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Influence of cosegregation on grain boundary diffusion: Experimental study in ultra high purity FeNiSb solid solutions
OOOI-6160/86$3.00+0.00
Acta metall. Vol. 34, No. 3, pp. 3955403, 1986 Printed in Great Britain. All rights reserved
Copyright
c
1986 Pergamon
Press Ltd
INFLUENCE OF COSEGREGATION ON GRAIN BOUNDARY DIFFUSION: EXPERIMENTAL STUDY IN ULTRA HIGH PURITY Fe-Ni-Sb SOLID SOLUTIONS P. GAS, Laboratoire
S. POIZE
and J.
BERNARDINI
de Mttallurgie-U.A. 443, Facultt des Sciences et Techniques, rue H. Poincari, 13397-Marseille Cedex 13, France
Centre
St Jkr8me,
(Received 25 June 1985) Abstract-We have studied the influence of cosegregation on grain boundary (G.B.) diffusion in Fe&b and Fe-Sb-Ni high purity solid solutions with radioactive tracers and Auger electron spectroscopy. Using these two techniques to measure respectively the grain boundary diffusivity and the G.B. composition, we were able to monitor the variations of the G.B. diffusion coefficients as a function of the G.B. chemical composition. We observe that antimony segregation (in Fe-Sb) and antimony and nickel cosegregation (in Fe-Ni-Sb) lead to a large decrease of the G.B. diffusion of the three species. This behavior is explained assuming a modification of the G.B. structure induced by the strong iron-antimony or nickel-antimony interactions. Iron and antimony G.B. diffusion coefficients are identical in Fe(Sb) and Fe(Ni-Sb) when the G.B. concentration of antimony is the same: the presence of nickel just increases the G.B. antimony content. In ternary alloys the segregation of nickel excludes the iron atoms from the G.B. core. Adding nickel in pure iron strongly affects the antimony G.B. heterodiffusion. This clearly indicates that the dispersion observed in G.B. heterodiffusion measurements can be explained by cosegregation effects due to highly active impurities. R&umC-Nous avons 6tudiC au moyen de radioisotopes 59Fe, 63Ni, ‘%b , la diffusion intergranulaire des constituants de solutions solides de haute puretk Fe(Sb) et Fe(Si+Ni) dont la composition chimique des joints a d&j$ & caracttris&e par spectromttrie d’Clectrons Auger. La skgrigation d’antimoine [dans Fe(Sb)] et la cos&grCgation d’antimoine et de nickel dans Fe(Ni-Sb) induisent une diminution importante des coefficients de diffusion intergranulaire D,, pour les trois Cl&ments. Cette diminution des coefficients D,, dans les alliages Fe(Sb) et Fe(Ni-Sb) est expliqute par une modification de la structure des joints rtsultant des interactions fer-antimoine et nickel-antimoine. A teneur identique en antimoine au joint, Di; et DE: sont identiques dans Fe(Sb) et Fe(Ni-Sb): la prCsence du nickel a pour seul effet d’augmenter la concentration intergranulaire en antimoine. Dans les solutions solides ternaires, la sigrkgation du nickel s’effectue aux d&pens du fer qui est au fur et g mesure exclu des joints de grains. Les rCsultats obtenus pour I’h&rodiffusion de l’antimoine dans le fer et les alliages fer-nickel permettent d’attribuer la dispersion des ttudes d’h&rodiffusion, g&ralement observi-e dans la litttrature B des effets de cos&gregation. Zusammenfassung-Wir haben den EinfluD der Cosegregation auf die Korngrenzdiffusion in den hochreinen Mischkristallen Fe-Sb und Fe-SbNi mit radioaktiven Tracern und mit der AugerelekronenSpektroskopie untersucht. Mit diesen beiden Techniken wurden Korngrenzdiffusion und -zusammensetzung gemessen, wodurch wir die Koeffizienten der Korngrenzdiffusion in Abhlngigkeit von der Korngrenzzusammensetzung bestimmen konnten. Antimonsegregation (im Fe-Sb) und die Cosegregation von Antimon und Nickel (im Fe-SbNi) fiihrten zu einer starken Verringerung der Korngrenzdiffusion aller drei Atomsorten. Dieses Verhalten wird damit erklHrt, daI3 eine durch die starke Wechselwirkung zwischen Eisen und Antimon oder Nickel und Antimon bedingte Vetinderung der Korngrenzstruktur angenommen wird. Wenn die Korngrenzkonzentration von Antimon gleich bleibt, d&n sind die Koeffizienten der Korngrenzdiffusion von Eisen und Antimon in Fe(Sb) und Fe(SbNi) identisch: vorhandenes Nickel erhlht nur den Antimongehalt der Korngrenze. In tern&en Legieiungen’schlieBt die Segregation von Nickel die Eisenatome vom Korngrenzkern aus. Zugabe von Nickel zu reinem Eisen beeinflul3t die Heterodiffusion von Antimon an der Korngrenze. Das weist deutlich darauf hin, daI3 die Streuung, die bei Messungen der Heterodiffusion an Korngrenzen beobachtet wird, mit Effekten der Cosegregation durch hochaktive Verunreinigungen erklHrt werden kann.
1. INTRODUCTION
Diffusion studies at interfaces is a very fruitful way to get information about these defects, their structure and, in the case of alloys, their composition [l]. On the one hand, used in conjunction with other techniques, these studies are useful to deduce the role of each individual species in the segregated layer [2]. On the other hand, due to the increasing use of thin films in microelectronic and coating technologies (where
mass transport at interfaces is predominant) it is quite important to understand, and if possible to predict, how mass transport properties are affected by such parameters as temperature, alloying elements and residual impurities. Previously, this subject has been developed by Bernardini et al. [3] who derived an analytical expression linking the change in diffusivity to the grain boundary (G.B.) adsorption in binary solid solutions. This relationship can be used to roughly predict the influence of a solute on G.B.
396
GAS
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ON
GRAIN BOUNDARY DIFFUSION
diffusion when its bulk solubility and its effect on bulk diffusion are known. The predicted behavior of the G.B. self diffusion coefficients as a function of the G.B. segregation of the solute was confirmed experimentally [3] by direct diffusion measurements in iron-tin solid solutions using radiotracer techniques and direct G.B. segregation measurements using Auger electron spectroscopy (A.E.S.). For more complex alloys, like ternary systems, the different solutes may interact at the G.B. and enhance or decrease segregation. This synergistic effect, which is the cause of most of intergranular failures in engineering materials has been studied in detail by Guttmann [4,5]. The model proposed by this author shows that the free energy of segregation of one species may be increased by the second if the interaction energy between the two species is negative (attraction). This conclusion has been validated by careful segregation experiment on surfaces [6] and grain boundaries [7]. This cosegregation effect, which affects the cohesion of the boundaries may also have a tremendous effect on the kinetics of mass transport at the G.B. To study the influence of cosegregation on G.B. diffusion, which is of great practical interest, is the first objective of the present paper. The second one is to study the properties of grain boundary diffusion in an effort to obtain complementary information on the structure and the composition of the segregated layer. The system we have chosen for this purpose, is the Fe-Ni-Sb ternary solid solution. Antimony segregation to G.B. in steel causes high G.B. embrittlement [8] and it has now been well established that the amount of antimony in the G.B. strongly depends on the presence of nickel [7]. Moreover, it is one of the rare ternary systems where the G.B. diffusion parameters can be measured for the three species, using radioactive-tracers, and discussed as a function of the G.B. chemical composition determined by A.E.S. We have also analysed G.B. diffusion in the binary Fe-Sb and Fe-Ni solid solutions; this was necessary to emphasize the role of cosegregation and was also an excellent way to test the accuracy of our model for binary alloys.
