ECC 211 Engineering Materials Lecture 19-Review PDF

ECC 211 Engineering Materials Prof. Mahmut A. Savaş Dec. 30, 2024  Final Exam Please note: The ECC 211 Final exam will be on January 6, 2025 at 16:30 in the VT1-D01, VT1-D02 and VT 2-D02 rooms. Do not miss it! Academic calender D...

ECC 211 Engineering Materials Prof. Mahmut A. Savaş Dec. 30, 2024  Final Exam Please note: The ECC 211 Final exam will be on January 6, 2025 at 16:30 in the VT1-D01, VT1-D02 and VT 2-D02 rooms. Do not miss it! Academic calender Deadline for the Project submission – 15 December 2024 - Remember: ECC 211 (ME 211) – ENGINEERING MATERIALS Course Objective Processing Structure Properties Engineering Application Failure ECC 433 ME 453 ME 475 ECC 211 (ME 211): Engineering Materials ECC 433 (ME 454): Heat Treatment ME 453: Materials Engineering ME 475: Materials Failure Investigation Please note: This course is given at the flipplearning.neu.edu.tr not at the uzebim site! See the uzebim page of the course. Sept. 24, 2024 Chapters: 1, 6, 8 and 17. W. D. Callister, e-copy is available at flippedlearning site Chapter 1 – W. D. Callister (Digital copy is available at uzebim) Soft drinks can be kept in: 1- Glass bottle. 2- PET bottle. 3- Metal can. Have 3 alternative materials. Which one to choose? Why?  ECC 211 (ME 211) – ENGINEERING MATERIALS Course Objective Processing Structure Properties Engineering Application Failure ECC 433 ME 453 ME 475 ECC 211 (ME 211): Engineering Materials ECC 433 (ME 454): Heat Treatment ME 453: Materials Engineering ME 475: Materials Failure Investigation  What is meant by structure and properties of engineering materials? See the textbook: W. D. Callister Chapter 1: Introduction Structure: Chapter 2: Atomic structure and bonding between atoms Chapter 3: Crystal structures Chapter 4: Crystal defects (imperfections) Properties: Chapter 6: Mechanical properties Chapters 18, 19, 20, 21: Electrical, thermal, magnetic, optical properties  Chapter 1: An introduction – Engineering materials and a brief classification PS: There are more that 100,000 materials used in engineering applications! A BRIEF CLASSIFICATION of ENGINEERING MATERIALS I - METALS - Have metallic bonding – Therefore, ductile (not brittle) and good conductors. Examples: Pure Copper (Cu), Copper alloys such as brass (Cu-Zn), bronze (Cu-Sn), monel (Cu-Ni). Iron (Fe) – carbon (C) alloys with C ≤ 2% are called steels. II - Non – METALS - a) Ceramics and glasses - Have ionic and/or covalent bonds – Therefore, strong but brittle and insulator. Examples: Ceramics such as Al2O3 called alumina. Glasses such as SiO2 called quartz.  A BRIEF CLASSIFICATION of ENGINEERING MATERIALS b) Polymers – Macromolecules - Have secondary bonds – Therefore, mechanically weak and also often poor conductors. Examples: PET bottles, PVC pipes, etc. III - Composites – Mixtures of I and II. Examples: CFRP (Carbon Fibre Reinforced Polymer). Concrete reinforced with steel bars. Human bone. IV – Others – Semiconductors, Superconductors, Biomaterials, Smart materials, etc. HW 1: Read Chapter 1 and watch the video 1.  HW 1: List the materials group, advantages and disadvantages of each group of drinking water pipes that has been used in the Gönyeli Municipality till to date. Chapter 2 – W. D. Callister Chapter 2 - 15 Chapter 2: Atomic Structure & Interatomic Bonding Processing Structure Properties Engineering Application Failure ISSUES TO ADDRESS... What promotes bonding? What types of bonds are there? What properties are inferred from bonding? Chapter 2 - 16 8 October 2024 Chaps. 1&2 – A Brief summary Processing Structure Properties Engineering Application Failure 1- Name a metal, given an example, its bonding and the resultant properties. 2- Ceramic 3- Glass 4- Polymer 5- Composite 6- Biomaterial 7- Smart material Chapter 2 - 17 Chapter 2 - 18  Gönyeli Manucipality in Lefkoşa - Materials used for drinking water pipes Materials used: An old exam question: Chronological order: a) Advantages vs disadvantages of each pipe 1- Asbestos pipe. material? 