- Email: [email protected]
Influence of silicon content on intergranular self-diffusion of iron silicon alloys. Correlation with intergranular brittleness and grain boundary segregation
INFLUENCE OF SILICON CONTENT ON INTERGRANULAR SELF-DIFFUSION OF IRON SILICON ALLOYS. CORRELATION WITH INTERGRANULAR BRITTLENESS AND GRAIN BOUNDARY SEGREGATION D. TREHEUX,
L. VINCENT
and P. GU~~ALDENQ
Laboratoire Mttaliurgie-Physique-Matiriaux (ERA 732), Ecole Centrale de Lyon-BP 16349130 Ecully. France (Received 8 October 1980) Abatraet-Self diffusion of 59Fe in iron silicon alloys is measured in the paramagnetic field. Bulk and grain boundary diffusions are character&i by a slight decrease of constants for alloys up to Zat.% silicon, and then by a regular increase. The grain boundary results are not to be related to a segregation coefficient but perhaps to an alteration of the grain boundary structures of Fe-Si alloys. These conciusions well agree with the complex behaviour of the very first fatigue crack in relation to the grain boundaries of the same ailoys. R&u&--L’autodifiusion du fer 59 darts des alliages Fe-Si (0 a 121 at%) a Cte mesuree dans ie domaine paramagnetique. Aussi bien en volume qu’aux joints de grain, on note une faible decroissance des coefficients de diffusion jusqu’a environ 2 at.% Si puis une croissance rigulibre. Dans le cas des joints, les variations enregistrtcs ne peuvcnt pas itre dues au coefficient de segregation mais pourraient Otre l&s a une modification de la structure des joints des a&ages fer-silicium. Zasammatfasaung-Die Selbstdiffusion von 59Fe wurde in Eisen-Silizium im paramagnetischen Bereich gemessen. In Kristallen bis zu etwa 2At.-% Si wurde ein leichter Rbckgang der Koeffixienten sowohl fib die Volum- als such fiir die Korng~~iffusion auf~funden, dariiber ergab sich ein regelt&Biger Anstieg. Bei der Kom~~iff~ion lassen sich die Ergebnisse nicht mit den Segregationskoe%ximten verbinden, m&glicherweise aber mit einer ~nde~ng in dcr Komgre~struktur dieser Fe-Si-Legienmgen. Die Folgerungen entsprechcn den kompliiierten Wechselwirkungen zwischen den ersten Ermiidungsrissen. und den in diesen Legierungen beobachteten’K&ngrenzen.
1. LNTBODUCTION Odin andGoux [l] have shown that the complex phenomena leading to intergranular brittleness of iron-siiicon alloys can be related to silicon content and also to carbon content. For carbon contents higher than lOOppm, alloys, water quenched from 8OO”C, have mechanical properties independent of carbon level [l]. On the other hand, for lower carbon contents, we obtain a threshold value: room temperature fractures are intergranular for upper carbon and intracrystalline for lower one. This critical value decreases with the increase in silicon content: it is 22 ppm for 2 wt% silicon ferrites and 12 ppm for 3wt% ones. Moreover, for the same alloys authors gave evidence of a GB silicon-segregation. Thus, from GB energy measurements at 133O”C, Nondros and Stuart [2] found a GB abso~tion of 7.2 x X0” moles/cm2 for a Fe-3 wt% Si alloy. This corresponds to an “enrichment factor” r~equal to 3. This value was also obtained for the same alloy by direct measurement after heat treatment at 850°C [3] using Auger Electron Spectroscopy (A.E.S.). Recently, always with A.E.S., Watanabe er al. [4] measured at 1250°C the evolution of GB silicon-segregation vs the misorientation of grains for Fe-2.53 wt% Si. The width of the segregated region was estimated at 12-16 nm.