IpJ I
0.02
0.05
0.1
0.2
1
I
0.5
1.0
Fig. 1. Segregation isotherms of Sb in solid solutions Fe-Sb (a), Fe-SbNi
1% (b), and
Fe-SbNi
2% (c) at 550°C.
can form. A suitable condition for such experiments was to use ultra pure metals as starting materials and a pure flowing gas atmosphere to carry out the heat treatments. The iron and nickel were ultra high purity Fe and Ni supplied by the “Ecole des Mines” in Saint Etienne. The antimony was 6NSb supplied by FLUKA. The alloys were melted in a high frequency induction furnace under an atmosphere of flowing high purity argon 6N. The samples were then prepared by rolling and annealing at 850°C for 24 h under flowing (6N) hydrogen to provide an equiaxed grain structure with a grain size of about 0.5 mm. The samples where then aged at 550°C for 8 days in order to produce isothermal equilibrium segregation before the diffusion treatment. The G.B. chemical composition of the alloys was determined for in situ fractured alloys by scanning Auger Electron Spectroscopy. This allows the identification of pure G.B. facets. The calculation procedure used to convert Auger Peak to Peak amplitudes into surface concentrations is described in
2. MATERIALS AND G.B. CHEMICAL COMPOSITION
The general procedure for the fabrication of the binary and ternary high purity solid solutions and the evolution of G.B. composition in relation to bulk Sb and Ni contents have been previously described [7]. Only the major points are summarized here. The concentrations were chosen to be within the range of solubility for Sb at 55O”C, (9): 0.03 < Ctb < 0.69 at.% in pure Fe, 0.03 < Ci” < 0.36 at.% in Fe-Ni 1 at.%, and 0.03 < Cib < 0.146 at.% in Fe-Ni 2 at.%. So any segregation and diffusion measurements in binary Fe-Sb and ternary Fe-Ni-Sb alloys were made in solid solutions where no new 3D phases
20
40
60
Fig. 2. Relationship between Ni and Sb coverages at the G.B. in Fe-St+Ni 1% (b) and Fe-SbNi 2% (c).
GAS et al.: ON GRAIN BOUNDARY DIFFUSION
y6” [lo-
397
cm6’s J
Fig. 3. The G.B. ~n~tration curves (t = 14 j, T = 550°c) for ‘%b in Fe, and different Fe-Sb solid solutions. a previous publication [7]. It should be pointed out that we have only reported on Fig. 1 the shape of the segregation isotherms. The accurate values of G.B. composition and the scatter corresponding to the variations of Sb/Fe ratio among the different intergranular facets of each analysed sample are given in Fig. 2 of Ref. [7]. It can be seen in Figs 1 and 2 that the slope of the segregation isotherms are considerably steepened by the addition of Ni. On the other hand, the Ni coverage at the G.B. increases linearly with the Sb coverage {Fig. 2) for a given bulk Ni content. These results are in quantitative agreement with the regular solution model of cosegregation [4,.5]. They are consistent with a strong NiSb attractive interaction and reveal the existence of a weaker Sb-Sb attraction. 3. GRAIN BOUNDARY DIFFUSIVITY MEASUREMENTS To measure the diffusivity, the samples were prepared as follows. Radioisotopes 59Fe and 63Ni were electrodeposited on one face of the specimen; L24Sb was vacuum deposited by evaporation. Diffusion treatments were then completed under flowing 6N hydrogen for 15 days. The radiotracer penetration profiles were obtained by removing thin layers from the surface by chemical dissolution and then, after sectioning, counting the residual activity of the sample with a low background detector for 63Ni or the activity of the dissolved slices with a scintillation counter for 59Fe and 124Sb. G.B. diffusivity parameters P were calculated from In(c) vs y6/’ plots using Suzuoka’s method IlO]
(1) [ t1-$-PO.“”
a In C 4Db “‘0.578 P(m3s-‘f=-.-----
aps
To deduce the parameters P from equation (l), the bulk diffusion coefficients Db must be known. In iron, the determination of bulk diffusion coefficients at low temperature is very difficult, and, for this reason a large scatter is observed in the published values. In fact, by using very sensitive techniques over a wide range of temperatures (550°C < T < 850°C) it may be shown that Arrhenius plot, log Db =f(l/T) is not a straight line and that a discontinuity exists near the Curie tem~rature (T z 770°C) Ill]. Therefore, we have decided to introduce into equation (1) our own diffusion coefficients measured on the same samples, with the technique used for the G.B. diffusion measurements. However, the sensitivity of this technique is only sufficient to get information in a narrow range of tem~ratures under the Curie point (680°C < T < 75OOC) and a linear extrapolation at 550°C is necessary. Even though the absolute values of the so obtained bulk diffusion coefficients are subject to caution, this procedure allows for the determination of relative diffusivity as a function of the change in the composition. This type of determination is far more important than an obsolute determination. The so obtained bulk diffusion coefficients D, are: Dp = 2.7, 10wt6cm2 SK’, Dp = 3.7. lo-l6 cm* s-l, and Dp = 3.6, lO-1s cm2 SK’ at 550°C. It should be pointed out that antimony is a “fast element” in the bulk. Bulk diffusion of Fe and Ni are almost identical. So it may be assumed that 1 or 2% of Ni does not affect bulk diffusion in Fe and Fe-Sb solid solutions. We have observed that antimony addition enhances the bulk diffusion of iron in proportion to the antimony concentration
where C is the activity of the radioisotope at depth y and /3 is given by p = P/2 D,I D,t 1‘I*. To apply the relation (1) B must be higher than 10. Typical results for antimony diffusion in the different binary alloys at 550°C are given in Fig. 3.
I),F”:F”sb= L),“‘“( 1 + bC,sb)
with b = 254 at 55O”C, and has practically no effect on antimony diffusion. This influence is quite similar to the one observed for tin in iron-tin alloys [3]. The variations of G.B. diffusivity for Fe, Ni and Sb as a function of bulk Sb concentrations are reported respectively in Fig. 4(a-c).
398
GAS et al.: ON GRAIN BOUNDARY
DIFFUSION
(cl
Fig.4. The G.B. diffusivity P for Fe (a), Sb (b), Ni (c) in Fe-% (O), Fe-SbNi 1% (O), and Fe-SbNi 2% (m) as a function of Sb bulk concentration at 550°C. ary, C,. Both C,, and C, are expressed in mole per unit volume. pgb is the G.B. excess concentration of diffusing element expressed in moles per unit area. It is worth noting that both models represent the G.B. as an isotropic slab of material of different width within which diffusion occurs according to Fick’s law with a constant G.B. diffusion coefficient neglecting its possible variation with the penetration depth y. So, even when segregation and diffusion measure4. DISCUSSION ments have been carried out under the same conditions in the same G.B., the two relations (2) and (3) The following discussion will focus on the informaonly lead to a “macroscopic” coefficient D,, which tion provided by these simultaneous measurements does not take into account the atomistic configurof G.B. diffusivity and G.B. segregation. However, ation of the G.B. In particular, D,, will be calculated before examining this point, it may be useful to recall assuming that all the atoms of solute adsorbed at the some assumptions to calculate the G.B. diffusion G.B. take part in the G.B. diffusion, i.e. that the coefficients D,, from the experimental diffusivity and values of the ratio 6a = SC,,/C, (or pgb/ph) are idensegregation parameters. tical in both kinetic and equilibrium measurements. 4.1. Calculation of the G.B. dzjiision coejicients On the other hand, different possibilities may be used to calculate the solute and the solvent G.B. In the conventional theoretical analysis for G.B. diffusion coefficients when the chemical G.B. compodiffusion, a matching condition linked to the presence sition has been obtained from A.E.S. measurements. of a boundary enrichment of solute leads to the fact For the solute B, two possibilities may be used to that the transport quantity measured is not the G.B. diffusion coefficient D,, but a complex parameter P obtain the solute G.B. concentration per unit area (pib) from A.E.S. data (Xi) using fracture speciwhich can be written mens. They are dependent on the location of the P = D,,.~.cc (2) fracture path. If one is within the region in which Sb or and Ni are enriched, then both surfaces of the fracture will show enrichment and p,” = 2 Xg(p,“), where (3) ( ptb),, is the quantity of solute (in mole per unit area) p = (@gb/cdD,b contained in one monoatomic layer. If the fracture depending on the model assumed to describe the G.B. (respectively the Fisher’s or the Ghez’s model [ 12, 131. path is along the boundary between the enriched region and the matrix, only one fracture surface will In these relations, 6 is the boundary width, c[ the show enrichment and p$ = Xi. ( p,“), .To calculate equilibrium ratio between the atomic concentrations of diffusing element in the boundary Cgb, and in the Dib (B = Sb or Ni), we have used the first possibility in aereement with the results obtained bv Moulder et bulk atom layer immediately adjacent to the bound-
We observed a strong decrease in the diffusivity for the three components: PSb decrease from 34 to 0.5. 10-‘6cm3 s-i; PFe from 5.4 to 0.12. 10-‘6cm3 s-l, and PNi from 23 to 5. lo-i6cm3 s-i. This change is not proportional to the bulk Sb content: it principally takes place in dilute solid solutions where it is greatly increased by the presence of Ni.
