Diffusion [8]€¦ · ¾The surface of a 0.1% C steel gears is to be hardened by carburizing. In gas carburizing, the steel gears are placed in an atmosphere that provides 1.2% C

Diffusion [8]

1>

Diffusion transport by atomic motion.

Inhomogeneous material can become homogeneous by diffusion. Temperature should be high enough to overcome energy barrier.

Applications of Diffusion

2>

Life - BreathingNitriding / Carburizing - Surface Hardening of Steelsp-n junction - Dopant Diffusion for Semiconductor Devices Manufacturing of Plastic Beverage Bottles/MylarTM

BalloonsSputtering, Annealing - Magnetic Materials for Hard Drives Coatings and Thin FilmsThermal Barrier Coatings for Turbine Blades

Diffusion of oxygen into a single-celled organisms

3>

oxygen

carbon dioxide

maximum distance is 0.1 mm

In a single-celled organism (such as Amoeba) the distance is so small that diffusion is rapid enough for the cell’s needs

Diffusion of oxygen into an earthworm

4>

CO2 diffusesoutO2 diffuses in

Section throughworm’s skin

the blood vesselsabsorb the O2 andcarry it to the body

0.04mm

diffusion takes place through the thin skin of the worm

the air passages in the lungbranch into finer and finer tubes

each tube ends up ina cluster of tiny air sacs.

diffusion ofoxygen

diffusion ofcarbon dioxide

O2

CO2

0.03 mm

Diffusion of oxygen into a human body

6>

blood supply to air sac

air breathedin and out

HumanLung

Surface Hardening of Steels

6>

Furnace for heat treating steel using the carburization process.

• Case Hardening:-- Diffuse carbon atoms

into the host iron atomsat the surface.

-- Example of interstitialdiffusion is a casehardened gear.

Electronic solid state devices

7>

Schematic of a n-p-n transistor.

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Surface corrosion protection

8>

Hot dip galvanized parts and structures prevent corrosion.

Surface heat protection

9>

A thermal barrier coating on nickel-based superalloy.

Mechanisms for Diffusion

10>

Self-diffusion - The random movement of atoms within an essentially pure material.Vacancy diffusion - Diffusion of atoms when an atom leaves a regular lattice position to fill a vacancy in the crystal.Interstitial diffusion - Diffusion of small atoms from one interstitial position to another in the crystal structure.


11>

Self-diffusion: in an elemental solid, atoms also migrate.

Label some atoms

A

B

C

D

After some time

AB

C

D


12>Source: William Callister 7th edition, chapter 5, page 112, figure 5.3(a)

Vacancy or Substitutional Diffusion: Atom from normal lattice position changes position with an adjacent vacancy (vacancy lattice site). So, the atoms and vacancies travel in opposite directions. Both self-diffusion and inter (impurity)-diffusion can

occur thus.


13>

Interstitial Diffusion: Atoms move from one interstitial site to another (vacant) interstitial site.

Source: William Callister 7th edition, chapter 5, page 112, figure 5.3(b)


14>

100%

Concentration Profiles0

Cu Ni

Interdiffusion: In an alloy, atoms tend to migratefrom regions of large concentration.

Initially After some time

100%

Concentration Profiles0

Adapted from Figs. 5.1 and 5.2, Callister 6e.

Activation Energy for Diffusion

15>

Activation energy: energy is required to squeeze atoms past one another during diffusion.

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Q (substitutional) > Q (interstitial)

Diffusion coefficient and temperature

16>

Diffusion coefficient: a constant which is a function of diffusing species and temperature.

Diffusion coefficient increases with increasing T

D = Do exp⎛

⎝⎜

⎞

⎠⎟−

Qd

RT

= pre-exponential [m2/s]= diffusion coefficient [m2/s]

= activation energy [J/mol or eV/atom] = gas constant [8.314 J/mol-K]= absolute temperature [K]

DDo

Qd

RT

Activation Energy for Diffusion

16>

Diffusion coefficient

18>

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Si

Diffusion Paths

19>

Qsurface < Qgrain boundary < Qlattice

Experimentally determined activation energies for diffusion

Core of dislocation lines offer paths of lower resistance → (PIPE DIFFUSION)

Lower activation energy implies higher diffusivity

1/T →

Log

(D) →

Schematic

Polycrystal

Singlecrystal

Qgrain boundary = 110 kJ /mole

QLattice = 192 kJ /mole

Ag self-diffusion:

Type of Diffusion

20>

Rate of Diffusion – Some Definitions

21>

Diffusion coefficient (D) - A temperature-dependent coefficient related to the rate at which atoms, ions, or other species diffuse.

