Some Aspects of lmpurity Grain Boundary Segregation in Low Alloy Cr-Mo-V Steels
Segregacije nečistoč v nizko legiranih Cr-Mo-V jeklih
J. Janovec1, Institute of Materials Research, Košice, Slovakia V. Magula, VVelding Research Institute, Bratislava, Slovakia P. Sevc, Institute of Materials Research, Košice, Slovakia
Prejem rokopisa - received: 1996-10-04; sprejem za objavo - accepted for publication: 1996-11-01
The present work is focused on theories of grain boundary segregation. An overvievv of different approaches to solution of surface enrichment phenomenon is given in the first part. The second part is devoted to the verification of introduced theories by means of
experimental results.
Key words: low alloy steels. phosphorus, grain boundary segregation, non-equilibrium segregation, kinetics
V članku so predstavljene teorije različnih avtorjev o segregaciji po mejah zrn. V prvem delu je podan pregled različnih razlag obogatitve prostih površin. V drugem delu smo obravnavane teorije verificirali z eksperimentalnimi rezultati.
Ključne besede: nizko legirana jekla, segregacija po mejah zrn, neravnotežne segregacije, kinetika segregacije po mejah zrn
1 Introduction
Enrichment of solute or solvent atoms from bulk at the grain boundaries is referred to as grain boundary segregation. Segregation is mostly attributed to the grain boundary weakening due to lowering the interface cohe-sion. As a consequence, an intergranular embrittlement occurs. Because segregation phenomenon decisively in-fluences properties of commertial materials, the grain boundary segregation has been intensively studied in last decades1"8.
The present vvork deals vvith segregation theories9-15 and their experimental verification. By use of multicom-ponential alloys in the verification, the introduction of some simplifications is necessary because the segregation theories vvere mostly derived for binary or ternary solid solutions. For example, lovv alloy steels containing Fe, Cr, Mo, V, Mn, Si, C and P vvere considered to be binary Fe-P or ternary Fe-Mo-P systems13"15.
2 Segregation theories
2.1 Non-interactive equilibrium segregation
The theory of equilibrium segregation for dilute bi-nary solid solution Fe-I (Fe - solvent, I - solute impurity) vvas derived by McLean to be the grain boundary analo-gous of Langmuir adsorption at free surfaces1,16. The Langmuir-McLean isotherm yields:
CFC<I C?
l-CfC4 l-cj
, Ag, exP(-w)
(D
Dr.Sc. Jožef JANOVEC
Institute I)f Materials Research. Slovak Academy of Sciences VVatsonova 47. (14353 Košice. Slovakia
vvhere CiEeq is the equilibrium grain boundary concentration of impurity, CiB is the bulk concentration of im-purity, Agi is the free energy of impurity segregation, and k is the Boltzmann constant.
The equilibrium segregation kinetics can be calculated as1:
Cf(t)-C?
£Eeq _ £E0
= 1 - exp
4D,t
erfe
Vry~
af dE
. (2)
_(af)2 (dE)2
where CiE(t) is the grain boundary concentration of im-purity for the time t, CiE0 = CiE(t=0) is the initial concentration of impurity, dE is the grain boundary thick-ness, Di is the diffusion coefficient of impurity, and aiE = CiEecVCiE0 is the enrichment factor.
2.2 Interactive equilibrium segregation (co-segregation)
Guttmann417 modified the Langmuir-McLean isotherm to be suitable for the calculation of interaetive equilibrium segregation in ternary Fe-M-I systems. He assumed for this system an attractive interaetion betvveen the impurity I and the solute metalic element M. If the M-I competition for convenient sites at the grain bound-ary exists, impurity grain boundary concentration can be calculated according to:
Cf=i	Cf	Agj
-r5-T~ ~-i-T exp (_ 7"^r) . i=I. M (3)
1-Cf-Cgj kT; '
The interaetion leading to the M-I co-segregation vvas defined in terms of segregation free energy, Agi, i = I, M:
Ag, = Ag? - 2ccFeICp« + a'MI (Cj? - C&) , (4) AgM = AgM - 2aPeI (C*'" - Cm) + a' MI Cf* , (5)
vvhere Agi0 and AgM0 are the free energies of segregation for I and M in their respeetive binary systems vvith
Fe, vvhile a'mi and aFei are the relative chemical interac-tion energies between M-I and Fe-I, respectively. For non-competitive segregation the follovving expression was obtained17,18
CEcq CB	A<?