GAS
et al.:
ON GRAIN
BOUNDARY
399
DIFFUSION
1c
112
/
I \
‘w
c
(a)
30-
NE 0
6
m
NE ”
‘0 l-z_l
z 2‘0
.(
“0”
“2
. 10
-
2 .O
l=---r-.
-O_q_m_
40
20
60
20
60
40 c;;p
%]
lo=-
(c)
1 t 40
20
60
C
(d)
la-,.20 c,“p
40 %J
G.B. diffusion coefficients as a function of Sb (or Ni) content at 550°C in Fe (A), Fe+Ni 2% (a), Fe-Sb-Ni 1% (O), Fe-SbNi 2% (W). Diz are calculated with the assumptions: Fig. [5(b)] p,‘b’= ct; Fig. [5(c)] pgFbeia”oy = pit’pure- p,“d.
Fig. 5. The calculated
Fe-Sb (a),
al. [ 141. These authors have indeed confirmed that the varying distribution of (Sb + Ni) on the fracture surface in temper embrittled low alloy steels is not caused by a fracture path proceeding between the Sb-Ni enriched region and the matrix. For the solvent, no information may be obtained from A.E.S. measurements; so it is difficult to define a numerical value of p,‘b’and its evolution without a G.B. model and a segregation model. Two simple cases may be considered: every atom of solute absorbed at a G.B. site takes the place of one atom of iron; p$ decreases as pgb ’ increases. Consequently any change in PFe may be attributed individually or jointly to pF’/C”’ &, & h and DF’. every atom of solute adsorbed at a G.B. site forms a new adsorption site comparable with
the first one occupied. Thus pii may be taken as equivalent to a constant value, say two monolayers or 64 pmol m-*. In this case the decrease of PFe is linked to the evolution of
4.2. Evolution of the G.B. d@sion function of C$ and C,Nd
coejficients as a
G.B. diffusion coefficients of Fe, Sb and Ni are shown in Fig. S(a-d). To calculate D,, coefficients from P experimental parameters, Pgb values in mol/ cm* are calculated from C& values in at.% (Figs 1 and 2) using the relation pgb = 2( pBb)OC,,, where ( Pg& is the quantity of solute (solvent) in mole per unit area contained in a monoatomic layer [(pi:), = 32~molm~*, (P!$)~= 17~molm-*, (p,Nd&=33.7 ~molm~*]. For brevity the dependence of Dzk, D,F,‘(Dr;) on Ni(Sb) content are not reported.
GAS et nl.: ON GRAIN BOUNDARY
DIFFUSION
(b)
ternary
alloys
20
40 C:: [at
% ]
I
I
8
I
20
40
60
c3[ot
v.]
Fig. 6. The G.B. diffusivity P for Fe (a), Sb (b), Ni (c) in Fe-Sb (e), Fe-SbNi 1% (O), Fe-Sl+Ni 2% (W) as a function of Sb G.B. concentration at 550°C.
The salient features presented by the evolution of the D,, coefficients as a function be summarized as follows:
of C$ or Cik may
3. Regardless of the assumptions made to calculate these coefficients are always higher than Dit. This result is quite different from the bulk one, as antimony is a “fast element” in iron. 4. 0:: or D$ are almost the same in binary and ternary alloys when Cik values are identical. In other words the effect of Ni is only to increase the G.B. concentration of Sb. D$,
1. The values for D$, 0:; and D$ all reduce as the Sb solute content increases. 2. For the solvent, Fe, the evolutions of the D$ value calculated assuming p,’ = ct or p$@““y)= (P $ pure- p:i) are almost identical. The evolution observed for D$ values calculated assuming pii”‘Oy 4.3. Evolution of the G.B. chemical composition between the binary and the ternary alloys ‘(P i;Pure- pii - px) allows us to give up this By plotting the variation of the parameters PSb, assumption as we observe a minimum in the values PFe and PNi, against Cik (Fig. 6), we observe that of D,“b’which would increase for Cj > 40 at.%.
GAS et al.:
ON GRAIN
the differences between the binary and the ternary alloys disappear for the dilute solid solutions (C$ < 5 at.%). In contrast, the three curves PFe, PN’ and PSb = f’(C$) are quite different at the higher Cik concentrations: for any value of C,“: > 5 at.%, it is seen that the difference between the values of PSb in binary and ternary alloys are weak, (P’“) in Fe-Ni-Sb being however higher than (PSb) in Fe-Sb; the values of (P”) in FeeNi-Sb are significantly lower than those in FeeSb and (PN’) in Fe-Ni-Sb are higher than (P”‘) in Fe-Sb. In view of the evolution of the G.B. diffusion coefficients D,,, discussed in the preceding section, these differences in the behavior of P values may be solely attributed to the different behavior of the ratio pgb/Ch and we can obtain information about the localization of segregated nickel in the ternary alloys. At a given value ]ps] corresponds to only one value of 0;: (Fig. 5) but the bulk Sb contents (ptb) in equilibrium with ]p$] are different in binary and ternary alloys (Fig. 1): they are indeed dependent on the nickel concentration. Consequently PSb in Fe-SbNi will be higher than PSb in Fe-Sb. Concerning the nickel, the values of PNi are higher in Fe-Sb-Ni than in FeeSb for a given value ]p$‘] (Fig. 6) and are in fair agreement with the results reported in Fig. 2: the grain boundary nickel concentration I p$ I increases strongly in the ternary alloys, leading to an increase in the ratio p:i/Cr’. The dependence of PFe on the Ni content observed on Fig. 6 is only consistent with a decrease of (pi{) in the ternary alloys. Clearly if (p[l) was identical in binary and ternary alloys, D$ [which is almost independent on Ni content at a given (pi,“) concentration] and PFc, of course, would also not be dependent on the presence of Ni. So the assumption pi: is identical in binary and ternary alloys disagrees with the evolution of the measured PFe (Fig. 6). Lower P” values in ternary than in binary alloys must be explained by postulating that each atom of Ni adsorbed at a grain boundary site takes the place of one atom of Fe, thus decreasing pii. These results confirm, if necessary, the presence of a large amount of nickel at the grain boundaries of cosegregated alloys. This important point (which has recently been suspected [15], without real experimental evidence, owing to the small bulk antimony concentrations used in the alloys) proves that the “cosegregation effect” is due to interactions between nickel and antimony leading to the mutual presence of both species at the grain boundary. 4.4. Segregation G.B.