D0 - a constant which is a function of jump frequency, jump distance and coordination number of vacancies.

Concentration gradient - The rate of change of composition with distance in a nonuniform material, typically expressed as atoms/cm3.cm or at%/cm.

Fick’s first law - The equation relating the flux of atoms by diffusion to the diffusion coefficient and the concentration gradient.

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Flux

22>

( )( ) smkgor

scmmol

timearea surfacediffusing mass) (or molesFlux 22=≡≡J

Simplest Case: Steady-State Diffusion

dxdCDJ −=

This model is captured as Fick’s first law of diffusionC1

C2

x

C1

C2

x1 x2

D ≡ diffusion coefficient which is a function of diffusing species and temperature

The rate of diffusion is independent of time∴ Flux is proportional to concentration gradient =

dxdC

12

12 linear ifxxCC

xC

dxdC

−−

=ΔΔ

≅

For steady state diffusion concentration gradient = dC/dx is linear23>

Example: Chemical Protective Clothing (CPC)

24>

Methylene chloride is a common ingredient in 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:

C2 = 0.02 g/cm3

C1 = 0.44 g/cm3


25>

scmg 10 x 16.1

cm) 04.0()g/cm 44.0g/cm 02.0(/s)cm 10 x 110( 2

5-33

28- =−

−=J

12

12- xxCCD

dxdCDJ

−−

−≅=

Dtb 6

2l=

gloveC1

C2

skinpaintremover

x1 x2

Solution – assuming linear concentration gradient

D = 110x10-8 cm2/s

C2 = 0.02 g/cm3

C1 = 0.44 g/cm3

x2 – x1 = 0.04 cm

Data:


26>

If a person is in contact with the irritant and more than about 0.5 gm of the irritant is deposited on their skin they need to take a wash break.

If 25 cm2 of glove is in the paint thinner can, How long will it take before they must take a wash break?

52

52

2

2 4

4

gcm -s

if the exposed area of the gloves are 25 cm

how long will it take to get 0.5g of M-C onto the hands?

gF 1.16 10cm -s

1.16 10

25 2.9 10

0.5gExposure time= 1724 0.48 2.9 10

lux

lux

F

gcm s

s hrgs

−

−

−

−

×

= ×

= ∗ = ×

≅ =×

Non-steady State Diffusion

Concentration,C, in the box

J(right)J(left)

dx

27>

The concentration of diffusing species is a function of both time and position C = C(x,t)This is more common – the flux varies with time!

• To conserve matter: • Fick's First Law:

• Governing Eqn.:dCdt

= Dd2C

dx2

−dx

= −dC

dtJ = −D

dC

dxor

J(left)J(right)

dJ

dx= −

dC

dt

dJ

dx= −D

d2C

dx2

(if D does not vary with x)

equate

Fick’s Second Law

Non-steady State Diffusion

28>

Fick’s Second Law Solution

2

2

xCD

tC

∂∂

=∂∂ ( )

⎟⎠

⎞⎜⎝

⎛−=−−

Dtxerf

CCCtxC

os

o

21,

Error Function Table

29>

( )⎟⎠

⎞⎜⎝

⎛−=−−

Dtxerf

CCCtxC

os

o

21,

Example: Design of a Carburizing Treatment

30>

The surface of a 0.1% C steel gears is to be hardened by carburizing. In gas carburizing, the steel gears are placed in an atmosphere that provides 1.2% C at the surface of the steel at a high temperature. Carbon then diffuses from the surface into the steel. For optimum properties, the steel must contain 0.45% C at a depth of 0.2 cm below the surface. Design a carburizing heat treatment that will produce these optimum properties. Assume that the temperature is high enough (at least 900oC) so that the iron has the FCC structure.