It seems that intergranular brittleness can be explained by silicon segregation phenomena or better by silicon-carbon interactions of GB segregation as well as by an intrinsic brittleness of ferritic grains related to high stresses as proposed by [I]. The inffuence of segregations on the direct m~surement of inter~nu~r ~~f~iffusion is now well admitted [5,6], so the aim of this paper is a study of 59Fe self diffusion of several iron-silicon alloys. MATERIALS AND METHODS Iron-silicon alloys, melted in the Research Center of Creusot-Loire in Unieux (France), have a constant carbon level of 50ppm. Silicon contents are given in Table 1. Other minor elements are about 50 ppm for sulphur and phosphorus and 30 ppm for nitrogen. Self diffusion measurements of iron alloys are made by means of a 59Fe radioactive tracer electrodeposited on specimens. After diffusion heat treatments at constant temperatures, diffusion data are obtained by Gruzin’s method [7]. After successive abrasions, the residual activity is measured by means of a scintillation counter for y rays. Of course, GB self diffusion is made after the determination of lattice data for all studied alloys. 931
932
D. TREHEUX et al:
SILICON CONTENT OF IRON SILICON ALLOYS
Table 1. Silicon contents of studied alloys Weight Percent
0
0.75
0.95
3.41
4.54
Atomic Percent
0
1.48
1.87
6.55
8.64
3. BULK SELF-DIFFUSION
OF IRON
Several studies already enable us to know the influence of silicon on self-diffusion of iron [8-l 11. This leads to the general expression of lattice diffusion data versus silicon content, given in (1) @c-Fe%
=
dceFLsi is the GB diffusion constant and 6 the mean GB width of the grain boundary. Recently, Bernardini and Martin [5] showed that the measured quantity gives a “diffusivity” expression: ppB-FeSi
A GRAIN BOUNDARY SELF DIFFUSION OF IRON 4.1 Analysis of quantities measured by intergranular difficion
On the same alloys, we studied the kinetics of diffusion at iron grain boundaries by means of radioactive tracers. As for bulk constants, we used Gruzin’s method on poiycrystalline specimens. These specimens, with grain sizes inferior to 2OO,nm, were homogenized at the diffusion temperature. Until these last years, one determined by such experiences the product D~~MFeSiS. Let us remember that
Dot 2*-t (cm )
::3 0:63 2.1 3.4
_PGBFC
where poBFc iS the INdW Of kOII atOIIIS for a Unit grain boundary surface and ptFe this number for a unit bulk. To again obtain the “X’ width in the diffusivity term P2B*FeSi,one can write:
(kj m:e,239 253 250 238 228 244 212 212 219 216
1)
Ref.
ct21 Cl11
Fe-FeSi .6.
p&- Fcsi =
sc
DGE
c IFC
where Gee, and CIFc are the number of atoms in a unit volume in grain boundaries and in lattice respectively. Using concentrations defined by atom fractions x, we have PGBF~ PGS
=
XlFc
=
PlFe -
PI
with Pee and pl as the numbers of sites by unit surface in GB and by unit volume in the lattice. Thus, we obtain: Fe-FeSi PGB
. POE. XG.9h
F~-F& DGB
I
PI
=
XIFe
Fe-F&.&.+ DGB xlF.
where S’ is an apparent GB width different from the previous 6. The former expression also states:
Fe-F&i PGB
Table 2. Lattice diffusion data of iron-silicon alloys
:.:5 1:38
DFe-FeSi GB
PFC
XGBF.
1.6 4.4
=
(1)
WSJ
where xsi is the atomic fraction and b a constant found to be about 20 at 900°C (1173 K). Table 2 gives the main results, especially of Million. The standard 0% silicon data were obtained by Million er al. [ 1l] and by the working group of Friedberg et al. [12]. Our results, obtained in a paramagnetic field, are given in table 3 and in Fig. 1 where comparison is made with [8,11,12]. With the increase in silicon content from PA, we notice first a slight decrease in diffusion data. Then, we verify the general law given in (1) with b varying from 26.5 (1073 K) to 15.9 (1273 K) for silicon contents superior to 5 at%.
0 0 5.5 6.4 7.64 7.8 11.1 11.6 15.3 19.2
12.1
Dp-Fe ev
Silicon content at.%
6.48
_
,,&
FeSi .S ‘ . 1 1 -
XGSSI x191
Table 3. Lattice diffusion data of iron-silicon alloys of the present study Silicon content at.%
Do, (cmZ s- ‘)
(kJ medIe_‘)
2.73 1.03 76.7 5.2 4.93 0.8
242 276 276 242 236 213
[ii 0
;;; E:;
C81 PI
1.48 1.87 6.55 8.64 12.1
D. TREHEUX et al:
933
SILICON CONTENT OF IRON SILICON ALLOYS TV
iooo
900
so0
700
z
104
To Fig. 1. Lattice diffusion coefficients in Fe Si alloys -1: 0 at.% Si; 2: 1.87at.% Si; 3: 6.55 at.% Si; 4: 8,64 at.% Si; 5: 12,l at.% Si; --- 0 at.% Si [12]; -.Million’s results [S] a: 5,5 at.% Si; b: 6,4 at.%; c: 7,s at.%; d: 11,6at.%; e: 15,3at.%; f: 19,2at.%. if we neglect impurities in iron except silicon. Thus the experimental measurement PG;+FISi leads us to take into account three parameters: the diffusion coefficient, a segregation expression and a’, or Gvalue, that depends on the GB structure. These last three factors can vary with solute concentrations. 4.2 Experimental
rite GB, A an expression of the vibration entropy and XGmi the GB concentration. GB concentration is then 4 .
results
We tried to obtain an order of magnitude segregation expression a, _ 1 l
of the
-xGIlSi -
xJSi
from literature data about silicon segregation [2, j] and with the use of McLean’s relationship [13].
