Ngày tải lên :
23/12/2013, 00:15
... Inc.
Æ
À1
¼1=5boundaryisoneinwhich1in5ofthegrainboundaryatoms
match,asshowninFig.2.8(c).
Twinboundariesmayformwithincrystals.Suchboundarieslieacross
deformationtwinplanes,asshowninFig.2.8(d).Notethattheatomson
eithersideofthetwinplanesaremirrorimages.Stackingfaultsmayalsobe
formedwhentheperfectstackinginthecrystallinestackingsequenceis
disturbed,Figs2.8(e)and2.8(f).Thesemaybethoughtofastheabsence
ofaplaneofatoms(intrinsicstackingfaults)ortheinsertionofrowsof
atomsthatdisturbthearrangementofatoms(extrinsicstackingfaults).
IntrinsicandextrinsicstackingfaultsareillustratedschematicallyinFigs
2.8(e)and2.8(f),respectively.NotehowtheperfectABCABCstackingof
atomsisdisturbedbytheinsertionorabsenceofrowsofatoms.
2.3.4VolumeDefects
Volumedefectsareimperfectionssuchasvoids,bubble/gasentrapments,
porosity,inclusions,precipitates,andcracks.Theymaybeintroducedintoa
solidduringprocessingorfabricationprocesses.Anexampleofvolume
defectsispresentedinFig.2.9.ThisshowsMnSinclusionsinanA707
steel.AnotherexampleofavolumedefectispresentedinFig.1.16(d).
This ... Inc.
whichisgivensimplybyÀðC
A
ÀC
B
Þ=r
0
,thediffusionflux,J,maythenbe
expressedas
J¼D
0
exp
Àq
kT
dC
dx
ð2:9Þ
IfwescalethequantityqbytheAvogadronumber,thentheenergyterm
becomesQ¼N
A
qandR¼kN
A
.Equation(2.9)maythusbeexpressedas
J¼ÀD
0
exp
ÀQ
RT
dC
dx
ð2:10Þ
IfwenowsubstituteD¼ÀD
0
exp
ÀQ
RT
intoEq.(2.10),weobtainthe
usualexpressionforJ,i.e.,Jisgivenby
J¼ÀD
dC
dx
ð2:11Þ
TheaboveexpressionisFick’sfirstlawofdiffusion.Itwasfirstpro-
posedbyAdolfHicksin1855.Itisimportanttonoteherethatthediffusion
coefficientforself-diffusion,D,canhaveastrongeffectonthecreepproper-
ties,i.e.,thetime-dependentflowofmaterialsattemperaturesgreaterthan
$0.3–0.5ofthemeltingtemperatureindegreesKelvin.Also,theactivation
energy,Q,inEq.(2.10)isindicativeoftheactualmechanismofdiffusion,
whichmayinvolvethemovementofinterstitialatoms[Fig.2.11(a)]and
vacancies[Fig.2.11(b)].
Diffusionmayalsooccuralongfastdiffusionpathssuchasdislocation
pipesalongdislocationcores[Fig.2.12(a)]orgrainboundaries[Fig.2.12(b)].
This ... associated with the disappearance of smal-
ler grains and the enhanced growth of larger grains. Due to the combined
effects of these factors, a limiting grain size is soon reached. The rate at
which...