and structural
mod$cation
of the
A large amount of Ni and Sb can be adsorbed at the G.B. So it is difficult to assume only a substitution of iron by the solutes. Moreover D,, values, calculated in binary alloys for the solute, all reduce as the solute content increases for the systems Fe-Sb and
BOUNDARY
401
DIFFUSION
Fe-Sn [3] where the solutes are “fast elements” in the bulk. If this reduction in diffusivity is really a direct result of the strong solute segregation, as suggested in [3], it may indicate a modification of the structure of the “segregated G.B.“. However, as mentioned above, these coefficients are calculated assuming that the quantity of solute measured in the segregation experiments is identical to that taking part in the mass transport process. This procedure may induce under-estimated D,, values. Moreover, the effect of segregation on P parameters and D,, values is particularly important in the dilute alloys, over a range of solute concentrations where the segregation measurements are very difficult to perform by the means of the A.E.S. technique (intergranular embrittlement concerned only some G.B. at low Sb concentration). Lastly, infinite dilute G.B. heterodiffusion coefficients Dib measured in the pure solvent are concerned with a solute G.B. concentration pib-+O; so they cannot be calculated from the expressions (2) and (3) and then compared with self diffusion coefficients calculated in alloys: indeed during the solute diffusion in the pure solvent, the G.B. composition always varies during the diffusion anneal. So it is not easy to conclude about the exact role of segregation on this diffusion coefficient. Some of these difficulties disappear when dealing with the ternary solid solutions. In Fe(Ni-Sb) alloys, for instance, the effect of Sb addition on the nickel within a range parameter PN1 could be determined of Sb bulk or G.B. concentration including ChSb= 0 (i.e. pi: = 0) as th e self diffusion coefficient of Ni may be measured in Fe-Ni solid solution. The main features of these results (reported in Table 1) may be summarized as follows: the presence of 1 or 2 per cent of nickel in pure iron did not change the parameters PN’ and PFe [Fig. 6(a, c)]. Assuming no segregation of nickel in Fe-Ni, this result indicates that the presence of some 1 or 2 at.% nickel in iron grain boundaries do not change G.B. diffusion; in presence of antimony (0.03 bulk, PNi decreased strongly, even Sb concentration, when Ni and in the G.B. are very weak (3 respectively)
at.%) in the with this low Sb contents and 4at.%
calculated D$ values are identical in iron and Fe-Ni-2 at.% but we observe a decrease of a factor of 20, increasing C,“b from 2 to 4 at.% in presence of antimony [Fig. 5(d)]. Even if the segregation values used to calculate D,“d are a little too high (owing to a certain selectivity of A.E.S. measurements and our assumption concerning the identity between the nickel quantity segregated and those taking part in the diffusion process) these results improve the conclusions drawn in binary solid solutions. That is the segregation implies a large decrease in mobility for the G.B. atoms. Indeed, even
402
GAS et al.:
ON GRAIN BOUNDARY
DIFFUSION
Table 1. Calculated G.B. diffusion coefficients of Ni in Fe, Fe-Ni and Fe-Ni-Sb Solvent Fe
C,” (at. %) -
C;b (at. %) -
PN’
(cm~.s-‘) 2.3.10-‘5
Fe-Ni
2
-
2.1.10rn’5
Fe-Ni-Sb
I
0.0290 0.1520 0.0300 0.0950
5,10-‘6 4.10-‘6 4.1.10rn’6 4.6.10-16
1 2 2
Cp”b
(at. %)
solid solutions at 550°C c;b”
(at. %) -
2” 4 26 13 45
0; (cn&sm’) 4.6.10-” 4.1.10rn”
3 56 IO 63
2.6. 10m9 3.2. IO-” 1.3.10m9 4.3.10-‘0
‘Assuming no segregation of Ni in Fe-Ni.
if all of the nickel atoms segregated in the G.B. does not take part in the mass transport, i.e. calculating O,“biwith a nickel quantity identical in the bulk and in the G.B., the nickel G.B. diffusion coefficients will be still lower in the ternary solid solutions than in the binary one. So the nickel diffusion behavior is more linked to the mutual presence of both Sb and Ni than to the G.B. composition itself. The most plausible explanation for the decrease of the G.B. mass transport is that the modification of the chemical composition of the G.B. is linked to the formation of a “new phase” where the ratio D,,/D, is lower than in iron. We can assume, for example, as proposed by Cabane [16], a special structure with highly correlated jumps which decrease the efficiency of the high energy sites. The shape of the G.B. segregation isotherms (Fig. 1) may be taken as an evidence of the presence of a “segregated phase” even if the Ni-Sb intergranular interaction energy (largely attractive) is smaller (10 kJ.mol-‘) than the value determined [9] in the three dimensional Ni-Sb antimonide (18 kJ.mol-I). 4.5. Segregation scattering
and heterod@ision
measurements
Surveys in the literature of heterodiffusion measurements show the data to be sparse. It is important to note that this dispersion, which is several times greater than the error associated with layerwise analysis and temperature determination, is often observed for solute having strong interfacial segregation. In a previous paper [17], we have discussed the role of the grain boundary solute saturation on the apparent scattering of heterodiffusion measurements observed for slightly soluble solute. Another effect of segregation on the hereodiffusivity can be deduced from the present results. It can be seen from Fig. 4 that iron and nickel diffusion parameters are identical in iron and iron-nickel alloys while the antimony diffusion parameter, PSb, is strongly increased in the presence of nickel. This effect may be related to a variation of D$ or an increase of c(~, the segregation ratio at infinite bulk antimony dilution. As the antimony diffusion coefficients only depend on the Sb content [cf. Fig. 5(a)] this effect can only be attributed to the increase in antimony segregation in the presence of nickel. The cosegregation of Ni and Sb observed in ternary
Fe(Ni-Sb) solid solutions and the decrease in antimony solubility in presence of nickel [9] are in fair agreement with this explanation. Thus, the chemical affinity between two solutes or one solute and residual impurities must be taken into account in G.B. heterodiffusion measurements to explain the dispersion of the results observed in the literature.
5. CONCLUSION We have performed intergranular mass transport measurements in Fe(Sb) and Fe(Ni-Sb) solid SO~Utions using 59Fe, 63Ni and lz4Sb radioisotopes. This study has been concurrently carried out on the same samples as those previously used to measure the G.B. chemical composition by scanning A.E.S. From both sets of measurements we calculate the evolution of the G.B. diffusion coefficients of Fe, Ni and Sb as a function of the G.B. nickel or antimony concentration. The following conclusions can be drawn. 1. Antimony segregation in F&b and nickelantimony cosegregation in Fe-Ni-Sb largely decrease the G.B. mass transport parameters of Fe, Ni and Sb. 2. Calculated G.B. diffusion coefficients for Fe, Ni, Sb all decrease as the G.B. antimony concentration increases. 3. Fe and Sb G.B. diffusion coefficients are almost the same in Fe(Ni) and Fe(Ni-Sb) when the G.B. antimony concentrations are identical: the presence of nickel only increases the G.B. antimony concentration in equilibrium with the same bulk Sb concentration. 4. The behavior of mass transport parameters in binary and ternary alloys may be explained by assuming that nickel atoms take the place of iron atoms in Fe(Ni-Sb) and thus decrease the G.B. iron concentration. 5. The presence of nickel in the G.B. does not influence the G.B. diffusion of nickel in Fe(Ni) but largely decreases this parameter in Fe(Ni-Sb). Thus the nickel behavior is more linked to the mutual presence of antimony and nickel than to the G.B. composition itself. This result improves the conclusions previously reported in binary solid solutions: a large segregation implies a large decrease in mobility for the G.B. atoms. This is tentatively related to a structural modification of the G.B. induced by the formation of a 2D phase according to the large Ni-Sb
GAS
et al.:
ON GRAIN
interactions and the shape of the segregation isotherms. 6. The large scatter observed in heterodiffusion measurements may be explained by a cosegregation effect induced by the chemical affinity between the solutes and residual impurities. REFERENCES I, P. Gas and J. Bernardini, Surf Sci. 72, 365 (1978). 2. P. Gas, These d’Etat, Marseille (1982). 3. J. Bernardini, P. Gas, E. D. Hondros and M. P. Seah, Proc. R. Sot. Lond. A379, 159 (1982). 4. M. Guttmann, Surf. Sci. 53, 213 (1975) 5. M. Guttmann, D. McLean, in Proc. ASM Mater. Sci. Semin. Interfacial Segregation (edited by W. C. Johnson and J. M. Blakely), p. 261. Am. Sot. Metals, Metals Park, Ohio (1979). 6. Ph. Dumoulin and M. Guttmann, Mater. Sci. Engng 42, 249 (1980).
BOUNDARY
DIFFUSION
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and J. Bernardini, Acta merall. 7. P. Gas, M. Guttmann 30, 1309 (1982). Jr and R. A. 8. H. Ohtani, H. C. Feng, C. J. McMahon Mulford, Metall. Trans. A 7A, 87 (1976). 9. M. C. Cadeville, M. Maurer and J. M. Friedt, Mafer. Sci. Engng 51, 147 (1981). 10. T. Suzuoka, J. Phys. Sot. Japan 19, 839 (1964). II. G. Hettich, H. Mehrer and K. Maier, Scripta metall. 11, 795 (1977). 12. J. C. Fisher, J. appl. Phys. 22, 74 (1951). 13. R. Ghez, Surf. Sci. 20, 326 (1970). and A. Joshi, Metall. Trans. 12, 139 14. J. F. Moulder (1981). 15. C. L. Briant and A. M. Ritter. Acta metall. 32, 2031 (1984). 16. J. Cabane, Studies in Physical and Theoretical Chemislry (edited by P. Lacombe), p. 201. Elsevier, Amsterdam (1984). 17. P. Gas, S. Poize and J. Bernardini, Scripta metall. 18, 19 (1984).