, .
#I
.
AxIsi exp - $
X GBSi
5
=
L
% at.Si
1 + AXlsi exp - $ Fig. 2. Concentration
where U is the interaction energy of silicon with fer-
IO
dependencies of Fe Lattice diffusion
coefficient in Fe-Si alloys for temperatures 800. 850,900”C.
934
D. TREHEUX et al:
T
.
.
.
.
I
SILICON CONTENT OF IRON SILICON ALLOYS
I.)
IO
5
at. Y. si Fig. 3. Grain boundaries Concentration relationship).
XGmi (MacLean
defined as the ratio of the number of silicon atoms to the number of sites favourable to segregation. Thus, we can express the atom fractions by XGBSI =
a? ,8
Y &ilSi
where y is an expression related to GB structure and disorder. y is inferior to 1 and often taken as l/3 in a first approximation [ 133. From Hondros’s results given in appendix, we obtain a value of U energy about -33 KJ/mole (-8OC0cal/mole) (attraction) and thus we can plot GB concentration (XGBsi)vs lattice concentration and temperature (Fig. 3). The evaluation of the corrective expression
-I
t
L
a
9
IO
IO’ T(K)
is also considered with a mean value of l/3 taken for constant whatever silicon content (Fig. 4). We shall notice that GE concentration slowly varied beyond 8 at.% for lattice silicon levels and that the corrective expression is at its minimal value for this same concentration (then for this value, correction becomes maximal).
Fig 5. Grain boundaries Diffusion in Fe-Si alloys Diffusivity P,,; 1: Oat.% Si; 2: 1.48at.% Si; 3: 6.55at.x Si; 4: 8.64at.% Si; 5: 12.1 at.% Si --- Coefficients DGB6).
On Fig. 5, Arrhenius diagram gives the evolution of the PGB apparently difhrsivity-as given by Fisher’s method Cl]-and of Do& (as obtained from PGlr while taking into account the co&&on of Fig. 4). It first appears that the correction is very slight and that PGB is not far different from Do&‘. An Arrhenius law is verified for the several alloys studied by measured energies have very high values compared to GB diffusion. (Table 4). As for lattice diffusion, we notice different evolutions following the silicon content: for low silicon alloys, diffusivity de? creases and for upper values, diffusivity strongly increases to abnormally high values of activation energies. 4.3 Explanation
0.8
;
’
’
’
’
5
’
’
’
’
’
IO
n
’
x, SI Fig, 4. Concentration dependence of corrective expression 01’for temperatures 800, 900, 1000°C.
’
Recently, Gas and Bernardini [6] have studied silver-tin alloys. For these authors, the pGrAISn self diffusivity linearly increases with tin lattice concentration up to a C1 value beyond which PGB seems to be no longer modified. This result is explained if we consider that a grain boundary may be saturated and
D. TREHEUX Edal:
SILICON CONTENT OF IRON SILICON ALLOYS
Table 4. POGBand QG,,values obtained for the five alloys Silicon content at:; 0 1.48 6.55 8.64 12.1
(;q
1)
2.1 10-S 6 lo+ 279 i.1 x 10’ 7.3 x IO6
QGB
kJ mole- ’ 237 193 334 422 413
935
At last, one cannot neglect the carbon effect and especially the possible silicon-carbon interaction. However, it appears very difficult to analyse the mutual segregation of these two elements. First of all, direct measurements by A.E.S. (and explanation of mutual segregation) are not yet well known and furthermore our ailoys do not generally exhibit intergranular fractures after impact test [l], particularly when they are not of a very high purity. However this parameter may strongly influence the mechanical behaviour of grain boundaries.