2- Galvanized steel pipe. 3- Polyethelene pipe. b) Bonding? c) Tensile properties? Processing Structure Properties Engineering Application Failure  Processing Structure Properties Engineering Application Failure October 14 - 15, 2024 Mechanical properties of engineering materials Chap.6- W. D. Callister Chapter 2 - 21 14 October 2024  ECC 211 (ME 211) – ENGINEERING MATERIALS Course Objective Processing Structure Properties Engineering Application Failure ECC 433 ME 453 ME 475 ECC 211 (ME 211): Engineering Materials ECC 433 (ME 454): Heat Treatment ME 453: Materials Engineering ME 475: Materials Failure Investigation  Chapter 6: Mechanical Properties - Tensile test Mechanical properties obtained from tension test PS: Watch the video Engineers follow international standars  What is an International Standard? International Standards are technical standards developed by experts belonging to international organizations under the coordination of entities such as ISO, the International Organization for Standardization. ISO is the world’s largest developer of voluntary international standards and facilitates world trade by providing common standards between nations.  EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM EN ISO 6892-1 August 2009 ICS 77.040.10 Supersedes EN 10002-1:2001 English Version Metallic materials - Tensile testing - Part 1: Method of test at room temperature (ISO 6892-1:2009) Matériaux métalliques - Essai de traction - Partie 1: Méthode d'essai à température ambiante (ISO 6892- 1:2009) Metallische Werkstoffe - Zugversuch - Teil 1: Prüfverfahren bei Raumtemperatur (ISO 6892-1:2009) This European Standard was approved by CEN on 13 March 2009. CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN Management Centre or to any CEN member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG Management Centre: Avenue Marnix 17, B-1000 Brussels © 2009 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 6892-1:2009: E Copyright British Standards Institution Provided by IHS under license with BSI - Uncontrolled Copy Licensee=Bogazici University/5964815002 No reproduction TS EN ISO 6892-1: Turkish standard for tension test  Stress-Strain Testing Typical tensile test Typical tensile machine specimen Adapted from extensometer specimen Fig. 6.2, Callister & Rethwisch 8e. gauge length Adapted from Fig. 6.3, Callister & Rethwisch 8e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.) Chapter 6 - 28  Engineering stress and Engineering strain Stress→ Strain→ Mechanical properties found from tension test  Mechanical properties found from tension test Yield strength → End of elastic deformation region. (Ultimate) tensile strength → Maximum load (stress) that can be carried by the material. Young’s modulus (Modulus of elasticity) → E → Measure of stiffness ? E=Stress/Strain in the elastic deformation region Fracture elongation → ? Toughness → ? Ductile or brittle material ? Brittle materials (ceramics and glasses), Ductile materials (metals and alloys), Plastic materials (plastics) Stiffness - Young’s modulus and Density Strength and Toughness Carbon Fibre Reinforced Polymer Relation between Brinell hardness (HB) and tensile strength (TS) TS (MPa) = 3.45 x HB  Hardness: Measurement Table 6.5 Chapter 6 - 37  Variability in Material Properties Elastic modulus is material property Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability. Statistics n  xn – Mean x= n 1 n  ( ) 2 2   xi − x  – Standard Deviation s =   n −1    where n is the number of data points Chapter 6 - 38  Design or Safety Factors Design uncertainties mean we do not push the limit. Factor of safety, N Often N is y between working = 1.2 and 4 N Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5. d y working = 1045 plain carbon steel: N y = 310 MPa Lo 220,000N TS = 565 MPa 5 (  d /42 ) F = 220,000N d = 0.067 m = 6.7 cm Chapter 6 - 39  Summary Stress and strain: These are size-independent measures of load and displacement, respectively. Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches y. Toughness: The energy needed to break a unit volume of material. Ductility: The plastic strain at failure. Chapter 6 - 40 HW- Example Problems from W. D. Callister An old exam question HW: 1- Describe an international standard and its importance in engineering practice. 2- Solve problem 6.10. An old exam question Hint:  Mechanical properties found from tension test Yield strength → ? (Ultimate) tensile strength →? Young’s modulus (Modulus of elasticity) → E → ? Fracture elongation → ? Toughness → ? Ductile or brittle material ? Hardness ? Safety factor ?  Processing Structure Properties Engineering Application Failure October 21 - 22, 2024 Crystal structures of solids Chap.3- W. D. Callister Chapter 2 - 51 21 October 2024  ECC 211 (ME 211) – ENGINEERING MATERIALS Course Objective Processing Structure Properties Engineering Application Failure ECC 433 ME 453 ME 475 ECC 211 (ME 211): Engineering Materials ECC 433 (ME 454): Heat Treatment ME 453: Materials Engineering ME 475: Materials Failure Investigation  Metallic Crystal Structures Tend to be densely packed. Reasons for dense packing: - Typically, only one element is present, so all atomic radii are the same. - Metallic bonding is not directional. - Nearest neighbor distances tend to be small in order to lower bond energy. - Electron cloud shields cores from each other Have the simplest crystal structures. We will examine three such structures... Cubic crystal systems. SC, BCC and FCC Chapter 3 - 54  Simple Cubic Structure (SC) Rare due to low packing density (only Po has this structure) Close-packed directions are cube edges. Coordination # = 6 (# nearest neighbors) Click once on image to start animation (Courtesy P.M. Anderson) Chapter 3 - 55  Atomic Packing Factor (APF) Volume of atoms in unit cell* APF = Volume of unit cell *assume hard spheres APF for a simple cubic structure = 0.52 volume atoms atom a 4 unit cell 1  (0.5a) 3 3 R=0.5a APF = a3 volume close-packed directions unit cell contains 8 x 1/8 = atom/unit 1 cell Adapted from Fig. 3.24, Callister & Rethwisch 8e. Chapter 3 - 56  Body Centered Cubic Structure (BCC) Atoms touch each other along cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. ex: Cr, W, Fe (), Tantalum, Molybdenum Coordination # = 8 Adapted from Fig. 3.2, Click once on image to start animation Callister & Rethwisch 8e. (Courtesy P.M. Anderson) 2 atoms/unit cell: 1 center + 8 corners x 1/8 Chapter 3 - 57  Atomic Packing Factor: BCC APF for a body-centered cubic structure = 0.68 3a a 2a Close-packed directions: Adapted from R length = 4R = 3 a Fig. 3.2(a), Callister & Rethwisch 8e. a atoms volume 4 unit cell 2  ( 3a/4) 3 3 atom APF = volume APF = 0.68 a 3 unit cell Chapter 3 - 58  Face Centered Cubic Structure (FCC) Atoms touch each other along face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. ex: Al, Cu, Au, Pb, Ni, Pt, Ag Coordination # = 12 Adapted from Fig. 3.1, Callister & Rethwisch 8e. Click once on image to start animation (Courtesy P.M. Anderson) 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8 Chapter 3 - 59  Atomic Packing Factor: FCC APF for a face-centered cubic structure = 0.74 maximum achievable APF Close-packed directions: length = 4R = 2 a 2a Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell a Adapted from Fig. 3.1(a), Callister & atoms volume Rethwisch 8e. 4 unit cell 4  ( 2a/4) 3 3 atom APF = APF = 0.74 3 volume a unit cell Chapter 3 - 60  HW Problems from W. D. Callister – Chapter 3 HW : Derive the Atomic Packing Factors (APF) for SC, BCC and FCC crystal structures.  