31>


32>

Diffusion and Materials Processing

33>

Sintering - A high-temperature treatment used to join small particles compacted by powder metallurgy.

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Diffusion processes during sintering and powder metallurgy. Atoms diffuse to points of contact, creating bridges and reducingthe pore size


34>

Microstructure of BMT ceramics obtained by compaction and sintering of BMT powders.

Particles of barium magnesium tantalate (BMT) (Ba(Mg1/3 Ta2/3)O3) powder are shown. This ceramic material is useful in making electronic components known as dielectric resonators that are used for wireless communications.


35>

Grain growth - Movement of grain boundaries by diffusion in order to reduce the amount of grain boundary area.


Grain growth occurs as atoms diffuse across the grain boundary from one grain to another


36>

Grain growth in alumina ceramics can be seen from the SEM micrographs of alumina ceramics. (a) The left micrograph shows the microstructure of an alumina ceramic sintered at 1350oC for 150 hours. (b) The right micrograph shows a sample sintered at 1350oC for 30 hours.

The steps in diffusion bonding: (a) Initially the contact area is small; (b) application of pressure deforms the surface, increasing the bonded area; (c) grain boundary diffusion permits voids to shrink; and (d) final elimination of the voids requires volume diffusion


37>

Diffusion bonding - A joining technique in which two surfaces are pressed together at high pressures and temperatures.


Kirkendall effect

38>

Inert Marker – thin rod of a high melting material which is basically insoluble in A & B

Materials A and B welded together with inert marker underdiffusionUsually the lower melting component diffuses faster (say B)

A B

Marker motion

Kirkendall effect

39>Porosity occurs in the copper because copper diffuses faster in the nickel.

D(Cu)>D(Ni)

Summary: Structure & Diffusion

39>

Diffusion FASTER for...

• open crystal structures

• lower melting T materials

• materials w/secondarybonding

• smaller diffusing atoms

• cations

• lower density materials

Diffusion SLOWER for...

• close-packed structures

• higher melting T materials

• materials w/covalentbonding

• larger diffusing atoms

• anions

• higher density materials

CALLISTER JR, W. D. AND RETHWISCH, D. G. Materials Science and Engineering: An Introduction, 9th edition.

John Wiley & Sons, Inc. 2014, 988p. ISBN: 978-1-118-32457-8.ASHBY, M. and JONES, D. R. H.

Engineering Materials 1: An Introduction to Properties, Applications and Design. 4th Edition. Elsevier Ltd. 2012, 472p. ISBN 978-0-08-096665-6.

CALLISTER JR, W. D. AND RETHWISCH, D. G. Fundamentals of Materials Science and Engineering: An Integrated Approach, 4th ed.

John Wiley & Sons, Inc. 2012, 910p. ISBN 978-1-118-06160-2.MITTEMEIJER, E. J.

Fundamentals of Materials Science: The Microstructure–Property Relationship Using Metals as Model Systems. Springer-Verlag Berlin. 2010, 594p. ISBN 978-3-642-10499-2.

ASKELAND, D. AND FULAY, P. Essentials of Materials Science & Engineering, 2nd Edition.

Cengage Learning. 2009, 604p. ISBN 978-0-495-24446-2.ABBASCHIAN, R., ABBASCHIAN, L., AND REED-HILL, R. E.

Physical Metallurgy Principles, 4th Ed. Cengage. 2009, 750p. ISBN 978-0-495-08254-5.SMALLMAN, R. E. and NGAN, A.H.W.

Physical Metallurgy and Advanced Materials, 7th Edition. Elsevier Ltd. 2007, 650p. ISBN 978-0-7506-6906-1.

References

41Nota de aula preparada pelo Prof. Juno Gallego para a disciplina Ciência dos Materiais de Engenharia.® 2016. Permitida a impressão e divulgação. http://www.feis.unesp.br/#!/departamentos/engenharia-mecanica/grupos/maprotec/educacional/

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Diffusion [8]€¦ · ¾The surface of a 0.1% C steel gears is to be hardened by carburizing. In gas carburizing, the steel gears are placed in an atmosphere that provides 1.2% C