thus remain identical beyond the C, value. Now, we want to compare our results to AgSn ones. 5. FATIGUE PROPERTIES OF In both results, the self diffusivity coefficient inIRON SILICON FERRITES creases with solute content for the investigated temperatures. Measurements for higher silicon contents The importance of grain boundaries in the dynamic (13.9 and 17.3 at.%) at 900°C (1173 K) show that PGB process of fatigue crack initiation has been studied by no longer increases beyond 12 at.% silicon concenmeans of ball-plane fatigue tests. This device, detration. This gives evidence of a maximal level of difscribed in [I93 permits a stress of 35 x 10s Pa at the fusivity as for AgSn. surface of the plane specimen (standard balls are By considering the evolution of GB concentration made in A120J with a 10mm diameter). These con(Fig. 3), one would conclude that boundaries are satuditions give a maximal shearing stress of 10 x 10s Pa rated. However, we must notice that this saturation at a crystal depth of 0.22 mm as indicated by Hertz’s occurs for concentratio? about 50% of the limit bulk theory, After 4.5 x lo6 cycles (at 25 hz), specimens solubility of silicon in iron while this value is less than mounted in “half-shell” pattern are observed in the 10% for Ag-Sn. most stressed zones and then we can obtain the place Borisov’s relationship [15,16] gives increasing of the very first cracks in a diametral plane of plane energies with solute concentrations (EGB defined by Strain. Borisov is pro~~ional to RT Log DEEDS), which Fatigue tests were conducted on iron siliuin alloys does not agree with either direct measurements (2) or up to 6.48 Wt% -silicon cuntents, after heat treatment a segregation process. With the same formulation, at 800°C (30mn) and water quenchihg (mean grain Gupta [ I73 did obtain decreasing energies for Au-Ta. sizes = 50 m). The main results of these observations In fact. we must not use Borisov’s relationship for are summed up below) self diffusion in alloys and this approach is character1. For pure iron ferrites, cracks are always related istic of GB properties but not of GB energy. Now it to slip lines and never grain boundaries (Fig. 6). becomes obvious that for decreasing energies with solute concentration, one may find either an increase 2. For high silicon ferrites, grain boundaries are the (Ag-Sn, Fe-Si) or a decrease (Au-Ta [lq) of the self main ways of cracking. Especially, in such brittle diffusivity. For a same binary system, the. evolution alloys, cracks initiate in sublayers and go up to the may change for a critical temperature (for instance surface by means of GB networks (Fig. 7). Then, 350°C with Au-Ta). Thus, we can conclude that difpropagation can be inter or transcrystalline. fusivity and GB energies have not the same evolution 3. The intermediate silicon alloys (4 wt%) exhibit a vs the lattice concentration. mixed feature (inter and transcrystalline cracks. Figs We cannot explain diffusivity measurements and es8, 9). In fact, grain boundaries appear to be of the pecially the high activation energies only by segregagreatest importance and some observations indicate tion effect of silicon and hence by the GB concenthat cracks accompany a grain boundary at a very tration of silicon (indeed this last value slightly varies short distance (Fig. 10). This feature is to be related to with temperature). We think that we have to consider the problem of the GB width and thus shows all the an increasing evolution of GB structure with lattice importance of a better knowledge of the GB structure. ~ncentration and tempwature, in addition to segre4. At last in 4wt% ferrites quenched from higher gation phenomena. This would lead to an alteration temperatures (950°C) and with coarse grains. cracks initiate in the grain boundary, in the most stressed Of DGB and probably of 6’ (and hence P,,) values. This agrees quite well with Odin’s and Goux’s results zones below the surface. Then, we can observe several and with the large width of segregation (12-16nm) slip planes and especially we notice that one system measured by Watanabe et al. [43 though the profile of seems to appear before the crack at the opposite of distribution of segregation silicon. Usually the conthe other succeeding ones (Fig. 11). Thus, the GB centration profile of segregating species gives width influence upon fatigue properties seems to be related up to 1.5 nm (18), then. it may be possible that the to three fields: A the grain boundary itself, B a thin increase of PGB with s’ilicon content would be a consezone all around GB and at last C the grain unaltered quence of the increase in GB width beyond 4 a?.“/, Si. by any GB- p~enomenom. The B zone, in which
936
D. TREHEUX et al:
SILICON CONTENT OF IRON SILICON ALLOYS
Fig. 6. Feature of cracking for pure iron ferrites.
secondary slips are mainly observed, is mainly noticed for 4 wt% silicon ferrites. For lower silicon contents, the slip bands in “C” region are the main places of cracking. This is probably due to a better accomodation of stresses at GB due to the greater fitness to cross slips of low silicon ferrites (indeed fault energy decreases when silicon decreases). Our fatigue results agree with those of McEvily [ZO] but the influence of fitness to cross slips on intergranular cracking is not yet understood and opposite results can be noticed in b.c.c. or f.c.c. structures [Zl, 22). 6. CONCLUSION In this study, we wanted to get an accurate analysis of grain boundaries in iron-silicon alloys and es-
pecially of the influence of GB segregations. A.E.S. measurements and intergranular fractures that are usually employed for such considerations were not fitted for our alloys, particularly because of their too high carbon content,which increases the GB strength. Thus we chose diffusion measurements using radioactive tracers. This defines the nature of grain boundaries at the very temperature of the segregation process. Furthermore, the mechanical behaviour of grain boundaries was studied through the initiating period of fatigue cracks. The main advantage is that fatigue tests can be performed on the pieces used for diffusion measurements. Experimental results show that diffusivity data cannot be explained only by segregation effect or silicon contents. From fatigue tests, we noticed that inter-
Fig. 7. Superficial cracks observed on Fe 6.5 wt.% Si aPoys.
