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Comment on “on the quasi-chemical model of interface decohesion”
Scripta
METALLURGICA
P e r g a m o n Press Ltd. All r i g h t s r e s e r v e d
Vol. 15, pp. 4 5 7 - 4 6 0 , 1981 P r i n t e d in the U.S.A.
COMMENT ON "ON THE QUASI-CHEMICAL MODEL OF INTERFACE DECOHESION"
M.P. Seah National Physical Laboratory Teddington, Middlesex, UK. (Received
February
5, 1981)
Introduction Some points in the paper by Hartweck (I) deserve further comment in order that the earlier publication "Adsorption-induced interface decohesion" (2) should not be misconstrued. These points, only concern the aspects relating to decohesion and not to Hartweck's adhesion results. The earlier publication (2) presents an analysis of the effects of different grain boundary segregants on their power to modify grain boundary cohesion. The analysis is presented there by two separate routes which, within the regular solution approximation, lead to the same relation for the change in fracture energy of the grain boundary, arising from segregation. The two routes used are the thermodynamic work of fracture approach, reviewed recently by Hirth and Rice (3), and the pair-bonding or quasi-chemical approach. For moderate levels of segregation the equations obtained are shown in (I) and (2) and may be summarised by:
zg[H~ub"
FE(Xb)-FE(o) = - Z- ~
-
z1
.sub*_ H A ~
(I)
where FE(0) is the fracture energy of a clean grain boundary in matrix A, FE(X b) is that for a grain boundary with a fractional monolayer, Xb, of segregant B, Zg is the ~-ordination across the boundary (not as given by Hartweck (I)), Z is the total co-ordination, H~ ~ is the sublimation enthalpy of pure A per unit area, ~ is the regular solution parameter and a B2 the area of a B atom in the fracture surface. Comment
Numerical analysis (2) of the terms in the brackets in Eq (I) shows that the regular solution parameter, m, has an effect typically of I J m -2 in the fracture energy change for many segregants in iron over a range of 25 J m -2. (The average effect for the 16 segregants for which thermodynamic heat of mixing data (h) is available, is in fact, 1.27 J m-2). Thus, since, the regular solution parameter involves such a small term, a general remedial/embrittlement plot is presented in the earlier publication (2) to classify all segregants in all matrices in the ideal solution approximation of Eq (I) with ~ omitted. This is important to show how embrittlement experience in ferrous systems can be extended to other materials. In the full regular solution model, however, the remedial/emhrittlement plots for all the segregants have to be presented for each matrix material separately, as exampled, for iron, in Fig h of ref (2). Inspection of Fig 3 of ref (2), in the ideal solution approximation, and Fig 4 of ref (2), in the regular solution approximation, shows that the ideal solution is, in fact, an excellent guide and that errors only occur in the relative positions of close points. Thus, as must be evident, the model in the earlier publication (2) is, in fact, presented in the regular solution approximation and cannot be criticised because "the assumption of an ideal solution is too restrictive" (I). The second main comment in the paper by Nartweck (I) purports to show that the quasi-chemical model leads to P and S strengthening grain boundaries in iron, at low segregation levels, in contradiction with observations and hence disproving the appropriateness of the model. Two approaches are used by him to show the strengthening. In the first he uses Eq (I), or actually one of its
457 0036-9748/81/040457-04502.00/0 C o p y r i g h t (c) 1981 P e r g a m o n Press
Ltd.
4S8
COMMENT ON INTERFACE DECOHESION
Vol.
15,
No.