Acta metall. Vol. 34, No. 3, pp. 3955403, 1986 Printed in Great Britain. All rights reserved
Copyright
c
1986 Pergamon
Press Ltd
INFLUENCE OF COSEGREGATION ON GRAIN BOUNDARY DIFFUSION: EXPERIMENTAL STUDY IN ULTRA HIGH PURITY Fe-Ni-Sb SOLID SOLUTIONS P. GAS, Laboratoire
S. POIZE
and J.
BERNARDINI
de Mttallurgie-U.A. 443, Facultt des Sciences et Techniques, rue H. Poincari, 13397-Marseille Cedex 13, France
Centre
St Jkr8me,
(Received 25 June 1985) Abstract-We have studied the influence of cosegregation on grain boundary (G.B.) diffusion in Fe&b and Fe-Sb-Ni high purity solid solutions with radioactive tracers and Auger electron spectroscopy. Using these two techniques to measure respectively the grain boundary diffusivity and the G.B. composition, we were able to monitor the variations of the G.B. diffusion coefficients as a function of the G.B. chemical composition. We observe that antimony segregation (in Fe-Sb) and antimony and nickel cosegregation (in Fe-Ni-Sb) lead to a large decrease of the G.B. diffusion of the three species. This behavior is explained assuming a modification of the G.B. structure induced by the strong iron-antimony or nickel-antimony interactions. Iron and antimony G.B. diffusion coefficients are identical in Fe(Sb) and Fe(Ni-Sb) when the G.B. concentration of antimony is the same: the presence of nickel just increases the G.B. antimony content. In ternary alloys the segregation of nickel excludes the iron atoms from the G.B. core. Adding nickel in pure iron strongly affects the antimony G.B. heterodiffusion. This clearly indicates that the dispersion observed in G.B. heterodiffusion measurements can be explained by cosegregation effects due to highly active impurities. R&umC-Nous avons 6tudiC au moyen de radioisotopes 59Fe, 63Ni, ‘%b , la diffusion intergranulaire des constituants de solutions solides de haute puretk Fe(Sb) et Fe(Si+Ni) dont la composition chimique des joints a d&j$ & caracttris&e par spectromttrie d’Clectrons Auger. La skgrigation d’antimoine [dans Fe(Sb)] et la cos&grCgation d’antimoine et de nickel dans Fe(Ni-Sb) induisent une diminution importante des coefficients de diffusion intergranulaire D,, pour les trois Cl&ments. Cette diminution des coefficients D,, dans les alliages Fe(Sb) et Fe(Ni-Sb) est expliqute par une modification de la structure des joints rtsultant des interactions fer-antimoine et nickel-antimoine. A teneur identique en antimoine au joint, Di; et DE: sont identiques dans Fe(Sb) et Fe(Ni-Sb): la prCsence du nickel a pour seul effet d’augmenter la concentration intergranulaire en antimoine. Dans les solutions solides ternaires, la sigrkgation du nickel s’effectue aux d&pens du fer qui est au fur et g mesure exclu des joints de grains. Les rCsultats obtenus pour I’h&rodiffusion de l’antimoine dans le fer et les alliages fer-nickel permettent d’attribuer la dispersion des ttudes d’h&rodiffusion, g&ralement observi-e dans la litttrature B des effets de cos&gregation. Zusammenfassung-Wir haben den EinfluD der Cosegregation auf die Korngrenzdiffusion in den hochreinen Mischkristallen Fe-Sb und Fe-SbNi mit radioaktiven Tracern und mit der AugerelekronenSpektroskopie untersucht. Mit diesen beiden Techniken wurden Korngrenzdiffusion und -zusammensetzung gemessen, wodurch wir die Koeffizienten der Korngrenzdiffusion in Abhlngigkeit von der Korngrenzzusammensetzung bestimmen konnten. Antimonsegregation (im Fe-Sb) und die Cosegregation von Antimon und Nickel (im Fe-SbNi) fiihrten zu einer starken Verringerung der Korngrenzdiffusion aller drei Atomsorten. Dieses Verhalten wird damit erklHrt, daI3 eine durch die starke Wechselwirkung zwischen Eisen und Antimon oder Nickel und Antimon bedingte Vetinderung der Korngrenzstruktur angenommen wird. Wenn die Korngrenzkonzentration von Antimon gleich bleibt, d&n sind die Koeffizienten der Korngrenzdiffusion von Eisen und Antimon in Fe(Sb) und Fe(SbNi) identisch: vorhandenes Nickel erhlht nur den Antimongehalt der Korngrenze. In tern&en Legieiungen’schlieBt die Segregation von Nickel die Eisenatome vom Korngrenzkern aus. Zugabe von Nickel zu reinem Eisen beeinflul3t die Heterodiffusion von Antimon an der Korngrenze. Das weist deutlich darauf hin, daI3 die Streuung, die bei Messungen der Heterodiffusion an Korngrenzen beobachtet wird, mit Effekten der Cosegregation durch hochaktive Verunreinigungen erklHrt werden kann.
1. INTRODUCTION
Diffusion studies at interfaces is a very fruitful way to get information about these defects, their structure and, in the case of alloys, their composition [l]. On the one hand, used in conjunction with other techniques, these studies are useful to deduce the role of each individual species in the segregated layer [2]. On the other hand, due to the increasing use of thin films in microelectronic and coating technologies (where
mass transport at interfaces is predominant) it is quite important to understand, and if possible to predict, how mass transport properties are affected by such parameters as temperature, alloying elements and residual impurities. Previously, this subject has been developed by Bernardini et al. [3] who derived an analytical expression linking the change in diffusivity to the grain boundary (G.B.) adsorption in binary solid solutions. This relationship can be used to roughly predict the influence of a solute on G.B.
396
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ON
GRAIN BOUNDARY DIFFUSION
diffusion when its bulk solubility and its effect on bulk diffusion are known. The predicted behavior of the G.B. self diffusion coefficients as a function of the G.B. segregation of the solute was confirmed experimentally [3] by direct diffusion measurements in iron-tin solid solutions using radiotracer techniques and direct G.B. segregation measurements using Auger electron spectroscopy (A.E.S.). For more complex alloys, like ternary systems, the different solutes may interact at the G.B. and enhance or decrease segregation. This synergistic effect, which is the cause of most of intergranular failures in engineering materials has been studied in detail by Guttmann [4,5]. The model proposed by this author shows that the free energy of segregation of one species may be increased by the second if the interaction energy between the two species is negative (attraction). This conclusion has been validated by careful segregation experiment on surfaces [6] and grain boundaries [7]. This cosegregation effect, which affects the cohesion of the boundaries may also have a tremendous effect on the kinetics of mass transport at the G.B. To study the influence of cosegregation on G.B. diffusion, which is of great practical interest, is the first objective of the present paper. The second one is to study the properties of grain boundary diffusion in an effort to obtain complementary information on the structure and the composition of the segregated layer. The system we have chosen for this purpose, is the Fe-Ni-Sb ternary solid solution. Antimony segregation to G.B. in steel causes high G.B. embrittlement [8] and it has now been well established that the amount of antimony in the G.B. strongly depends on the presence of nickel [7]. Moreover, it is one of the rare ternary systems where the G.B. diffusion parameters can be measured for the three species, using radioactive-tracers, and discussed as a function of the G.B. chemical composition determined by A.E.S. We have also analysed G.B. diffusion in the binary Fe-Sb and Fe-Ni solid solutions; this was necessary to emphasize the role of cosegregation and was also an excellent way to test the accuracy of our model for binary alloys.
