Table Of ContentMagneticoriginofchemical balanceinalloyedFe-Crstainlesssteels: first-principles andIsing
model study
E. Airiskallio, E. Nurmi, I. J. Väyrynen, and K. Kokko∗
Department of Physics and Astronomy, Universityof Turku, FI-20014 Turku, Finlandand
Turku University Centre for Materials and Surfaces (MatSurf), Turku, Finland
M. Ropo
Department of Information Technology, Åbo Akademi, FI-20500 Turku, Finland
M. P. J. Punkkinen
Department of Physics and Astronomy, Universityof Turku, FI-20014 Turku, Finlandand
Applied Materials Physics, Department of Materials Science and Engineering,
Royal Institute of Technology, SE-10044 Stockholm, Sweden
2
1
B. Johansson
0
Applied Materials Physics, Department of Materials Science and Engineering,
2
Royal Institute of Technology, SE-10044 Stockholm, Sweden and
n Department of PhysicsandMaterialsScience, Uppsala University, SE-75121 Uppsala, Sweden
a
J
L. Vitos
0
Applied Materials Physics, Department of Materials Science and Engineering,
2
Royal Institute of Technology, SE-10044 Stockholm, Sweden
DepartmentofPhysicsandMaterialsScience, UppsalaUniversity,Box516, SE-75120Uppsala, Swedenand
]
i Research InstituteforSolidStatePhysicsand Optics, Budapest H-1525, P.O.Box49, Hungary
c
(Dated:11January2012)
s
-
l Iron-chromium formsthebasisofmost ofthestainlesssteel gradesinthemarkets. Recentlynew insights
r
intothephysicalandchemicalpropertiesofFe-Crbasedalloyshavebeenobtained.Someofthenewresultsare
t
m quiteunexpectedandcallforfurtherinvestigations. Thepresentstudyaddressesthemagneticcontributionin
theatomicdrivingforcesbehindthechemicalcompositioninFe-CralloyedwithAl,Ti,V,Mn,Co,Ni,andMo.
.
t Usingtheabinitioexactmuffin-tinorbitalsmethodandanIsing-typespinmodel,itisfoundthatthemagnetic
a
m momentofthesoluteatomcombinedwiththeinducedchangesinthemagneticmomentsofthehostatomsform
themainframeworkindeterminingthemixingenergyandchemicalpotentialsoflow-CrFe-Crbasedalloys.
-
Theresultsobtainedinthepresentworkarerelatedtotuningofthemicrostructureandcorrosionprotectionof
d
n low-Crsteels.
o
c
[ I. INTRODUCTION observedsteepincreaseofthecorrosionresistanceofthefer-
riticstainlesssteelsstartswhentheCrcontentinbulkreaches
1 the levelof about10 at.%.1 This bulk thresholdof Cr corre-
v Thesuperbpropertiesof stainlesssteel, like resistance to
latessurprisinglywellwiththecalculatedreversalpointofthe
6 corrosion,highstrength, ductility,low maintenance,andrel-
magnitudesofthebulkandsurfaceeffectivechemicalpoten-
3 atively low cost make it an ideal base material for a host of
3 commercial applications. For example, stainless steels are tialdifferences.Thisreversalofthechemicalpotentialsisthe
4 causefortheoutburstofCrontheotherwisepureFesurfaceof
used in cook-ware, cutlery, hardware, surgical instruments,
. Fe-Cralloys.2 InadditiontoCrmanyotherelementsarefre-
1 majorappliances,industrialequipment,asanautomotiveand
0 aerospace structural alloy, and construction materialin large quentlyusedasminoralloyingadditionsinstainlesssteelsto
2 furtherimprovethepropertiesofstainlesssteelsgrades.How-
buildings.