4
derivatives, with thermodynamic data from Guttmann (5) to estimate the regular solution term. If this data is used to calculate the terms in the brackets of Eq (I) these in fact become (5.66-13.33+ 3.87) for P in iron and (5.2h-13.33+3.64) J m -2 for S in iron, both of which are negative and therefore show a severe embrittlement propensity. The numbers given above can be improved since the use of a compound will overestimate the value of the interaction parameter (6). The extent of this overestimate seems typically to be around a factor of two as was shown by Guttmann's (7) reassessment of the interaction parameters from metallurgical phase diagram data when compared with the earlier work (5) cited by Hartweck (I). This fine tuning gives final figures for the term in brackets in Eq (I) as -5.7h and -6.27 J m -2 for P and S in iron respectively, in full agreement with the text of the earlier publication (2) and experimental observations. The reason why Hartweck (I) fails to obtain these results appears to come from the use of an equation similar to Eq (I) but which is, in fact, derived early in the previous publication (2) for segregant atoms equal in size to those of the matrix (Equations (I) or (2) of Hartweck's paper (I)). The atom size is very important and cannot be ignored since the work of fracture concerns the product of bond energy and the number of bonds per unit area. Thus, Hartweck's criticism of the model appears to be founded on the use of the wrong equation and is therefore itself wrong. In the second attempt at demonstrating that the pair-bonding model leads to P and S strengthening grain boundaries the grain boundary is viewed as composed of sites V, which behave like vacancies, and other sites, akin to normal lattice sites, to make up the grain boundary monolayer. This model leads to improved cohesion for all segregants since it puts all of the excess grain boundary energy into the V sites and in the initial stages of segregation bonds across the boundary are formed but none are broken. In the previous publication (2) the sites are all assumed to be fairly equal and P and S then directly give embrittlement as discussed both in that publication and above. It is therefore important to see which of these two models fits the experimental observations best. With Hartweck's (I) model segregation will occur to the V sites with a high negative free energy and to the other sites with a low energy. An estimate of the proportion of the V sites, from the known ratio of grain boundary and surface free energies of 0.35 in iron (8) would be around 17%. It is
1.01
o
'
'
o
'
o
•
•
'
o
o
i
is
%P
.o
g
0.5
o.o,i. °. io,
i
,o.o~~,~o Annealing tempm'atuce(~)
Fig I: Equilibrium grain boundary segregation in the system Fe-P for different Fe-P (wt%) alloys as a function of temperature, after K~pper et al (9).
Vol.
15,
No.
4
COMMENT ON INTERFACE DECOHESION
459
possible to test for the presence of the V sites from measurements of grain boundary segregation where a plateau should be found around the first 10-25% of a monolayer. Excellent measurements for P in iron have recently been reported by K~pper et al (9) and these are reproduced in Fig I. An average of the quantification calibrations for P segregation in iron (10, 11, 12) shows that the saturation value is nearly one monolayer. No plateau is visible over the range 2.5% to 100% of a monolayer and the experimental results show smooth monotonic reductions as the temperature increases over the whole segregation range. Estimates of the free energies of segregation, using the Langmuir-McLean adsorption theory, to the extreme results at high and low levels of segregation show free energy values which diverge by less than 10%. Thus the V site model does not appear to describe the segregation of P in iron. Results at low segregation levels are not available for S in iron but measurements for S in copper (13) and 0 in molybdenum (14) show constant free energies of segregation over a very wide range of segregation levels. Thus the experimental evidence favours a model for the grain boundaries in which the segregation sites all have very close free energies of segregation and not as inherent in the V-site model. The experimental evidence of segregation therefore supports the model in the earlier publication (2) and not as proposed by Hartweck (I). Supportive evidence for the correct predictive power of the original model (2) comes from the recent work of Dumoulin et al (15). In their studies of the effect of P in Mo bearing steels they show that, for a constant level of P segregation, subsequent segregation of Mo lowers the degree of embrittlement. From the regular solution remedial/embrittlement plot of Fig 4 in the earlier publication (2) it is seen that Mo atoms should be about 0.6 times as remedial as the P atoms are detrimental, per unit area of grain boundary. This prediction and Dumoulin et al's results (15) are shown in Fig 2. The segregation values have been changed from Dumoulin et al's publication since they express concentrations per two monolayers at the grain boundary and in this work segregations are expressed per monolayer, also their quantification for P in iron appears to give about twice that used by others (10). It is seen that the predictions and experiments fit exceedingly well and far better than the predictions of any alternative current theory.
300
P S e g r e g a t i o n , Xp = 35 -40°1.
20~ o
u
10(
01 0
•. 0.2
.
.
.
.
.
I 0.4
Monolayers Mo segregated
Fig 2: The remedial effect of Mo atoms segregated to a grain boundary in steel with 35-40% of a monolayer of P, deduced from the data of Dumoulin et al (15), after Seah (16). The points show the experimental results (15) and the line the theoretical prediction.
460
COMMENT
ON I N T E R F A C E
DECOHESION
Vol.
15, No.
4
Conclusions I)
The previous publication (2) is not limited to the ideal solution model but is presented in the regular solution approximation.