-=-L—r exp (- T-=f) , i=I, M (6)
1 _Cfeq 1 — C® kT
where Agi has the same meaning as in the previous čase.
Kinetics of interactive segregation can be described by means of the regular solution model proposed by Seah18. In the model it is assumed a local equilibrium betvveen concentrations of impurity at the grain bound-ary, CiE(t), and in adjacent bulk layers, CiB(t). Then
C? (t)


1 - Cf (t)
= Cf(t) exp (-^r)
(7)
	/
Ef	exp
V	v
■ Ef Eh - Ef
kT„ kT
where Eb is the vacancy-impurity atom binding energy and Ef is the energy of vacancy formation. The kinetic equation of non-equilibrium segregation has a form27:
VdJ^
■<r
cr (o ■
£<Nmax _
= 1- exp
4D,t
(a»y-(dy
erfc
a, dN
(9)
where CiN(t) is the grain boundary concentration of im-purity for time t, CiN0 = CiN(t=0) is the initial concentration of impurity, Dc is the diffusion coefficient of com-plexes, dN is the thickness of grain boundary, and aiN = CiNmax/CiN0 is the enrichment factor. The equation (9) is used for times of impurity diffusion shorter than the critical time. The critical time tc is given by27
The combination of equations (4) and (7) is fre-quently used in kinetic calculations, as firstly by Tyson19.
In recently proposed theories, the grain boundary segregation is assumed to be a bulk-diffusion-controlled process. There are also kinetic models favouring other controlling mechanisms, for instance the fast diffusion path20'21 or the grain boundary diffusion22,23. Du Plessis and Van Wyk24, for instance, proposed a model consider-ing the chemical potential gradient as a driving force of the grain boundary segregation.
2.3 Non-equilibrium segregation
Non-equilibrium segregation theory was established by Aust et al.25 and Anthony26. They supposed that va-cancies and impurities form vacancy-impurity complexes with a binding energy higher than the thermal energy. The controlling mechanism of non-equilibrium segregation is the vacancy concentration gradient. The higher temperature the higher is the equilibrium concentration of vacancies. The temperature decrease during rapid cooling leads to a loss of vacancies along grain boundaries due to their annihilation. This process is in accord-ance vvith the tendency to achieve a lower equilibrium concentration of vacancies at lovver temperature. The va-cancy concentration decrease near the grain boundaries results in the dissociation of vacancy-impurity com-plexes in this region. In the interior of grains, where less vacancy sinks are present, the concentrations of vacancies and vacancy-impurity complexes decrease lesser. Consequently, the diffusion of the complexes from interior to the grain boundaries occurs due to the concentration gradient betvveen these tvvo areas. The process leads to an excessive impurity concentration near the grain boundaries and causes the non-equilibrium segregation.
The model of non-equilibrium segregation vvas proposed by Faulkner6 and extended by Xu Tingdong27. When a sample is held at the solution-treatment temperature To and then quickly cooled to the lovver temperature T, the maximum of the impurity grain boundary concentration CiNmax induced during holding at the temperature T is calculated as6-27:
t,=
f In (D./D,) 45 (Dc - D,)
(10)
vvhere y is the average austenite grain size and a is the critical time constant28. For times of impurity diffusion longer than the critical time the process of desegrega-tion occurs.
The concentration level of impurity at grain boundaries during the desegregation can be calculated according
to29-30:
Cf (t) = C? + [C,N (tc) - Cf] ■
HN/9 -dN/2 ■[erf (- ,/2) - erf (-; t>tc (11)
[4D,(t-tc)]	[4D,(t-tc)]
The process in vvhich the desegregation is dominant can only occur vvhen CiN(tc) > CiEeci for a given temperature. It means the desegregation is limited by reaching the equilibrium grain boundary concentration. The mi-gration of grain boundaries during austenitizing and re-crystallization can also contribute to the non-equilibrium segregation in term of a svveep effect. The nature of this phenomenon resides in embedding and subsequent drag-ging of solute species by moving grain boundary. As a consequence the grain boundary enrichment of solute species occurs31'32.
