Mechanical Properties of Structural Materials
Mechanical Properties of Structural Materials MSE 200
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MSEZOO Lecture 4 CHAPTER 36311 Crystal Structures and Crystal Geometry Instructor Yuntian Zhu Ob jectivesoutcomes You will learn the following List the directions of in a direction family and planes of a family Determine Miller s indices of planes in the cubic system Determine What direction lies on a plane Describe the atomic packing of fee and hop structures Calculate the density om unit cells Calculate the planar and linear atomic densities Describe XRay dif action 3quotIlttpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Direction Indices in a direction famil form Equivalent directions indices of a family ltuvwgt lt100gt lt110gt lt111gt lt121gt 339 tl wwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Miller Indices Miller Indices describe speci c lattice planes of atoms Miller Indices 111 3MMWW mse ncsu eduresearchZhu Department of Materlals 5C1 amp Eng NC STATE UNIVERSITY Determine Miller Indices 100 4632 339at pjwwwmsencsueduresearchzhu Department of Materlals Sclv amp Ehgv NC STATE UNIVERSITY Miller Indices Planes of a family form 100 100 010 001 110 110 Z 111 y X 121 WWWmSE ncsu eduresearchzhu Department of Materlals SCl amp Eng NC SIATE UNIVERS TY Miller lndices hkl Important Relationship Direction indices of a direction nemendicular to a crvstal plane are same as miller indices of the plane Example Z 11390 x Determine if a directions is on a plane Interplanar spacing hzk dth Z Z 3 www mse ncsu eduresearchZhu Department of Materials 5C1 amp Eng NC SIAIE UNIVERSITY Structural Difference between HCP and FCC HCP packing FCC packing Plane A Plane A Plane B Plane B Plane A Plane C 3 www mse ncsu eduresearchZhu Department of Materlals 5C1 amp Eng NC SIAIE UNIVERSITY Volume DensitV MassU nit cell Volume density of metal pv V1 U t u oume n1 ce Examplez Copper FCC has atomic mass of 6354 gmol and atomic radius of 01278 nm 339wwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Planar Atomic Density Planar atomic density pp of atoms per unit plane area Example In Iron BCC a028 D The 110 plane intersects center of 5 atoms Four 1A and 1 full atom gt 172al0ms 172 gtlt1013 51 H p 2 2 nm mm 339lwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Linear Atomic Density Linear atomic density pl of atoms per unit line length Examplez For a FCC copper crystal a0361 the 110 direction intersects 2 half diameters and 1 full diameter gt Therefore it intersects 12 12 1 2 atomic diameters Length of line J x 0361nm 2at0ms 3 92at0ms 392 X 106at0ms gt y p1 J5 X 0361nm mm mm H0 3 312lwwwmsencsueduresearchlzhul Department of Materials Sci amp Eng Planes and Directions in Hexagonal Unit Cells Four indices are used hkil called as MillerBravais indices 0 Four axes are used a1 a2 a3 and c Reciprocal of the intercepts that a crystal plane makes with the al a2 a3 and c axes give the hkI and l indices respectively v quot H J jw 1 n 71 7 Department of Materials Sci amp Eng httpwwwmsencsueduresearchzhu Hexagonal Unit Cell Examples Ulmll Basal Planes Intercepts a1 00 212 00 a3 00 c 1 hkli 0001 Prism Planes For plane ABCD Intercepts a1 1 212 00 a3 1 c 00 hkli 1010 mmccpl ls l amp Eng NC STATE UNIVERSITY 339ZQJJwwmsencsueduresearchzhu Department of Materials Sci The closest packed plane and direction 0 BCC2lt111gt no FCC lt110gt 111 httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY XRay Diffraction Crystal planes of target metal act as mirrors re ecting Xray beam Destructive interference WM km V7 w n0 reinforced beam is produced lquot HIM NLmL Constructive interference in phase Relicdud 39 rruys Egg 1 H Fiure 328 339a vwvwMerrkSBL BiureselamhHneh EWsm bysj alIMemHnagys 3d edampAltElig1nWe NC SYATE UNIVERSITY reinforced beams are produced V XRay Diffraction Cont 0 For rays re ected from different planes to be in phase the extra