Theoretical Density,  Mass of Atoms in Unit Cell Density =  = Total Volume of Unit Cell nA  = VC NA where n = number of atoms/unit cell A = atomic weight VC = Volume of unit cell = a3 for cubic NA = Avogadro’s number = 6.022 x 1023 atoms/mol Chapter 3 - 62  Theoretical Density,  Ex: Theoretical density of Cr (BCC): A = 52.00 g/mol R = 0.125 nm n = 2 atoms/unit cell R Adapted from Fig. 3.2(a), Callister & a a = 4R/ 3 = 0.2887 nm Rethwisch 8e. atoms g unit cell 2 52.00 theoretical= 7.18 g/cm3 mol = actual = 7.19 g/cm3 a3 6.022 x 1023 volume atoms unit cell mol Chapter 3 - 63  Densities of Material Classes In general Graphite/ metals > ceramics > polymers Metals/ Composites/ Ceramics/ Polymers Alloys fibers Semicond 30 Why? Platinum Based on data in Table B1, Callister *GFRE, CFRE, & AFRE are Glass, 20 Gold, W Metals have... Tantalum Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on close-packing 60% volume fraction of aligned fibers 10 Silver, Mo in an epoxy matrix). (metallic bonding) Cu,Ni Steels often large atomic masses Tin, Zinc Zirconia  (g/cm3 ) 5 Ceramics have... 4 Titanium Al oxide less dense packing 3 Diamond Si nitride Aluminum Glass -soda often lighter elements Concrete Silicon PTFE Glass fibers GFRE* 2 Carbon fibers Polymers have... Magnesium Graphite Silicone CFRE* Aramid fibers PVC low packing density PET PC AFRE* 1 HDPE, PS (often amorphous) PP, LDPE lighter elements (C,H,O) 0.5 Composites have... 0.4 Wood intermediate values 0.3 Data from Table B.1, Callister & Rethwisch, 8e. Chapter 3 - 64  HW Problems from W. D. Callister – Chapter 3 HW : Find the theoretical density of copper (Cu) which has a FCC crystal structure.  Polymorphism Two or more distinct crystal structures for the same material (allotropy/polymorphism) iron system titanium liquid , -Ti 1538ºC BCC -Fe Delta ferrite carbon diamond, graphite 1394ºC FCC -Fe Austenite 912ºC BCC -Fe Ferrite Chapter 3 - 66  Crystal Systems Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal. 7 crystal systems 14 crystal lattices Bravais lattices a, b, and c are the lattice constants Fig. 3.4, Callister & Rethwisch 8e. Chapter 3 - 67  Crystallographic Planes Adapted from Fig. 3.10, Callister & Rethwisch 8e. Chapter 3 - 68  Crystallographic Planes Miller Indices: Reciprocals of the (three) axial intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices. Algorithm 1. Read off intercepts of plane with axes in terms of a, b, c 2. Take reciprocals of intercepts 3. Reduce to smallest integer values 4. Enclose in parentheses, no commas i.e., (hkl) Chapter 3 - 69  Crystallographic Planes z example a b c 1. Intercepts 1 1  c 2. Reciprocals 1/1 1/1 1/ 1 1 0 3. Reduction 1 1 0 y a b 4. Miller Indices (110) x z example a b c 1. Intercepts 1/2   c 2. Reciprocals 1/½ 1/ 1/ 2 0 0 3. Reduction 2 0 0 y 4. Miller Indices (100) a b x Chapter 3 - 70  Crystallographic Planes z example a b c c 1. Intercepts 1/2 1 3/4 2. Reciprocals 1/½ 1/1 1/¾ 2 1 4/3 y 3. Reduction 6 3 4 a b 4. Miller Indices (634) x Family of Planes {hkl} Ex: {100} = (100), (010), (001), (100), (010), (001) Chapter 3 - 71 Crystallographic Planes and their atomic densities HW: a) Draw (100) and (111) crystallographic planes for Fe. b) Calculate the planar density for each of these planes. Chapter 3 - 72  X-Ray Diffraction Diffraction gratings must have spacings comparable to the wavelength of diffracted radiation. Can’t resolve spacings   Spacing is the distance between parallel planes of atoms. Chapter 3 - 73  X-Rays to Determine Crystal Structure Incoming X-rays diffract from crystal planes. reflections must be in phase for a detectable signal extra  Adapted from Fig. 3.20,   distance Callister & Rethwisch 8e. travelled by wave “2” spacing d between planes Measurement of X-ray n critical angle, c, intensity d= (from 2 sin c allows computation of detector) planar spacing, d.  c Chapter 3 - 74 Chapter 3 - 75  X-Ray Diffraction Pattern z z z c c c y (110) y y a b a b a b Intensity (relative) x x x (211) (200) Diffraction angle 2 