Diffusion and carburizing-1.pdf

(1)

DIFFUSION IN SOLIDS

ISSUES TO ADDRESS

DIFFUSION IN SOLIDS

ISSUES TO ADDRESS...

• How does diffusion occur?

How does diffusion occur?

• Why is it an important part of processing?

• How can the rate of diffusion be predicted for

some simple cases?

• How does diffusion depend on structure

and temperature?

• How to control diffusion process?

H

t

t l

b i i

?

1

• How to control carburizing process?

DIFFUSION DEMO

• Glass tube filled with water.

At ti

t 0 dd

d

f i k t

d f

DIFFUSION DEMO

• At time t = 0, add some drops of ink to one end of

the tube.

• Measure the diffusion distance x over some time

Measure the diffusion distance, x, over some time.

• The concentration of ink is a function of time and

distance x.

t

_o

t

x (mm)

t

₁

t

₂

t

₃

x

_o

x

₁

x

₂

x

₃

time (s)

x

_o

x

₁

x

₂

x

₃

(2)

DIFFUSION: THE PHENOMENA (1)

• Interdiffusion

:

In an alloy, atoms tend to migrate

from regions of high concentration to low concentration.

DIFFUSION: THE PHENOMENA (1)

g

Initially After some time

Adapted from Figs. 5.1 and 5.2, C lli t 6

Cu

_Ni

Callister 6e.

100%

Cu

Ni

_100%

Concentration Profiles

0 Concentration Profiles

0

3

Concentration Profiles

_{Concentration Profiles}

t=0

t > 0

DIFFUSION: THE PHENOMENA (2)

• Self-diffusion

:

In an elemental solid, atoms also migrate.

DIFFUSION: THE PHENOMENA (2)

Label some atoms _{After some time}

C

A

C

D

A

D

B

D

A

B

Diffusion:

The movement of atoms or molecules from an area of

higher concentration to an area of lower

(3)

DIFFUSION MECHANISMS

Substitutional

Diffusion:

DIFFUSION MECHANISMS

• applies to substitutional impurities

• atoms exchange with vacancies

• rate depends on:

Both

self-diffusion and

i t diff i

• rate depends on:

--number of vacancies

--activation energy to exchange.

inter-diffusion

occur

increasing elapsed time

5 increasing elapsed time

INTERSTITIAL SIMULATION

(Courtesy P.M. Anderson)

• Applies to interstitial

INTERSTITIAL SIMULATION

Applies to interstitial

impurities.

• More rapid than

vacancy diffusion.

• Simulation:

shows the jumping of a

Interdiffusion of impurities

--shows the jumping of a

smaller atom

(gray)

from

one interstitial site to

Interdiffusion of impurities

such as H, C, N and O;

which have atom small

another in a BCC

structure. The

interstitial sites

enough to fit into the

interstitial position

interstitial sites

considered here are

at midpoints along the

Atomic radius Iron 0.124 nm

(4)

Diff

i

h

i

t i l ( )

Diffusion mechanisms in material: (a) vacancy or

substitutional atom diffusion and (b) interstitial diffusion

7

Background - Steel

Background Steel

• Pure iron is relatively soft and would not last very long if used as a tool • Luckily, when a small amount of carbon (up to about 1.5%) is added to

the iron it is called steel and can be made much harder by a heat

t t t ll d it i l h d i

treatment called quite simply, hardening.

• If some other metals, such as chromium, nickel and manganese are added to the steel it can be made much stronger and tougher and is called alloy to the steel it can be made much stronger and tougher and is called alloy steel

• In simple terms:

– The amount of carbon in the steel determines how hard it will be after hardening

Th i l i h hi h i i ll d d i h

– The various metals with which it is alloyed determine how strong or tough it will be, after hardening

(5)

MECHANICAL PROP:

Fe-C SYSTEM (1)

MECHANICAL PROP:

Fe C SYSTEM (1)

• Effect of wt%C

Pearlite (med)

Cementite

Adapted from Fig. 9.27,Callister 6e. (Fig. 9.27 courtesy Republic Steel Corporation )

Co>0.77wt%C Hypereutectoid Co<0.77wt%C

Hypoeutectoid

Pearlite (med)

ferrite (soft) Cementite(hard)

Adapted from Fig. Steel Corporation.) United States Steel Corporation.)

100 %EL ft-lb) 80 1100 YS(MPa) TS(MPa) yp Hypo Hyper Hypo Hyper 10.20, Callister 6e. (Fig. 10.20 based on data from Metals Handbook: Heat Treating, Vol. 4, 9th 50 rgy (Izod, 40 700 900 hardness Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.) 50 m pact ene 0 300 500

• More wt%C: TS and YS increase, %EL decreases. wt%C 0 0.5 1 0 Im wt%C 0 0.5 1 0.77 0.77 9 ,

PROCESSING USING DIFFUSION (1)

• Case Hardening

:

Diffuse carbon atoms

Fig 5 0

PROCESSING USING DIFFUSION (1)

--Diffuse carbon atoms

into the host iron atoms

at the surface.