2.4 Segregation under stress
Stress and thermal energy does not affect the equilib-rium grain boundary concentration of impurities during the tempering (aging) significantly, but it influences segregation kinetics. Grain boundary segregation of impurities vvith higher diffusivity can be enhanced effectively by applied stress. Atoms of some impurities (e.g. carbon, nitrogen, boron) fastly occupy the convenient sites on grain boundaries and they prevent subsequently due to competition effect the segregation of other elements33"35.
Shinoda and Nakamura36 studied the grain boundary segregation of phosphorus in lovv carbon steel during long-term tempering and subsequent aging under stress at the same temperature. In the first step of aging under
tension (compression) phosphorus grain boundary concentration increases (decreases), then its value approxi-mate to the initial one36. Changes in impurity concentration at the grain boundaries oriented normal to the applied stress ACis can be calculated as follovvs37:
4<|)CfDIpCTAt
"f RT
(12)
where 0 is a numerical factor of the order of unity, Ciso is the initial grain boundary concentration of impurity, p is the specific volume of alloy, c is the stress related to the grain boundary, and At is the aging time under stress.
3 Verification of segregation theories
To verify the above described theories the phosphorus grain boundary segregation in five low alloy steels was investigated, Table 1. Schedules of heat treatment and phases identified in individual investigated steels termed 1, 2, 3, 4, and 5 are given in Table 2. Grain boundary concentrations of relevant elements were calculated after Daviš et al.38 from Auger spectra. Peaks of Pl20eV, Sl52eV, M0l86eV, C272eV, N379eV, V473ev, Cr529eV and Fe703eV were used in calculation. The peak of oxygen was not considered because of additional adsorption of this element on freshly fractured surface. Parameters, at which Auger spectra were achieved are given in Ref.13,15.
Table 1: Chemical composition of investigated steels in wt.%
Steel C
Mn Si Cr Mo
Ni
1	0.110 0.004	0.525	0.385	2.685	0.694	0.355	-	0.010
2	0.100 0.014	0.700 0.270	2.620	0.690	0.330	-	0.007
3	0.110 0.027	0.665	0.340	2.700	0.733	0.357	-	0.010
4	0.060 0.013	0.650	0.290	2.660	0.700	0.310	-	0.009
5	0.160 0.014	0.460	0.290	2.700	0.640	0.300	0.060 0.015
Table	2: Schedules of heat treatment and phases	identified in
investigated steels
Steel	Heat treatment	Phases identified
1	1250°C/0.75h, water quenching. 680°C/20 h, water cooling, Ferrite+M7C3+MC aging at 500°C for 0.33h,lh,5h,150h	
2		
3		
4	1250°C/0.16h, water quenching, 680°C/20h, water cooling, aging 580°C for 5 min and 150h	Ferite+M7C3+MC
5	welding cycle:Tmax=1300°C At«/5=30s, 580°C/100h	Ferrite+MjC+IvbCi
	welding cycle:Tmas=l 300°C,Atn/5=30s, 600°C/120s under stress(strain rate 300mm.h"1)	Ferrite+M3C
Phosphorus grain boundary concentrations measured for steels 1, 2, 3 aged at 500°C for different times shovved the best fit with McLeans non-interactive kinetic equation (2), (Figure 1). The segregation can be characterized as slow, because after 150 h aging the equilibrium vvas not reached for any of the steels. A completely different situation vvas observed for steel 4 aged at 580°C
50 45 40 35 30 25 20 15 10 5 0 50 45 40 35 30 25 20 15 10 5 0 50 45 40 35 30 25 20 15 10 5 0
iT.......