distance traveled by a ray should be a integral multiple of wave length l nl 2 dbwsme quidenl My 1 Reflected n 12 439H 39 rmys n is order of diffraction 39 Ray 2 H r M N w I dhkl is interplanar distance I Figure 328 1 Iquot saga aAimigwrWe MC SYAHT UNIVERSITY Interpreting Diffraction Data 3 A Mme Iln HU m JIM Innmu m unran 1m w 1m xn Dm mm In 4 110 no my 0 vmWHV L V m m W W w W m n MW 4 3917 h A quot 2 r mm M um m M w m mmmm A Lt mhun 398 Hm m mummy m mm 331 wwwmsencsweduresearchzhu Department of Materials 5C1 amp Eng NC STAIE UNIV HSITY mHmw W w m m u u u mum mumqu WWW Homework Example Problems 37 38 39 310 311 Regular Problems Chapter 3 38 39 40 41 43 4446 47 48 49 5051 52 5456 57 58 59 697071 72 Reading assignment for the next class 4344 httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY MSEZOO Lecture 7 CH 6264 Mechanical Properties I Instructor Yuntian Zhu Objectivesoutcomes You will learn the following Stresses and strains in solids Norma1 and shear stresses Elastic and plastic deformation The tensile test and the engineering stressstrain curves Y0ung s modulus the yield strength the ultimate tensile strength the percent elongation and percent reduction in area True stress and true strain Hardness and hardness testing 339 ttpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Elastic and Plastic Deformation in Metals Elastic deformation Metal returns to its original dimension after the force is removed Plastic deformation The metal is deformed to such an extent such that it cannot return to its original dimension after the load is removed httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Engineering Stress and Strain under tensioncompression Engineering stress a T A0 T M Units of Stress are Nm2 Pascals or Pa or PSI T K A Z 0 0 Engineering strain e z z 0 M 6 0 6 0 Force F N DepanmentofM v m i rquot NC STATE UNIVERSITV Poisons Ratio 6 latera e Poisons ratio V L e longltudlnal e 2 Usually poisons ratio ranges from 025 to 04 Example Stainless steel 9 028 Copper gt 033 http Ilwww mse ncsu eduresearchZhu Department of Materials Sol amp Eng NC STA IE UNIVERSITY Shear Stress and Shear Strain S Shear force Shear stress 1 A Area of shear force appllcatlon a Unxl fussed burly Surface am 4 8 shear I39mce Amount of shear displacement Distance h over which shear acts Shear Modulus G 17 Y httpmmwmsencsueduresearchzhu Department of Materials Sci amp Eng quotc STAIE U N39VERS l TY Shear strain 7 Tensile testThe most common test 0 Strength of materials can be tested by pulling the metal to failure Load Cell http llwww mse ncsu eduresearchZhu Department of Materlals Sol amp Eng Specimen Extensometer Force data is obtained from Load cell Strain data is obtained from Extensometer NCSTAlEil EHSHV Tensile Test Cont Round bar sample Flat sheet sample Ulumm mile many K7 HUI hi 4001 NIP q 7 777 Ih39llihi39il kme A 600 H in 39mln39ll 39 mm 39 1 mm 8 gt7 7 Rum Ti iJTIL 00 HU 1mm imam mun km l mm 5 quot quot Rm 39 W 3min nun3 9 quot Iquotquot cm inn1h 400 E Figure 621 W ii39 5 quot5 50 W Commonly used in g 7 3m 5 L Test specimen ASTM standard gives 3 more information 7 i 00 Typical Stressstrain W curve U 0 nmn 0040 0050 noxn U 100 Engineering strain inin httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIV Young s Modulus Young s Modulus 1E Stress and strain are linearly related in elastic region Hooks laW Linear panic at the erai stress Higl1er the bonding strength higl1er is the modulus of elasticity Largelv determined bV Insensitive t0 the grain size hllp Ilwwwmse ncsu eduresearchzhu Depanment of MaLeHals Sc amp Eng Yield Strength 02 o set yield stren gth is that strength at which 02 plastic deformation takes place 4m Construction line starting at 02 strain and parallel to elastic region is drawn to find 02 offset yield strength In E mu ing mwumii u nun mm 4mm 4mm Hmn DepanmentofM v m i rquot NC STATE UNIVERSITV Ultimate tensile strength Ultimate tensile strength UTS is