Fig. 5.0, Callister 6e. (Fig. 5.0 is courtesy of Surface Di i i

--Example of interstitial

diffusion is a case

hardened gear

Division, Midland-Ross.)

hardened gear.

• Result: The "Case" is

--hard to deform: C atoms

hard to deform: C atoms

"lock" planes from

shearing

.

--hard to crack: C atoms put

th f

i

the surface in

compression

.

Improve

:

Wear resistance

Wear r=kw/H,

l d H h d

10

w-load, H-hardness

(6)

Carburizing

The process:

• Pack carburizing

• Gas carburizing

• Liquid carburizing

• Vacuum carburizing

• Plasma carburizingg

Depth of Hardening:

Case depths from as light as 0.08 mm (0.003") to as deep as 6.4 mm (0.250") may be specified, depending on the service requirements of the product

service requirements of the product.

11

Application Depth of Case

High wear resistance, low to moderate loading-Small and delicate

machine parts subject to wear Cases to 0.51 mm (0.020")

High wear resistance, moderate to heavy loading-Light industrial i

0.51 mm to 1.02 mm (0 020" t 0 040")

gearing (0.020" to 0.040")

High wear resistance, heavy loading, crushing loads or high magnitude

alternating bending stresses-Heavy duty industrial gearing 1.02mm to 1.52mm (0.040" to 0.060")

High wear resistance shock resistance high crushing loads Bearing 1 52 mm to 6 4mm

High wear resistance, shock resistance, high crushing loads-Bearing

surfaces, mill gearing, rollers (0.060" to 0.250") 1.52 mm to 6.4mm

Carburizing Time: 4 to 72 hours

Carburizing Temperature: 850-950 °C (1550-1750 °F) (i.e., above the upper

iti l t t t it )

critical temperatures - austenite area)

Quenching: After carburizing, the part is either slow cooled for later quench hardening, or quenched directly into various liquid quenches The part is then hardening, or quenched directly into various liquid quenches. The part is then tempered to the desired hardness to achieve the optimum properties with acceptable levels of dimensional change.

(7)

Materials

Most steels specified for carburizing contain less than 0.25%

b

i h

ffi i

ll

i

d

carbon, with sufficient alloys to improve case and core

hardenability. Depending on the application, any of numerous

grades may be used In general steels that are applicable to

grades may be used. In general, steels that are applicable to

carburizing are the following:

1. Low-carbon steels

2. Resulfurized low-carbon steels

3. Low-carbon alloy steels

4. Low-carbon powder metal (P/M) compacts

p

(

)

p

13

Resulfurized low-carbon steels

esu u ed ow ca bo s ee s

Sulfur - is usually an undesirable impurity in steel

h

ll i

l

I

rather than an alloying element. In amounts

exceeding 0.05% it tends to cause brittleness and

d

ld bili

All i

ddi i

f

lf i

reduce weldability. Alloying additions of sulfur in

amounts from 0.10% to 0.30% will tend to improve

h

hi bili

f

l S h

b

the machinability of a steel. Such types may be

referred to as "resulfurized" or "free-machining".

F

hi i

ll

i

d d f

h

Free-machining alloys are not intended for use where

welding is required.

(8)

Pack carburizing

The part is packed in a steel container so that it is completely surrounded by granules of charcoal. The charcoal is treated with an activating chemical (a catalyst) such as barium carbonate (BaCO₃) that promotes the formation of carbon dioxide (CO₂). This gas in turn reacts with the excess carbon in the charcoal to produce carbon monoxide, CO. Carbon monoxide reacts with the low-carbon steel surface to form atomic carbon

hi h diff i h l b id li h b

which diffuses into the steel. Carbon monoxide supplies the carbon gradient that is necessary for diffusion. The carburizing process does not harden the steel. It only increases the carbon content to some

d t i d d th b l th f t ffi i t l l t ll

predetermined depth below the surface to a sufficient level to allow subsequent quench hardening.

Heat

Part to be

carburized

Steel _{Figure Pack}

C CO CO Charcoal Steel container Figure. Pack carburizing process 15 Heat

Pack carburizing-continued

Pack carburizing continued

Quenching Process:

It is difficult to quench the part immediately, the sealed pack has to be It is difficult to quench the part immediately, the sealed pack has to be opened and the part must be removed from the pack. One technique that is used often is to slow cool the entire pack and subsequently harden and temper the part after it is removed from the sealed pack.p p p

Depth of Hardening:

There is no technical limit to the depth of hardening with carburizing techniques but it is not common to carburize to depths in excess of 1 3 techniques, but it is not common to carburize to depths in excess of 1.3 mm (0.050").

Carburizing Time: 4 to 10 hours

The degree of carburizing depends on

- Substrate (its carbon content and alloy content)( y ) - Carburizing temperature, and

(9)

Advantages of Pack Carburizing

1. It can be done in almost any type of furnace

2. The equipment requirement is minimal (furnace, box, compound)

3. A wide variety of parts can be accommodated (as many as could be fitted and separated in a box, or as large as the box that will fit in the available furnace)p g ) 4. Requires lower operator skills than other processes.