1 evertheirimpactonthechemicalpotentialofthehostmatrix
: Stainlesssteeldiffersfromcorrodiblecarbonsteelmainly isnotwelldocumented.
v
bytheamountofchromiuminthebulk. Stainlesssteelshave
i
X sufficientamountofchromiumpresentsothatathinandtrans- Alloyingelementsinsteels canbe dividedintotwo main
r parentfilmofchromiumoxiderapidlyformstotheopensur- categoriesnamely austenite and ferrite stabilizers. From the
a faceofthemetalwhichpreventsfurthersurfacecorrosionand elementsdiscussedinthepresentworkCr,Ti,Mo,V,andAl
blockscorrosionfromspreadingintotheinternalstructureof belongtotheferritestabilizersandNi,Mn,andCoareausten-
the material. More importantly, this oxide layer quickly re- itestabilizers. Inadditiontotheeffectontheaustenite/ferrite
forms when the surface is scratched. This phenomenon is stabilization, these elements affect many other properties of
called’self-healingpassivation’andisseenalsoinothermet- steels. Inthefollowingwelistsometypicalapplicationsofal-
als,suchasaluminumandtitanium. loying.Aluminumisoftenusedinhightemperaturecorrosion
Highoxidation-resistanceinairatambienttemperatureis resistantmaterials3–5 duetoitsabilitytoformahighlystable
normally achieved with chromium additions in steels. The andprotectiveoxidescaleontheopensurfacewhenexposed
2
tooxidizingenvironment. Thephysicalpropertiesandcorro- one-center expansion of the full charge density, we adopted
sionresistanceofFe-Cr-Alasafunctionofthechemicalcom- anl-cutoffof8andthetotalenergywascalculatedusingthe
position of the alloy have been studied quite extensively.6–22 full charge-density technique.38,42 For each alloy the calcu-
Titaniumisanelementaddedtosteelsbecauseitincreasesthe latedequilibriumlatticeconstantwasused. Theconvergence
strengthandresistancetocorrosion.Furthermore,Tiprovides ofthetotalenergywithrespecttothenumberofk-vectorswas
a desirable property to alloys: lightness. Its density is less tested. Itwasfoundthat1240uniformlydistributedk-vectors
than half that of steel, so a titanium-steel alloy weighs less withintheirreduciblewedgeoftheBrillouinzonewasenough
thanpuresteelandismoredurableandstronger.Thesephysi- forthepresentpurposes.
calandmechanicalpropertiesmaketitaniumsteelsapossible The Fe-rich Fe-Cr alloys adopt the body centered cubic
material for example in aircraft and spacecraft engineering, (bcc)phaseofα-Fe.Anumberofpreviousworksdemonstrate
chemical industry, and medicine.23–27 Vanadium is a com- thatbelowthemagnetictransitiontemperature(900-1050K)
mon component, for instance, in tool steels. Vanadium ad- theenergeticsofFe-Cralloyswith lessthan 10%Cr iswell
ditionto Fe-Cr increasesthe hardness, tensile strength, wear describedusingthesubstitutionallydisorderedferromagnetic
resistance,andimpactresistance.28,29However,littlehasbeen bccphase.45,46
published on the corrosion properties of the Fe-Cr-V alloys Sinceinthepresentinvestigationwemapalargeconcen-
and on the role of vanadium in the passivation process.30–32 trationregionwith Cr contentapproachingzero, theconven-
Molybdenumis used to increase the strength to weightratio tional supercell method would require enormously large su-
andweldability.33 percells. Here, we resolve this difficulty by employing the
Nickel is the most frequent alloying element to stabilize CoherentPotentialApproximation(CPA).47 WithintheCPA,
Fe-Cr alloysin the austenitestructure. Thiscrystalstructure the alloy componentsare embeddedin an effectivemedium,
makes such steels paramagnetic and less brittle at ambient which is constructed in such a way that it represents, on the
conditions. Also manganese has been used in many stain- average, the scattering properties of the alloy. The EMTO
less steel compositions. Manganese preserves the austenite approachincombinationwiththeCPAhasbeenappliedsuc-
structureinsteelsasdoesnickel,butatalowercost. Austen- cessfullyinthetheoreticalstudyofvariousstructuralandelec-
itegradesareperhapsthemostwidelyusedstainlesssteelsin tronic properties of alloys and compounds38 demonstrating
modernapplications.23,34 Cobaltis used to increase heatand the accuracyand efficiencyneededfor the presentinvestiga-
wear resistance (improve anti-galling property) and to pro- tion.