D. TREHEUX er al:
SILICON CONTENT OF IRON SILICON ALLOYS
931
Fig. 8. Typical feature of cracking for Fe-4 wte< Si alloys. Fig. 9. Typical feature of cracking for Fe 4 wt% Si alloys. granular cracking is strongly favored by high silicon level and that grain boundaries play complex roles. So, we think that grain boundaries structure evolves with both silicon lattice concentrations and temperature. However a better knowledge of grain
Fig. IO
boundaries in iron silicon alloys needs extensive work on carbon effect and especially on the mutual segregation due to silicon, carbon and other minor elements such as oxygen or sulphur. Now, still in relation with
Cracks near a grain boundary
(Fe-4 wtqo Si)
938
D. TREHEUX et al:
SILICON CONTENT OF IRON SILICON ALLOYS 7. P. L. Gruzin, Dokl Akad Nauk SSSR 86,289 (1952). 8. B. Million, Czech. J. Phys. B 27, 928 (1977). 9. H. V. M. Mirani, R. Harthoom, P. J. Zuurendonk, S. J. Herlmerhorst and G. de Vries, Physica status Solidi (a)
29, 115 (1975). 10. R. J. Borg and 0. Y. F. Lai, J. appl. Phys. 41, 5193 (1970). 11. J. Kucera, B. Million, J. Ruzidkova. V. Foldyna and A. Jakobova, Acta metall. 22, 135 (1974). 12. J. Friedberg, L. E. Tomdahl and M. Hillert, Jernkontorets nnn. 153. 263 (1969). in Metals, p. 117. Claren13. D. McLean, G&in b&d&es don Press, Oxford (1957). 14. J. C. Fischer, J. Appl. Phys. 22, 74 (1951). 15. V. T. Borisov, V. M. Golikov and G. V. Schetbedinskiy, Fizikza Metall. 17, 881 (1964). 16. P. Guiraldenq, J. Phys. suppl. 36, C4 201 (1975). 17. D. Gupta and R. Rosenberg, Thin solid Films 25, 171 (1971). 18. E. D. Hondros, J. Phys. suppl. 36. C4 117 (1975). 19. L. Vincent, B. Coquillet and P. Guiraldenq, 1 Vth Bolton Landing-Co&
Grain Boundaries
in Engineering
Materials, p. 410 Claitor’s Pub. Div. (1974). 20. A. J. McEvily and T. L. Johnston, Inc. Con& Fract., Sendai Japan p. 45 (1965). 21. A. W. Thompson and W. A. Backofen. Acta metall. 19. 597 (1971). 22. H. Ishii and J. Weertman, Metal Trans. 2, 3444 (1971).
APPENDIX
Fig. 11. Intergranular cracking for large grain ferrites (Fe-4 wt% Si). the fatigue initiating process, we want to continue this analysis of GB segregation on iron-silicon alloys with a higher purity.
Hondros et al. C2.33 have been working on an iron 3 wt”< silicon alloy that is, xni = 5.7 at.%. Then, they obtain an 18% of segregated monolayer and thus a segregation ratio 9 = 18/5.7 = 3. After McLean. this gives a GE concentration of 0.5 with y = j[lfl. This is obtained as well as A.E.S. as by measuring GB energy. With McLean’s relationship [13],
u
hi XGLW
=
623 (1966). 2. E. D. Hondros and L. E. S. Stuart. Phil. Maa. _ 17. 711 (1968). 3. E. D. Hondros and M. P. Seah. Scripta metall. 6, 1007 (1972). 4. T. Watanabe, T. Murakami and S. Karashima, Scripta metall. 12, 361 (1978). 5. J. Bernardini and G. Martin. Scriota . metall. 10. 833 (1976). 6. P. Gas and J. Bemardini, XIXe Colloque Metallurgie Speciale (edited by C. E. N. Saclay) 459 (1976).
,l
1 + hi ev -
REFERENCES 1. G. Odin and C. Goux, MPm. scient. Rev. M&all 7/8,
exp-- RT
”
RT
we obtain --
rJ RT
=
log
XGSSi %I(1 -
xGBSi*)
For us, U = -2.86RT A.E.S. measurements were made near 1125 K and GB ones near 16OOK. thus we considered a mean value of silicon-GB interaction energy as LI = - 8000 cal/mole.