Diffraction pattern for polycrystalline -iron (BCC) Adapted from Fig. 3.22, Callister 8e. Chapter 3 - 76 Chapter 3 - 77  HW from W.D. Callister – Prob: 3.67 Solve - An old midterm question 3.67 - Determine the expected diffraction angle for the first-order reflection from the (310) set of planes for BCC chromium (Cr) when monochromatic radiation of wavelength 0.0711 nm is used. (Hint: Bragg’s law) Chapter 3 - 78 Chapter 3 - 79 Chapter 3 - 80 Chapter 3 - 81  Processing Structure Properties Engineering Application Failure October 28 - 29, 2024 Crystal defects / imperfections solids Chap.4- W. D. Callister Chapter 2 - 82 Chapter 3 - 83  Chapter 4: Imperfections in Solids ISSUES TO ADDRESS... What are the solidification mechanisms? What types of defects arise in solids? Can the number and type of defects be varied and controlled? ECC 433 Heat treatment How do defects affect material properties? Are defects undesirable or desirable? Chapter 4 - 84  Types of Imperfections (Defects) Vacancy atoms Interstitial atoms Point defects Substitutional atoms Dislocations Line defects Grain Boundaries Area defects Chapter 4 - 85  Imperfections in Solids Dislocations are visible in electron micrographs Fig. 4.6, Callister & Rethwisch 8e. Chapter 4 - 86  Microscopic Examination Crystallites (grains) and grain boundaries. Vary considerably in size. Can be quite large. – ex: Large single crystal of quartz or diamond or Si – ex: Aluminum light post or garbage can - see the individual grains Crystallites (grains) can be quite small (mm or less) – necessary to observe with a microscope. Chapter 4 - 87  Optical Microscopy Useful up to 2000X magnification. Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal orientation. crystallographic planes Adapted from Fig. 4.13(b) and (c), Callister & Rethwisch 8e. (Fig. 4.13(c) is courtesy of J.E. Burke, General Electric Co.) Micrograph of brass (a Cu-Zn alloy) 0.75mm Chapter 4 - 88  Optical Microscopy Grain boundaries... are imperfections, are more susceptible to etching, may be revealed as polished surface dark lines, change in crystal surface groove orientation across grain boundary (a) boundary. Adapted from Fig. 4.14(a) and (b), Callister & ASTM grain Rethwisch 8e. (Fig. 4.14(b) is courtesy size number of L.C. Smith and C. Brady, the National Bureau of N = 2n-1 Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].) number of grains/in2 Fe-Cr alloy at 100x (b) magnification Chapter 4 - 89 Chapter 4 - 90 Chapter 4 - 91 Chapter 4 - 92 Chapter 4 - 93 Chapter 4 - 94 Chapter 3 - 95 4 Nov. 2024 Review Chapter 3 - 96 18 Nov. 2024 After the Midterm Chapter 3 - 97  What is meant by structure and properties of engineering materials? See the textbook: W. D. Callister Chapter 1: Introduction Structure: Chapter 2: Atomic structure and bonding between atoms Chapter 3: Crystal structures Chapter 4: Crystal defects (imperfections) Diffusion in solids Phase diagrams Failure modes (mechanisms) Properties: Chapter 6: Mechanical properties Chapters 18, 19, 20, 21: Electrical, thermal, magnetic, optical properties Chapter 5: Diffusion in solids, W. D. Callister Case (Surface) hardened steel gear by carburization Internal combustion engine Electrical car  Chapter 5: Diffusion in Solids Diffusion - Meaning - Mass transport by atomic motion in solids. Mechanisms Gases & Liquids – random (Brownian) motion - Fast Solids – vacancy diffusion or interstitial diffusion in crystal structure - Slow Fick’s diffusion laws Industrial / Technological importance Chapter 5 - 102 Please note: Diffusion is very important in the human body for the movement of substances: Examples: 1- Movement of oxygen from the air into the blood and carbon dioxide out of the blood into the air in the lungs, or 2- Movement of glucose from the blood to the cells.... Cell membranes are partially permeable. 