DIFFUSION IN SOLIDSISSUES TO ADDRESS... ADDRESS 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? How H to t control t l carburizing b i i process? ?1

DIFFUSION DEMO Glass tube filled with water. At time ti t=0 0, add dd some d drops of fi ink kt to one end d of f the tube. distance, x x, over some time time. Measure the diffusion distance The concentration of ink is a function of time and distance x.

to t1 t2 t3 xo x1 x2 x3

x (mm)

time (s)2

DIFFUSION: THE PHENOMENA (1) Interdiffusion: In an alloy, atoms tend to migratefrom regions g of high g concentration to low concentration.Initially After some time

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

100% 0

Cu

Ni

100% 0 Concentration Profiles 3 t>0

Concentration Profilest=0

DIFFUSION: THE PHENOMENA (2) Self-diffusion: In an elemental solid, atoms also migrate.Label some atoms After some time

C A D B

C A B D

Diffusion: The movement of atoms or molecules from an area of higher concentration to an area of lower concentration. (Interdiffusion or impurity diffusion)4

DIFFUSION MECHANISMSSubstitutional Diffusion: applies to substitutional impurities atoms exchange with vacancies rate depends on: --number of vacancies --activation energy to exchange.

Both selfdiffusion and i t diff i inter-diffusion occur

increasing elapsed time5

INTERSTITIAL SIMULATION Applies to interstitial impurities. More rapid than vacancy diffusion. Simulation:--shows shows the jumping of a smaller atom (gray) from one interstitial site to another in a BCC structure. The interstitial sites considered here are at midpoints along the unit cell edges.(Courtesy P.M. Anderson)

Interdiffusion of impurities such as H, C, N and O; which have atom small enough to fit into the interstitial positionAtomic radius Iron C 0.124 nm 0.071 nm6

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

Diffusion Diff i mechanisms h i i in material: t i l (a) ( ) vacancy or substitutional atom diffusion and (b) interstitial diffusion

7

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 treatment t called ll d quite it simply, i l hardening. h d i 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 steel In simple terms: The amount of carbon in the steel determines how hard it will be after hardening Th The various i metals l with i h which hi h it i is i alloyed ll d determine d i how h strong or tough it will be, after hardening8

MECHANICAL PROP: Fe Fe-C C SYSTEM (1) Effect of wt%CPearlite (med) ferrite (soft)Adapted from Fig. 9.27,Callister 6e. (Fig. 9.27 courtesy Republic Steel Corporation.) Corporation )

Co0.77wt%C Hypereutectoid yp HypoAdapted from Fig. 9.30,Callister 6e. (Fig. 9.30 copyright 1971 by United States Steel Corporation.) Corporation )

100 hardness 50

80

Im mpact energy (Izod, ft-lb)

TS(MPa) 1100 YS(MPa) 900 700 500 300

Hypo

%EL

Hyper

40

Handbook: Heat Treating, Vol. 4, 9th

Adapted from Fig. 10.20, Callister 6e. (Fig. 10.20 based on data from Metals ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.)

0 1 0

0.77

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

0

0.77

0.5

1

PROCESSING USING DIFFUSION (1) Case Hardening:--Diffuse Diffuse carbon atoms into the host iron atoms at the surface. --Example of interstitial diffusion is a case hardened gear. gearFig 5.0, Fig. 50

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

Result: The "Case" is--hard hard to deform: C atoms "lock" planes from shearing. --hard to crack: C atoms put th surface the f in i compression. i

Improve: Wear resistance Wear r=kw/H, w-load, l d H-hardness Hh d Fatigue life compress stress

10

CarburizingThe process: Pack carburizing Gas carburizing Liquid carburizing Vacuum carburizing g Plasma carburizing

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. product

11

Application High wear resistance, low to moderate loading-Small and delicate machine parts subject to wear High wear resistance, moderate to heavy loading-Light industrial gearing i High wear resistance, heavy loading, crushing loads or high magnitude alternating bending stresses-Heavy duty industrial gearing High wear resistance resistance, shock resistance resistance, high crushing loads-Bearing loads Bearing surfaces, mill gearing, rollers