Disadvantages of Pack Carburizing

1 C b i i i l h f f h h

1. Carburizing times are longer than for some of the other processes 2. Not suitable for continuous production

3. Labour intensive (pack loading, box maintenance, sealing, pack handling etc) 4. Unsuitable for thin, carefully controlled case depths.

At carburizing temperatures, say 900 °C, the following reactions occur:

(

initial

air

in

charcoal

)

CO

C

CO

O

C

+

₂

→

₂ ₂

+

→

.

(1)

(

C

in

solution

)

CO

C

CO

Fe

CO

Fe

+ 2

CO

→

Fe

(

C

in

solution

)

+

CO

+

C

→

CO

(2)

Fe

+

2 →

+

₂ ₂

+

→

.

(2)

CO

C

CO

BaO

BaCO

₃

→

+

₂ ₂

+

→

.

(3)

17

Gas Carburizing

The parts are heated above the upper critical temperature in a furnace with an atmosphere of carbon-containing gas such as methane, ethane, propane, an atmosphere of carbon containing gas such as methane, ethane, propane, natural gas, acetylene, manufactured gas or mixed hydrocarbon gases. Most carburizing gases are flammable and controls are needed to keep carburizing gas at 927 °C (1700 °F) from contacting air (oxygen) The carburizing gas at 927 C (1700 F) from contacting air (oxygen). The carburizing gases are often diluted with an endothermic carrier gas, mainly nitrogen (N₂) and CO along with smaller amounts of CO₂, H₂and

H O Of ll th N i i t d t l dil t t Th i

H₂O. Of all the gases, N₂ is inert and acts only as a dilutent. The carrier gas serves to control the amount of carbon supplied to the steel surface and prevents the formation of soot residue.

Mechanism

(1) Transport of gas molecules containing carbon to the surface of the steel part

steel part

(2) Reaction of the molecules at the surface to raise carbon content of steel, and

(3) Diff i f h b i h l

(10)

First, methane reacts with CO2 and H2O to generate CO and H2.

CH4 + CO2 ↔ 2CO + 2H2 . . .. . . (4) CH4 + H2O ↔ CO + 3H2 . . . (5) These reactions decrease the amounts of CO and H O but increase the amounts of CO These reactions decrease the amounts of CO2 and H2O but increase the amounts of CO and H2. Carbon monoxide is the primary gas responsible for raising the carbon content at surface of the steel.

Second, the CO decomposes to allow carbon to diffuse into the steel surface by the following reversible reactions

2CO ↔ C (in Fe) + CO2 . . . (6) CO + H2↔ C (in Fe) + H2O (7) CO + H2 ↔ C (in Fe) + H2O . . . .. . (7)

Thus, the carbon content on the surface of the steel may be controlled by either a constant CO2 content or a constant water vapor content determined by the dew point of the gas. If we combine Equations (4) and (6) or Equations (5) and (7), we have

CH4↔ C (in Fe) + 2H2 (8)

CH4 ↔ C (in Fe) + 2H2 . . . (8)

19

Advantages of Gas Carburizing (over pack carburizing)

(1) More accurate control of the composition and depth of the hardened case (2) Suitable for continuous production and high-volume production surface

hardeningg Disadvantages

(1) High equipment requirements

(2) Soaking time required is longer than for pack carburizing (2) Soaking time required is longer than for pack carburizing

(3) High safety demands. The gases used for gas carburizing can be explosive. (4) Requires experienced and skilled personnel and very reliable gas control

systems systems.

Fi G Figure. Gas

(11)

PROCESSING USING DIFFUSION (2)

• Doping

Silicon with P for n-type semiconductors:

P

PROCESSING USING DIFFUSION (2)

• Process:

1. Deposit Prich layers on surface

0.5mm

layers on surface.

silicon

magnified image of a computer chip

2. Heat it.

silicon

Fig. 18.0, Callister 6e. 3. Result: Doped semiconductor regions.

light regions: Si atoms

regions.

ili

light regions: Al atoms

21

silicon

light regions: Al atoms

MODELING DIFFUSION: FLUX

• Flux

:

MODELING DIFFUSION: FLUX

J

=

1 A

dM

dt

⇒

kg

m

2

s

⎡

⎣

⎢

⎤

⎦

⎥ or

atoms

m

2

s

⎡

⎣

⎢

⎤

⎦

⎥

• Directional Quantity

Jy

y

x-direction

Jx

Jy

y

Unit area A

• Flux can be measured for:

x

Jz

_x

z

through

which

atoms

• Flux can be measured for:

--vacancies

--host (A) atoms

atoms

move.

(12)

CONCENTRATION PROFILES & FLUX

• Concentration Profile

, C(x): [kg/m

3

]

CONCENTRATION PROFILES & FLUX

Concentration _{Concentration}

Cu flux

Ni flux

Adapted of Cu [kg/m3] Concentration of Ni [kg/m3] Adapted from Fig. 5.2(c), Callister 6e.