3- Osmosis. Chapter 5 - 103 Movement of oxygen from the air into the blood and carbon dioxide out of the blood into the air in the lungs Chapter 5 - 104  Processing Using Diffusion Case Hardening: Adapted from -- Diffuse carbon atoms chapter-opening into the host iron atoms photograph, Chapter 5, at the surface. Callister & Rethwisch 8e. -- Example of interstitial (Courtesy of Surface Division, diffusion is a case Midland-Ross.) hardened gear. Result: The presence of C atoms makes iron (steel) surface harder. This increases wear resistance. Chapter 5 - 105 Brittle and ductile materials Chapter 5 - 108 Chapter 5 - 109  Processing Using Diffusion Diode and transistor manufacture – p/n junction Doping silicon with phosphorus for n-type semiconductors: Process: 0.5 mm 1. Deposit P rich layers on surface. magnified image of a computer chip silicon 2. Heat it. 3. Result: Doped light regions: Si atoms semiconductor regions. light regions: Al atoms silicon Adapted from Figure 18.27, Callister & Rethwisch 8e. Chapter 5 - 110  Diffusion Interdiffusion: In an alloy, atoms tend to migrate from regions of high conc. to regions of low conc. Initially After some time Adapted from Figs. 5.1 and 5.2, Callister & Rethwisch 8e. Chapter 5 - 111  Diffusion Self-diffusion: In an elemental solid, atoms also migrate. Label some atoms After some time C C A D A D B B Chapter 5 - 112  Diffusion Mechanisms Vacancy Diffusion: atoms exchange with vacancies applies to substitutional impurities atoms rate depends on: -- number of vacancies -- activation energy to exchange. increasing elapsed time Chapter 5 - 113  Diffusion Mechanisms Interstitial diffusion – smaller atoms can diffuse between atoms. Adapted from Fig. 5.3(b), Callister & Rethwisch 8e. More rapid than vacancy diffusion Chapter 5 - 114  Diffusion How do we quantify the amount or rate of diffusion? moles (or mass) diffusing mol kg J  Flux  = or (surface area)(time) 2 cm s m2s Measured empirically – Make thin film (membrane) of known surface area – Impose concentration gradient – Measure how fast atoms or molecules diffuse through the membrane M= M l dM mass J  slope J= = diffused At A dt time Chapter 5 - 115  Steady-State Diffusion Rate of diffusion independent of time dC Flux proportional to concentration gradient = dx C1 C1 Fick’s first law of diffusion dC C2 C2 J = −D dx x1 x2 x D  diffusion coefficient dC C C2 − C1 if linear  = dx x x2 − x1 Chapter 5 - 116 Textbook – W. D. Callister, e-copy is available Chapter 5 - 117 Example: Chemical Protective Clothing (CPC) Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn. If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the glove? Data: – diffusion coefficient in butyl rubber: D = 110 x10-8 cm2/s – surface concentrations: C1 = 0.44 g/cm3 C2 = 0.02 g/cm3 Chapter 5 - 118  Example (cont). Solution – assuming linear conc. gradient glove C1 dC C2 − C1 tb = 2 J =-D  −D paint 6D dx x2 − x1 skin remover C2 Data: D = 110 x 10-8 cm2/s x1 x2 C1 = 0.44 g/cm3 C2 = 0.02 g/cm3 x2 – x1 = 0.04 cm -8 2 (0.02 g/cm3 − 0.44 g/cm3 ) g J = − (110 x 10 cm /s) = 1.16 x 10 -5 (0.04 cm) cm2s Chapter 5 - 119  Diffusion and Temperature Diffusion coefficient increases with increasing T.  Qd  D = Do exp−   RT  D = diffusion coefficient [m2/s] Do = pre-exponential [m2/s] Qd = activation energy [J/mol or eV/atom] R = gas constant [8.314 J/mol-K] T = absolute temperature [K] Chapter 5 - 120  Diffusion and Temperature D has exponential dependence on T 1500 1000 600 300 T(C) 10-8 D (m2/s) Dinterstitial >> Dsubstitutional C in -Fe Al in Al 10-14 C in -Fe Fe in -Fe Fe in -Fe 10-20 0.5 1.0 1.5 1000 K/T Adapted from Fig. 5.7, Callister & Rethwisch 8e. (Date for Fig. 5.7 taken from E.A. Brandes and G.B. Brook (Ed.) Smithells Metals Reference Book, 7th ed., Butterworth-Heinemann, Oxford, 1992.) Chapter 5 - 121 Example: At 300ºC the diffusion coefficient and activation energy for Cu in Si are D(300ºC) = 7.8 x 10-11 m2/s Qd = 41.5 kJ/mol What is the diffusion coefficient at 350ºC? D transform ln D data Temp = T 1/T Qd 1 Qd  1 lnD2 = lnD0 −   and lnD1 = lnD0 −   R  T2  R  T1  D2 Qd  1 1   lnD2 − lnD1 = ln =−  −  D1 R  T2 T1  Chapter 5 - 122  Example (cont.)  