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IntroMaterials Science & Engr

by: Eudora Blick

IntroMaterials Science & Engr MSE 201

Eudora Blick
GPA 3.61


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Class Notes
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This 12 page Class Notes was uploaded by Eudora Blick on Monday October 26, 2015. The Class Notes belongs to MSE 201 at University of Tennessee - Knoxville taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/229814/mse-201-university-of-tennessee-knoxville in Materials Science Engineering at University of Tennessee - Knoxville.

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Date Created: 10/26/15
Introduction To Materials Sclmce FOR ENGJNEERS ch 5 Introduction To Materials Sclmce FOR ENGJNEERS ch 5 Goals Diffusion how do atoms move through solids Fundamental concepts and language Diffusion mechanisms 7 Vacancy diffusion 7 Interstitial diffusion 7 Impurities Diffusion equations 7 Fick s rst law 7 Fick s second law Factors that in uence diffusion 7 Diffusing species 7 Host solid 7 Temperature 7 Microstructure Introduction To Materials Science FOR ENGJNEERS Ch 5 What is diffusion Diffusion is material transport by atomic motion Atoms of type A Atoms of type B I w zoooramare A Inhomogeneous materials can become homogeneous by diffusion For an active diffusion to occur the temperature should be high enough to overcome energy barriers to atomic motion Introduction To Materials Science FOR ENGJNEERS Ch 5 Atomic Vibrations Heat causes atoms to vibrate Vibration amplitude increases with temperature Melting occurs when vibrations are suf cient to rupture bon s Vibrational frequency N 1013 Hz Average atomic electronic energy due to thermal excitation is of order kT with a distribution around this average energy PE N exp EkT k Boltzmann s constant 138x1039Z3JK or 862 x 10395 eVK T Absolute temperature Kelvin imitation nlaanssam poaancmms Ch 5 What is diffusion Inlerdiffusion and Selfrdiffusion Diffusion is material transport by atomic motion Intzrdl usmn occurs in response to a concentration gradient mm rigorously to a gr cm in chemical potential mammalian Maunalssclznce m2 momma Ch 5 Din 39on Mechanisms 39 To move from lattice site to lattice site atoms need energy to break bonds With neighbors and to cause the necessary lattice distortions during motion from site to another T is energy comes from atomic vibrations Eav N k Atom migration Vacancy migration 39 O Before After Atomic migration by a mechanism or vacancy migration Materials now the atom is opposite the vacancy ow direction 6 madam iiitsiiiissmm m momma Ch 5 Interstitial diriusion depends on tem erature T jump to Requires small impur39 y eg c1l 0 to lit into interstices in host Pwi unolhmd d AkinM aimmi n interstitial sites because 0 39 Imaducum Ta Mitsiiils Scimce mm ENGINEERS Ch 5 Diiiusion Flux e ux oi diiiusing atoms J is used to quantify how fast diffusion occur The 11 is de ned as nteims o the mass ux mass 0 atoms 39ffusing through unit area per unit time eg kgmZseco m J gt 2 or 2 A dt m s m s gt xdirection Unit area A through which atoms move Introduction To Materials Scimce FUR ENGINEERS Ch 5 SteadyState Diffusion Steady state diffusion the diffusion flux does not change wi time Concentration profile concentration of atomsmolecules of interest as function of position in the sample Concentration gradient dCdx Kg mquot the slope at a particular point on concentration profile chgicAicB Exam Yhmmemn ak dX AX X A 7 XB c 5 at mm vs Ga 2quot mm PA Dwnchnn m mtmsmn m Ecnccn mm m Avea A IN my Introduction To Materials Scimce FUR ENGINEERS Ch 5 SteadyState Diffusion Fick s first law Fick s first law the diffusion ux along direction X is proportional to the concentration gradient J D where D is the diffusion coefficient X J flux of atoms across plane with area1 we I The concentration gradient is o en called the driving force in diffusion but it is not a force in the mechanistic sense The minus sign in the equation means that diffusion is down the concentration gradient 10 Introduction To Materials Science FUR ENGINEERS Ch 5 Diffusion Temperature Dependence 1 dc Diffusion coef cient is the measure of J 7D 3 mobility of diffusing species Q D 7 D0 exp7 0 RT D0 7 temperatureindependent preexponential mls Q01 7 the activation energy for diffusion Jmol or eVatom R 7 the gas constant 831 JmolK or 862x10395 eVatomK T 7 absolute temperature K The above equation can be rewritten as 1 1 lnD lnD0 or logDlogD0 7 Qd R T 23R T The activation energy Q01 and preexponential D0 therefore can be estimated by plotting lnD versus 11quot or logD versus 11quot Such plots are Arrhenius plots Introduction To Materials Science FUR ENGLN39EERS Ch 5 Diffusion Temperature Dependence II i i i i 1071 7 7777 N3 10437 7 E g 10 7 7 10715 7 E 1 107167 1 7 i i w 1 1 1 07 05 09 10 11 12 Rectpvoca tempevztuve lOODK Graph oflog D vs 11quot has slop ondZBR intercept of In DO logD17logDZ 1T1 71T2 inunducum Ta Mnenets Semee