• Fick's First Law:

Position, x

Diffusion coefficient [m2/s] fl d

J

x

= −D

dC

dx

Diffusion coefficient [m /s] concentration di t [k / 4] flux in x-dir. [kg/m2-s]

• The steeper the concentration profile,

the greater the flux!

x

dx

gradient [kg/m4]

23

the greater the flux!

ense. emark used herein under lic e T homson L earning ™ is a tr ad

Illustration of the

concentration

of Thomson L earning , I nc. T

gradient

03 B rooks/Cole, a division o ©20 0

(13)

STEADY STATE DIFFUSION

• Steady State

:

the concentration profile doesn't

change with time

STEADY STATE DIFFUSION

change with time.

Jx

(left)

=

Jx

(right)

Steady State:

Jx

(right)

Jx

(left)

Jx

(left)

Jx

(right)

Concentration C in the box doesn’t change w/time

Jx

(right)

Jx

(left)

x

• Apply Fick's First Law:

Concentration, C, in the box doesn t change w/time.

J

_x

= −D

dC

dx

• stop 12/03

dx

dC

dx

⎛

⎝

⎜

⎞

⎠

⎟

=

dC

dx

⎛

⎝

⎜

⎞

⎠

⎟

• If

J

x

)

left

=

J

x

)

right

, then

• Result: the slope,

dC/dx

, must be constant

dx

⎝

⎠

_left

⎝

dx

⎠

_right

25

p ,

,

(i.e., slope doesn't vary with position)!

EX: STEADY STATE DIFFUSION

• Steel plate at

C 1 = 1. 2kg/m

3

8kg/m 3

EX: STEADY STATE DIFFUSION

or 0.015% of C 0 010% f C

• Steel plate at

700C with

geometry

Adapted C 1 C2 = 0 .8kg Carbon rich Steady State = straight line! or 0.010% of C

g

y

shown:

Adapted from Fig.

5.4, Callister 6e. rich gas _Carbon deficient gas g

• Q: How much

₁ gas

x1

x2

0

₅ D=3x10-11m2/s

carbon transfers

from the rich to

th d fi i

t id ?

C

2

− C

1 9

kg

10_m m

5m m

the deficient side? J = −DC

2

C

1

x

₂

− x

₁

= 2.4 × 10

−9

kg

m

2

s

26

005 .

0

01 .

0

2 .

1

8 .

0

10

3

11

−

×

−

=

−

J

(14)

27

NON STEADY STATE DIFFUSION

• Concentration profile,

C(x) changes

dx

NON STEADY STATE DIFFUSION

C(x), changes

w/ time.

T

tt

Concentration, C i th b J_(right) J_(left)

• To conserve matter:

• Fick's First Law:

C, in the box

−

J

_(left)

d

C

_J

_D

d

C

J

_(right)

dx

= − d

C

dt

J

= −D

dx

or

J

_(left)

J

_(right)

d

J

d

C

d

J

d2

C

(if D does

d

J

dx

= − d

C

dt

d

J

dx

= −D d

C

dx2

( not vary with x)

• Governing Eqn.:

d

C

D

d

2 C

equate

= D

(15)

EX: NON STEADY STATE DIFFUSION

• Copper diffuses into a bar of aluminum.

Surface conc.,

bar

EX: NON STEADY STATE DIFFUSION

pre-existing conc., Co of copper atoms

Cs of Cu atoms bar

Cs

C(

x

,t)

_f

z _t

_d

∫

2

2 )

(

Cs

t2

t3

Adapted from Fi 5 5

dt

e

z

erf

=

∫

−t 0

)

(

π

Co

to

t1

t2 3

Fig. 5.5, Callister 6e.

• General solution:

_C(

_x

_,

_{t) − C}

o

= 1−

_erf

⎛

x

⎝

⎜

⎞

_⎠

⎟

position, x

(1)

C

_s

− C

_o

1 erf

⎝

⎜

2 D

t

⎠

⎟

Assuming: C

_s

and D

are constants

29

Co: Constant when t=0; Cs: Concentration at surface it is independent to time.

Error Function Value

Tabulation of Error Function Values

z erf(z) z erf(z) z erf(z)

0 0 0.55 0.5633 1.3 0.934 0.025 0.0282 0.6 0.6039 1.4 0.9523 0.05 0.0564 0.65 0.642 1.5 0.9661 0.1 0.1125 0.7 0.6778 1.6 0.9763 0.15 0.168 0.75 0.7112 1.7 0.9838 0.2 0.2227 0.8 0.7421 1.8 0.9891 0.25 0.2763 0.85 0.7707 1.9 0.9928 0.3 0.3286 0.9 0.797 2 0.9953 0.35 0.3794 0.95 0.8209 2.2 0.9981 0.4 0.4284 1 0.8427 2.4 0.9993 0.45 0.4755 1.1 0.8802 2.6 0.9998 0 5 0 5205 1 2 0 9103 2 8 0 9999 0.5 0.5205 1.2 0.9103 2.8 0.9999

x

z

=

When z<0 6, erf(z) ≈ z

Dt

z

2

When z<0.6, erf(z) z

(16)

