Solid Diffusion of Metal

8/10/2019 Solid Diffusion of Metal

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THE WAY TOSOMEWHERE

1

Sub-topics

DiffusionDiffusion processes in industry


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NON+SPONTANEOS PROCESSES

State 1

State 2

Q=activation energy

Involves reduction in energy

Or

Energy change is negative

1.2.

-or proess to be started,t"e atoms s"ould "a!esuffiient ener#y too!erome an 'cti#'tion

ener%y barrier(

)


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DI--SION

As T of t"e system is inreased, more and more moleules .ill attain t"eati!ation ener#y le!el(

In statistial me"anis, M'*ell+,olt&'nn st'tistics desribes t"edistribution of material partileso!er !arious ener#y states and

probabilities to find a partile indefinite state/

Probability 0 ep(-E/RT)

R Boltzman constant = 1.38

x10 -23 J/atom K .


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12AT IS DI--SION3

/


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SEL-+DI--SION

A

B

C

DA

B

C

D

t

0


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4ACANC5 OR S6STITTIONAL DI--SION1"y, in #eneral, ist"e ati!ation ener#yfor self diffusion "i#"erfor materials of "i#"meltin# point3

7 Atoms mo!e into t"e!aanies plaes(7 8ore !aanies arereated at "i#"ertemperature(

7 Diffusion rate is "i#"erat "i#" temperatures(


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2O1 -AST DOES DI--SION OCCR3

Concentration

of Cu [kg/m3]

Concentration

of Ni [kg/m3]

Position, x

Cu flux Ni flux

Concentration Profile, C(x) [kg/m3]

!x = D

"C

"x

Diffusion coefficient [m#/s]

concentration

gra"ient [kg/m$]

flux in x%"ir&[kg/m#%s]

3

T"e rate at ."i" atoms, ions, partilesor ot"er speies diffuse in a material

T"e flu' is defined as t"e number ofatoms passin# t"rou#" a plane of unitarea per unit time


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STEAD5+STATE DI--SIONo Diffusion is a time dependent proess and t"e rate of mass transfer ist"e diffusion flu "4$5

o In a steady+state ondition t"e onentration #radient is onstant(

Fic67s First l'*8

Net flo. of atomsPer unit area pernit time ; RADIENT

1)

T"e onentration #radient s"o.s "o.t"e omposition of t"e material !aries.it" distane/c

is t"e differene in onentrationo!er t"e distane x

G#mFG#m s

atomsm s


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PRO6LE8 + SE8ICONDCTOR DOPIN>One .ay to manufature transistors, ."i" amplifyeletrial si#nals, is to diffuse impurity atoms into a

semiondutor material su" as silion $Si&( Problem/ Suppose a silion .afer @(B m t"i:, ."i"

ori#inally ontains one p"osp"orus atom for e!ery B@million Si atoms, is treated so t"at t"ere are H@@ P+atoms for e!ery B@ million Si atoms(

Calulate t"e onentration #radient $a& in atomiperentm and $b& in atoms$mF ' m&

1.

T"e lattieparameter ofsilion is (HF@? A(


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DI--SI4IT5Diffusi#ity depends on

9 Type of diffusion / 1"et"er t"e diffusion isinterstitial or substitutional(9 Temperature/ As t"e temperature inreasesdiffusi!ity inreases(9 Type of rystal struture/ 6CC rystal "as lo.erAP- t"an -CC and "ene "as "i#"er diffusi!ity(9 Type of rystal imperfetion/ 8ore open strutures

$#rain boundaries& inreases diffusion(9 T"e onentration of diffusin# speies/ 2i#"eronentrations of diffusin# solute atoms .ill affetdiffusi!ity( 1/


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DI--SION COE--ICIENT

10


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E--ECT O- TE8PERATRE ON DI--SION