duceexcellentmagneticpropertiesandgoodductility.35 The EMTO results are analyzedby using a spin model48
InthisReport,weinvestigatetheroleofminoralloyingel- wherethemagneticmomentsobtainedfromtheEMTOcalcu-
ements(Al,Ti,V,Mn,Co,Ni,Mo)ontherelativeenergetics lationsaretheinputdataandtheoutputenergyisusedtocal-
of Fe and Cr and its possible consequencesto surface prop- culatetheeffectivechemicalpotential. Thisprocedureallows
erties. The basic data is obtained by an ab initio electronic amoretransparentwaytounderstandtheeffectofmagnetism
structuremethodandinthe analysisoftheresultswe use an onthechemistryoftheFe-Cr-Xalloys.
Ising-typespinmodelinordertoelucidatetheeffectsofmag-
neticinteractionsontheenergeticsofthealloy.Therestofthe
paperisdividedintotwomainsectionsandconclusions. The III. RESULTSANDDISCUSSION
theoreticaltoolisbrieflyreviewedinSectionIIandtheresults
arepresentedanddiscussedinSectionIII.
A. Corrosionrateversusbalancebetweenbulkandsurface
chemicalpotentials
II. METHOD Ourpreviousinvestigationsdemonstratethatthechemical
compositionoftheclosepackedsurfacesofFe-Cralloysfol-
The calculations are based on the density functional lows closely the characteristic threshold-likebehavior of the
theory36,37andperformedusingtheExactMuffin-TinOrbitals corrosionrateofferriticstainlesssteels.2,49Indilute,corrodi-
(EMTO) method.38,39 The EMTO method is an improved ble, Fe1−xCrx alloys (x<∼0.05) the surfaces are exclusively
screened Korringa-Kohn-Rostokermethod,40 where the one- covered by Fe, whereas the Cr-containing surfaces become
electronpotentialisrepresentedbylargeoverlappingmuffin- favorable when the bulk Cr concentration exceeds 10 at.%,
tin potentialspheres. By using overlappingspheres, one de- whichisclosetothegenerallyacceptedCrthresholdforcor-
scribesmoreaccuratelythecrystalpotential,whencompared rosionresistantalloys. Thediscoveredthresholdpointinthe
totheconventionalnonoverlappingmuffin-tinapproach.41–43 concentration of bulk Cr was found to be a consequence of
The EMTO basis set included s, p, d, and f orbitals. thereversaloftherelativemagnitudesofthebulkandsurface
The one-electron equations were solved within the scalar- effective chemical potentials (µFe −µCr), which in turn re-
relativisticandsoft-coreapproximation.Thegeneralizedgra- flectsthepeculiarelectronicandmagneticstructureofFe-rich
dient approximation in the PBE form was used for the ex- Fe-Cralloys.45,46,48,50–57
changecorrelationfunctional.44TheEMTOGreen’sfunction Inthepresentworkweextendthepreviousinvestigations
wascalculatedself-consistentlyfor32complexenergypoints toquestionstowhatextentthebalanceofthechemicalpoten-
distributed exponentially on a semi-circular contour, which tialsofFeandCrinbulkalloycanbetunedbydopingFe-Cr
included states within 1 Ry below the Fermi level. In the withtypicalminoralloyingelementscommonlyusedincom-
3
mercialsteels. Asa referenceforthe alloyingeffect, we use (i) Theincreasedvolumeisrelatedtothedecreasedbond-
the aforementioned threshold value of bulk Cr which corre- ing between the atoms, and consequently to the in-
spondstothebreakingofthepureFe surfaces. We calculate creasedtotalenergyofthealloy.
