Decrease of segregation energy of the impurity at its Table 1 Composition at.% of the Fe–P and Fe–P–Mo Alloys Chemical composition, at.% Figure 14 Change of Esegof phosphorus with its vo
Trang 1bulk and on the interface As seen in Fig 14, the elastic interaction energy of the P atoms with grain boundaries in iron is equal to 0.53 eV=at and decreases significantly at molybdenum alloying to 0.24 eV=at in the alloy Fe–3.1at.% Mo Decrease of segregation energy of the impurity at its
Table 1 Composition (at.%) of the Fe–P and Fe–P–Mo Alloys
Chemical composition, at.%
Figure 14 Change of Esegof phosphorus with its volume concentration in Fe (1) and Fe–3.1 at.% Mo–P alloys (2) Auger electron spectroscopy of free surface segregations at 823K
Trang 2volume concentration growth is caused by chemical pair interaction of the atoms in alloy
Using the example of the Fe–P system, we could determine chemical interaction of elements by applying the approach proposed in Ref [34] Analyzing the solidus and liquidus equilibrium (volume and GB) on the equilibrium phase diagram at three temperatures permits the construction
of a system of three equations that describe this equilibrium
kT qa ln100 Xs
100 Xl
¼ X2
sW0 X2
where k is the Boltzmann constant; Ta is the melting temperature of Fe; qa is melting entropy per atom divided by Boltzmann constant;
W0 and W00 are the mixing energies in solid and liquid states; Xs and
Xl are the impurity concentration in solid and liquid phases at the tem-perature T
Solving these equations for the phase diagram of Fe–P binary sys-tem [35], the sign and value of mixing energy in liquid phase equal 0.425 eV=at were determined The positive value (in accordance with phy-sical sense) means that binding force of P–P and Fe–Fe atoms is higher than for Fe–P atoms:
W ¼ WFeP1
emphasizing the tendency for solid solution tendency for stratification or intercrystalline internal adsorption
D Effect of Solute Interaction in Multicomponent System
on the Grain Boundary Segregation
Guttman has expanded the concept for synergistic co-segregation of alloy-ing elements and harmful impurities at the grain boundaries His theory is very important for analysis of steels and alloys that contain many impuri-ties and alloying elements In accordance with the theory, the interaction between alloying elements and the impurity atoms could be estimated from enthalpy of formation of the intermetallic compounds (NiSb, Mn2Sb, Cr3P, etc.) The alloying elements could influence on the solubility of impurities in the solid solution Only the dissolved fraction of the impurity takes part in the segregation [36] When preferential chemical interaction exists between
M (metal) and I (impurity) atoms with respect to solvent, the energy of
Trang 3segregation becomes functions of the intergranular concentrations of I and M:
DGI¼ DG0
IþbbMI
Cb YbMb
a MI
Ca X
a
DGM¼ DG0
MþbbMI
ab YbI b
a MI
aa X
a
where Cband abare the fractions of sites available in the interface for I and
M atoms, respectivelyðabþ Cb¼ 1Þ; Yb
is the partial coverage in the inter-face; Xa is the concentration in the solid solution a; bMIis the interaction coefficient of M and I atoms in a-solid solution (a) or on the grain boundary (b) For a preferentially attractive M–I interaction, the bMIare positive and the segregation of each element enhances that of the other If the interaction
is repulsive, the bMIare negative and the segregations of both elements will
be reduced For a high attractive M–I interaction in the a-solid solution, the impurity can be partially precipitated in the matrix into a carbide, or inter-metallic compound The interface is then in equilibrium with an a-solution where the amount of dissolved I, XI a, may become considerably smaller than its nominal content
In the ternary solid solutions, the segregation of impurity (I) could be lowered or neglected at several critical concentrations of the alloying element (M) whose value (CMa) depends on surface activity of each compo-nent (ESegI,M) and interaction features of the dissolved atoms (bMI):
I Seg
bMIðexpðEM
The critical concentration of alloying element is accessible for segregation of impurity and alloying element EISeg;M > 0 and repulsion of different atoms