the maximum strength reached by the engineering stress strain curve Necking starts after UTS is reached Al ltil lr lullgxrul S T More ductile the metal is more R Necmng POint is the necking before failure 1S3 S A12024Annealed True stress level at necking section MPa Eng Strain Engineering Stress strain curves of A12024 With two different heat treatments Ductile annealed sample necks more hllplwwwmsencsuedulresearchzhul Department of Materials 3m s Eng NC STATE UNIVERSITY Percent ElongationDuctility 0 Percent elongation elongation to failure is a measure of ductility of a material 0 It is the elongation of the metal before fracture expressed as percentage of original length Elongation to failure 0 ie Ductility er http www mse ncsu eduresearchzhu Department ur Materials Sm amp Eng NC STATE UNIVERSITY Percent Reduction in Area Percent reduction area is also a measure of ductility Reduction Initial area Final area Area Final area i 1 BMFBr39 ttle Percent reduction in area in metals decreases in case of presence of porosity NC STATE UNIVERSITV Depanmem ofM v m i i Fquot True Stress True Strain True stress and true strain are based upon instantaneous crosssectional area and length F 39 True Stress 6t Ai instantaneous area True Strain at Ln5 Ln 10 A St 6 1 6 St ln 1 6 httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNVERSITY Hardness and Hardness Testing Hardness is a measure of the resistance of a metal to permanent plastic deformation General procedure WW a Press the indenter that is harder than the metal Into metal surface mu m i my mum Withdraw the indenter Measure hardness by measuring depth or width of indentation DepanmentofM v m Fn NC STATE UNIVERSITV Home work 0 Example Problems 64 65 66 67 68 0 Regular Problems Chapter 6 18 19 23 24 25 29 30 0 Reading assignment section 6568 httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY MSEZOO Lecture 3 CHAPTER 3135 Crystal Structures and Crystal Geometry Instructor Yuntian Zhu Obj ectives Outcomes Describe crystal lattices and the unit cell Describe the principal metallic crystal structures the bodycentered cubic the facecentered cubic and the hexagonal closepacked structures Determine directions in the cubic system 3quotIlttpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY The Space Lattice and Unit Cells Atoms arranged in repetitive 3 D pattern in long range order give rise to crystal structure Why do we care An imaginary network of lines with points at intersections representing the arrangement of atoms is called space lattice Space Lattice Unit cell Amorphous materials Unit Cell 3 3npMWW mse ncsu eduresearchZhu Department of Materials 5C1 amp Eng NC SIAIE UNIVERSITY Ciystal Systems and Bravais Lattice Fig 32 Only 7 different types of unit cells are necessary to create all point lattices According to Bravais 14 standard unit cells HumWWW msencsueduresearchZhu Department of Materials eel t Eng NC STATE tnwmmv Types of Unit Cells T e 1 Cubic Unit Cell L x m gt a b c ndy Centered bcc Face centered fcc Figure 32 Type 2 Tetragonal gt a b 75 c 39 39 r 39l gtaBy900 V l i I 11 I Simple Body Centered 3quot J Vm39 g 39 Nmtmsx vol NZ STM E UMI JFRSITY Types of Unit Cells Cont I h Type 3 Orthorhomblc gt 21 b c t l r 1 gt a B v 900 5 u C b 47 V Simple Base Centered y 1 l Body Centered Face Centered T I Type 4 Rhombohedral Figure 32 gt a b c a gtaBv 90 1 r a I gimple 35rtmmww IMMM T39 39 I quot Mmmwol NC STATE quotNHTWWYY Types of Unit Cells Cont Type 5 Hexagonal gt a b c gt aB 900 gty120 0 Type 6 Monoclinic gt 21 b c gt ay90 B 0 Type 7 Triclinic gt 21 b c gt a B Y 90 NDMA T39 I Simple r L I l l il I I I l Base w Centered Figure 32 lIIntcw mk vo N53 STATE C39Nl39b39f WlTY Principal Metallic C stal Structures 90 of the metals have either Body Centered Cubic BCC Face Centered Cubic FCC or Hexagonal Close Packed HCP crystal structure HCP is denser version of simple hexagonal crystal structure r HCP Structure BCC Structure