theeffectivechemicalpotentialinbulk((µFe−µCr)bulk)for
(ii) The increasing total energy of dilute Fe-Cr alloys de-
Fe-Cr-Xalloyscontaining5at.%X(X=Al,Ti,V,Mn,Co,Ni,
tMheo)coanrrdescpoomndpianrgetehfefeccatilvceulcahteedm(icµaFlep−oteµnCtria)lbualtkt(hFeigsu.r1f)actoe cinregaseensththaelpmyaogfniFtued1−exoCftrhxeantegxati≈ves0lo.peTohfistheismdiuxe-
wofobrkin.2a,r5y8,5F9e-Cr((µFe−µCr)surface),determinedinourearlier tFoe1t−hexCcrhxaraalcloteyrsisatitcsmshaallpex.2of the mixing enthalpy of
Inalloysforwhichthesurfaceenergyofthethirdcompo- (iii) Therelationbetweentheeffectivechemicalpotentialof
nentX ishigherthanthatofFe, thesurfacesareexpectedto bulkFe-Cr andtheslope ofthe mixingenthalpy(∆H)
becoveredmainlybyFeatoms. Therefore,inthesecasesthe ofthealloy61
effective chemicalpotential µFe −µCr at the surface can be
∂∆H
approximated by that of the binary Fe-Cr alloy and in these (µFe−µCr)bulk ≈− +constant (1)
∂x
alloys the threshold value of bulk Cr corresponds to the on-
set of the breaking of the pure Fe surface by Cr atoms. On shows that the effective chemical potential at x ≈ 0
the other hand, for those alloys where the surface energy of consequentlydecreases.
the third component X is lower than that of Fe (Al and Ni, (iv) Finally,thedecreaseof(µFe−µCr)bulkatsmallxshifts
Ref. 60), the surfaces of the Fe-Cr-X alloys are expected to
thethresholdvaluecthrtolowerCrcontents.
becoveredmainlybyXatoms.Inthesecasestheloweringof
the threshold value of bulk Cr correspondsto the increasing Atthispointitshouldbenotedthatvanadiumdeviatessignifi-
ofthedrivingforceformovinganFeatom,comparedtothat cantlyfromthegeneraltrendofcthrwithvolumeshowingthe
ofCr,fromthesurfacestothebulkofthealloy. largestreductioninthebulkCrthresholdwithincreasingvol-
BycomparingtheeffectivechemicalpotentialµFe−µCrin ume(Fig.2). Therefore,thethresholdvalueofthebulkCras
bulkandatthesurfaceweareabletoestimate,forFe-Cr-Xal- afunctionofminoralloyingelementneedstobeinvestigated
loys,thethresholdconcentrationsofbulkCr,whichagainare inmoredetail.
expectedtoberelatedtotheonsetofthecorrosionresistance
in Fe-Cr basedalloys. Thefirst-principlesEMTOresultsfor
C. Establishingtheroleofmagneticinteractionsinthe
thethresholdvalues(cthr)ofbulkCrinFe1−x−0.05CrxX0.05
thermodynamicsofFe-Cranditsderivatives
alloysarelistedinTableI.