Factors affect the diffusion

C(

x

,

t) − C

_o

_{= 1−}

erf

⎛

_⎝

⎜

x

⎞

_⎠

⎟

Factors affect the diffusion

C

_s

− C

_o

1 erf

⎝

⎜

2 D

t

⎠

⎟

1) Diffusion coefficient

2) C

i i l

b

2) C

_o

original carbon content

in the steel

3) C

_s

Surface concentration

4) X distance from Surface

)

5) t: Time

Adapted from Fig 5.6 Callister 6e

31

Adapted from Fig 5.6 Callister 6e

DIFFUSION AND TEMPERATURE

• Diffusivity increases with T.

pre-exponential [m2/s] (see Table 5.2, Callister 6e) activation energy activation energy

D

=

_Do

_{exp −}

Qd

R

T

⎛

⎝

⎜

⎞

⎠

⎟

diffusivity

[J/mol],[eV/mol] (see Table 5.2, Callister 6e)

• Experimental Data:

T(C) 5 00 0 00 ₀0 ₀0 D h d d T

gas constant [8.31J/mol-K]

R

T

D (m2/s) _{C in} C i n γ-F e 10-8 1 T(C) 5 1

0 ₆0 ₃0 _{D has exp. dependence on T}

Recall: Vacancy does also!

( ) _{in α} -Fe e Al Zn in_C Fe 10-14 Dinterstitial >> Dsubstitutional C in α-Fe C in γ-Fe Al in Al Cu in Cu 1000K/T Al _in A_l C u in_C u n C_u Fe in _α -F_e e i_{n γ} -F_e 10-20 C in γ Fe Zn in Cu Fe in α-Fe Fe in γ-Fe 1000K/T e 0.5 1.0 1.5 2.0 10

(17)

erein under license. rning ™ is a t radem ark used h e

Figure 5 8 The

earning , I nc. Thomson L ea r

Figure 5.8 The

Arrhenius plot of in

(rate) versus 1/T can

ole, a division of Thomson L

(

)

be used to determine

the activation energy

i

required for a

reaction

Diffusion coefficient

₌

₂

_.

₃

_×

₁₀

−5

_exp(

₋

148000

₎

D

)

1173

31 .

8 exp(

10

3 .

2 ×

D

(18)

Diffusion coefficient

35

Carburizing

Three steps:

ee s eps:

• Transfer C from the gas to steel surface

C diff i

f

t i t i

f t l

• C diffusion from surface to interior of steel

section

Q

h/

i

hi

h d

• Quench/tempering treatment to achieve hard

case with a tough interior

Aim

To obtain specified carbon profile and

hardness distribution through section

thickness of the component

p

(19)

MECHANICAL PROP:

Fe-C SYSTEM (1)

MECHANICAL PROP:

Fe C SYSTEM (1)

• Effect of wt%C

Pearlite (med)

Cementite

Adapted from Fig. 9.27,Callister 6e. (Fig. 9.27 courtesy Republic Steel Corporation )

Co>0.77wt%C Hypereutectoid Co<0.77wt%C

Hypoeutectoid

Pearlite (med)

ferrite (soft) Cementite(hard)

Adapted from Fig. Steel Corporation.) United States Steel Corporation.)

100 %EL ft-lb) 80 1100 YS(MPa) TS(MPa) yp Hypo Hyper Hypo Hyper 10.20, Callister 6e. (Fig. 10.20 based on data from Metals Handbook: Heat Treating, Vol. 4, 9th 50 rgy (Izod, 40 700 900 hardness Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.) 50 m pact ene 0 300 500

• More wt%C: TS and YS increase, %EL decreases. wt%C 0 0.5 1 0 Im wt%C 0 0.5 1 0.77 0.77 37 ,

MECHANICAL PROP:

Fe-C SYSTEM (2)

MECHANICAL PROP:

Fe C SYSTEM (2)

• Fine vs coarse pearlite vs spheroidite 320 ss fine 90 A R) spheroidite Hypo Hyper Hypo Hyper

240 l hardne s _pearlite coarse pearlite spheroidite 60 c tility (% A spheroidite 80 160 Brinel l 0 30 Du c fine pearlite coarse pearlite

Adapted from Fig. 10.21, Callister 6e. (Fig. 10.21 based on data from

• Hardness: fine > coarse > spheroidite wt%C

0 0.5 1 0

wt%C

0 0.5 1

( g

Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, pp. 9 and 17.)