FCC Structure Figure 33 NC STATE UNIVERSITY Department of Materials Sci amp Eng 3 zttpjvvmlmlmsencsu eduresearchzhu BodV Centered Cubic BCC Crvstal Structure Represented as one atom at each corner of cube and one at the center of cube coordination number Examples gt Chromium a0289 nm gt Iron a0287 nm gt Sodium a0429 nm Figure 34 aampb 3 ellpjwwwmsencsueduresearchzhu Department of Materlals scr amp Eng NC SIATE UN39VEHSITY BCC Crystal Structure Cont of atoms in the unit cell Atoms contact each other at cube diagonal Lattlce 4R constant a 5 Example 31 Packing factor 3398ttplwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNlVERSITY Face Centered Cubic gFCCQ Cmstal Structure FCC structure 1 atom at each corner and face center Coordination number Atomic Packing Factor Examples gt Aluminum a 0405 gt Gold a 0408 igure 36 aampb 39 V 3 MplwvwvmsencsueduresearchZhul Department of Materials 351 amp Engv NC STATE UNIVERSITV FCC Crystal Structure C0r1t of atoms in a unit cell Lattice constant 4R a45 J lzmwwwmsencsueduresearchzhu Department of Materlals SCl amp Eng NC STATE UNIVERSITY Hexagonal ClosePacked Structure 0 The HCP structure is represented as an atom at each of 12 corners of a hexagonal prism 2 atoms at top and bottom face and 3 atoms in between top and bottom face 0 The coordination number is 12 ackin factor 074 339filfbjwwvmmsencsueduresearchlzhul Department of Materlals Sclv amp Engv NC SIATE UNIVERSITY HCP Crystal Structure Cont of atoms in each HCP unit cell Examples gt Zinc a 02665 nm da 185 gt Cobalt a 02507 nm da 162 Ideal ca ratio is 1633 NC STAIE UNIVERSITY Atom Positions in Cubic Unit Cells In a cubic unit cell gt Lilly 1 gamp4m 1 I Atom positions are located using unit distances along the axes Figure 310 b 3 M www mse ncsu eduresearchZhu Department of Materials 5C1 amp Eng NC SIAIE UNIVERSITY Find Direction Indices Example 34 339 tl wwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Homework Example Problems 31 32 34 35 36 Regular Problems Chapter 3 6 78 9 10 11 12 13 14 15 16 1820 21 22 31 32 33 3436 Reading assignment for the next class 36311 httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY MSEZOO Lecture 5 CH 4344 Crystal Imperfections Defects Instructor Yuntian Zhu Ob jectivesoutcomes You will learn the following Describe point defects solid solutions vacancies and interstilialcies Describe line defects dislocations Burger39s vector edge and screw dislocations Describe grain boundaries and grain size Understand metallography httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Metallic Solid Solutions Solid solution is a simple type of alloy in which elements are dispersed in a single phase The crystal structure of the solvent is maintained Why do we care There are two types of solid solutions Example gt httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Substitutional Solid Solution Solute atoms substitute for solvent atom in a crystal lattice The structure remains unchanged Lattice might get slightly distorted Solvent artoms j Solute atoms httpMwwmse ncsu eduresearchZhu Department of Materlals 5m amp Eng NC STATE UNUVEHSITY Substitutional Solid Solution Cont The solubility of solids is greater if gt Similar diameter difference lt 15 gt Same crystal structures gt Similar electronegativity else compounds will be formed gt Same valence Examples Atomic Electro Solid System radius negativity Difference difference CuZn 39 01 383 CuPb 367 02 017 CuNi 23 0 100 httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Interstitial Solid Solution Solute atoms t in between the voids interstices of solvent atoms Solute atoms is much smaller than solvent atoms Calculate the radius of the biggest interstitial void 7 Example problem 3 Iron atoms r0129nm a xv Carbon atoms n0075nm HllpUWWW mse ncsu eduresearchZhu Department of Materials 5C1 amp Eng NC SIATE UNIVERSITV Crystalline Imperfections defects N0 crystal is perfect Why do we care about