bMI > 0; or without segregation of alloying element EM
Seg< 0 and with attraction of different atoms bMI< 0
In this case, the dependence of ESegI,Mon the dissolved element concentra-tion is not taken into account Indeed, for systems with limited solubility, the alteration of value and sign of segregation energy is possible at a definite con-tent of alloying element The phase equilibrium diagram analysis allows the determination of mutual influence of components on their surface activity The equilibrium distribution of solute elements between solid and liquid phases in iron-base ternary system (distribution interaction coefficient
K0) is known to be an important factor in relation to microsegregation dur-ing the solidification of steels As it was shown above, these analogies are useful for the prediction of GBS and for impurity segregation energy
Trang 4determination in the given solvent The K0of some elements, especially in multicomponent systems, is considered to be different from those in binary systems because of the possible existence of solute interactions, but the mechanisms are so complicated that detailed information has not yet been obtained Therefore, it would be very useful if the effect of an addition of
an alloying element on the distribution could be determined by the use of
a simple parameter
Equilibrium distribution coefficient K0 1
of various elements in Fe–C base ternary system is calculated from equilibrium distribution coefficient in iron-base binary systems [40–43] In Fig 15, the calculated results are com-pared with the measured values by various investigators The changes of the
K0 1
of P and S with various alloying elements are shown inFig 16(a, b)in Fe–P and Fe–S base ternary system, respectively
These data could be applied for calculation of phosphorus segregation energy change under the alloying element influence in Fe–Me–0.1at.% P alloys (Fig 17) or for calculation of the segregation energy change of alloying elements with concentration of carbon in Fe–0.1Me–C alloys (Fig 18).For the growth of carbon volume content, the segregation energy
of C and P decreases which means lowering of the segregation stimulus for these elements
Figure 15 Change of the equilibrium distribution coefficient of some elements with carbon concentration in Fe–C-based ternary systems (From Ref 37.)
Trang 5tion are developed, but rich segregations dissolve Distinguishing diffusion mobility and mutual influence of elements on their diffusion coefficients determines much of their segregation ability Amplification or suppression
of adsorption could be due to a kinetic factor This peculiarity determines the fundamental factor of distinguishing adsorption from gas phase to free surface when comparing it to intercrystalline internal adsorption: GBS is controlled by diffusion during heat treatment of steels and alloys
Many GBS features in multicomponent systems cannot be predicted adequately using the equilibrium segregation thermodynamic accounting basis Particularly, the thermodynamic concept of the cooperative (synergis-Figure 16 (Continued)
Trang 6where Xb(t) is the interfacial coverage of element, at time t; Xb(0) — is its initial value and Xb its equilibrium value as defined by Eq (7); Xi a — is its volume concentration; Diis the bulk diffusivity of i and d is the interface thickness
Assuming Xb=Xi a¼ const, using Laplace transformation for (22), one can obtain the approximate expression
XbðtÞ Xbð0Þ
Xb Xbð0Þ ¼
2Xai Xbd
ffiffiffiffiffiffiffiffiffiffi FDti p
r
ð23Þ where F¼ 4 for grain boundaries and F ¼ 1 for free surface
The kinetics of segregation dissolution could be described by these equations (22) and (23) But, in this case, the variables Xb(0) and Xb
exchange places The influence of Mo, Cr, and Ni additions on kinetics of
P segregation has been studied in six Fe–Me–P alloys, whose base composi-tions are listed in Table 1 These materials were austenitized for 1 hr at 1323K and quenched in water The tempering of foils at 773K was carried out in a work chamber of an electron spectrometer ESCALAB MK2 (VG) The kinetics of P segregation studied for Fe–Me–P alloys(Figs 20–22)show that equilibrium is reached within several hours Based on the starting posi-tion of adsorpposi-tion isotherms, the phosphorus diffusion coefficients in these alloys were calculated using Eq (22) The data are presented in Table 2