Depth of Case Cases to 0.51 mm (0.020") 0.51 mm to 1.02 mm (0 020" to (0.020" t 0.040") 0 040") 1.02mm to 1.52mm (0.040" to 0.060") 1 52 mm to 6.4mm 1.52 6 4mm (0.060" to 0.250")

Carburizing Time: 4 to 72 hours Carburizing Temperature: 850-950 C (1550-1750 F) (i.e., above the upper critical iti l temperatures t t - austenite t it area) ) Quenching: After carburizing, the part is either slow cooled for later quench hardening, or quenched directly into various liquid quenches. quenches The part is then tempered to the desired hardness to achieve the optimum properties with acceptable levels of dimensional change.12

MaterialsMost steels specified for carburizing contain less than 0.25% carbon, b with i h sufficient ffi i alloys ll to improve i case and d core hardenability. Depending on the application, any of numerous grades may be used. used In general general, steels that are applicable to carburizing are the following: 1. Low-carbon steels 2. Resulfurized low-carbon steels 3. Low-carbon alloy steels powder metal (P/M) ( ) compacts p 4. Low-carbon p

13

Resulfurized esu u ed low-carbon ow ca bo steels s ee s

Sulfur - is usually an undesirable impurity in steel rather h than h an alloying ll i element. l In I amounts exceeding 0.05% it tends to cause brittleness and reduce d weldability. ld bili Alloying All i additions ddi i of f sulfur lf in i amounts from 0.10% to 0.30% will tend to improve the h machinability hi bili of f a steel. l Such S h types may be b referred to as "resulfurized" or "free-machining". F Free-machining hi i alloys ll are not intended i d d for f use where h welding is required.14

Pack carburizingThe 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 which hi h diffuses diff i into the h steel. l Carbon b monoxide id supplies li the h carbon b gradient that is necessary for diffusion. The carburizing process does not harden the steel. It only increases the carbon content to some predetermined d t i d depth d th below b l th surface the f t a sufficient to ffi i t level l l to t allow ll subsequent quench hardening.Heat Part to be carburized Steel containerC

CO

CO

Figure Pack Figure. carburizing processCharcoal

Heat

15

Pack carburizing carburizing-continued continuedQuenching Process: 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 p the p part after it is removed from the sealed p pack. temper 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, 13 mm (0.050"). Carburizing Time: 4 to 10 hours The degree of carburizing depends on - Substrate ( (its carbon content and alloy y content) ) - Carburizing temperature, and - Time that the part is soaked at the carburizing temperature.16

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 p in a box, or as large g as the box that will fit in the available furnace) ) separated 4. Requires lower operator skills than other processes. Disadvantages of Pack Carburizing 1 Carburizing 1. C b i i times i are longer l than h for f some of f the h other h 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: (1) C + O2 (initial air in charcoal ) CO2 CO2 + C CO . (2) Fe + 2CO Fe(C in solution) + CO2 CO2 + C CO . . (3) BaCO3 BaO + CO2 CO2 + C CO17

Gas CarburizingThe parts are heated above the upper critical temperature in a furnace with an atmosphere of carbon carbon-containing 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 C (1700 F) F) from contacting air (oxygen). (oxygen) The carburizing gases are often diluted with an endothermic carrier gas, mainly nitrogen (N2) and CO along with smaller amounts of CO2, H2 and H2O. O Of all ll the th gases, N2 is i inert i t and d acts t only l as a dilutent. dil t t The Th carrier i 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 (2) Reaction of the molecules at the surface to raise carbon content of steel, and (3) Diffusion Diff i of f the h carbon b i into the h steel. l18

First, methane reacts with CO 2 and H 2 O to generate CO and H 2 . CH 4 + CO 2 2CO + 2H 2 . . .. . . CH 4 + H 2 O CO + 3H 2 . . . .

. .