Hardness: fine coarse spheroidite • %AR: fine < coarse < spheroidite

(20)

MECHANICAL PROP:

Fe-C SYSTEM (3)

• Fine Pearlite vs Martensite:

MECHANICAL PROP:

Fe C SYSTEM (3)

s

Hypo Hyper

Adapted from Fig. 10.23,

Callister 6e. (Fig. 10.23 adapted from Edgar C Bain

400 600

hardnes

s

martensite

adapted from Edgar C. Bain,

Functions of the Alloying Elements in Steel, American Society for Metals, 1939, p. 36; and R.A. Grange, C.R. Hribal,

d L F P t M t ll T 200

400

Brinell

fine pearlite and L.F. Porter, Metall. Trans. A, Vol. 8A, p. 1776.)

0

wt%C

0 0.5 1

fine pearlite

• Hardness: fine pearlite << martensite.

39

Martensite

(b)

( ) H d f t it f ti f b t t (b) Mi h f t it t i i

(a) Hardness of martensite, as a function of carbon content. (b) Micrograph of martensite containing 0.8% carbon. The gray platelike regions are martensite; they have the same composition as the original austenite (white regions). Magnification: 1000X. Source: Courtesy of USX Corporation.

(21)

Quenching test

41

WHY Quench is required

• Fast cooling is required to form Martensite

RC 60

distance from quenched end (in)

H ardness, H 20 40 0 1 2 3 H 0 1 2 3 600 A → P T(°C) 0% 100% Adapted from Fig. 11.12, Callister 6e. (Fig. 11.12 d t d f 400 200 M(start) _{O l th} _iti adapted from H. Boyer (Ed.) Atlas of Isothermal Transformatio n and Cooling Transformatio 200 A → M M artMartFine Pe arl_ite ( ) 0 M(finish)

Only the position with ΔT/t > critical cooling rate will Transformatio n Diagrams, American Society for Metals, 1977, p. 376.) art_en site art_ens ite + P ea e P ea rlit_e te 0.1 1 10 100 1000 change to Martensite ea rlit_e Time (s)

(22)

Properties of Oil-Quenched Steel

Properties of Oil Quenched Steel

Figure 4.25 Mechanical properties of

il h d 4340 l f i

oil-quenched 4340 steel, as a function of tempering temperature. Source: Courtesy of LTV Steel Company

43

Surface carbon concentration

C

_s

: during process, it is the maximum solubility of carbon or

nitrogen in iron at the carburizing or nitriding temperature

nitrogen in iron at the carburizing or nitriding temperature.

It shows the approximate limits of carbon solubility in austenite for 8 common steels common steels

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Effective case depth

While we can specify the total case depth, a more meaningful specification in carburized parts is to require a certain hardness at a specific depth, x, from the surface which is called the effective case depth

surface, which is called the effective case depth.

In steels, the hardness specification is equivalent to carbon content. Thus, an effective case depth is defined as that depth at which a 0.40 wt% C concentration effective case depth is defined as that depth at which a 0.40 wt% C concentration is attained.In both case-depth definitions, a particular value of x can be achieved by varying the product, Dt, to give the particular z value for the particular C. Thus for a desired case depth x the parameters to be controlled are D and t Thus, for a desired case depth, x, the parameters to be controlled are D and t. However, D depends on temperature.

Th t l t th t t d ti f b i ti

The actual process parameters are the temperature and time of carburization. While there is an infinite number of combinations of these two variables, the desired properties of the carburized case are obtained when the temperature of desired properties of the carburized case are obtained when the temperature of carburization is limited to about 900-950°C.

C(

x

,

t) −C

_o

⎛

_⎜

x

⎞

_⎟

45

C(

x

,

t) C

_o

C

_s

−C

_o

=1−

erf

⎝

⎜

2 D

t

⎠

⎟

Limitation of sample size

The case depth discussed up to this point is for a concentration gradient beneath a plane surface on a solid of infinite magnitude. For solid slabs with finite a p a e su ace o a so d o te ag tude. o so d s abs w t te dimensions and diffusion from both surfaces, the equations are excellent approximations for case depth as long as ₀_.₂

2L < Dt

where 2L is the thickness of the slab. For the equation (1) to be valid, the finite thickness of the slab must be greater than twice the total case depth.

E At 900 o_{C 2 ho r 2L >} 5.9×10−12×2×3600 ₀₀₀₁₀₃ ₁

Ex. At 900 o_{C, 2 hour, 2L >} (use the data in Table 5.2)

h f h f b i b i d l i fl h d h mm m 1 00103 . 0 2 . 0 = ≈

The curvature of the surface being carburized also influences the case depth when the radius of curvature is comparable in magnitude with the case depth. For convex surfaces the case depth obtained is greater than that expected on For convex surfaces, the case depth obtained is greater than that expected on plane surfaces.

For concave surfaces, the case depth is lesser than that expected from plan , p p p surfaces.

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PROCESSING QUESTION-1

• Copper diffuses into a bar of aluminum.

• 10 hours at 600C gives desired C(x).

• How many hours would it take to get the same C(x)

if we processed at 500C?

Key point 1:

C(x t

500C

) = C(x t

600C

)

Constant

• Result:

Dt should be held constant

.