Molybdenum reduces significantly P surface activity and decelerates its diffusion Nickel is not a surface-active element in carbonless alloys, Fe– P–Ni It increases sharply P thermodynamic activity and equilibrium GB concentration, and accelerates its diffusion Chromium segregates poorly Figure 19 Kinetics of P GBS in steel 0.3C–1.6Mn–0.8Cr–008P (1) with adds of 0.047Ti (2) or (0.07Ti and 0.026V) (3), quenched from 1273K and tempered at 923K
Trang 7time at increasing temperature With temperature increase, the solubility of impurity in solid solution increases, and its GB concentration reduces It fol-lows that the probability to form the segregation with high impurity content reduces, and time for such segregation increases extensively The upper branch of isodose curves corresponds to dissolution of rich segregations and access to new equilibrium with lower impurity concentration The
Figure 23 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mo steel (seeTable 3).Auger electron spectroscopy of free surface segregations
Figure 24 The isodose C-curves of multicomponent interface segregation in 0.2C– Cr–Mn–Ni–Si steel (seeTable 3)under its tempering Auger electron spectroscopy of free surface segregations
Trang 8adsorption patterns for engineering steels have common as well as indivi-dual features As a rule, carbon segregates at temperatures lower than 523K, nitrogen—in 523–623K range, phosphorus—in 523–823K range, sul-fur segregates at temperatures higher than 723K
The substitual and interstitial element concurrence promotes blocking
of adsorption centers by mobile impurities and impedes P segregation at
Figure 25 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mn–Nb steel (see Table 3) under its tempering Auger electron spectroscopy of free surface segregations
Figure 26 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mn–V steel (see Table 3) under its tempering Auger electron spectroscopy of free surface segregations
Trang 9the thermokinetic diagrams for ternary Fe–Me–P alloys based on Eqs (23) and (6), the mutual influence of elements on their binding energy to GB was determined [36]
EPseg¼ 20:6 þ 183CP
a 4:8CAl
a 7:2CMo
a 3:4CNi
a 7141CB
a
þ 4:9CCr
a 444CS
a 183EMo
seg 87EN
ESseg¼ 6:9 151CS
a 1:5CAl
a þ 14:5CP
a 39ESn
ENseg¼ 16 2:6CAl
a þ 3CMo
a þ 4:2CCr
a 2625CTi
a þ 175EMo
seg ð26Þ
Figure 28 Influence of alloying on the kinetics isotherms of P free surface segregation at 723K The following steels were investigated (see Table 3): 1, 3C–Cr– Mn–Nb; 2, 3C–Cr–Mn–Si–Ti; 3, 2C–Cr–Mn–Ni–Si; 4, 3C–Cr–Mo; 5, 3C–Cr– Mn–V
Trang 10Eseg¼ 7:9 1:4Ca þ 5Ca þ 676Caþ 1:2Ca 130Eseg þ 116Eseg
ð27Þ
EMoseg ¼ 0:7 þ 32EN
seg 28EP
ETiseg¼ 17 þ 3CC
a EP
EAlseg¼ 1:4CAl
ESnseg¼ 21; ENi
seg¼ 14; EB
seg¼ 54; ECu
seg¼ 20 kJ/mol where EsegI is segregation energy of the I element, Cajis bulk concentration of
jimpurity
F Stability of the Segregation
The equilibrium GBS dissolves as temperature increases Analysis of the kinetic development of the equilibrium segregation level of P shown in
Fig 29gives the T–t plot of segregation directly Obviously that segregation level close to the maximum exists only within a specific temperature range This range is characterized by a maximum temperature stability Tmax, over which the intensive dissolution of the segregates is observed This tempera-ture can be calculated by computer analysis of Eq (7) at dCbmax=dT ¼ 0 The temperature Tmax depends on Eseg and temperature dependencies of solubility limits, which can be determined from analysis of phase equili-brium diagrams [43]
Using these dependencies as a generalizing criterion, it is possible to simplify the analysis of data on element segregation kinetics in iron alloys The interrelationship of maximum temperature of stability (Tmax) of rich equilibrium segregations and segregation energies of different elements is presented inFig 30
The common features of kinetics show the following groups:
1 enriching grain boundaries at low- and medium-tempering temperatures—B, C, N, and Cu;