Temperature "as a most profound influeneon t"e oeffiients and diffusion rates(

A lar#e ati!ation ener#y results in a relati!ely small diffusion oeffiient(

1

1"en t"e temperature inreases, t"e diffusion oeffiient D inreasesand, t"erefore, t"e flu' of atoms inreases as .ell(At "i#"er temperatures, t"e t"ermal ener#y supplied to t"e diffusin#atoms permits t"e atoms to o!erome t"e ati!ation ener#y barrier andmore easily mo!e to ne. sites in t"e atomi arran#ements(At lo. temperaturesoften belo. about @(H times t"e absolute

meltin# temperaturediffusion is !ery slo. and may not be si#nifiant(


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I8PRIT5 DI--SION INTO SILICON 1A-ER

Impurities are made to diffuseinto silion .afer to "an#e its

electric'l c;'r'cteristics57 sed in inte#rated iruits(7 Silion .afer is e'posed to!apour of impurity at BB@@C in

a %uartz tube furnae(7 T"e onentration ofimpurity at any point depends

on dept" and time of e'posure(

Do'ing ilicon it* P

silicon

+& De'osit P ric*

laers on surface&

#& -eat it&

3& .esult Do'e"

semicon"uctor

regions&

silicon 12

t"e ati!ationener#ies in ionimaterials are "i#"and t"e rates of

diffusion are lo. SiO2


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DESI>N PRO6LE8/ INTE>RATED CIRCITINTERCONNECTS

Top layers t"at ser!e as t"e .irefor t"is de!ie $interonnet&(Diffusion+layer doped silion t"at"a!e been oated .it" aninterlayer dieletri(

1"at material an be usedfor interonnets3

13


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DESI>N O- AN IRON 8E86RANE

A ylinder F m in diameterand B@ m lon# ontains a #as

t"at inludes @( 'B@@

N atomsper mF and @( 'B@@ 2 atomsper mF on one side of an ironmembrane(>as is ontinuously introdued to t"e pipe to assure a onstant

onentration of nitro#en and "ydro#en(T"e #as on t"e ot"er side of t"e membrane inludes a onstant B

B@B N atoms per mF and B ' B@B 2 atoms per mF(T"e entire system is to operate at ?@@ C $at t"is T iron "as t"e 6CC

struture&( Desi#n an iron membrane t"at .ill allo. no more t"an BJ of t"enitro#en to be lost t"rou#" t"e membrane ea" "our,

."ile allo.in# K@J of t"e "ydro#en to pass t"rou#" t"e membraneper "our( (:


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T5PES O- DI--SION

In #olu&e diffusion< t"e atoms mo!e t"rou#" t"e rystalfrom one re#ular or interstitial site to anot"er( 6eause oft"e surroundin# atoms, t"e ati!ation ener#y is lar#e andt"e rate of diffusion is relati!ely slo.(

Atoms an also diffuse alon# boundaries, interfaes, and

surfaes in t"e material( Atoms diffuse easily by %r'inbound'ry diffusion< beause t"e atom pa:in# isdisordered and less dense in t"e #rain boundaries(6eause atoms an more easily s%ueeze t"eir .ay t"rou#"

t"e #rain boundary, t"e ati!ation ener#y is lo.( Surf'ce diffusion is easier still beause t"ere is e!en less

onstraint on t"e diffusin# atoms at t"e surfae((1


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TN>STEN +T2ORI8 DI--SION COPLE Consider a diffusion ouple bet.een pure tun#sten

and a tun#sten alloy ontainin# B atJ t"orium(

After se!eral minutes of e'posure at @@@C, atransition zone of @(@B m t"i:ness is establis"ed( 1"at is t"e flu' of t"orium atoms at t"is time if

diffusion is due to $a& !olume diffusion, $b& #rain boundary diffusion, and $& surfae diffusion3

((

T"e lattie parameter of6CC tun#sten is F(BM (


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NONSTEAD5+STATE DI--SION

Fic67s Second ='*

>oncentr'tion of solute 'to&s 't 'ny point in &et'l c;'n%es *it;ti&e in t;is c'se5

Fic6s second l'*8

R'te of co&position'l c;'n%e is e?u'l to

diffusi#ity ti&es t;e r'te of c;'n%e ofconcentr'tion %r'dient5

C"an#e of onentration of solute atoms .it" "an#e in time in different planes

()


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Co''er "iffuses into a ar of aluminum&

+0

're%existing conc&, Coof co''er atoms

urface conc&,Csof Cu atoms

ar

Co

Cs

'osition, x

C(x,t)

tot+

t#t3

NON+STEAD5 STATE DI--SION

(.


