imperfection in Solids

MS 2130 HandMS 2130 Hand--out by Husaini Ardyout by Husaini Ardy

IMPERFECTION IN SOLIDSIMPERFECTION IN SOLIDS


Defects in MetalsDefects in MetalsDefects in CeramicsDefects in CeramicsDefects in PolymersDefects in Polymers


Point Defects in MetalsPoint Defects in Metals

The equilibrium number of The equilibrium number of vacancy :vacancy :

( )kTQNN Av /exp −=

Self interstitial


Point Defects in CeramicsPoint Defects in Ceramics

Ceramic is an ionic Ceramic is an ionic structurestructureCharge balance Charge balance ((electroneutralityelectroneutrality) shall ) shall be maintainedbe maintainedAnion vacancy = Anion vacancy = cationcationvacancyvacancyAnion interstitial is less Anion interstitial is less probableprobable

Anion vacancy


Point Defects in CeramicsPoint Defects in Ceramics

FrenkelFrenkel defect :defect :–– CationCation leaving its leaving its

normal position and normal position and move to the interstitial move to the interstitial sitesite

SchottkySchottky defect :defect :–– cationcation--anion pair anion pair

defectdefect Frenkel defect

Schottky defect


Point Defects in PolymersPoint Defects in Polymers

Point defects in polymers have been observed in Point defects in polymers have been observed in the crystalline region :the crystalline region :–– VacancyVacancy–– Interstitial atoms and ionsInterstitial atoms and ions

Chain ends are considered to be defect (vacancy)Chain ends are considered to be defect (vacancy)


Impurities in MetalsImpurities in Metals

Pure metals consists only of Pure metals consists only of one type of atomone type of atomDifficult to produce 100% Difficult to produce 100% metalmetalAlloy : addition of foreign Alloy : addition of foreign atoms for special purpose atoms for special purpose (strengthening, special (strengthening, special properties) : properties) : substitutionalsubstitutional and and interstitial atomsinterstitial atomsThe formation of solid solution The formation of solid solution ::–– Solvent : the major Solvent : the major

componentcomponent–– Solute : the minor componentSolute : the minor component


Impurities in CeramicsImpurities in Ceramics

SubstitutionalSubstitutional or interstitial or interstitial solid solution is possiblesolid solution is possible

Charge neutrality shall be Charge neutrality shall be maintainedmaintained

The ionic charge and size must The ionic charge and size must be very nearly the same as be very nearly the same as one the host ionsone the host ions

If the size and charge are If the size and charge are different, lattice defects will different, lattice defects will occur to maintained neutralityoccur to maintained neutrality


Line Defect Line Defect -- DislocationDislocation

Dislocation : one extra Dislocation : one extra atom planeatom planeThere are two types :There are two types :–– Edge dislocationEdge dislocation–– Screw dislocationScrew dislocation

Burgers vector ( b ) : the Burgers vector ( b ) : the magnitude and lattice magnitude and lattice distortiondistortion


Planar Defect Planar Defect –– Grain BoundariesGrain Boundaries

Atomic mismatch at the Atomic mismatch at the boundariesboundaries

There are two types :There are two types :–– High angle g b (High angle g b (θθ > 15> 15oo))–– Low angle g b (Low angle g b (θθ < 15< 15oo))

Based on rotation :Based on rotation :–– Tilt boundariesTilt boundaries–– Twist boundariesTwist boundaries


Twist BoundaryTwist Boundary


IntroductionIntroduction

Diffusion : material transport by the movement of atomsDiffusion : material transport by the movement of atoms

Affected by : Temperature and TimeAffected by : Temperature and Time

Diffusion types :Diffusion types :–– SubstitutionalSubstitutional diffusion (Vacancy diffusion)diffusion (Vacancy diffusion)–– Interstitial diffusionInterstitial diffusion


Steady State DiffusionSteady State Diffusion

Steady state diffusion : diffusion flux does not change with time

xCDJ∂∂

−=

J : diffusion flux [atom/m2-sec.]

D : diffusion coefficient [m2/sec.]