2 co-segregating with P at high tempering—P, Sn, Ti, and Mo;
3 segregating at high temperatures—S and Al
Phosphorus in Fe alloys has abnormally weak dependence of Tmax
on Eseg in reversible temper embrittlement temperature range In other
Trang 11Figure 31 presents the thermokinetic diagram of element segregation
in 0.35C–1.5Mn–0.1P–0.6Al steel The chemical composition of free surface segregations was determined by AES for a set of isothermal conditions in the spectrometer ESCALAB MK2 (VG) The temperature–time interval
of preferential segregation of chemical elements is the result of different dif-fusion mobility and binding energy of elements with GB The temperature interval of P preferential segregation is caused by concurrence of this impur-ity with mobile interstitial elements C and N This process determines temperature and exposition necessary for RTE development Direct investi-gation of grain boundary composition by AES confirms the conclusion about the prevailing role of concurrent segregation in RTE The composi-tion of several grain boundaries on brittle intercrystalline fracture of 0.35C–Mn–Al steel after heat treatment: quenching from 1223K, tempering
at 923K for 1 hr with rapid (a) and slow (b) cooling is presented inFig 32
[47] These data are in good correspondence with those inFig 31 Acceler-ated cooling of steel, does not provide enough time for the development of segregations with high P content, and GB are enriched by C During slow cooling, phosphorus has enough time to enrich the grain boundaries In this case, the carbon concentration on GB is sufficiently lower than at rapid cooling of steel Carbon segregations are unstable at temperatures higher than 500–673K, and they are dissolved At slow cooling, P segregates to grain boundaries, decreasing the GB redundant energy This circumstance lessens the thermodynamic stimulus for carbon segregation as the tempera-ture decreases Carbon and phosphorus in steels are responsible for RTE development They have high surface activity and diffusion mobility that Figure 31 Thermo-kinetics diagrams of multicomponent segregation on free surface in steel 0.35C–1.58Mn–0.1P–0.6Al
Trang 12enrichment of GB by carbon at rapid cooling [48] Undoubtedly, carbide transformation, internal stresses, substructure transformations are very important for RTE One should take into account such circumstances where kinetics of C and P segregation are dependent significantly on steel alloying
IV DYNAMIC SIMULATION OF GRAIN BOUNDARY
SEGREGATION
A Interface Adsorption During Tempering of Steel
1 Decomposition of Martensite
The common laws of multicomponent GBS and analysis of experimental diagrams on elements segregation kinetics in iron alloys are used to develop the computer models of these processes The exact solution of McLean’s diffusion Eq (21) accounting for temperature dependant of diffusion and element solubility is a complex problem In low-alloyed steels, the concen-tration of surface-active impurities (S, P, and N) is rather small, and based
on this reason, it is possible to analyze the diffusion of each element sepa-rately The model takes into account mutual influence of bulk and surface concentration of elements with respect to segregation energies
Carbon in solid solution has maximum influence on phosphorus GBS kinetics Concentration of C in martensite changes significantly during quenched steel tempering and mainly depends on alloying element content Based on this reason, one should take into account the solid solution com-position altering segregation processes modeling during tempering
Investigations of martensite tetragonality at alloyed steel tempering [6,7] are the basis for calculations of mutual influence of alloying elements
on martensite decomposition kinetics and carbon content in solid solution The carbon content change in solid solution during tempering of engineer-ing steels is well described by equation
DXC
a
XC
að0Þ¼ 1 exp KDotexp
Q RT
ð31Þ
where
DXC
a ¼ XC
að0Þ XC
XaC(0) and XaC(t) are the carbon content in quenched steel and after a time t;
Dois the carbon diffusion coefficient; Q is the activation energy associated with the interstitial diffusion of carbon atoms; K is the constant associated