L. VINCENT
and P. GU~~ALDENQ
Laboratoire Mttaliurgie-Physique-Matiriaux (ERA 732), Ecole Centrale de Lyon-BP 16349130 Ecully. France (Received 8 October 1980) Abatraet-Self diffusion of 59Fe in iron silicon alloys is measured in the paramagnetic field. Bulk and grain boundary diffusions are character&i by a slight decrease of constants for alloys up to Zat.% silicon, and then by a regular increase. The grain boundary results are not to be related to a segregation coefficient but perhaps to an alteration of the grain boundary structures of Fe-Si alloys. These conciusions well agree with the complex behaviour of the very first fatigue crack in relation to the grain boundaries of the same ailoys. R&u&--L’autodifiusion du fer 59 darts des alliages Fe-Si (0 a 121 at%) a Cte mesuree dans ie domaine paramagnetique. Aussi bien en volume qu’aux joints de grain, on note une faible decroissance des coefficients de diffusion jusqu’a environ 2 at.% Si puis une croissance rigulibre. Dans le cas des joints, les variations enregistrtcs ne peuvcnt pas itre dues au coefficient de segregation mais pourraient Otre l&s a une modification de la structure des joints des a&ages fer-silicium. Zasammatfasaung-Die Selbstdiffusion von 59Fe wurde in Eisen-Silizium im paramagnetischen Bereich gemessen. In Kristallen bis zu etwa 2At.-% Si wurde ein leichter Rbckgang der Koeffixienten sowohl fib die Volum- als such fiir die Korng~~iffusion auf~funden, dariiber ergab sich ein regelt&Biger Anstieg. Bei der Kom~~iff~ion lassen sich die Ergebnisse nicht mit den Segregationskoe%ximten verbinden, m&glicherweise aber mit einer ~nde~ng in dcr Komgre~struktur dieser Fe-Si-Legienmgen. Die Folgerungen entsprechcn den kompliiierten Wechselwirkungen zwischen den ersten Ermiidungsrissen. und den in diesen Legierungen beobachteten’K&ngrenzen.
1. LNTBODUCTION Odin andGoux [l] have shown that the complex phenomena leading to intergranular brittleness of iron-siiicon alloys can be related to silicon content and also to carbon content. For carbon contents higher than lOOppm, alloys, water quenched from 8OO”C, have mechanical properties independent of carbon level [l]. On the other hand, for lower carbon contents, we obtain a threshold value: room temperature fractures are intergranular for upper carbon and intracrystalline for lower one. This critical value decreases with the increase in silicon content: it is 22 ppm for 2 wt% silicon ferrites and 12 ppm for 3wt% ones. Moreover, for the same alloys authors gave evidence of a GB silicon-segregation. Thus, from GB energy measurements at 133O”C, Nondros and Stuart [2] found a GB abso~tion of 7.2 x X0” moles/cm2 for a Fe-3 wt% Si alloy. This corresponds to an “enrichment factor” r~equal to 3. This value was also obtained for the same alloy by direct measurement after heat treatment at 850°C [3] using Auger Electron Spectroscopy (A.E.S.). Recently, always with A.E.S., Watanabe er al. [4] measured at 1250°C the evolution of GB silicon-segregation vs the misorientation of grains for Fe-2.53 wt% Si. The width of the segregated region was estimated at 12-16 nm.
It seems that intergranular brittleness can be explained by silicon segregation phenomena or better by silicon-carbon interactions of GB segregation as well as by an intrinsic brittleness of ferritic grains related to high stresses as proposed by [I]. The inffuence of segregations on the direct m~surement of inter~nu~r ~~f~iffusion is now well admitted [5,6], so the aim of this paper is a study of 59Fe self diffusion of several iron-silicon alloys. MATERIALS AND METHODS Iron-silicon alloys, melted in the Research Center of Creusot-Loire in Unieux (France), have a constant carbon level of 50ppm. Silicon contents are given in Table 1. Other minor elements are about 50 ppm for sulphur and phosphorus and 30 ppm for nitrogen. Self diffusion measurements of iron alloys are made by means of a 59Fe radioactive tracer electrodeposited on specimens. After diffusion heat treatments at constant temperatures, diffusion data are obtained by Gruzin’s method [7]. After successive abrasions, the residual activity is measured by means of a scintillation counter for y rays. Of course, GB self diffusion is made after the determination of lattice data for all studied alloys. 931
932
D. TREHEUX et al:
SILICON CONTENT OF IRON SILICON ALLOYS
Table 1. Silicon contents of studied alloys Weight Percent
0
0.75
0.95
3.41
4.54
Atomic Percent
0
1.48
1.87
6.55
8.64
3. BULK SELF-DIFFUSION
OF IRON
Several studies already enable us to know the influence of silicon on self-diffusion of iron [8-l 11. This leads to the general expression of lattice diffusion data versus silicon content, given in (1) @c-Fe%
=
dceFLsi is the GB diffusion constant and 6 the mean GB width of the grain boundary. Recently, Bernardini and Martin [5] showed that the measured quantity gives a “diffusivity” expression: ppB-FeSi
A GRAIN BOUNDARY SELF DIFFUSION OF IRON 4.1 Analysis of quantities measured by intergranular difficion
On the same alloys, we studied the kinetics of diffusion at iron grain boundaries by means of radioactive tracers. As for bulk constants, we used Gruzin’s method on poiycrystalline specimens. These specimens, with grain sizes inferior to 2OO,nm, were homogenized at the diffusion temperature. Until these last years, one determined by such experiences the product D~~MFeSiS. Let us remember that
Dot 2*-t (cm )
::3 0:63 2.1 3.4
_PGBFC
where poBFc iS the INdW Of kOII atOIIIS for a Unit grain boundary surface and ptFe this number for a unit bulk. To again obtain the “X’ width in the diffusivity term P2B*FeSi,one can write:
(kj m:e,239 253 250 238 228 244 212 212 219 216
1)
Ref.
