The effects of Vanadium on the strength of a bcc Fe Σ3(111)[1-10] grain boundary

0.19 MB·English

by  Sungho Kim

Σ ¯1
The effects of Vanadium on the strength of a bcc Fe 3(111)[1 0] grain
boundary
Sungho Kim1, Seong-Gon Kim2, Mark F. Horstemeyer1, Hongjoo Rhee1
1Center for Advanced Vehicular Systems, Mississippi State University, P. O. Box 5405,Mississippi State,
MS 39762,USA
2
1 2Department of Physics and Astronomy, Mississippi State University, Mississippi State, MS 39762,USA
0
2
Keywords: Vanadium, Steel, Grain Boundary, DFT

n
a Abstract there is a corresponding increase in toughness. V
J
also increases hardness, creepresistance, and impact
7
The effects of micro-alloying element, vanadium, on resistance due to formation of hard vanadium car-
2
a bcc Fe Σ3(111)[1¯10]symmetric tiltgrainboundary bides limiting grain size. Since V is very effective
] strength are studied using density functional theory on aforementioned properties, it is added in minute
i
c calculations. The lowest energy configuration of the amounts. Atgreaterthan0.05%,however,theremay
s grainboundarystructureareobtainedfromthefirst- beatendencyforthesteeltobecomeembrittleddur-
-
l principles calculations. Thesubstitutionalandinter- ing thermal stress relief treatments [6, 13].
r
t stitialpointdefectformationenergiesofvanadiumin The cohesion at these grain boundaries affects the
m
thegrainboundaryarecompared. Thesubstitutional hardness, deformability, and toughness of the mate-
t. defect is preferedto interstitialone. The segregation rial and it can be enhanced or decreased by segre-
a energies of vanadium onto the grain boundary and gated impurities. Therefore, it is essential to under-
m
its fractured surfaces are computed. The cohesive stand the interfacial cohesion and impurity segrega-
d- energy calculation of the grain boundary with and tionindetail,andameaningfulgoalistofindgeneral
n without vanadium show that vanadium strengthen rulesthatdescribetherelationshipbetweenthesemi-
o the bcc iron Σ3(111)[1¯10] grain boundary. croscopic features and the macroscopic properties.
c
The vanadium(V) is the most common cohesion
[
Introduction enhancerthatchangesthestrengthofiron(Fe)metal
1 by the segregation at grain boundaries. The grain
v
The macroscopicbehaviorofsteelalloyandtheir ca- boundarysegregationoccurswithinafewatomiclay-
5
1 pabilitiesfortechnologicalapplicationsarevitallyin- ersatthegrainboundaryplane. Thegrainboundary
9 fluencedby the propertiesofmicro-alloyingelements cohesionenhancementiscausedbythechangeinthe
5 in their microstructures. Small amounts of microal- cohesivepropertiesofatomswithinafewatomiclay-
1. loyingelementssuchasvanadium(V),titanium(Ti), ers at the grain boundary plane.
0 or niobium (Nb) increase strength of steels by grain In 1989, Rice and Wang[12] developed their theo-
2 sizecontrol,precipitationhardening,and/orsolidso- reticalmodelforsolutesegregationintograinbound-
1
lution hardening[2, 1]. V, Nb, and Ti combine pref- ary and insisted that the energy required for inter-
:
v erentiallywithcarbonand/ornitrogentoformafine facial separation of grain boundary is the most im-
Xi dispersion of precipitated particles in the steel ma- portant contribution to embrittlement of the grain
trix. Nb may be added in high strength low al- boundary. They used the solutes (C, P, S, Sb, Sn)
r
a loy (HSLA) sheet to increase the strength predom- in iron to show that the segregation-induced change
inatedly via grain refinement, while other microal- of separation energy of grain boundary is roughly
loysapplythestrengtheningmechanismofprecipita- consistant with segregation-induced embrittlement.
tion hardening to a major extent(Ti) or totally(V) They estimated the separation energy from experi-
[14, 15]. The addition of small amounts of V in- mental segregation energies in fractured surface and
creases the yield strength and the tensile strength grain boundary.
of carbon steel. V is one of the primary contrib- A fracture of the grain boundary creates two sep-
utors to precipitation strengthening in microalloyed arate fractured surfaces under the action of stress.
steels. When thermomechanical processing is prop- The cohesive energy of grain boundary γcoh (J/m2)
erly controlled, the ferrite grain size is refined and is defined as the energy difference between the en-
ergy sum oftwo surfaces after fracture andthe grain
boundary energy before fracture.