IpJ I
0.02
0.05
0.1
0.2
1
I
0.5
1.0
Fig. 1. Segregation isotherms of Sb in solid solutions Fe-Sb (a), Fe-SbNi
1% (b), and
Fe-SbNi
2% (c) at 550°C.
can form. A suitable condition for such experiments was to use ultra pure metals as starting materials and a pure flowing gas atmosphere to carry out the heat treatments. The iron and nickel were ultra high purity Fe and Ni supplied by the “Ecole des Mines” in Saint Etienne. The antimony was 6NSb supplied by FLUKA. The alloys were melted in a high frequency induction furnace under an atmosphere of flowing high purity argon 6N. The samples were then prepared by rolling and annealing at 850°C for 24 h under flowing (6N) hydrogen to provide an equiaxed grain structure with a grain size of about 0.5 mm. The samples where then aged at 550°C for 8 days in order to produce isothermal equilibrium segregation before the diffusion treatment. The G.B. chemical composition of the alloys was determined for in situ fractured alloys by scanning Auger Electron Spectroscopy. This allows the identification of pure G.B. facets. The calculation procedure used to convert Auger Peak to Peak amplitudes into surface concentrations is described in
2. MATERIALS AND G.B. CHEMICAL COMPOSITION
The general procedure for the fabrication of the binary and ternary high purity solid solutions and the evolution of G.B. composition in relation to bulk Sb and Ni contents have been previously described [7]. Only the major points are summarized here. The concentrations were chosen to be within the range of solubility for Sb at 55O”C, (9): 0.03 < Ctb < 0.69 at.% in pure Fe, 0.03 < Ci” < 0.36 at.% in Fe-Ni 1 at.%, and 0.03 < Cib < 0.146 at.% in Fe-Ni 2 at.%. So any segregation and diffusion measurements in binary Fe-Sb and ternary Fe-Ni-Sb alloys were made in solid solutions where no new 3D phases
20
40
60
Fig. 2. Relationship between Ni and Sb coverages at the G.B. in Fe-St+Ni 1% (b) and Fe-SbNi 2% (c).
GAS et al.: ON GRAIN BOUNDARY DIFFUSION
y6” [lo-
397
cm6’s J
Fig. 3. The G.B. ~n~tration curves (t = 14 j, T = 550°c) for ‘%b in Fe, and different Fe-Sb solid solutions. a previous publication [7]. It should be pointed out that we have only reported on Fig. 1 the shape of the segregation isotherms. The accurate values of G.B. composition and the scatter corresponding to the variations of Sb/Fe ratio among the different intergranular facets of each analysed sample are given in Fig. 2 of Ref. [7]. It can be seen in Figs 1 and 2 that the slope of the segregation isotherms are considerably steepened by the addition of Ni. On the other hand, the Ni coverage at the G.B. increases linearly with the Sb coverage {Fig. 2) for a given bulk Ni content. These results are in quantitative agreement with the regular solution model of cosegregation [4,.5]. They are consistent with a strong NiSb attractive interaction and reveal the existence of a weaker Sb-Sb attraction. 3. GRAIN BOUNDARY DIFFUSIVITY MEASUREMENTS To measure the diffusivity, the samples were prepared as follows. Radioisotopes 59Fe and 63Ni were electrodeposited on one face of the specimen; L24Sb was vacuum deposited by evaporation. Diffusion treatments were then completed under flowing 6N hydrogen for 15 days. The radiotracer penetration profiles were obtained by removing thin layers from the surface by chemical dissolution and then, after sectioning, counting the residual activity of the sample with a low background detector for 63Ni or the activity of the dissolved slices with a scintillation counter for 59Fe and 124Sb. G.B. diffusivity parameters P were calculated from In(c) vs y6/’ plots using Suzuoka’s method IlO]
(1) [ t1-$-PO.“”
a In C 4Db “‘0.578 P(m3s-‘f=-.-----
aps
To deduce the parameters P from equation (l), the bulk diffusion coefficients Db must be known. In iron, the determination of bulk diffusion coefficients at low temperature is very difficult, and, for this reason a large scatter is observed in the published values. In fact, by using very sensitive techniques over a wide range of temperatures (550°C < T < 850°C) it may be shown that Arrhenius plot, log Db =f(l/T) is not a straight line and that a discontinuity exists near the Curie tem~rature (T z 770°C) Ill]. Therefore, we have decided to introduce into equation (1) our own diffusion coefficients measured on the same samples, with the technique used for the G.B. diffusion measurements. However, the sensitivity of this technique is only sufficient to get information in a narrow range of tem~ratures under the Curie point (680°C < T < 75OOC) and a linear extrapolation at 550°C is necessary. Even though the absolute values of the so obtained bulk diffusion coefficients are subject to caution, this procedure allows for the determination of relative diffusivity as a function of the change in the composition. This type of determination is far more important than an obsolute determination. The so obtained bulk diffusion coefficients D, are: Dp = 2.7, 10wt6cm2 SK’, Dp = 3.7. lo-l6 cm* s-l, and Dp = 3.6, lO-1s cm2 SK’ at 550°C. It should be pointed out that antimony is a “fast element” in the bulk. Bulk diffusion of Fe and Ni are almost identical. So it may be assumed that 1 or 2% of Ni does not affect bulk diffusion in Fe and Fe-Sb solid solutions. We have observed that antimony addition enhances the bulk diffusion of iron in proportion to the antimony concentration
where C is the activity of the radioisotope at depth y and /3 is given by p = P/2 D,I D,t 1‘I*. To apply the relation (1) B must be higher than 10. Typical results for antimony diffusion in the different binary alloys at 550°C are given in Fig. 3.
I),F”:F”sb= L),“‘“( 1 + bC,sb)
with b = 254 at 55O”C, and has practically no effect on antimony diffusion. This influence is quite similar to the one observed for tin in iron-tin alloys [3]. The variations of G.B. diffusivity for Fe, Ni and Sb as a function of bulk Sb concentrations are reported respectively in Fig. 4(a-c).
398
GAS et al.: ON GRAIN BOUNDARY
DIFFUSION
(cl
Fig.4. The G.B. diffusivity P for Fe (a), Sb (b), Ni (c) in Fe-% (O), Fe-SbNi 1% (O), and Fe-SbNi 2% (m) as a function of Sb bulk concentration at 550°C. ary, C,. Both C,, and C, are expressed in mole per unit volume. pgb is the G.B. excess concentration of diffusing element expressed in moles per unit area. It is worth noting that both models represent the G.B. as an isotropic slab of material of different width within which diffusion occurs according to Fick’s law with a constant G.B. diffusion coefficient neglecting its possible variation with the penetration depth y. So, even when segregation and diffusion measure4. DISCUSSION ments have been carried out under the same conditions in the same G.B., the two relations (2) and (3) The following discussion will focus on the informaonly lead to a “macroscopic” coefficient D,, which tion provided by these simultaneous measurements does not take into account the atomistic configurof G.B. diffusivity and G.B. segregation. However, ation of the G.B. In particular, D,, will be calculated before examining this point, it may be useful to recall assuming that all the atoms of solute adsorbed at the some assumptions to calculate the G.B. diffusion G.B. take part in the G.B. diffusion, i.e. that the coefficients D,, from the experimental diffusivity and values of the ratio 6a = SC,,/C, (or pgb/ph) are idensegregation parameters. tical in both kinetic and equilibrium measurements. 4.1. Calculation of the G.B. dzjiision coejicients On the other hand, different possibilities may be used to calculate the solute and the solvent G.B. In the conventional theoretical analysis for G.B. diffusion coefficients when the chemical G.B. compodiffusion, a matching condition linked to the presence sition has been obtained from A.E.S. measurements. of a boundary enrichment of solute leads to the fact For the solute B, two possibilities may be used to that the transport quantity measured is not the G.B. diffusion coefficient D,, but a complex parameter P obtain the solute G.B. concentration per unit area (pib) from A.E.S. data (Xi) using fracture speciwhich can be written mens. They are dependent on the location of the P = D,,.~.cc (2) fracture path. If one is within the region in which Sb or and Ni are enriched, then both surfaces of the fracture will show enrichment and p,” = 2 Xg(p,“), where (3) ( ptb),, is the quantity of solute (in mole per unit area) p = (@gb/cdD,b contained in one monoatomic layer. If the fracture depending on the model assumed to describe the G.B. (respectively the Fisher’s or the Ghez’s model [ 12, 131. path is along the boundary between the enriched region and the matrix, only one fracture surface will In these relations, 6 is the boundary width, c[ the show enrichment and p$ = Xi. ( p,“), .To calculate equilibrium ratio between the atomic concentrations of diffusing element in the boundary Cgb, and in the Dib (B = Sb or Ni), we have used the first possibility in aereement with the results obtained bv Moulder et bulk atom layer immediately adjacent to the bound-
We observed a strong decrease in the diffusivity for the three components: PSb decrease from 34 to 0.5. 10-‘6cm3 s-i; PFe from 5.4 to 0.12. 10-‘6cm3 s-l, and PNi from 23 to 5. lo-i6cm3 s-i. This change is not proportional to the bulk Sb content: it principally takes place in dilute solid solutions where it is greatly increased by the presence of Ni.