. (4) . (5)

These reactions decrease the amounts of CO 2 and H 2 O but increase the amounts of CO and H 2 . 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) + CO 2 CO + H 2 C (in Fe) + H 2 O . . . . . . . . . . .. . (6) . (7)

Thus, the carbon content on the surface of the steel may be controlled by either a constant CO 2 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 CH 4 C (in Fe) + 2H 2 . . . . . . (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 hardening g Disadvantages (1) High equipment requirements (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

Figure. Gas Fi G carburizing

20

PROCESSING USING DIFFUSION (2) Doping Silicon with P for n-type semiconductors: Process: P 0.5mm1. Deposit P rich layers on surface. surface

magnified image of a computer chip

silicon2. Heat it. 3. Result: Doped semiconductor regions.light regions: Si atomsFig. 18.0,

Callister 6e.

silicon ili

light regions: Al atoms21

MODELING DIFFUSION: FLUX Flux: J= atoms 1 dM kg or 2 A dt m2s m s

Directional Quantity y J y Jz Jx x

x-direction Unit area A through which atoms move.22

z Flux can be measured for:--vacancies --host (A) atoms --impurity (B) atoms

CONCENTRATION PROFILES & FLUX Concentration Profile, C(x): [kg/m3] Cu flux Ni fluxConcentration of Cu [kg/m3] Concentration of Ni [kg/m3]Adapted from Fig. 5.2(c),

Callister 6e.

Fick's First Law:flux in x-dir. fl d [kg/m2-s]

Position, xDiffusion coefficient [m2/s]

Jx = D

dC dx

concentration gradient di t [kg/m [k / 4]

The steeper the concentration profile, the greater the flux!23

200 03 Brooks/Cole, a division o of Thomson Learning, Inc. T Thomson Learning is a trademark used herein under lice ense.

Illustration of the concentration gradient

24

STEADY STATE DIFFUSION Steady State: the concentration profile doesn'tchange with time. timeSteady State:Jx(left) Jx(right)

Jx(left) = Jx(right)

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

dC Apply Fick's First Law: J x = D dx

stop 12/03

dC dC = If Jx)left = Jx)right , then dx left dx right Result: the slope, p , dC/dx, , must be constant(i.e., slope doesn't vary with position)!25

EX: STEADY STATE DIFFUSION Steel plate at 700C with Carbon geometry g y rich gas shown:3 or 0.015% of C m / g 3 .2k 1 = /m g C1 or 0.010% 0 010% of fC .8k =0 C2 Steady State = straight g line! Adapted

Carbon deficient gas

from Fig. 5.4,

Callister 6e.

Q: How much carbon transfers from the rich to th d the deficient fi i t side? id ?

0 x1 x2

D=3x10-11m2/s

m 10 m

J = D

J = 3 10 11

5m

m

kg C2 C1 = 2.4 109 x2 x1 m2s0.8 1.2 0.01 0.00526

27

NON STEADY STATE DIFFUSION Concentration profile, C(x) changes C(x), J(left) w/ time. To T conserve matter: ttJ(right) J(left) dx = dC dt dJ = dC dt dx equate

dxJ(right) Concentration, C i C, in th the b box

Fick's First Law: dC J = D or dx (if D does dJ = d2 C ( D not vary dx dx2 with x)

Governing Eqn.:

dC d2C =D dt dx 2

28

EX: NON STEADY STATE DIFFUSION Copper diffuses into a bar of aluminum.Surface conc., Cs of Cu atoms bar pre-existing conc., C o of copper atoms

Cs

C(x,t)

erf f ( z) =t t2 3 position, x

2

z

0

e t dt dAdapted from Fi 5.5, Fig. 55 Callister 6e.