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SOLTIONOne pratially important solution is for a semi+infinite solid in ."i" t"esurfae onentration is "eld onstant(-re%uently, t"e soure of t"e diffusin# speies is a #as p"ase, t"e partialpressure of ."i" is maintained at a onstant !alue(

-urt"ermore, t"e follo.in# assumptions are made/B(6efore diffusion, any of t"e diffusin# soluteatoms in t"e solid are uniformly distributed .it"onentration of C0.

( xat t"e surfae is zero and inreases .it"distane into t"e solid(F( T"e time is ta:en to be zero beforet"e diffusion proess be#ins(

(/


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F@>7S SE>OBD =AW+ SO=CT@OB

(0


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TA6LATION O- ERROR -NCTION 4ALES

(


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CAR6RIIN>

=o*

c'rbon

Steel p'rt

Diffusin% c'rbon

'to&s

>'rbon r'dients

@n >'rburied &et'ls

7 Result/++"ard to deform/ C atomslo: planes from s"earin#(

++"ard to ra:/ C atoms putt"e surfae in ompression( (2


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E--ECT O- TE8PERATRE ON DI--SION+

EA8PLE@f diffusi#ity 't t*o te&per'tures 're deter&ined< t*o

e?u'tions c'n be sol#ed for 'nd D:

):


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DI--SI4IT5DATA -OR SO8E 8ETALS

)(


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PRO6LE8

/ TI8E -OR DI--SION

))

>'rburiin%8 t"e steel piee is e'posed, at an ele!ated temperature, to anatmosp"ere ri" in a "ydroarbon #as, su" as met"ane $C2H &(

Consider an alloy t"at initially "as a uniform arbon onentration

of @( .tJ and is to be treated at K@ C( If t"e onentration of arbon att"e surfae is suddenly brou#"t to and maintained at B(@ .tJ,"o. lon# .ill it ta:e to a"ie!e a arbon ontent of @(@ .tJ at a position@( mm belo. t"e surfae3

T"e diffusion oeffiient for arbon in iron at t"is temperature is B(M ' B@+BB

ms(


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DESI>N PRO6LE8T"e .ear resistane of a steel #ear is to be impro!ed by "ardenin# itssurfae( T"is is to be aomplis"ed by inreasin# t"e arbon ontent.it"in an outer surfae layer as a result of c'rbon diffusion into t"esteel t"e arbon is to be supplied from an e'ternal arbon+ri" #aseousatmosp"ere at an ele!ated and onstant temperature(

T"e initial arbon ontent of t"e steel is @(@ .tJ, ."ereas t"e surfaeonentration is to be maintained at B(@@ .tJ( In order for t"is treatmentto be effeti!e, a arbon ontent of @(M@ .tJ must be establis"ed at aposition @(? mm belo. t"e surfae(Speify an appropriate "eat treatment in terms of temperature and time

for temperatures bet.een K@@C and B@@ C( se data in Table for t"ediffusion of arbon in +iron( T"e #as onst ; (FB


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DESI>N O- A 8ORE ECONO8ICAL 2EATTREAT8ENT

)/

B@ " are re%uired to suessfully arburize a bat" of @@ steel#ears at K@@C, ."ere t"e iron "as t"e -CC struture(

1e find t"at it osts UB@@@ per "our to operate t"e arburizin#furnae at K@@C and UB@@ per "our to operate t"e furnae atB@@@C(Is it eonomial to inrease t"e arburizin# temperature toB@@@C31"at ot"er fators must be onsidered3


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#1

Diffusion FASTER for555

7 open rystal strutures

7 lo.er meltin# T materials

7 materials .seondarybondin#

7 smaller diffusin# atoms

7 lo.er density materials

Diffusion S=OWER for(((

7 lose+pa:ed strutures

7 "i#"er meltin# T materials

7 materials .o!alentbondin#

7 lar#er diffusin# atoms

7 "i#"er density materials

S88AR5/

STRCTRE V DI--SION

)0

Solid Diffusion of Metal

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