightemperature.
The metals which have HCP structure [cadmium,zinc, titanium and magnesium] exhibit brittle fracture atlow temperature due to low number of slip system.
The metals which have FCC structure [Copper,Aluminium, Nickel, Platinum] is ductile because of largenumber of slip system results in low yield strength, whichcause plastic flow stress less than those required to causefracture.
1.32. MODES OF PLASTIC DEFORMATION
Two modes of plastic deformation may occur. They are
(i) DefinitionThe slip is defined as the shear deformation, which
moves the atoms through many interatomic distancesrelative to their initial positions.
1.32.2. Mechanism of Slip The mechanism of slip is actually due to the
movement or dislocation in the crystal lattice.Refer Fig. 1.20
The slip mode of deformation is the common modein many crystals at elevated temperatures.
By examination of the surface of a deformedcrystal under microscope shows groups of parallellines which correspond to steps on the surface.They are called as slip lines.
The shear stress required for producing a slip dueto the movement of dislocations is a small fractionof the theoretical value (i.e) G/b and it matchesthe observed shear strengths of metals.
The mechanism of slip requires the growth andmovement of dislocation line.
Therefore the energy required for this movementof dislocation line is given by the relation
(a) Before slip (b) After slipFig. 1.20
Introduction 1.51
E l Gb2
Where E young’s modulus
l length of dislocation line
G shear modulus
b unit slip vector (or) burgers vector
The energy required will be minimum when b(vector) and G are having the lowest value.
It means that the dislocation having the shortestslip vector is the easiest dislocation to generateand expand for plastic deformation by slip.
1.32.3. Deformation by TwinningThe next important mechanism by which metals
deformation occur is known as Twinning.
(i) Definition of twinningTwinning is the plastic deformation which takes place
along two planes due to a set of forces acting a given metal.The two planes are usually parallel to each other and arecalled the twin planes. Here each atom moves only afraction of an interatomic distance relative to its neighbour.The deformation of the crystal lattice caused by twinningis shown in Fig. 1.21
Twinning is the process in which the atoms in a partof a crystal subjected to stress, rearrange themselves in amanner that one part of the crystal becomes the mirrorimage of other part. This process of rearranging themselvesis defined as Twinning.
(ii) Twinning planesThe planes where the twinning almost takes place is
known as twinning planes. These planes are also called asspecial planes.
In most plastic deformation, twinning is relativelyinsignificant but it may have considerable influence on thetotal amount of deformation that occurs. It should be notedthat twinning is different from slip. In slip, every plane ofatoms suffer some movement and the positions of manyunit cells are altered.
(iii) Types of twinningThere are two types of twins, they are
(a) Mechanical twins
(b) Annealing twins
(a) Mechanical TwinsAs a result of mechanical deformation of crystals,
twins may occur and these twins that occur duringmechanical deformation are called ’Mechanical Twins’.
(b) Annealing TwinsThe twins that are produced by annealing are called
as annealing twins. Most of FCC metals (like copper) formannealing twins.
1.32.4. Mechanism of twinningIn twinning process, the movement of atoms is only
a fraction of interatomic distance. Fig 1.21 shows thecircles indicating the arrangement of atoms. The line ABand CD represents the planes of symmetry, from where thetwinning starts and ends respectively. These planes areknown as twinning planes.
Introduction 1.53
It has been observed that the crystals twin about thetwinning planes and the atoms in the regions to the leftof the twinning plane AB and the right of the twinningplane CD remain undisturbed.
Whereas in the twinned region each atom moves bya distance proportional to its distance from the twinningplane AB. The dark circles indicate the new position of theatoms.
The twinning occurs due to the growth and movementof dislocation in the crystal lattice.
Comparison Between Slip And Twinning
S.No
Slip Twinning
1. Plastic deformation occursbecause of the sliding ofatomic planes over theothers. The orientation ofthe slip plane remainsunchanged.
Plastic deformation takesplace due to theorientation of one part ofthe crystal with respect tothe other. The twinnedportion is a mirror imageof the original.
2. Slip occurs along a singleplane called the ’slipplane’.
Twinning occurs betweentwo planes called the’twin planes’.
3. The atoms move overlarge distances in slipping
The atoms move over afraction of the atomicdistance in twinning.
4. Slip occurs on widelyspaced planes
Deformation occurs onevery plane within thetwinned region of thecrystal.
5. It requires a lower stressfor atomic movement.
It requires a higher stressfor atomic movement.
1.33. SCHMID’S LAWS
Schmid’s law defines the relationship between shearstress, applied stress and the orientation of the slip system.Schmid’s law helps to explain the differences in behaviourof different metals when subjected to a unidirectional force.
cos cos
1.34. CRITICAL RESOLVED SHEAR STRESS FOR SLIP
The stress at which slip starts in a crystal dependson the relative orientations of the stress axis with respectto the slip plane and the slip direction.
The resolved shear stress, which is in the actualstress operating on the slip system resulting from theapplication of simple tensile stress.
FA
Introduction 1.55
F - externally applied force perpendicular to thecross-sectional Area (A)
A - Area of single crystal sample.
This resolved shear stress should reach a criticalvalue called as CRSS (Critical Resolved Shear Stress)for a plastic deformation to start.
The important concept here is that the fundamentalinformation mechanism is a shearing action based on theobjection of applied force onto the slip system.
- Angle between Normal to slip plane and F (Fig. 1.22)
- Angle between Normal to the slip-direction and F.
Force operating in the slip direction F cos
Slip plane on to the given area A
cos
As a result, the resolved shear stress is given by
F cos A/cos
FA
cos cos
cos cos
Where - applied tensile stress.
A value of to produce slip by dislocation motion iscalled as CRSS and is given by
c c cos cos
1.35. CORRECTION OF SLIP SYSTEM WITH PLASTIC
DEFORMATION IN METALS.
Slip is mainly the foremost cause of plasticdeformation. Generally dislocations in a metals donot movein all crystallographic plane and in all crystallographicdirection. The dislocation occurs in specific plane and atspecific direction, the plane where the dislocation motionoccurs are called slip plane and the corresponding directionis called slip direction. The combination of slip plane andslip direction are called slip system.
Introduction 1.57
The (111) plane, which is the plane of densest atomicpopulation, intersects the (001) plane in the line ac. When
the (001) plane is assumed to be the plane of the paperand many unit cells are taken together Refer Fig (1.23),slip is seen as a movement along the (111) planes in theclose packed direction (110), a distance of one latticedimension or multiple of that dimension.
Slip is always initiated in planes orientated at 45and happens thereafter on other planes from 0 to 45excluding 0. Therefore the crystal planes which are bothperpendicular and parallel to the applied force donotundergo slip process.
Metals with FCC (or) BCC crystal structures have arelatively large number of slip system. These metals arequite ductile because extensive plastic deformation isnormally possible along the various systems. Conversely,HCP metals have few active slip systems So hey arenormally brittle.