Key point 1:

C(x,t

500C

) = C(x,t

600C

)

.

Key point 2:

Both cases have the same C

o

and C

s

.

(Dt)500ºC =(Dt)600ºC

Result:

Dt should be held constant

.

C(

x

,

t) −C

_o

C

=1−

erf

x

2 D

t

⎛

⎝

⎜

⎞

_⎠

⎟

Note: values

5 3x10-

13

_m

2

_/s

_10hrs

Constant

C

_s

−C

_o

⎝

2 D

t

⎠

• Answer:

_t

of D areprovided here.

500 =

(

D

t)

₆₀₀

D

= 110hr

5.3x10

13

_m

2

_/s

_10hrs

47

500 _D

500 4.8x10-

14

_m

2

_/s

PROCESSING QUESTION-Carburizing C-

γFe

• 10 hour required at 900 C / Cost $1000/hour(500 parts).

• To get same C(x)at 1000 C, cost $1500/hour (500 parts).

g

γ

• Is it economical to operate at 1000 C?

• What other factor must be considered?

Key point 1:

C(x t

_900C

) = C(x t

_1000C

)

• Result:

Dt should be held constant

.

Key point 1:

C(x,t

_900C

) = C(x,t

_1000C

)

.

Key point 2:

Both cases have the same C

o

and C

s

.

(Dt)900ºC =(Dt)1000ºC

Result:

Dt should be held constant

.

C(

x

,

t) −C

_o

₌₁₋

erf

⎛

_⎝

⎜

x

⎞

_⎠

⎟

• Answer:

_D

137800

₎

₁₀

exp(

−

×

C

_s

−C

_o

1 erf

⎝

2 D

t

⎠

hours

D

t

3 .

3 )

1273

31

8 137800

exp(

10 )

1173

31 .

8 exp(

0 0 1273

₋

=

×

=

)

1273

31 .

8 p(

0

_×

(25)

QUESTION-continued

At 900°C, the cost per part is ($1000/h) (10 h)/500 parts = $20/part At 1000°C the cost per part is ($1500/h) (3 3 h)/500 parts = $9 90/part At 1000°C, the cost per part is ($1500/h) (3.3 h)/500 parts = $9.90/part

Considering only the cost of operating the furnace, increasing the temperature reduces the heat-treating cost of the gears and increases the production rate. reduces the heat treating cost of the gears and increases the production rate. Another factor to consider is if the heat treatment at 1000°C could cause

microstructural or some other changes? For example, would increased temperature cause grains to grow significantly? If this is the case, we will be weakening the bulk of the material. How does the increased temperature affect the life of the other equipmentq p such as the furnace itself and any accessories? y How long would the g cooling take? Will cooling from a higher temperature cause residual stresses? Would the product still meet all other specifications? These and other questions should be considered The point is, as engineers, we need to ensure that the solution we considered. The point is, as engineers, we need to ensure that the solution we

propose is not only technically sound and economically sensible, it should recognize and make sense for the system as a whole (i.e., bigger picture). A good solution is often simple solves problems for the system and does not create new problems

49

(26)

C(

x

,t

)−C

o

=1

_f

⎛

x

⎝⎜

⎞

⎠⎟

C(

x

,t

) C

o

C

s

−C

o

=1−

erf

⎝

2 D

t

⎜

_⎠

⎟

3

10

5

0 ×

−

25 .

0

8 .

0

1 −

t

11

10

6 .

1

2

10

5 .

0

−

×

25 .

0

2 .

1

1 −

−

00755

.

0 3794

.

0 4284

.

0

421 .

0 4284

.

0

35 .

0

4 .

0

4 .

0 ₌

−

=

−

− z

51

392 .

0 =

z

Worked example

A 25-mm diameter 8620 steel bar was carburized at 900°C for eight hours. The diffusion coefficient of carbon in austenite is

The diffusion coefficient of carbon in austenite is

) 314 . 8 137800 exp( 2 . 16 T D= − Determine:

(1) the location in the carburized case where a quenched hardness of 54 HRC may be obtained with a minimum of 95 percent martensite;

(2) whether the desired hardness can be obtained by quenching in agitated t i it t d il?

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Solution-1

Solution 1

The as-quenched hardness is 54 HRC.

Then, we use Fig. 1 to convert the asquenched hardness to carbon

content because the hardness of as-quenched martensite is only a

function of carbon content The carbon content is found to be

function of carbon content. The carbon content is found to be

0.45 percent C = C(x,t) in the carburizing equation

1 53

Solution-2

Solution 2

) 2 ( 1 ) , ( ₀ Dt x erf C C C t x C − ₌ ₋

from which we can solve for x, the location of C(x,t) = 0.45% of C. At 900°C (1173 K), Cs = 1.24 percent C for 8620 steel from Fig. A and the diffusion