2

t1 t o Co

General solution:Assuming: Cs and D are constants

x C(x, t) Co = 1 erf 2 Dt Cs Co

(1)

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

29

Error Function ValueTabulation of Error Function Values z erf(z) z 0 0 0.55 0.025 0.0282 0.6 0.05 0.0564 0.65 0.1 0.1125 0.7 0.15 0.168 0.75 0.2 0.2227 0.8 0.25 0.2763 0.85 0.3 0.3286 0.9 0.35 0.3794 0.95 0.4 0.4284 1 0.45 0.4755 1.1 05 0.5 0 5205 0.5205 12 1.2 erf(z) 0.5633 0.6039 0.642 0.6778 0.7112 0.7421 0.7707 0.797 0.8209 0.8427 0.8802 0 9103 0.9103 z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.2 2.4 2.6 28 2.8 erf(z) 0.934 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0 9999 0.9999

z=

x 2 Dt

When z Dsubstitutional C in -Fe C in -Fe Fe Cu in Cu Al in Al Fe in -Fe Fe in -Fe Zn in Cu32

C in FeZn

Ci

n -Fe

10-14

in Fe

Al in Al Cu Cu in -Fe in C u in Fe Fe -

10-20

0.5

1.0

1.5

2.0 1000K/T

Adapted from Fig. 5.7, Callister 6e. (Date for Fig. 5.7 taken from E.A. Brandes and G.B. Brook (Ed.) Smithells Metals Reference Book, 7th ed., Butterworth-Heinemann, Oxford, 1992.)

2003 Brooks/Co ole, a division of Thomson Learning, Inc. Thomson Lear rning is a trademark used he erein under license.

33

Figure 5.8 5 8 The Arrhenius plot of in (rate) ( ) versus 1/T can be used to determine the activation energy required i for a reaction

33

Diffusion coefficient

D = 2.3 10 5 exp(

148000 ) 8.31 1173

Q: Using Do and T to calculate

34

Diffusion coefficient

35

CarburizingThree ee s steps: eps: Transfer C from the gas to steel surface C diffusion diff i from f surface f to t interior i t i of f steel t l section Quench/tempering Q h/ i treatment to achieve hi hard h d case with a tough interior

Aim To obtain specified carbon profile and hardness distribution through section p thickness of the component36

MECHANICAL PROP: Fe Fe-C C SYSTEM (1) Effect of wt%CPearlite (med) ferrite (soft)Adapted from Fig. 9.27,Callister 6e. (Fig. 9.27 courtesy Republic Steel Corporation.) Corporation )

Co0.77wt%C Hypereutectoid yp HypoAdapted from Fig. 9.30,Callister 6e. (Fig. 9.30 copyright 1971 by United States Steel Corporation.) Corporation )

100 hardness 50

80

Im mpact energy (Izod, ft-lb)

TS(MPa) 1100 YS(MPa) 900 700 500 300

Hypo

%EL

Hyper

40

Handbook: Heat Treating, Vol. 4, 9th

Adapted from Fig. 10.20, Callister 6e. (Fig. 10.20 based on data from Metals ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.)

0 1 0

0.77

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

0

0.77

0.5

1

MECHANICAL PROP: Fe Fe-C C SYSTEM (2) Fine vs coarse pearlite vs spheroiditeHypo320 Brinell l hardnes ss 240 160 80 0 0.5 fine pearlite coarse pearlite spheroidite

HyperDuc ctility (%A AR)

90

Hypo

Hyperspheroidite

60

30

wt%C

1

0 0

coarse pearlite fine pearlite 0.5

wt%C

1

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

Adapted from Fig. 10.21, Callister (Fig. g 10.21 based on data from 6e. ( Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, pp. 9 and 17.)

38

MECHANICAL PROP: Fe Fe-C C SYSTEM (3) Fine Pearlite vs Martensite:HypoBrinell hardness s 600

Hyper

martensiteFunctions of the Alloying Elements in Steel, AmericanAdapted from Fig. 10.23, Callister 6e. (Fig. 10.23 adapted from Edgar C C. Bain, Bain

400

200 0 0

fine pearlite0.5

Society for Metals, 1939, p. 36; and R.A. Grange, C.R. Hribal, and dL L.F. F Porter, P t Metall. M t ll Trans. T A, Vol. 8A, p. 1776.)

wt%C

1

Hardness: fine pearlite critical cooling rate will change to Martensite

M

0.1

1

10

100

Time (s)

1000

42

Properties of Oil Oil-Quenched Quenched SteelFigure 4.25 Mechanical properties of oil-quenched il h d 4340 steel, l as a function f i of tempering temperature. Source: Courtesy of LTV Steel Company

43

Surface carbon concentrationCs: during process, it is the maximum solubility of carbon or nitrogen in iron at the carburizing or nitriding temperature. temperatureIt shows the approximate limits of carbon solubility in austenite for 8 common steels

Q: Determine Cs values for 4820, 1020 and 3115 steels at 800 and 900 C.