2)
Hartweck's (I) first prediction that P and S improve grain boundary cohesion arises through the use of the wrong equation.
3)
Hartweck's (I) second prediction of improved grain boundary cohesion arises through the use of a V-site model not supported by observations.
h)
The predictions of the previous model (2) are therefore still in agreement with experiment and, in fact, accurately predict the more complex behaviour observed in co-segregating Mo and P in steel. Acknowledgements
The author would like to thank Drs K[~pper, Erhart and Grabke for the material prior to publication involving Fig I. References I. 2. 3. h.
W.G. Hartweck, Scripta Met. previous paper this issue. M.P. Seah, Acta Met. 28, 955 (1980). J.P. Hirth and J.R. Rice, Met. Trans. 11A, 1501 (1980). O. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry, 5th Edn. Pergamon, Oxford
5. 6. 7. 8.
M. Guttmann, Surface Sci. 53, 213 (1975). A.H. Cottrell, An Introduction to Metallurgy, Arnold, London (1967). M. Guttmann, Met. Sci. 10, 337 (1976). E.D. Hondros, In Interfaces, Proc. Conf. Melbourne (~d. R.C. Gifkins) pp 77-100 Butterworths, London (1969). J. K[~pper, H. Erhart and H.J. Grabke, Corros. Sci. to be published. M.P. Seah, J. Vac. Sci. Technol. 17, 16 (1980). L. Marchut and C.J. McMahon, Applications of ~lectron and Position Spectroscopies in Materials Science and Engineering, Ed. O. Buck, Academic Press, to be published. B.C. Edwards, H.E. Bishop, J.C. Riviere and B.L. Eyre, Acta Met. 24, 957 (1976). S.P. Clough and D.F. Stein, Scripta Met. 9, 1163 (1975). A. Kumar and B.L. Eyre, Proc. R. Soc. Lond. A 370, ~31 (1980). Ph. Dumoulin, M. Guttmann, M. Foucoult, M. Palmier, M. Wayman and M. Biscondi, Met. Sci. 14, I (1980). M.P. Scab, Proceedings of Gef~ge der Metalle, November 1980, Bad - Nauheim, Deuts. Ges. f. Metall., to be published.
(1979).
9. 10. 11. 12. 13. lb. 15. 16.
METALLURGICA
P e r g a m o n Press Ltd. All r i g h t s r e s e r v e d
Vol. 15, pp. 4 5 7 - 4 6 0 , 1981 P r i n t e d in the U.S.A.
COMMENT ON "ON THE QUASI-CHEMICAL MODEL OF INTERFACE DECOHESION"
M.P. Seah National Physical Laboratory Teddington, Middlesex, UK. (Received
February
5, 1981)
Introduction Some points in the paper by Hartweck (I) deserve further comment in order that the earlier publication "Adsorption-induced interface decohesion" (2) should not be misconstrued. These points, only concern the aspects relating to decohesion and not to Hartweck's adhesion results. The earlier publication (2) presents an analysis of the effects of different grain boundary segregants on their power to modify grain boundary cohesion. The analysis is presented there by two separate routes which, within the regular solution approximation, lead to the same relation for the change in fracture energy of the grain boundary, arising from segregation. The two routes used are the thermodynamic work of fracture approach, reviewed recently by Hirth and Rice (3), and the pair-bonding or quasi-chemical approach. For moderate levels of segregation the equations obtained are shown in (I) and (2) and may be summarised by:
zg[H~ub"
FE(Xb)-FE(o) = - Z- ~
-
z1
.sub*_ H A ~
(I)
where FE(0) is the fracture energy of a clean grain boundary in matrix A, FE(X b) is that for a grain boundary with a fractional monolayer, Xb, of segregant B, Zg is the ~-ordination across the boundary (not as given by Hartweck (I)), Z is the total co-ordination, H~ ~ is the sublimation enthalpy of pure A per unit area, ~ is the regular solution parameter and a B2 the area of a B atom in the fracture surface. Comment
Numerical analysis (2) of the terms in the brackets in Eq (I) shows that the regular solution parameter, m, has an effect typically of I J m -2 in the fracture energy change for many segregants in iron over a range of 25 J m -2. (The average effect for the 16 segregants for which thermodynamic heat of mixing data (h) is available, is in fact, 1.27 J m-2). Thus, since, the regular solution parameter involves such a small term, a general remedial/embrittlement plot is presented in the earlier publication (2) to classify all segregants in all matrices in the ideal solution approximation of Eq (I) with ~ omitted. This is important to show how embrittlement experience in ferrous systems can be extended to other materials. In the full regular solution model, however, the remedial/emhrittlement plots for all the segregants have to be presented for each matrix material separately, as exampled, for iron, in Fig h of ref (2). Inspection of Fig 3 of ref (2), in the ideal solution approximation, and Fig 4 of ref (2), in the regular solution approximation, shows that the ideal solution is, in fact, an excellent guide and that errors only occur in the relative positions of close points. Thus, as must be evident, the model in the earlier publication (2) is, in fact, presented in the regular solution approximation and cannot be criticised because "the assumption of an ideal solution is too restrictive" (I). The second main comment in the paper by Nartweck (I) purports to show that the quasi-chemical model leads to P and S strengthening grain boundaries in iron, at low segregation levels, in contradiction with observations and hence disproving the appropriateness of the model. Two approaches are used by him to show the strengthening. In the first he uses Eq (I), or actually one of its
457 0036-9748/81/040457-04502.00/0 C o p y r i g h t (c) 1981 P e r g a m o n Press
Ltd.