2

0 Dt

C Cs −

(1173 K), Cs 1.24 percent C for 8620 steel from Fig. A and the diffusion coefficient is s mm D ) 1.183 10 / ) 273 900 ( 314 . 8 137800 exp( 2 . 16 ₌ _× −5 2 + × − = ) 2 ( 1 2 . 0 24 . 1 2 . 0 45 . 0 Dt x erf − = − − ) 273 900 ( 314 . 8 +

Then

and

) 1 0.24 0.76 2 ( = − = Dt x erf

And from erf table x

And from erf table ₀_.₈₄

2 Dt = x

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Solution-3

(2) We need to know now whether we can obtain the desired as-quenched hardness of 54 HRC at 0.98 mm from the surface by quenching in water or oil. We need to know the Jominy equivalent cooling rate at this location and then use a hardenability curve. Rounding the location to 1 mm, this location from the centre of the 25-mm diameter bar is (11.5/12.5 = 0.92R).

For agitated water quenching, the Jominy equivalent rate at 0.92R (very close to surface) is 1mm.

To get the hardness at this location we look for the hardenability curve 8645 not 8620 since C = 0.45% at this location not 0.2% .The minimum at l mm for 8645 from Fig 9-51 it is 57 HRC

8645 from Fig. 9 51 it is 57 HRC.

Doing the same for the agitation in oil and using Fig. 9-53, the Jominy equivalent cooling rate at 0.92R location is found to be 2.5 mm, and using q g g 0.45% C, is 56 HRC.

We see that 57 HRC for water quenching and 56 HRC for oil quenching both

d h 54 HRC Th f i h h b il

55

exceed the 54 HRC. Therefore, we can use either quench, because oil quenching is less drastic, we should use oil quenching.

(29)

(30)

59

DIFFUSION DEMO: ANALYSIS

• The experiment:

we recorded combinations of

t and x that kept C constant.

DIFFUSION DEMO: ANALYSIS

p

to t1 t2 t₃ xo x1 x2 x3

C(x

_i

, t

_i

)

− C

_o

= 1− erf

⎛

⎜

x

i

⎜

⎞

⎟

= (constant here)

• Diffusion depth given by:

C

_s

− C

_o

= 1 erf

_⎝

⎜

_{2 Dt}

_i

_⎠

⎟

= (constant here)

• Diffusion depth given by:

x

_i

∝ Dt

i

(31)

DATA FROM DIFFUSION DEMO

B B B B B B B 3 5 4

(

)

DATA FROM DIFFUSION DEMO

B B B B B B B B B B B 2.5 3 3.5 1 1.5

2 _{Linear regression fit to}_data:

ln[x(mm)] = 0.58ln[t(min)] + 2.2 R2 = 0 999 0 0.5 1 R2 = 0.999 0 0.5 1 1.5 2 2.5 3

ln[t(min)]

• Experimental result: x ~ t

0.58

• Theory predicts x ~ t

0.50 61

• Reasonable agreement!

Other Applications

• Processing of microelectronic

i

The ability to produce a large number of circuits on such a small surface arises from the techniques of masking and then patterning by lithography. The procedure is

circuits

then patterning by lithography. The procedure is illustrated here. The "mask" used is the oxide of silicon that is grown by thermal oxidation, referred to as thermox in the industry. The thicknessof this oxide can be carefully

ll d f i i A l f i

controlled from previous experience. A layer of an organic material called photoresist is applied over the oxide layer on which lithography is done. Webster's Dictionary defines lithography as the process of printing from a plane de es og ap y as e p ocess o p g o a p a e surface (smooth stone or metal plate) on which the image to be printed is receptive and the blank area ink-repellant. In microelectronics processing, a masking

tt i l d th h t i t d lt i l t li ht pattern is placed over the photoresist and ultraviolet light is passed through. Depending on whether the photoresist is positive (or negative), the area exposed (or unexposed) is washed away by a suitable developer to provide a

S h ti f th lith hi th d t t

y y p p

window over the oxide. The oxide is etched away by ydrofluoric acid to expose the silicon surface onto which dopants are predeposited and driven-in or where metallic i t t i d it d

62 Schematics of the lithographic methods to create

metallic pattens and selected areas for infusion of dopent atoms

(32)

Example: Silicon Device Fabrication

Devices such as transistors are made by doping semiconductors with different dopants to generate regions that have p or n type semiconductivity [1] The dopants to generate regions that have p- or n-type semiconductivity.[1] The diffusion coefficient of phosphorus (P) in Si is D = 65 × 10-13 _cm2_{/s at a}

temperature of 1100o_{C. Assume the source provides a surface concentration of}

1020_atoms/cm3_{and the diffusion time is one hour Assume that the silicon}

1020_atoms/cm3_{and the diffusion time is one hour. Assume that the silicon}

wafer contains no P to begin with.

(a) Calculate the depth at which the concentration of P will be 1018_atoms/cm3_.

( ) p

State any assumptions you have made while solving this problem.

(b) What will happen to the concentration pro.le as we cool the Si wafer containing P?

containing P?

(c) What will happen if now the wafer has to be heated again for boron (B) diffusion for creating a p-type region?g p yp g