Qd  1 1  D2 = D1 exp −  −   R  T2 T1  T1 = 273 + 300 = 573 K T2 = 273 + 350 = 623 K −11 2  − 41,500 J/mol  1 1  D2 = (7.8 x 10 m /s) exp   −   8.314 J/mol - K  623 K 573 K  D2 = 15.7 x 10-11 m2/s Chapter 5 - 123 Chapter 5 - 124 Chapter 5 - 125  Non-steady State Diffusion The concentration of diffusing species is a function of both time and position C = C(x,t) In this case Fick’s Second Law is used Fick’s Second Law: C  2C =D 2 t x Chapter 5 - 126  Non-steady State Diffusion Copper diffuses into a bar of aluminum. Surface conc., Cs of Cu atoms bar pre-existing conc., Co of copper atoms Cs Adapted from Fig. 5.5, Callister & Rethwisch 8e. B.C. at t = 0, C = Co for 0  x   at t > 0, C = CS for x = 0 (constant surface conc.) C = Co for x =  Chapter 5 - 127  Solution: C (x , t ) − Co  x  = 1 − erf   Cs − Co  2 Dt  C(x,t) = Conc. at point x at CS time t erf (z) = error function 2 z −y 2 C(x,t) =   0 e dy Co erf(z) values are given in Table 5.1 Adapted from Fig. 5.5, Callister & Rethwisch 8e. Chapter 5 - 128 Chapter 5 - 129 Simplified version → Foreman’s formula: Textbook – W. D. Callister, e-copy is available Chapter 5 - 131 Chapter 5 - 132 Chapter 5 - 133  HW 1- Chap.5, W.D. Callister Chap Solution? Watch the video. Chapter 5 - 134 HW 2- Chap.5, W.D. Callister Chapter 5 - 136 HW 3- Chap.5, W.D. Callister Chapter 5 - 137  Summary Diffusion FASTER for... Diffusion SLOWER for... open crystal structures (SC) close-packed structures (FCC) materials w/secondary bonding (Polymers) materials w/covalent bonding (Ceramics) smaller diffusing atoms (C in Fe) larger diffusing atoms lower density materials higher density materials Chapter 5 - 138 Chapter 5 - 139 Chapter 5 - 140 Chapter 5 - 141  What is meant by structure and properties of engineering materials? See the textbook: W. D. Callister Chapter 1: Introduction Structure: Chapter 2: Atomic structure and bonding between atoms Chapter 3: Crystal structures Chapter 4: Crystal defects (imperfections) Diffusion in solids Phase diagrams Failure modes (mechanisms) Properties: Chapter 6: Mechanical properties Chapters 18, 19, 20, 21: Electrical, thermal, magnetic, optical properties 25 Nov. 2024 – Phase Diagrams I Chap. 9 in W. D. Callister Chapter 5 - 143  ECC 211 (ME 211) – ENGINEERING MATERIALS Course Objective Processing Structure Properties Engineering Application Failure ECC 433 ME 453 ME 475 ECC 211 (ME 211): Engineering Materials ECC 433 (ME 454): Heat Treatment ME 453: Materials Engineering ME 475: Materials Failure Investigation  Water has three phases  Chapter 9: Phase Diagrams ISSUES TO ADDRESS... When we combine two elements... Such as copper (Cu) and nickel (Ni) → Alloy → called Monel what is the resulting equilibrium state? In particular, if we specify... -- the composition (e.g., wt% Cu - wt% Ni), and -- the temperature (T ) then... How many phases form? What is the composition of each phase? What is the amount of each phase? Phase A Phase B Cu-Ni (Monel) phase diagram Nickel atom Copper atom Chapter 9 - 146  OUTCOMES I) Phase diagrams are useful tools to determine: a) -- the number and types of phases present, -b) - the composition of each phase, c)-- and the weight fraction of each phase given the temperature and composition of the system. II) The microstructure of an alloy depends on -- its composition, and -- whether or not cooling rate allows for maintenance of equilibrium. III) Important phase diagram phase transformations include eutectic, eutectoid, and peritectic. IV) Some important commercial alloys → Monels, Solders, Steels, Cast irons Chapter 9 - 147  Classification of Metal Alloys Metal Alloys Monel Adapted from Fig. Ferrous Nonferrous 11.1, Callister & Rethwisch 8e. Steels Steels Cast Irons Cast Irons