a
Steel 1
♦ T
0,001
0,01
0,1
10 m,-1
100
1000 ™r
b
Steel 2
0,001
0,01
0,1
10
100
1000
c
Steel 3
i-
0,001
0,01
0,1 1 time [h]
10
100
1000
Figure 1: McLean's non-interactive equilibrium kinetic equation fitted to values of phosphorus grain boundarv concentration for steels: 1 (a), 2 (b), and 3 (c), aged at 500°C (after15)
-th
-t/-l
■ calculated after (4) and (7) experiment
I ' 1 ' I 1 I 1 I 1 I 1 I // 1 1 I 1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 500 550 600
time [ks]
Figure 2: Interactive kinetic equations (4) and (7) fitted to values of phosphorus grain boundary concentration for steel 4 aged at 580°C (after13)
(Figure 2). Here, the measured values of phosphorus grain boundary concentrations correlate vvith the curve, calculated according to equations (4) and (7). The equi-Iibrium vvas reached after 5 min, and that indicates to very rapid segregation process. The obtained results shovved that both rate of equilibrium segregation and also participations of interactions in this process are temperature dependent. McLean's non-interactive kinetic theory seems to be available for the description of segregation kinetics at lower aging temperatures (slovver segregation rates) and interactive equations are more con-venient for higher ones (accelerated segregation rates).
In Figure 3 Auger spectra for the steel 5 after tem-pering (a) and short-term aging under stress (b) are shown. For loaded state the peaks of C, S, N, and Cr vvere evidently higher than for tempered one (Table 3). Differences betvveen carbon, sulphur and phosphorus grain boundary concentrations for the loaded state can be explained by different diffusivity of these elements in iron at 600°C20'39'40. Atoms of carbon and sulphur dif-fuse faster than phosphorus atoms and occupy earlier convenient sites at grain boundaries. Site competition betvveen P-C and P-S5'41 make impossible an additional phosphorus enrichment at grain boundaries. With pro-longing the aging an inerease in phosphorus and a de-crease in carbon grain boundary concentrations occur because of carbide precipitation5'42,43.
Table 3: Experimentally measured grain boundary concentrations of C, S. P, N, Cr. Mo, and V for steel 5 in at.%
C	S P	N	Cr	Mo V
tempered 9.5±1.0	- 4.411.6	-	4.9±0.5	1,4±0.5 2.7±0.4
stressed 26.9	17.7 5.4	9.3	9.6	2.1 2.5
Higher grain boundary concentrations of chromium and nitrogen in the first period of aging under stress are probably caused by Cr-N interactive segregation. Misra and Balasubramanian34'35 supposed a Cr-N co-segrega-tion (stressing up to 5 min at 580°C) due to strong chemical interaetion betvveen these elements. After reaching the maximum coverage (depending on aging temperature), a continuous decrease in Cr and N grain boundary concentrations occurs.
The shape of carbon peaks (Figure 3) indicates the occurence of carbide particles on the grain boundaries44. Then, also peaks of alloying elements, preferentially Cr, must originate partially from these particles45"47. Re-flexes originating from intergranular carbide particles mostly influence the achieved spectra and they can not be neglected in interpretation of grain boundary segregation in multicomponential alloys.
4 Concludig remarks
An overvievv of the theones of grain boundary segregation is given in the present vvork. The verification of
E[eV]
Figure 3: Characteristic Auger spectra taken on intergranular facets of steel 5: a) tempered at 580°C for 100 h, b) aged under stress for 120 s at 600°C
the theories for multicomponential Cr-Mo-V lovv alloy steels leads to the follovving findings:
1.	The McLean's non-interactive equation is the most convenient for the description of equilibrium segregation kinetics at lovver temperatures (500°C), vvhile the interactive equations are more suited for the description of equilibrium segregation kinetics at higher temperatures (580°C)
2.	In comparision vvith unstressed aging, the higher rates of C, S, N and Cr grain boundary segregation in the first period of the aging under stress (600°C) vvere observed
3.	In the investigated multicomponential steels, an influence of carbide particles on achieved Auger spectra can not be neglected.
Ackno\vledgment - This study vvas supported by the Grant Agency of Slovak Republic under grant No. 2/2001/96.
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