4S8
COMMENT ON INTERFACE DECOHESION
Vol.
15,
No.
4
derivatives, with thermodynamic data from Guttmann (5) to estimate the regular solution term. If this data is used to calculate the terms in the brackets of Eq (I) these in fact become (5.66-13.33+ 3.87) for P in iron and (5.2h-13.33+3.64) J m -2 for S in iron, both of which are negative and therefore show a severe embrittlement propensity. The numbers given above can be improved since the use of a compound will overestimate the value of the interaction parameter (6). The extent of this overestimate seems typically to be around a factor of two as was shown by Guttmann's (7) reassessment of the interaction parameters from metallurgical phase diagram data when compared with the earlier work (5) cited by Hartweck (I). This fine tuning gives final figures for the term in brackets in Eq (I) as -5.7h and -6.27 J m -2 for P and S in iron respectively, in full agreement with the text of the earlier publication (2) and experimental observations. The reason why Hartweck (I) fails to obtain these results appears to come from the use of an equation similar to Eq (I) but which is, in fact, derived early in the previous publication (2) for segregant atoms equal in size to those of the matrix (Equations (I) or (2) of Hartweck's paper (I)). The atom size is very important and cannot be ignored since the work of fracture concerns the product of bond energy and the number of bonds per unit area. Thus, Hartweck's criticism of the model appears to be founded on the use of the wrong equation and is therefore itself wrong. In the second attempt at demonstrating that the pair-bonding model leads to P and S strengthening grain boundaries the grain boundary is viewed as composed of sites V, which behave like vacancies, and other sites, akin to normal lattice sites, to make up the grain boundary monolayer. This model leads to improved cohesion for all segregants since it puts all of the excess grain boundary energy into the V sites and in the initial stages of segregation bonds across the boundary are formed but none are broken. In the previous publication (2) the sites are all assumed to be fairly equal and P and S then directly give embrittlement as discussed both in that publication and above. It is therefore important to see which of these two models fits the experimental observations best. With Hartweck's (I) model segregation will occur to the V sites with a high negative free energy and to the other sites with a low energy. An estimate of the proportion of the V sites, from the known ratio of grain boundary and surface free energies of 0.35 in iron (8) would be around 17%. It is
1.01
o
'
'
o
'
o
•
•
'
o
o
i
is
%P
.o
g
0.5
o.o,i. °. io,
i
,o.o~~,~o Annealing tempm'atuce(~)
Fig I: Equilibrium grain boundary segregation in the system Fe-P for different Fe-P (wt%) alloys as a function of temperature, after K~pper et al (9).
Vol.
15,
No.