GAS
et al.:
ON GRAIN
BOUNDARY
399
DIFFUSION
1c
112
/
I \
‘w
c
(a)
30-
NE 0
6
m
NE ”
‘0 l-z_l
z 2‘0
.(
“0”
“2
. 10
-
2 .O
l=---r-.
-O_q_m_
40
20
60
20
60
40 c;;p
%]
lo=-
(c)
1 t 40
20
60
C
(d)
la-,.20 c,“p
40 %J
G.B. diffusion coefficients as a function of Sb (or Ni) content at 550°C in Fe (A), Fe+Ni 2% (a), Fe-Sb-Ni 1% (O), Fe-SbNi 2% (W). Diz are calculated with the assumptions: Fig. [5(b)] p,‘b’= ct; Fig. [5(c)] pgFbeia”oy = pit’pure- p,“d.
Fig. 5. The calculated
Fe-Sb (a),
al. [ 141. These authors have indeed confirmed that the varying distribution of (Sb + Ni) on the fracture surface in temper embrittled low alloy steels is not caused by a fracture path proceeding between the Sb-Ni enriched region and the matrix. For the solvent, no information may be obtained from A.E.S. measurements; so it is difficult to define a numerical value of p,‘b’and its evolution without a G.B. model and a segregation model. Two simple cases may be considered: every atom of solute absorbed at a G.B. site takes the place of one atom of iron; p$ decreases as pgb ’ increases. Consequently any change in PFe may be attributed individually or jointly to pF’/C”’ &, & h and DF’. every atom of solute adsorbed at a G.B. site forms a new adsorption site comparable with
the first one occupied. Thus pii may be taken as equivalent to a constant value, say two monolayers or 64 pmol m-*. In this case the decrease of PFe is linked to the evolution of
4.2. Evolution of the G.B. d@sion function of C$ and C,Nd
coejficients as a
G.B. diffusion coefficients of Fe, Sb and Ni are shown in Fig. S(a-d). To calculate D,, coefficients from P experimental parameters, Pgb values in mol/ cm* are calculated from C& values in at.% (Figs 1 and 2) using the relation pgb = 2( pBb)OC,,, where ( Pg& is the quantity of solute (solvent) in mole per unit area contained in a monoatomic layer [(pi:), = 32~molm~*, (P!$)~= 17~molm-*, (p,Nd&=33.7 ~molm~*]. For brevity the dependence of Dzk, D,F,‘(Dr;) on Ni(Sb) content are not reported.
GAS et nl.: ON GRAIN BOUNDARY
DIFFUSION
(b)
ternary
alloys
20
40 C:: [at
% ]
I
I
8
I
20
40
60
c3[ot
v.]
Fig. 6. The G.B. diffusivity P for Fe (a), Sb (b), Ni (c) in Fe-Sb (e), Fe-SbNi 1% (O), Fe-Sl+Ni 2% (W) as a function of Sb G.B. concentration at 550°C.
The salient features presented by the evolution of the D,, coefficients as a function be summarized as follows:
of C$ or Cik may
3. Regardless of the assumptions made to calculate these coefficients are always higher than Dit. This result is quite different from the bulk one, as antimony is a “fast element” in iron. 4. 0:: or D$ are almost the same in binary and ternary alloys when Cik values are identical. In other words the effect of Ni is only to increase the G.B. concentration of Sb. D$,
1. The values for D$, 0:; and D$ all reduce as the Sb solute content increases. 2. For the solvent, Fe, the evolutions of the D$ value calculated assuming p,’ = ct or p$@““y)= (P $ pure- p:i) are almost identical. The evolution observed for D$ values calculated assuming pii”‘Oy 4.3. Evolution of the G.B. chemical composition between the binary and the ternary alloys ‘(P i;Pure- pii - px) allows us to give up this By plotting the variation of the parameters PSb, assumption as we observe a minimum in the values PFe and PNi, against Cik (Fig. 6), we observe that of D,“b’which would increase for Cj > 40 at.%.
GAS et al.:
ON GRAIN
the differences between the binary and the ternary alloys disappear for the dilute solid solutions (C$ < 5 at.%). In contrast, the three curves PFe, PN’ and PSb = f’(C$) are quite different at the higher Cik concentrations: for any value of C,“: > 5 at.%, it is seen that the difference between the values of PSb in binary and ternary alloys are weak, (P’“) in Fe-Ni-Sb being however higher than (PSb) in Fe-Sb; the values of (P”) in FeeNi-Sb are significantly lower than those in FeeSb and (PN’) in Fe-Ni-Sb are higher than (P”‘) in Fe-Sb. In view of the evolution of the G.B. diffusion coefficients D,,, discussed in the preceding section, these differences in the behavior of P values may be solely attributed to the different behavior of the ratio pgb/Ch and we can obtain information about the localization of segregated nickel in the ternary alloys. At a given value ]ps] corresponds to only one value of 0;: (Fig. 5) but the bulk Sb contents (ptb) in equilibrium with ]p$] are different in binary and ternary alloys (Fig. 1): they are indeed dependent on the nickel concentration. Consequently PSb in Fe-SbNi will be higher than PSb in Fe-Sb. Concerning the nickel, the values of PNi are higher in Fe-Sb-Ni than in FeeSb for a given value ]p$‘] (Fig. 6) and are in fair agreement with the results reported in Fig. 2: the grain boundary nickel concentration I p$ I increases strongly in the ternary alloys, leading to an increase in the ratio p:i/Cr’. The dependence of PFe on the Ni content observed on Fig. 6 is only consistent with a decrease of (pi{) in the ternary alloys. Clearly if (p[l) was identical in binary and ternary alloys, D$ [which is almost independent on Ni content at a given (pi,“) concentration] and PFc, of course, would also not be dependent on the presence of Ni. So the assumption pi: is identical in binary and ternary alloys disagrees with the evolution of the measured PFe (Fig. 6). Lower P” values in ternary than in binary alloys must be explained by postulating that each atom of Ni adsorbed at a grain boundary site takes the place of one atom of Fe, thus decreasing pii. These results confirm, if necessary, the presence of a large amount of nickel at the grain boundaries of cosegregated alloys. This important point (which has recently been suspected [15], without real experimental evidence, owing to the small bulk antimony concentrations used in the alloys) proves that the “cosegregation effect” is due to interactions between nickel and antimony leading to the mutual presence of both species at the grain boundary. 4.4. Segregation G.B.