mm ENGINEERS ch 5 Diffusion Coefficient t t men Exetertnexegentnm tenemmenm tenement 3 we e E men 8 5 7 m a 5 w m n e t e 1 t x D 07 a o 9 1 u x 1 necwmcaw temvevalule wooKy Determine activatinn Energy 1313 expectkn InIHIn 12104th Graph nfln D vs1kT has yzdiem nerd intercept in Du inunducum Ta Mnenets Semee mm ENGINEERS ch 5 D39 usinn Pmpem39es fur Several Mater39 quotn MW nee 0 mm We W we we mum t quotW e an 1x 039 e Mt n n t m n eplot ofthe loganunn of the e M t Mqu several metals N Introduction To Materials Science FOR ENGINEERS Ch 5 NonsteadyState Diffusion Fick s second law not tested In most real situations the concentration pro le and the concentration gradient are changing with time The changes of the concentration pro le is given in this case by a differential equation F ick is second law W79 2 6C a Dg Dac 6X 6X2 Solution of this equation is concentration pro le as function of time CXt t3gtt2gttl Cancentrahun m muusmg species Dwstznce n c r 39 39 Funinnmin Introduction To Materials Science FOR ENGlNEERS Ch 5 no es e Equations Governing Diffusion 2 Time Varying Fick s 2ndLaw Tlme varylng d1ffus10n equatlon Le non steady state 6C6t aaxa aC 6x 62C axr Assumes D independent afx which it isn I Solute conc CD 7 z erf z 2I1rl expcyz dz 0 Characteristic Dijfu sion Len gth University m n r Funinnmin Introduction To Materials Scimce FOR ENGINEERS Ch 5 not tested The solution to this differential equation with the given boundary conditi n 39s h C 39 th I CCo1erfx2D t ff 5 quotMm CSCO con ant Cu is the initial bulk Gaussian error function 2 2 L 5 erl z 24 expoy dz 0 an function 7 Gaussian error function based on integau39on oi the bell shaped curve 17 Univu39sity nf T n Fm n min Introduction To Materials Scimce FOR ENGINEERS Ch 5 not tested Tabulation of Error Function Values quotm i J UHll l 4 0952 I5 mm in wnm L7 LVKSK l N H quotW i 39 l NZA u m1 0095 09003 WINS L l l Li 0 MN 18 Univa39sity nf T n c Fm n min Introduction To Materials Sctmce FOR ENGJNEERS ch 5 Diffusion 7 Thermally Activated Process 1 In order for atom to jump into a vacancy site it needs to posses enough energy thermal energy to to break the bonds and squeeze through its neighbors The energy necessary for motion Em is called the activation energy for vacancy motion Energy Distance 393 333 Schematic representation of the diffusion of an atom from its original position into a vacant lattice site At activation energy Em has to be supplied to the atom so that it could break interatomic bonds and to move into the new position 19 Introduction To Materials Sctmce FOR ENGJNEERS ch 5 Diffusion 7 Thermally Activated Process 11 The average thermal energy of an atom kBT 0026 eV for room temperature is usually much smaller that the activation energy Em N l eVatom and al e uctuation in energy When the energy is pooled together in a small volume is needed for a 39ump The probability of such uctuation or frequency of jumps R1 depends exponentially from temperature and can b described by equation that is attributed to Swedish chemist enius Arrh E Where R0 is an attempt frequency proportional to the frequency of atomic vibrations Introduction To Matauals Science FOR ENGINEERS ch 5 Diffusion 7 Thermally Activated Process 111 For the vacancy diffusion mechanism the probability for any atom in a solid to move is the product of the probability of nding a vacancy in an adjacent lattice site see Chapter 4 Q P CNex 7 V Pl m and the probability of thermal uctuation needed to overcome the energy barrier for vacancy motion E The diffusion coef cient therefore can be estimated as N 2 Em Q D CNR a expE kaTjexp V kETj 7 DUexpltEmQvgtkBTDoexp QdkBTj Tempemture dependence of the diffusion coef cient follows the Arrhenius dependence 21 Introduction To Materials Science FOR ENGINEERS ch 5 T K 20m 15m 1000 5 n l l 1040 Xi39anA boundary Diffusivily mzs 1042 u Volume Icr 7 1046 l l 05 m 15 20 1 4 fvmuo K Selfdiffusion coef cients for Ag depend on the diffusion path In general the diffusivity is greater through less restrictive structural regions n Introduction To Matauals Scimce FOR ENGINEERS Ch 5 Factors that In uence Diffusion Diffusion mechanism interstitial faster than vacancy Diffusing and host species Do Qd is different for every solute solvent pair Temperature diffusion rate increases very rapidly with increasing temperature Qd 1 5 eV Microstructure diffusion faster in polycrystalline vs single crystal materials because grain boundary diffusion is faster than bulk diffusion larger spaces between atoms Accelerated diffusion can also occur along dislocation cores n Introduction TW WWEERS ch 5 STRUCTURE amp DIFFUSION Dl uslon FASTER for 0 open crystal structures 0 lower melting T materials 0 materials wsecondary bondin smaller diffusing atoms cations lower density materials Diffusion SLOWER for closepacked structures 0 higher melting T materials 0 materials wcovalent bonding larger diffusing atoms anions higher density materials n


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