4
COMMENT ON INTERFACE DECOHESION
459
possible to test for the presence of the V sites from measurements of grain boundary segregation where a plateau should be found around the first 10-25% of a monolayer. Excellent measurements for P in iron have recently been reported by K~pper et al (9) and these are reproduced in Fig I. An average of the quantification calibrations for P segregation in iron (10, 11, 12) shows that the saturation value is nearly one monolayer. No plateau is visible over the range 2.5% to 100% of a monolayer and the experimental results show smooth monotonic reductions as the temperature increases over the whole segregation range. Estimates of the free energies of segregation, using the Langmuir-McLean adsorption theory, to the extreme results at high and low levels of segregation show free energy values which diverge by less than 10%. Thus the V site model does not appear to describe the segregation of P in iron. Results at low segregation levels are not available for S in iron but measurements for S in copper (13) and 0 in molybdenum (14) show constant free energies of segregation over a very wide range of segregation levels. Thus the experimental evidence favours a model for the grain boundaries in which the segregation sites all have very close free energies of segregation and not as inherent in the V-site model. The experimental evidence of segregation therefore supports the model in the earlier publication (2) and not as proposed by Hartweck (I). Supportive evidence for the correct predictive power of the original model (2) comes from the recent work of Dumoulin et al (15). In their studies of the effect of P in Mo bearing steels they show that, for a constant level of P segregation, subsequent segregation of Mo lowers the degree of embrittlement. From the regular solution remedial/embrittlement plot of Fig 4 in the earlier publication (2) it is seen that Mo atoms should be about 0.6 times as remedial as the P atoms are detrimental, per unit area of grain boundary. This prediction and Dumoulin et al's results (15) are shown in Fig 2. The segregation values have been changed from Dumoulin et al's publication since they express concentrations per two monolayers at the grain boundary and in this work segregations are expressed per monolayer, also their quantification for P in iron appears to give about twice that used by others (10). It is seen that the predictions and experiments fit exceedingly well and far better than the predictions of any alternative current theory.
300
P S e g r e g a t i o n , Xp = 35 -40°1.
20~ o
u
10(
01 0
•. 0.2
.
.
.
.
.
I 0.4
Monolayers Mo segregated
Fig 2: The remedial effect of Mo atoms segregated to a grain boundary in steel with 35-40% of a monolayer of P, deduced from the data of Dumoulin et al (15), after Seah (16). The points show the experimental results (15) and the line the theoretical prediction.
460
COMMENT
ON I N T E R F A C E
DECOHESION
Vol.
15, No.
4
Conclusions I)
The previous publication (2) is not limited to the ideal solution model but is presented in the regular solution approximation.
2)
Hartweck's (I) first prediction that P and S improve grain boundary cohesion arises through the use of the wrong equation.
3)
Hartweck's (I) second prediction of improved grain boundary cohesion arises through the use of a V-site model not supported by observations.
h)
The predictions of the previous model (2) are therefore still in agreement with experiment and, in fact, accurately predict the more complex behaviour observed in co-segregating Mo and P in steel. Acknowledgements
The author would like to thank Drs K[~pper, Erhart and Grabke for the material prior to publication involving Fig I. References I. 2. 3. h.
W.G. Hartweck, Scripta Met. previous paper this issue. M.P. Seah, Acta Met. 28, 955 (1980). J.P. Hirth and J.R. Rice, Met. Trans. 11A, 1501 (1980). O. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry, 5th Edn. Pergamon, Oxford
5. 6. 7. 8.
M. Guttmann, Surface Sci. 53, 213 (1975). A.H. Cottrell, An Introduction to Metallurgy, Arnold, London (1967). M. Guttmann, Met. Sci. 10, 337 (1976). E.D. Hondros, In Interfaces, Proc. Conf. Melbourne (~d. R.C. Gifkins) pp 77-100 Butterworths, London (1969). J. K[~pper, H. Erhart and H.J. Grabke, Corros. Sci. to be published. M.P. Seah, J. Vac. Sci. Technol. 17, 16 (1980). L. Marchut and C.J. McMahon, Applications of ~lectron and Position Spectroscopies in Materials Science and Engineering, Ed. O. Buck, Academic Press, to be published. B.C. Edwards, H.E. Bishop, J.C. Riviere and B.L. Eyre, Acta Met. 24, 957 (1976). S.P. Clough and D.F. Stein, Scripta Met. 9, 1163 (1975). A. Kumar and B.L. Eyre, Proc. R. Soc. Lond. A 370, ~31 (1980). Ph. Dumoulin, M. Guttmann, M. Foucoult, M. Palmier, M. Wayman and M. Biscondi, Met. Sci. 14, I (1980). M.P. Scab, Proceedings of Gef~ge der Metalle, November 1980, Bad - Nauheim, Deuts. Ges. f. Metall., to be published.
(1979).
9. 10. 11. 12. 13. lb. 15. 16.