(δC/ δx) : concentration gradient [atom/m]

Fick’s first law :


ExampleExample

A plate of iron is exposed to A plate of iron is exposed to a carburizing atmosphere on a carburizing atmosphere on one side and a decarburizing one side and a decarburizing atmosphere on the other side atmosphere on the other side at 700 at 700 ooCC. If a condition of . If a condition of steady state is achieved, steady state is achieved, calculate the diffusion flux calculate the diffusion flux of carbon through plate if of carbon through plate if the concentrations of carbon the concentrations of carbon at position 5 and 10 mm at position 5 and 10 mm beneath the carburizing beneath the carburizing surface are 1.2 and 0.8 surface are 1.2 and 0.8 kg/mkg/m33. Assume a diffusion . Assume a diffusion coefficient of 3.10coefficient of 3.10--1111 mm22/s at /s at this temperaturethis temperature

xCDJ∂∂

−=

δC = (1.2 – 0.8) kg/m3

δx = (5 – 10) x 10-3 m

J = -(3 x 10-11) x (0.4/-5.10-3)

= 2.4 x 10-9 kg/m2-s


NonNon--Steady State DiffusionSteady State Diffusion

Diffusion flux and the Diffusion flux and the concentration gradient at concentration gradient at some particular point in a some particular point in a solid vary with time.solid vary with time.FickFick’’ss second law :second law :

2

2

xCD

tC

∂∂

=∂∂

The differential equation shall The differential equation shall be solved by considering the be solved by considering the boundary conditionsboundary conditions


Solution of diff. Solution of diff. eqneqn..–– Semi infinite solid exposed Semi infinite solid exposed

to diffusing species to diffusing species (carburizing, (carburizing, nitridingnitriding))

Boundary conditions :Boundary conditions :–– For t = 0, C = CFor t = 0, C = Coo at 0 at 0 ≤≤ x x ≤≤ ~~–– For t > 0, C = CFor t > 0, C = CSS (the (the

constant surface constant surface concentration) at x = 0concentration) at x = 0

–– C = CC = Coo at x = ~at x = ~

The solution is :The solution is :

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

−−

Dtxerf

CCCC

oS

ox

21


Carburizing of steelCarburizing of steel

Steel surface will be Steel surface will be carburized by exposing to carburized by exposing to CHCH44 gas.gas.Initial carbon content of Initial carbon content of steel = 0.25 wt%steel = 0.25 wt%Temperature = 950 Temperature = 950 ooCCCarbon content at the Carbon content at the surface = 1.20 wt%.surface = 1.20 wt%.D = 1.6 x 10D = 1.6 x 10--1111 mm22/s/sTime to achieve carbon Time to achieve carbon content of 0.80 wt% at a content of 0.80 wt% at a position 0.5 mm below the position 0.5 mm below the surfacesurface

CCoo = 0.25 wt%, C= 0.25 wt%, CSS = 1.20 wt%= 1.20 wt%CCxx = 0.80 wt%, x = 5.10= 0.80 wt%, x = 5.10--44 mmD = 1.6 . 10D = 1.6 . 10--1111mm22/s/s

(C(CSS –– CCoo)/(C)/(Css –– CCoo) = 0.4210) = 0.4210

0.4210 = 0.4210 = erferf (62.5/(62.5/√√t)t)

TabelTabel 6.1 : 6.1 : erferf (z) = 0.4210, (z) = 0.4210, z = 0.392z = 0.392

t = 25,400 s = 7.1 hourt = 25,400 s = 7.1 hour


Factors that Influence DiffusionFactors that Influence Diffusion

Diffusing species : diffusion coefficientDiffusing species : diffusion coefficientTemperature : affected D and diffusion ratesTemperature : affected D and diffusion rates ⎟

⎠⎞

⎜⎝⎛ −=

RTQDD d

o exp


Diffusion in Ionic CrystalDiffusion in Ionic Crystal

Involving the motion of Involving the motion of two ions to maintained two ions to maintained local charge neutralitylocal charge neutralityIt is a vacancy diffusion It is a vacancy diffusion typetypeDiffusion rate is Diffusion rate is determined by the determined by the slowest moving ion.slowest moving ion.Diffusion rate is less than Diffusion rate is less than that of metalsthat of metalsElectrical conductivity is a Electrical conductivity is a function of diffusion function of diffusion coefficientcoefficient

Anion vacancy


Diffusion in Polymeric MaterialsDiffusion in Polymeric Materials

Involve the motion of small molecules (OInvolve the motion of small molecules (O22, H, H22O, COO, CO22, , CHCH44), between the molecular chain), between the molecular chainPolymer permeability and absorption characteristics are Polymer permeability and absorption characteristics are related to the degree to which foreign substances diffuse related to the degree to which foreign substances diffuse into polymer material.into polymer material.Rates of diffusion in Rates of diffusion in ““amorphousamorphous”” region is higher than region is higher than that of that of ““crystallinecrystalline”” regionregionSmaller foreign molecules diffuse faster than that of Smaller foreign molecules diffuse faster than that of large moleculeslarge molecules

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