ct21 Cl11
Fe-FeSi .6.
p&- Fcsi =
sc
DGE
c IFC
where Gee, and CIFc are the number of atoms in a unit volume in grain boundaries and in lattice respectively. Using concentrations defined by atom fractions x, we have PGBF~ PGS
=
XlFc
=
PlFe -
PI
with Pee and pl as the numbers of sites by unit surface in GB and by unit volume in the lattice. Thus, we obtain: Fe-FeSi PGB
. POE. XG.9h
F~-F& DGB
I
PI
=
XIFe
Fe-F&.&.+ DGB xlF.
where S’ is an apparent GB width different from the previous 6. The former expression also states:
Fe-F&i PGB
Table 2. Lattice diffusion data of iron-silicon alloys
:.:5 1:38
DFe-FeSi GB
PFC
XGBF.
1.6 4.4
=
(1)
WSJ
where xsi is the atomic fraction and b a constant found to be about 20 at 900°C (1173 K). Table 2 gives the main results, especially of Million. The standard 0% silicon data were obtained by Million er al. [ 1l] and by the working group of Friedberg et al. [12]. Our results, obtained in a paramagnetic field, are given in table 3 and in Fig. 1 where comparison is made with [8,11,12]. With the increase in silicon content from PA, we notice first a slight decrease in diffusion data. Then, we verify the general law given in (1) with b varying from 26.5 (1073 K) to 15.9 (1273 K) for silicon contents superior to 5 at%.
0 0 5.5 6.4 7.64 7.8 11.1 11.6 15.3 19.2
12.1
Dp-Fe ev
Silicon content at.%
6.48
_
,,&
FeSi .S ‘ . 1 1 -
XGSSI x191
Table 3. Lattice diffusion data of iron-silicon alloys of the present study Silicon content at.%
Do, (cmZ s- ‘)
(kJ medIe_‘)
2.73 1.03 76.7 5.2 4.93 0.8
242 276 276 242 236 213
[ii 0
;;; E:;
C81 PI
1.48 1.87 6.55 8.64 12.1
D. TREHEUX et al:
933
SILICON CONTENT OF IRON SILICON ALLOYS TV
iooo
900
so0
700
z
104
To Fig. 1. Lattice diffusion coefficients in Fe Si alloys -1: 0 at.% Si; 2: 1.87at.% Si; 3: 6.55 at.% Si; 4: 8,64 at.% Si; 5: 12,l at.% Si; --- 0 at.% Si [12]; -.Million’s results [S] a: 5,5 at.% Si; b: 6,4 at.%; c: 7,s at.%; d: 11,6at.%; e: 15,3at.%; f: 19,2at.%. if we neglect impurities in iron except silicon. Thus the experimental measurement PG;+FISi leads us to take into account three parameters: the diffusion coefficient, a segregation expression and a’, or Gvalue, that depends on the GB structure. These last three factors can vary with solute concentrations. 4.2 Experimental
rite GB, A an expression of the vibration entropy and XGmi the GB concentration. GB concentration is then 4 .
results
We tried to obtain an order of magnitude segregation expression a, _ 1 l
of the
-xGIlSi -
xJSi
from literature data about silicon segregation [2, j] and with the use of McLean’s relationship [13].
, .
#I
.
AxIsi exp - $
X GBSi
5
=
L
% at.Si
1 + AXlsi exp - $ Fig. 2. Concentration
where U is the interaction energy of silicon with fer-
IO
dependencies of Fe Lattice diffusion
coefficient in Fe-Si alloys for temperatures 800. 850,900”C.
934
D. TREHEUX et al:
T
.
.
.
.
I
SILICON CONTENT OF IRON SILICON ALLOYS
I.)
IO
5
at. Y. si Fig. 3. Grain boundaries Concentration relationship).
XGmi (MacLean
defined as the ratio of the number of silicon atoms to the number of sites favourable to segregation. Thus, we can express the atom fractions by XGBSI =
a? ,8
Y &ilSi
where y is an expression related to GB structure and disorder. y is inferior to 1 and often taken as l/3 in a first approximation [ 133. From Hondros’s results given in appendix, we obtain a value of U energy about -33 KJ/mole (-8OC0cal/mole) (attraction) and thus we can plot GB concentration (XGBsi)vs lattice concentration and temperature (Fig. 3). The evaluation of the corrective expression
-I
t
L
a
9
IO
IO’ T(K)
is also considered with a mean value of l/3 taken for constant whatever silicon content (Fig. 4). We shall notice that GE concentration slowly varied beyond 8 at.% for lattice silicon levels and that the corrective expression is at its minimal value for this same concentration (then for this value, correction becomes maximal).