γ =2γ −γ (1)
coh s gb
where γs is the surface energy of the two fracture
surfaces after fracture, and γ is the grain bound-
gb
ary energy before fracture. The cohesive energy in
the presence of segregations of solute atoms can be
defined as follows:
NEseg NEseg
γcsoegh = (2γs− As )−(γgb− Agb )
N Figure 1: The schematic of the cohesion enhance-
= γ −(Eseg−Eseg) (2)
coh s gb A ment effect on the grain boundary by solute atom
whereEseg andEseg arethe segregationenergyon segregationat the grain boundary.
s s
thesurfaceandgrainboundary. TheNisthenumber
of atoms in the unitcell. The A is the areaof surface
ory (DFT) [7, 24] using the projector-augmented-
or grain boundary.
wavemethod.[5,16]Allcalculationswerespinpolar-
The grain boundary segregation and trapping of
ized and the Voskown analysis is used for the mag-
vanadiumatomsatthefracturesurfaceaffecttheco-
netic moment calculations. The wave function of
hesive energy of the grain boundary[10, 26, 4, 19,
electrons are expanded in terms of plane-wave ba-
8, 9, 22, 3, 28, 27, 18, 25, 21, 26, 17, 23]. If the
sis set and all plane waves that have kinetic en-
fracture surfacesegregationenergyis largerthanthe
ergy less than 250 eV are included in expanding
grain boundary segregation energy for a solute ele-
the wave functions. For the treatment of electron
ment, this element canreduce the cohesive energyof
exchange and correlation, we use the generalized
the grain boundary; it indicates that this element is
gradientapproximation(GGA)usingPerdew-Burke-
an embrittling element. If the grain boundary seg-
Ernzerhof scheme.[11] For the determination of the
regation energy is larger than the fracture surface self-consistent electron density 4×1×3 Monkhorst-
segregationenergy for a solute element, onthe other
Pack k-point set has been used. The structure opti-
hand, this element is a strengthening element. We
mizations were performeduntil the energy difference
assume that the total amount of segregated solute between successive steps becomes less than 10−3 eV.
atomsdoesnotchangeduringfracture. Thisassump-
Fig. 2 shows simulation box and atom configura-
tionisvalidforelementslikevanadium. Fig.1shows
tion. Two layers are in the periodic cell in [¯112] di-
the schematic of the cohesion enhancement effect on
rection. The grey balls represent iron atoms. Four
a grain boundary by solute atom segregation at the
layers are periodic in [1¯10] direction. The Fe bcc
grainboundary. Theenergydifferencebeforeandaf-
Σ3(111)[1¯10]grainboundaryisindicatedwithablack
ter the grain boundary fracture is affected by solute
arrow. The total number of atoms in the simulation
atom segregation at the grain boundary. If the seg-
boxis88. Theperiodicboundaryconditionsareused
rationlowerthefractureenergydifference,thesolute
in all three direction. Spin is not considered.
atom have embrittlement effect on the grain bound-
ary, otherwise cohesion enhancement effect.
Vanadium interaction with the grain
Computational Methods boundary and the fractured surface
All computation in this paper employed the elec- We obtained the optimized grain boundary struc-
tronic structure calculations based on the first prin- ture of Fe bcc Σ3(111)[1¯10] shown in Fig. 2. The
ciples density-functional theory [7, 20, 24]. The atoms in first neighbor layers near the grain bound-
total-energy calculations and geometry optimiza- ary are relaxed from regular bcc site most signifi-
tions were performed within density-functional the- cantly. The other atoms doesn’t change their posi-
Figure 3: The optimized structure of interstitially
Figure2: Theoptimizedgrainboundarystructureof
Fe BCC Σ3(111)[1¯10], and simulation box and con- segregated vanadium atom on Fe bcc Σ3(111)[1¯10]
grain boundary. The grey balls representiron atoms
figuration. There are no vacuum and periodic condi-
and white vanadium.
tions apply in three directions. Two layers are peri-
odic in [¯112] direction. The grain boundary is indi-
cated by a black arrow. The atoms in first neighbor on the grain boundary as a substitutional form.
