12-Imperfection in Solids

7/26/2019 12-Imperfection in Solids

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MS 2101 Hand-out by Husaini Ardy

IMPERFECTION IN SOLIDS


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Defects in Metals


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Point Defects in Metals

The equilibrium number of

vacancy :

kTQNN Av /exp

Self interstitial


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Impurities in Metals

Pure metals consists only of

one type of atom

Difficult to produce 100% metal

Alloy : addition of foreignatoms for special purpose

(strengthening, special

properties) : substitutional and

interstitial atoms

The formation of solid solution:

Solvent : the major component

Solute : the minor component


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Line Defect - Dislocation

Dislocation : one extra

atom plane

There are two types :

Edge dislocation

Screw dislocation

Burgers vector ( b ) : the

magnitude and lattice

distortion


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Planar Defect Grain Boundaries

Atomic mismatch at the

boundaries

There are two types :

High angle g b (> 15o)

Low angle g b (< 15o)

Based on rotation :

Tilt boundaries

Twist boundaries


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Twist Boundary


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Introduction

Diffusion : material transport by the movement of atoms

Affected by : Temperature and Time

Diffusion types : Substitutional diffusion (Vacancy diffusion)

Interstitial diffusion


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Steady State Diffusion

Steady state diffusion : diffusion flux does not change with time

x

CDJ

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

D : diffusion coefficient [m2/sec.]

(C/ x) : concentration gradient [atom/m4]

Ficks first law :


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Example

A plate of iron is exposed toa carburizing atmosphere onone side and a decarburizingatmosphere on the other sideat 700 oC. If a condition of

steady state is achieved,calculate the diffusion fluxof carbon through plate ifthe concentrations of carbonat position 5 and 10 mm

beneath the carburizingsurface are 1.2 and 0.8kg/m3. Assume a diffusioncoefficient of 3.10-11m2/s atthis temperature

x

CDJ

C = (1.2 0.8) kg/m3

x = (5 10) x 10-3m

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

= 2.4 x 10-9kg/m2-s


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Non-Steady State Diffusion

Diffusion flux and the

concentration gradient at

some particular point in a

solid vary with time.

Ficks second law :

2

2

x

CD

t

C

The differential equation shall

be solved by considering the

boundary conditions


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Solution of diff. eqn.

Semi infinite solid exposed

to diffusing species

(carburizing, nitriding)

Boundary conditions : For t = 0, C = Coat 0 x ~

For t > 0, C = CS(the constantsurface concentration) at x = 0

C = Coat x = ~

The solution is :

Dt

xerf

CC

CC

oS

ox

21


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Carburizing of steel

Steel surface will be

carburized by exposing toCH4gas. Initial carbon content of

steel = 0.25 wt% Temperature = 950 oC

Carbon content at thesurface = 1.20 wt%. D = 1.6 x 10-11m2/s Time to achieve carbon

content of 0.80 wt% at aposition 0.5 mm below thesurface

Co= 0.25 wt%, CS= 1.20 wt%

Cx= 0.80 wt%, x = 5.10-4m D = 1.6 . 10-11m2/s

(CxCo)/(CsCo) = 0.5790

0.4210 = 1 - erf (62.5/t)

Tabel 6.1 : erf (z) = 0.4210,z = 0.392

t = 25,400 s = 7.1 hour


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Factors that Influence Diffusion

Diffusing species : diffusion coefficient

Temperature : affected D and diffusion rates

RT

QDD d

o

exp

12-Imperfection in Solids

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