and structural
mod$cation
of the
A large amount of Ni and Sb can be adsorbed at the G.B. So it is difficult to assume only a substitution of iron by the solutes. Moreover D,, values, calculated in binary alloys for the solute, all reduce as the solute content increases for the systems Fe-Sb and
BOUNDARY
401
DIFFUSION
Fe-Sn [3] where the solutes are “fast elements” in the bulk. If this reduction in diffusivity is really a direct result of the strong solute segregation, as suggested in [3], it may indicate a modification of the structure of the “segregated G.B.“. However, as mentioned above, these coefficients are calculated assuming that the quantity of solute measured in the segregation experiments is identical to that taking part in the mass transport process. This procedure may induce under-estimated D,, values. Moreover, the effect of segregation on P parameters and D,, values is particularly important in the dilute alloys, over a range of solute concentrations where the segregation measurements are very difficult to perform by the means of the A.E.S. technique (intergranular embrittlement concerned only some G.B. at low Sb concentration). Lastly, infinite dilute G.B. heterodiffusion coefficients Dib measured in the pure solvent are concerned with a solute G.B. concentration pib-+O; so they cannot be calculated from the expressions (2) and (3) and then compared with self diffusion coefficients calculated in alloys: indeed during the solute diffusion in the pure solvent, the G.B. composition always varies during the diffusion anneal. So it is not easy to conclude about the exact role of segregation on this diffusion coefficient. Some of these difficulties disappear when dealing with the ternary solid solutions. In Fe(Ni-Sb) alloys, for instance, the effect of Sb addition on the nickel within a range parameter PN1 could be determined of Sb bulk or G.B. concentration including ChSb= 0 (i.e. pi: = 0) as th e self diffusion coefficient of Ni may be measured in Fe-Ni solid solution. The main features of these results (reported in Table 1) may be summarized as follows: the presence of 1 or 2 per cent of nickel in pure iron did not change the parameters PN’ and PFe [Fig. 6(a, c)]. Assuming no segregation of nickel in Fe-Ni, this result indicates that the presence of some 1 or 2 at.% nickel in iron grain boundaries do not change G.B. diffusion; in presence of antimony (0.03 bulk, PNi decreased strongly, even Sb concentration, when Ni and in the G.B. are very weak (3 respectively)
at.%) in the with this low Sb contents and 4at.%
calculated D$ values are identical in iron and Fe-Ni-2 at.% but we observe a decrease of a factor of 20, increasing C,“b from 2 to 4 at.% in presence of antimony [Fig. 5(d)]. Even if the segregation values used to calculate D,“d are a little too high (owing to a certain selectivity of A.E.S. measurements and our assumption concerning the identity between the nickel quantity segregated and those taking part in the diffusion process) these results improve the conclusions drawn in binary solid solutions. That is the segregation implies a large decrease in mobility for the G.B. atoms. Indeed, even
402
GAS et al.:
ON GRAIN BOUNDARY
DIFFUSION
Table 1. Calculated G.B. diffusion coefficients of Ni in Fe, Fe-Ni and Fe-Ni-Sb Solvent Fe
C,” (at. %) -
C;b (at. %) -
PN’
(cm~.s-‘) 2.3.10-‘5
Fe-Ni
2
-
2.1.10rn’5
Fe-Ni-Sb
I
0.0290 0.1520 0.0300 0.0950
5,10-‘6 4.10-‘6 4.1.10rn’6 4.6.10-16
1 2 2
Cp”b
(at. %)
solid solutions at 550°C c;b”
(at. %) -
2” 4 26 13 45
0; (cn&sm’) 4.6.10-” 4.1.10rn”
3 56 IO 63
2.6. 10m9 3.2. IO-” 1.3.10m9 4.3.10-‘0
‘Assuming no segregation of Ni in Fe-Ni.
if all of the nickel atoms segregated in the G.B. does not take part in the mass transport, i.e. calculating O,“biwith a nickel quantity identical in the bulk and in the G.B., the nickel G.B. diffusion coefficients will be still lower in the ternary solid solutions than in the binary one. So the nickel diffusion behavior is more linked to the mutual presence of both Sb and Ni than to the G.B. composition itself. The most plausible explanation for the decrease of the G.B. mass transport is that the modification of the chemical composition of the G.B. is linked to the formation of a “new phase” where the ratio D,,/D, is lower than in iron. We can assume, for example, as proposed by Cabane [16], a special structure with highly correlated jumps which decrease the efficiency of the high energy sites. The shape of the G.B. segregation isotherms (Fig. 1) may be taken as an evidence of the presence of a “segregated phase” even if the Ni-Sb intergranular interaction energy (largely attractive) is smaller (10 kJ.mol-‘) than the value determined [9] in the three dimensional Ni-Sb antimonide (18 kJ.mol-I). 4.5. Segregation scattering
and heterod@ision
measurements
Surveys in the literature of heterodiffusion measurements show the data to be sparse. It is important to note that this dispersion, which is several times greater than the error associated with layerwise analysis and temperature determination, is often observed for solute having strong interfacial segregation. In a previous paper [17], we have discussed the role of the grain boundary solute saturation on the apparent scattering of heterodiffusion measurements observed for slightly soluble solute. Another effect of segregation on the hereodiffusivity can be deduced from the present results. It can be seen from Fig. 4 that iron and nickel diffusion parameters are identical in iron and iron-nickel alloys while the antimony diffusion parameter, PSb, is strongly increased in the presence of nickel. This effect may be related to a variation of D$ or an increase of c(~, the segregation ratio at infinite bulk antimony dilution. As the antimony diffusion coefficients only depend on the Sb content [cf. Fig. 5(a)] this effect can only be attributed to the increase in antimony segregation in the presence of nickel. The cosegregation of Ni and Sb observed in ternary
Fe(Ni-Sb) solid solutions and the decrease in antimony solubility in presence of nickel [9] are in fair agreement with this explanation. Thus, the chemical affinity between two solutes or one solute and residual impurities must be taken into account in G.B. heterodiffusion measurements to explain the dispersion of the results observed in the literature.
5. CONCLUSION We have performed intergranular mass transport measurements in Fe(Sb) and Fe(Ni-Sb) solid SO~Utions using 59Fe, 63Ni and lz4Sb radioisotopes. This study has been concurrently carried out on the same samples as those previously used to measure the G.B. chemical composition by scanning A.E.S. From both sets of measurements we calculate the evolution of the G.B. diffusion coefficients of Fe, Ni and Sb as a function of the G.B. nickel or antimony concentration. The following conclusions can be drawn. 1. Antimony segregation in F&b and nickelantimony cosegregation in Fe-Ni-Sb largely decrease the G.B. mass transport parameters of Fe, Ni and Sb. 2. Calculated G.B. diffusion coefficients for Fe, Ni, Sb all decrease as the G.B. antimony concentration increases. 3. Fe and Sb G.B. diffusion coefficients are almost the same in Fe(Ni) and Fe(Ni-Sb) when the G.B. antimony concentrations are identical: the presence of nickel only increases the G.B. antimony concentration in equilibrium with the same bulk Sb concentration. 4. The behavior of mass transport parameters in binary and ternary alloys may be explained by assuming that nickel atoms take the place of iron atoms in Fe(Ni-Sb) and thus decrease the G.B. iron concentration. 5. The presence of nickel in the G.B. does not influence the G.B. diffusion of nickel in Fe(Ni) but largely decreases this parameter in Fe(Ni-Sb). Thus the nickel behavior is more linked to the mutual presence of antimony and nickel than to the G.B. composition itself. This result improves the conclusions previously reported in binary solid solutions: a large segregation implies a large decrease in mobility for the G.B. atoms. This is tentatively related to a structural modification of the G.B. induced by the formation of a 2D phase according to the large Ni-Sb
GAS
et al.:
ON GRAIN
interactions and the shape of the segregation isotherms. 6. The large scatter observed in heterodiffusion measurements may be explained by a cosegregation effect induced by the chemical affinity between the solutes and residual impurities. REFERENCES I, P. Gas and J. Bernardini, Surf Sci. 72, 365 (1978). 2. P. Gas, These d’Etat, Marseille (1982). 3. J. Bernardini, P. Gas, E. D. Hondros and M. P. Seah, Proc. R. Sot. Lond. A379, 159 (1982). 4. M. Guttmann, Surf. Sci. 53, 213 (1975) 5. M. Guttmann, D. McLean, in Proc. ASM Mater. Sci. Semin. Interfacial Segregation (edited by W. C. Johnson and J. M. Blakely), p. 261. Am. Sot. Metals, Metals Park, Ohio (1979). 6. Ph. Dumoulin and M. Guttmann, Mater. Sci. Engng 42, 249 (1980).
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DIFFUSION
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and J. Bernardini, Acta merall. 7. P. Gas, M. Guttmann 30, 1309 (1982). Jr and R. A. 8. H. Ohtani, H. C. Feng, C. J. McMahon Mulford, Metall. Trans. A 7A, 87 (1976). 9. M. C. Cadeville, M. Maurer and J. M. Friedt, Mafer. Sci. Engng 51, 147 (1981). 10. T. Suzuoka, J. Phys. Sot. Japan 19, 839 (1964). II. G. Hettich, H. Mehrer and K. Maier, Scripta metall. 11, 795 (1977). 12. J. C. Fisher, J. appl. Phys. 22, 74 (1951). 13. R. Ghez, Surf. Sci. 20, 326 (1970). and A. Joshi, Metall. Trans. 12, 139 14. J. F. Moulder (1981). 15. C. L. Briant and A. M. Ritter. Acta metall. 32, 2031 (1984). 16. J. Cabane, Studies in Physical and Theoretical Chemislry (edited by P. Lacombe), p. 201. Elsevier, Amsterdam (1984). 17. P. Gas, S. Poize and J. Bernardini, Scripta metall. 18, 19 (1984).