There are four candidate iron site around grain
layers near the grainboundary are relaxedfrom reg-
boundary for vanadium substitution. The best sub-
ular bcc site most significantly.
stitution site is the iron atom exactly on the grain
boundary to lower system energy. Fig. 4 show the
substitutionally vanadium-segregated grain bound-
tions much in the optimization process. Our calcu- ary structure of Fe bcc Σ3(111)[1¯10]. The vana-
lated grainboundary formationenergy per unit area
dium atoms are white to distinguish from grey iron
is0.113eV/˚A2 whichistheenergyrequiredthegrain
atoms. The optimized vanadium substituted struc-
boundary to form from the Fe bcc bulk.
ture is very similar to the grain boundary structure
The grain boundaries usually have many hollow
without vanadium.
sites bigger than normalbetween atoms. The hollow
The vanadium substitutional formation energy on
sites are good candidate for micro-alloying element
the grain boundary is -6.08 eV from a isolated vana-
segregation. Inourunitcelltherearetwohollowsites.
dium atom and -0.75 eV from a vanadium atom in
Wecalculatedthevanadiuminterstitialformationen-
bulk. The negative sign means that the vanadium
ergyinonehollowsiteoutoftwo. Avanadiumatom
substitution for iron atom on grain boundary is an
is placed at a few different places in a hollow site
exothermic process. Compared to interstitutional
to find the best vanadium site to lower the system
formation energy, the substitutional formation en-
energy. Fig. 3 show the best interstitially vanadium-
ergyislowerby1.8eVwhichmeansthatsubstitution
segregatedgrain boundary structure. The vanadium
defects occur far more often than interstitial defects
atom is in the plane of front layer and shifted a lit-
in real world. Therefore we only consider the substi-
tle bit in [1¯10] direction. The vanadium push away
tutional segregationat the grain boundary.
a little bit the upper and lower neigher iron atoms
The vanadium segregation energy into the grain
becausethetwoironatomsaretooclosetothevana-
boundaryis the difference ofthe grainboundaryfor-
dium atom.
mation energy from vanadium defect formation en-
The vanadiuminterstitialformationenergyonthe ergy in bulk. In order to calculate the vanadium
grainboundaryis -4.20eVfroma isolatedvanadium segregationenergyintothegrainboundarywecalcu-
atom and 1.13 eV from a vanadium atom in bulk. lated two vanadium point defect formation energies
The isolated vanadium atom lower the system en- in bulk. One is interstitial point defect formation
ergyalotbyformingainterstitialinthegrainbound- energies which are -1.36 eV for tetrahedral intersti-
aryandformingmanybondingwithitsneighboriron tialfromisolatedvanadiumatomand3.97frombulk
atoms. vanadium atom while octahedral interstitial defect
The micro-alloyingelement can also be segregated energiesarehigherby0.43eV.Theotherissubstitu-
Summary and Conclusions
Insummary,westudiedtheeffectsofVanadiumona
bcc iron Σ3(111)[1¯10] grain boundary strength. We
calculated the optimized grain boundary structure
and the best vanadium segregation site on the grain
boundary. We compared the interstitial defect for-
mation energy to the substitutional one in bulk and
thegrainboundary. Thesubstitutionalformationen-
ergyislowerthaninterstitialsegregationenergy. Our
results indicate thatthe substitutional segregationis
more desirable. We also calculated vanadium segre-
gation energies on the fractured surface of the grain
boundary. Based on those segregation energies we
Figure4: Theoptimizedstructureofsubstitutionally
calculatedthe cohesiveenergyofthe grainboundary
segregated vanadium atom on Fe bcc Σ3(111)[1¯10]
andvanadiumsegregationeffectoncohesiveenergies.
grain boundary. The grey balls represent iron atoms
In conclusion, vanadium atom mostly exist as
and white vanadium. substitutional defects ratner than interstitial de-
fects in both bulk and grain boundary. Our first-
principle calculations show consistantly with experi-
tionalpointdefectformationenergywhichis-6.06eV
mentthatvanadiumis aFe grainboundarycohesion
from isolated atom and -0.73 eV from bulk atom.
enhancer and strengthens the Fe bcc Σ3(111)[1¯10]
The substitutional defect formation energies in bulk
grain boundary.
areagainlowerthaninterstitialoneby4.70eV.From
the calculatatedenergies we can conclude that vana-
dium atoms exist mostly as substitutional defects in References
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