BecausethephasestabilityofFe-Cralloysdependssignif-
X Al Ti V Mn Co Ni Mo Cr icantly on the magnetic interactions between the constituent
cthr(at.%) 5 4 1 9 6 3 1 8 atoms,2,48–50,62,63 it is instructive to concentrate on the mag-
netic propertiesin the presentcase too. In orderto trace the
role of the additionalalloying elements (X) on the magnetic
TABLEI:TheoreticalresultsforthethresholdvaluesofbulkCrcor- contributiontothebulkthresholdofCrinFe-Cr-Xalloyswe
respondingtothereversalofthedirectionsoftheCrandFedriving analyzeourabinitioresultsbyusingaspinHamiltonian
forcestowardsthesurfaceinFe1−x−0.05CrxX0.05 alloys. Thedata H =(S +S )σ σ /2+(1−S S )σ σ /2. (2)
is obtained by determining the intersection point of the calculated ij i j i j i j i j
(µFe−µCr)bulk(Fig.1)and(µFe−µCr)surface.2 Thelastcolumn A similar Hamiltonian was employed by Ackland (Ref. 48)
(Cr)showsthethreshold valueforFe-Cralloys, whichagreeswell
inhisstudyoftheFe-Crsystems. ThetotalenergyoftheN
withtheexperimentallyobservedonsetpointofcorrosionprotection
inFe-Cr. atomsystem(Etot)peratomthenreads
N 14 N
1 1 1
Etot/atom= X XHij = XHi =<Hi >,
N 2 N
i=1 j=1 i=1
(3)
B. Chromiumthresholdasanindicationoftheenergeticsof wherethej summationrunsoverthenearestandnextnearest
theFe-Crbasedalloys neighborsofthesitei(14sitesinthebcclattice48). Applying
equation(3)tobinaryFe-Cralloy,weadoptSFe =−1,SCr =
PlottingthedatashowninTableIasafunctionofthelat- 1, and σFe and σCr are the magnetic moments of Fe and Cr
ticeparameter(a)ofthealloy(Fig.2)revealsanapproximate atoms,respectively.ThisyieldsferromagneticFe-Fecoupling
decreasingtrendoftheCrthresholdvaluewiththevolumeof andantiferromagneticcouplingofCrtoitsneighbors.Within
the alloy. The observed general trend shown in the relation theCPAformalism,weobtainfortheFe1−xCrxalloy
between the Cr threshold value and the volume of the alloy
canbeunderstoodbyconsideringthetotalenergyofthealloy. <Hi > = x<HCr >+(1−x)<HFe >
Theapproximateconnectionbetweenthethresholdvalueand = 7(x2σC2r+2x(1−x)σCrσFe
thevolumecanbeelucidatedasfollows: − (1−x)2σ2 ). (4)
Fe
4
2.87 2.4
Al Al
2.86 Ti Ti
V ) 2.3 V
B
°A) 2.85 Mn µ( Mn
a ( Co Fe Co
Ni m 2.2 Ni
2.84
Mo Mo
2.83 2.1
0 5 10 15 20 25 30 0 5 10 15 20 25 30
-0.5 2.0
Al 1.5 Al
Ti Ti
1.0
µ)B -1.0 MVn µ)B 0.5 MVn
(Cr Co m (X 0.0 Co
m Ni -0.5 Ni
-1.5 Mo -1.0 Mo
-1.5
0 5 10 15 20 25 30
0 5 10 15 20 25 30
at. % Cr
-6035.8
Al
V) -6036.0 Ti %) 0.0
e V
(Cr -6036.2 Mn (at. -5.0
µµ-Fe -6036.4 MCNooi ∆c thr -10.0 Al V Co Mo
Ti Mn Ni
-6036.6
0 5 10 15 20 25 30 0 2 4 6
at. % Cr at. % X
FIG.1: (Coloronline) Resultsof theEMTOcalculations. Latticeparameter (a),magnetic moment peratom(m, inBohr magnetons µB),
effective chemical potential in bulk (µFe −µCr) and the shift of the Cr threshold ∆cthr of Fe1−x−0.05CrxX0.05 where X is the alloying
component (Al,Ti, V,Mn, Co, Ni,Mo). ContinuousblackcurveshowstheresultsforFe-Cr. ∆cthr asafunctionofXcontent isalinear
approximationbasedon5at.%Xdata.