44

Effective case depthWhile 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, 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 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, Thus, depth x, x the parameters to be controlled are D and t. t However, D depends on temperature. Th actual The t l process parameters t are the th temperature t t and d time ti of f carburization. b i ti 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 carburization is limited to about 900-950C.

C(x,t) Co = x 1 erf 2 Dt Cs Co

45

Limitation of sample sizeThe case depth discussed up to this point is for a concentration gradient beneath a plane p a e surface su ace on o a solid so d o of infinite te magnitude. ag tude. For o solid so d s slabs abs w with t finite te dimensions and diffusion from both surfaces, the equations are excellent approximations for case depth as long as Dt < 0.2 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 oC, Ex. C 2 ho hour, r 2L > (use the data in Table 5.2)5.9 10 12 2 3600 = 0.00103m 1mm 0.22L

The h curvature of f the h surface f b being i carburized b i d also l influences i fl the h case depth d h when the radius of curvature is comparable in magnitude with the case depth. For convex surfaces, surfaces the case depth obtained is greater than that expected on plane surfaces. For concave surfaces, , the case depth p is lesser than that expected p from plan p surfaces.

46

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? Constant Key point 1: C(x,t C(x t500C) = C(x,t C(x t600C). ) Key point 2: Both cases have the same Co and Cs.

Result: Dt should be held constant.

C(x,t) Co = x 1 erf 2 Dt Cs Co5.3x10 5 3x10-13m2/s 4.8x10-14m2/s

(Dt)500C =(Dt)600C 10hrsNote: values of D are provided here.47

Constant

Answer:

t 500 =

(Dt)600 = 110 hr D500

PROCESSING QUESTION-Carburizing g C-Fe 10 hour required at 900 C / Cost $1000/hour(500 parts). To get same C(x)at 1000 C, cost $1500/hour (500 parts). Is it economical to operate at 1000 C? What other factor must be considered? Key point 1: C(x,t C(x t900C) = C(x,t C(x t1000C). ) Key point 2: Both cases have the same Co and Cs.

Result: Dt should be held constant.

C(x,t) Co = x 1 erf 2 Dt Cs Cot1273 = D0 exp(

(Dt)900C =(Dt)1000C

Answer:

137800 ) 10 8.311173 = 3.3hours 137800 p( ) D0 exp( 8.31127348

QUESTION-continuedAt 900C, the cost per part is ($1000/h) (10 h)/500 parts = $20/part At 1000C, 1000C the cost per part is ($1500/h) (3 (3.3 3 h)/500 parts = $9 $9.90/part 90/part Considering only the cost of operating the furnace, increasing the temperature reduces the heat-treating heat treating cost of the gears and increases the production rate. Another factor to consider is if the heat treatment at 1000C 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 equipment q p such as the furnace itself and any y accessories? How long g would the 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. 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, simple solves problems for the system, system and does not create new problems. problems49

50

x C (x,t) Co = 1 erf f 2 Dt Cs Co

0.5 10 3 1 0.8 0.25 1.2 0.25 2 1.6 10 11 t0.4 z 0.4284 0.421 = = 0.00755 0.4 0.35 0.4284 0.3794 z = 0.392

51

Worked exampleA 25-mm diameter 8620 steel bar was carburized at 900C for eight hours. The diffusion coefficient of carbon in austenite isD = 16.2 exp( 137800 ) 8.314T

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 water t or in i agitated it t d oil? il?