defects Imperfections can be classi ed as gt Zero dimensional point defects gt One dimensional line defects dislocations gt Two dimensional defects grain boundaries httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Point Defects Vacancy Vacancy is formed due to a missing atom Vacancies are equilibrium defects HiipUWWW mse ncsu eduresearchZhu Department of Materials 5C1 amp Eng NC SIATE UNIVERSITY Point Defects Interstitials Atom in a crystal sometimes occupies interstitial site How can this happen Effect on crystal lattice httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Point Defects in Ionic Clystals Complex as electric neutrality has to be maintained If two appositely charged palticles are missing cation anion divacancy is created This is Scllottky imperfection Frenkel imperfection is created when cation moves to interstitial site Fre kel unp rlecnnn3quot Department of Materlals 5C1 amp Eng NC STAIE UNIVERSITY http WWW mse ncsu eduresearchZhu Line Defects Dislocations Lattice distortions are centered around a line Different types of line defects are gt Edge dislocation gt Screw dislocation gt Mixed dislocation httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Edge Dislocation Created b insertion of extra half lanes of atoms 39 I Positive edge dislocation 39 I Negative edge dislocation Burgers vector lllllllmlll Shows displa ll lilllllmjllll 1quot39l cement of 39 1 atoms slip ElElllllll httpvaNmsencsueduresearchzhu Department of Materials sciv amp Engv NC STAIE UNIVERSITY Screw Dislocation Created due to shear stresses applied to regions of a perfect crystal separated by cutting plane Distortion of lattice in form of a spiral ramp Lb Sm ahlmmm Dulnl imw Im 39quotN o o 0 30 ruuw Nun T he Bur ers Vector is arallel to the dislocation line HiipUWWW mse ncsu eduresearchZhu Department of Materials 5C1 amp Eng NC SIATE UNIVERSITV Mixed Dislocation Most crystal have components of A 7 a 77 7 both edge and screw dislocation u Each dislocation has only one Burgers vector b Dislocation appear as dark lines when observed under electron microscope When a dislocation glide across a crystal it produce a plastic deformation by b Examples of edge screw and mixed dislocations httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Grain Boundaries Grain boundaries separate grains Width 25 atomic diameters Atoms in grain boundaries have higher energy Grain boundary httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE LH HVERSITY Twin Boundaries Twin A region in which mirror image pf structure exists across a boundary Formed during plastic deformation and recrystallization Strengthens the metal httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Observing Grain Boundaries Metallography 0 Sample surface is polished The surface is then etched chemically Tiny groves are produced W W M at grain boundaries 39 Groves do not intensely mm Nu m Rel Imam mu 1mm spi ulmm reflect light Hence observed by optical 4C I ii ihmg microscope 5 l q 3 r 39 V i i quot I 39 Huuuhwnlny 4 l l r t39wq Xg httpmemsencsueduresearchlzhul Department of Materials Sci amp Eng NC STATE UNIVERSITY Grain Size Why do we care Smaller grains lead to stronger materials httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY Homework Example Problems 43 Regular Problems Chapter 4 l7 19 21 22 24 Reading assignment for the next class 5154 httpwwwmsencsueduresearchzhu Department of Materials Sci 3 Eng NC STATE UNIVERSITY MSEZOO Lecture 6 CH 5154 Diffusion Instructor Yuntian Zhu Objectivesoutcomes You will learn the following Describe the rate processes in solids the activation energy 39Describe atomic diffusion and diffusion mechanisms Describe substitutional and interstitial diffusion Describe steady state diffusion and apply Fick s first law Describe transient diffusion and apply Fick s second law Describe effect of temperature on diffusion rate List a few industrial applications of diffusion httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Rate Process in Solids At a given temperature not all atoms have activation energy AE It should be supplied to them AEa AE rate 2 Ce H 2 Ce RT Ea quot1 AE AEquot Activation Energy kB0ttzmann s constant Actlvatlon Energy 138x103923 Jatom K E x Reactants Energy released R 8314 Jmol K D e to reaction EP quotquotquotquotquotquotquotquotquotquotquotquot quotmedia39squot 39 R i n r 1n httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNVERSITY Vacancy concentration The number of vacancies at equilibrium at a particular temperature in a metallic crystal lattice is given by EV Q N nV Number of vacancies per m3 of metal N Number of atoms per m3 of metal EV Activation Energy to form a vacancy T Absolute Temperature K Boltzmann s Constant 138 x 103923 Jatom IQ C Constant httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Atomic Diffusion in Solids Diffusion is a process by which a matter is transported through another matter or itself self diffusion Examples NC STATE UNIVERSITY httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng Vacanc or Substitutional Diffusion A A v v Actlvatlon Activation Activation Energy of Energy to Energy to Self diffusion form a move a Vacancy vacancy E Puxiiilm requirement Vacancy As the melting point increases quot quot energv also increases gwhy DepanmentofM v m i rquot NC STA1E UNIVERSITY Interstitial Diffusion mechanism Atoms move from one interstitial site to another Interstitial atoms Matrix atom s DepanmentofM v m Fn NC STATE UNIVERSITV Steady State Diffusion No chan e in concentration with time No chemical reaction occurs Only net ow of atoms Solute atom ow C oncentration Of diffusing atoms Distance x gt Net flow of atoms Diffusing Unit Per unit area per atoms Area Umt time J DepanmentofM v m t rquot NC STATE UNIVERSITY Fick s First Law for steady state diffusion The ux or ow of atoms is given by dc J Flux or net ow of atoms J D D Diffusion coef cientdiffusivity dx Concentration Gradient dx Temperature effect D 2 D0 eXp httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY NonSteady State Diffusion Concentration of solute atoms at am point in metal changes with time in this case Ficks second law httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Fick s Second Law Solution Cs C e CsC0 rf L NE Cs Surface concentration of element in gas diffusing into the surface C0 Initial uniform concentration of element in solid CX Concentration of element at distance x from surface at time tl X Distance x x distance from surface D diffusivity of solute t time NC SIATE UNIVERSITY Depanmem ofM v m i i Fquot Carburizing Low carbon Diffusing carbon Steel part atoms no 7 r 7 w N THE UNIVERSITV Effect of Temperature on Diffusion Dependence of rate of diffusion on temperature is given by D Diffusivity mZS D0 Proportionality constant mZS Q Q Activation energy of diffusing s ecies Jmol D D Oe RT R RIiolar gas constant 8314 JmolK 01 Q T Temperature K lnD 1n D0 RT 539 wwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSlTY Effect of Temperature on DiffusionExample If diffusivity at two temperatures are determined two equations can be solved for Q and D0 Example The diffusivity of silver atoms in silver is 1 X 103917 at 5000C and 7 X 103913 at 10000C Therefore 01000 expQRT2 Q 1 1 a a R exp D500 eXpQRT1 7x1013 Q 1 1 1x10 R 1273 773 Solving for activation energy Q Q 183KJmol httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Home work Example Problems 51 52 53 54 55 56 Regular Problems Chapter 53 l3 16 21 25 Reading assignment for the next class after test 1 5154 httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY Test 1 review and policy Understand the underlined concept in the VG Example problems Homework problems 35 multiple choices at 3 points each Bring your student ID Have you ID for the score sheet httpwwwmsencsueduresearchzhu Department of Materials Sci amp Eng NC STATE UNIVERSITY