SinceweareinterestedintherelativeenergybalanceofCrin bulkCrthresholds∆cthr bydeterminingthepositionsofthe
bulk,weextendtheabovespinmodeltoFe-Cr-Xbymerging intersections of the (µFe −µCr)bulk and (µFe −µCr)surface
theXatomswiththeFeatomstoformaneffectiveFematrix curves. These estimated critical compositions are shown by
intowhichCratomsaredissolved. Forindividualspinsσ we greencrossesinFig.2.ThespinmodelbasedCrthresholdde-
usethecalculatedmagneticmoments(Fig.1). Thespinofthe viatessignificantlyfromthatoftheEMTOcalculationsinthe
effectiveFematrixistakentobetheaverageofthemagnetic caseofVandMo.Whatcomestothequalitativeagreement,it
momentsoftheFeandXatomsweightedbytheirconcentra- isofcourseexpectedthatthespinmodelcannotcompetewith
tions. As Fig. 3 shows, the alloying of Fe-Cr changes both theabinitio calculations,butwhatismoreimportanthereis
the curvature and the position of the minimum of the total thatthegeneraltrendpredictedbythespinmodelagreeswith
energy (mixing enthalpy), particularly around the point of 5 theEMTOresult. Thissuggeststhatthespin modeliscapa-
at.%Crwhichisanimportantregionwithrespecttothebulk ble of capturing the main features of the Fe-Cr-X alloy and
Cr threshold. Because the bulk effective chemical potential torevealthe underlyingmagneticinteractions. Theobtained
(µFe−µCr)bulk isakeyquantityindeterminingthebulkCr shiftsofthethresholdsofbulkCr(∆cthr)duetothealloying
threshold and since the effective potential is approximately inthespinmodelagreesurprisinglywellwiththoseobtained
the derivative of the total energy (Eqn. (1)) we calculate the directly by the EMTO calculation (Fig. 5). Presenting the
derivativesofthespinmodeltotalenergiesfromFig.3. The resultsusingrelativequantities,
result is shown in Fig. 4. The derivatives of the total en-
ergy of the spin model have approximately the same shape ∆cthr = cthr(Fe−Cr−X)−cthr(Fe−Cr) (5)
as the EMTOeffectivechemicalpotentials(µFe −µCr)bulk, cthr(Fe−Cr) cthr(Fe−Cr)
shown in Fig. 1. Plotting in Fig. 4 the surface chemical po- showninFig.6,itisrealizedthatthereisasignificantcorrela-
tential(µFe−µCr)surface ofFe-Cralloy,wecanestimatethe tionbetweentherelativethresholdsoftheEMTOcalculation
5
10.00 120
Mn
base Fe-Cr
8.00 s) 100 Fe-Cr-Al
nit Fe-Cr-Ti
u
%) 6.00 Co Al y 80 Fe-Cr-V
(at.hr 4.00 Ti rbitrar 60 FFFeee--CC-Crr--rMC-Noni
ct Ni m (a Fe-Cr-Mo
2.00 ato 40
V Mo c/
d
0.00 /ot 20
2.845 2.850 2.855 2.860 2.865 Et
° d
a (A) -
0
FIG. 2: (Color online) Threshold of the Cr concentration in
Fe1−x−0.05CrxX0.05 alloys (X =Al, Ti, V, Mn, Co, Ni, Mo; base 5 10 15 20
refers to Fe-Cr) as a function of the lattice parameter. The brown Cr at. %
circlesshowtheEMTOresultsandthegreencrossesshowthespin-
model results. The straight line is a guide for an eye showing the FIG.4: (Coloronline)Thederivativeofthespinmodeltotalenergy
generaltrendwiththevolume. per atom (spin model, Fig. 3) multiplied by −1 and shifted to the
common zero value at Cr at.% = 20. The short gray line segment
shows the level of the EMTO surface effective chemical potential
((µFe−µCr)surface,fromRef.2)relativetotheFe-Crcurve.
-30
)
s -32
nit 2 EMTO
u spin model
ry -34
ra 0
bit )
ar -36 Fe-Cr %
m ( Fe-Cr-Al at. -2
(
/atoot -38 FFFeee-C--CCr-rrM--VTn i ∆c thr -4
Et
-40 Fe-Cr-Co
Fe-Cr-Ni -6
Fe-Cr-Mo
-42
-8
0 5 10
Mn - Co V Ni Al Ti Mo
Cr at. %
FIG. 5: (Color online) The shifts of the bulk Cr threshold ∆cthr
FIG.3: (Coloronline)Thetotalenergyperatomobtainedfromthe
fromthatoftheFe-Crcase(EMTOresult:8at.%,spinmodelresult:
spinmodel.Thesymbolsrefertotheresultsofthespinmodel(Eqn.