52

Solution 1 Solution-1The 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. content The carbon content is found to be 0.45 percent C = C(x,t) in the carburizing equation

1

53

Solution 2 Solution-2C ( x, t ) C0 x ) = 1 erf ( C s C0 2 Dt

from which we can solve for x, the location of C(x,t) = 0.45% of C. At 900C (1173 K), Cs = 1.24 percent C for 8620 steel from Fig. A and the diffusion coefficient is 137800 D = 16.2 exp( ) = 1.183 10 5 mm 2 / s 8.314 (900 + 273)

Then and

0.45 0.2 x = 1 erf ( ) 1.24 0.2 2 Dt erf (

x ) = 1 0.24 = 0.76 2 Dt x And from erf table = 0.84 2 Dt

and

x = 1.68 1.183 10 5 8 3600 = 0.9806mm54

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. Fig 9 9-51 51 it is 57 HRC HRC. Doing the same for the agitation in oil and using Fig. 9-53, the Jominy equivalent q cooling g rate at 0.92R location is found to be 2.5 mm, and using g 0.45% C, is 56 HRC. We see that 57 HRC for water quenching and 56 HRC for oil quenching both exceed d the h 54 HRC HRC. Th Therefore, f we can use either i h quench, h because b oil il quenching is less drastic, we should use oil quenching.

55

Water q quenched

oil q quenched

56

57

58

59

DIFFUSION DEMO: ANALYSIS The experiment: we recorded combinations ofp C constant. t and x that keptto t1 t2 t3 xo x1 x2 x3

x C(x i , t i ) Co i = 1 erf Cs Co 2 Dt i

= (constant here)

Diffusion depth given by:

x i Dt i60

DATA FROM DIFFUSION DEMO4 35 3.5 3 2.5 2 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3B B B B

(

)

B B B B BBB B BB

Linear regression fit to data:

ln[x(mm)] = 0.58 ln[t(min)] + 2.2 R2 = 0.999 0 999

ln[t(min)]

Experimental result: x ~ t0.58 Theory predicts x ~ t0.50 Reasonable agreement!61

Other Applications Processing of microelectronic circuits i iThe 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 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 controlled ll d from f previous i experience. i A layer l of f an organic i material called photoresist is applied over the oxide layer on which lithography is done. Webster's Dictionary defines de es lithography og ap y as the ep process ocess of o printing p g from o a plane pa e surface (smooth stone or metal plate) on which the image to be printed is ink-receptive and the blank area inkrepellant. In microelectronics processing, a masking pattern tt is i placed l d over the th photoresist h t i t and d ultraviolet lt i l t light li ht is passed through. Depending on whether the photoresist is positive (or negative), the area exposed (or unexposed) is washed away y by y a suitable developer p to p provide a 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 interconnect t is i deposited. d it d62

S h Schematics ti of f the th lithographic lith hi methods th d to t create t metallic pattens and selected areas for infusion of dopent atoms

Example: Silicon Device FabricationDevices such as transistors are made by doping semiconductors with different dopants to generate regions that have pp or n n-type type semiconductivity semiconductivity.[1] [1] The -13 2 diffusion coefficient of phosphorus (P) in Si is D = 65 10 cm /s at a temperature of 1100oC. Assume the source provides a surface concentration of 1020 atoms/cm3 and the diffusion time is one hour. hour Assume that the silicon wafer contains no P to begin with. ( ) Calculate the depth (a) p at which the concentration of P will be 1018 atoms/cm3. 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? (c) What will happen if now the wafer has to be heated again for boron (B) diffusion for creating g a p-type p yp region? g

63

Schematic of a n-p-n transistor. Diffusion plays a critical role in formation of the different regions created in the semiconductor substrates. The creation of millions of such transistors is at the heart of microelectronics technology64

2003 Brooks/Cole, a div vision of Thomson Learning, , Inc. Thomson Learning is s a trademark used herein un nder license.

SOLUTION

65

SUMMARY: STRUCTURE & DIFFUSIONDiffusion FASTER for... open crystal structures lower melting T materials materials w/secondary bonding smaller diffusing atoms cations lower density materials

Diffusion SLOWER for... close-packed structures higher melting T materials materials w/covalent bonding larger diffusing atoms anions higher density materials66