7at.%)dueto5%alloyingwithAl,Ti,V,Mn,Co,Ni,andMo,ob-
(4))andcurvesarefunctionsfittedtothespinmodeldata. Theinset
tainedbytheEMTOmethod(brownbars)andthespinmodel(green
shows the same results but from 1 to 20 at.% Cr emphasizing the
bars).
almostlinearbehavioroftheenergyasobtainedfromthespinmodel
withinthe10–20at.%Crrange.
Critincreases(µFe−µCr)bulk.
andthespinmodelestimatedemonstratingdefinitelythatthe MaybethemostinterestingdatainFig.1isrelatedtothe
effective chemical potential of Fe and Cr in the investigated magneticmomentsofMn. Itprovidesanillustrativeevidence
alloys is to a large extent determined by magnetic interac- for the decisive role of the magnetic moments of the alloy-
tions.WecloseourdiscussionbyanalyzingtheEMTOresults ingelementsintherelativebalancebetweenthebulkchemi-
shown in Fig. 1. The general trend seen in Fig. 1 is that all calpotentialsofFeandCrinFe-Cr-Xalloys. WhileCrcon-
investigatedalloying componentslower the (µFe −µCr)bulk centrationchangesfrom0to5at.%theMnmomentchanges
for low-Cr alloys. When Cr content increases, this trend is approximatelyfrom−1to+1Bohrmagneton(µB)i.e.prac-
diminished or reversed (Mn). When Cr content reaches 15– ticallythroughthewholerangeofthemomentsoftheinves-
20 at.% the effect of the additional alloying is small. Man- tigated additional alloying elements (from V to Co). Corre-
ganese shows the most peculiar behavior: below 5 at.% Cr, spondinglythe(µFe−µCr)bulkchangesfromthevalueofthe
Mnstronglydecreases(µFe−µCr)bulkwhereasabove10at.% Fe-Cr-V case to thatof the Fe-Cr-Co case revealingthe cru-
6
fective chemical potential (µFe − µCr)bulk and showed that
the magnetic momentof the dopingatom plays a significant
0.20
O) base Mn roleintheenergybalanceofFeandCratomsinFe-Cr-Xal-
T 0.00 loys. The employedcomputationalmethod providesan effi-
M
E Co cienttooltoscantheeffectsofdifferentalloyingcomponents
r) ( -0.20 Al atanyconcentrationlevel. SincethestainlesspropertyofFe-
C
CrbasedalloysisrelatedtothepresenceofCrnearthealloy
e- -0.40
F Ti surface,ourfindingsareusefulinunderstandingandexplain-
(hr -0.60 Ni ingthecorrosionresistanceoftheFe-richFe-Crbasedalloys.
ct
c/thr -0.80 Mo V mUsaitnegthteheefofebctationfeadtrheisrudlctsomfoprotnheenbtuolnkthiteirseplaotsivsiebcleontotenetstoi-f
∆
FeandCratthesurface.
-1.00
-0.80 -0.60 -0.40 -0.20 0.00 0.20
∆c /c (Fe-Cr) (spin model)
thr thr
FIG.6: (Coloronline)RelativeshiftofthethresholdCrconcentra-
tion∆cthr/cthr(Fe−Cr)inFe1−x−0.05CrxX0.05with(X=Al,Ti,
V,Mn, Co, Ni, andMo; base referstoFe-Cr). Thelineshowsthe V. ACKNOWLEDGEMENTS
linearfittothedataf(x)=a+bx,a=−0.028b=1.29.
ThecomputerresourcesoftheFinnishITCenterforSci-
cial role of the magneticmomentof the alloying elementon ence (CSC) and Mgrid project are acknowledged. Financial
thechemicalpotentialsinFe-Cralloys. support from the Academy of Finland (Grant No. 116317)
(EA, EN, KK) and Outokumpu Foundation (EA) are ac-
knowledged. The Swedish Research Council, the European
IV. CONCLUSIONS Research Council, the Swedish Steel Producer’s Associa-
tion (LV, BJ), the Hungarian Research Fund (OTKA project
Using density functional theory, implemented in the 84078) (LV) and the Göran Gustafson Foundation (MP) are
EMTO formalism, and a spin model, we investigatedthe ef- alsoacknowledged.
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