Fig 5. Grain boundaries Diffusion in Fe-Si alloys Diffusivity P,,; 1: Oat.% Si; 2: 1.48at.% Si; 3: 6.55at.x Si; 4: 8.64at.% Si; 5: 12.1 at.% Si --- Coefficients DGB6).
On Fig. 5, Arrhenius diagram gives the evolution of the PGB apparently difhrsivity-as given by Fisher’s method Cl]-and of Do& (as obtained from PGlr while taking into account the co&&on of Fig. 4). It first appears that the correction is very slight and that PGB is not far different from Do&‘. An Arrhenius law is verified for the several alloys studied by measured energies have very high values compared to GB diffusion. (Table 4). As for lattice diffusion, we notice different evolutions following the silicon content: for low silicon alloys, diffusivity de? creases and for upper values, diffusivity strongly increases to abnormally high values of activation energies. 4.3 Explanation
0.8
;
’
’
’
’
5
’
’
’
’
’
IO
n
’
x, SI Fig, 4. Concentration dependence of corrective expression 01’for temperatures 800, 900, 1000°C.
’
Recently, Gas and Bernardini [6] have studied silver-tin alloys. For these authors, the pGrAISn self diffusivity linearly increases with tin lattice concentration up to a C1 value beyond which PGB seems to be no longer modified. This result is explained if we consider that a grain boundary may be saturated and
D. TREHEUX Edal:
SILICON CONTENT OF IRON SILICON ALLOYS
Table 4. POGBand QG,,values obtained for the five alloys Silicon content at:; 0 1.48 6.55 8.64 12.1
(;q
1)
2.1 10-S 6 lo+ 279 i.1 x 10’ 7.3 x IO6
QGB
kJ mole- ’ 237 193 334 422 413
935
At last, one cannot neglect the carbon effect and especially the possible silicon-carbon interaction. However, it appears very difficult to analyse the mutual segregation of these two elements. First of all, direct measurements by A.E.S. (and explanation of mutual segregation) are not yet well known and furthermore our ailoys do not generally exhibit intergranular fractures after impact test [l], particularly when they are not of a very high purity. However this parameter may strongly influence the mechanical behaviour of grain boundaries.
thus remain identical beyond the C, value. Now, we want to compare our results to AgSn ones. 5. FATIGUE PROPERTIES OF In both results, the self diffusivity coefficient inIRON SILICON FERRITES creases with solute content for the investigated temperatures. Measurements for higher silicon contents The importance of grain boundaries in the dynamic (13.9 and 17.3 at.%) at 900°C (1173 K) show that PGB process of fatigue crack initiation has been studied by no longer increases beyond 12 at.% silicon concenmeans of ball-plane fatigue tests. This device, detration. This gives evidence of a maximal level of difscribed in [I93 permits a stress of 35 x 10s Pa at the fusivity as for AgSn. surface of the plane specimen (standard balls are By considering the evolution of GB concentration made in A120J with a 10mm diameter). These con(Fig. 3), one would conclude that boundaries are satuditions give a maximal shearing stress of 10 x 10s Pa rated. However, we must notice that this saturation at a crystal depth of 0.22 mm as indicated by Hertz’s occurs for concentratio? about 50% of the limit bulk theory, After 4.5 x lo6 cycles (at 25 hz), specimens solubility of silicon in iron while this value is less than mounted in “half-shell” pattern are observed in the 10% for Ag-Sn. most stressed zones and then we can obtain the place Borisov’s relationship [15,16] gives increasing of the very first cracks in a diametral plane of plane energies with solute concentrations (EGB defined by Strain. Borisov is pro~~ional to RT Log DEEDS), which Fatigue tests were conducted on iron siliuin alloys does not agree with either direct measurements (2) or up to 6.48 Wt% -silicon cuntents, after heat treatment a segregation process. With the same formulation, at 800°C (30mn) and water quenchihg (mean grain Gupta [ I73 did obtain decreasing energies for Au-Ta. sizes = 50 m). The main results of these observations In fact. we must not use Borisov’s relationship for are summed up below) self diffusion in alloys and this approach is character1. For pure iron ferrites, cracks are always related istic of GB properties but not of GB energy. Now it to slip lines and never grain boundaries (Fig. 6). becomes obvious that for decreasing energies with solute concentration, one may find either an increase 2. For high silicon ferrites, grain boundaries are the (Ag-Sn, Fe-Si) or a decrease (Au-Ta [lq) of the self main ways of cracking. Especially, in such brittle diffusivity. For a same binary system, the. evolution alloys, cracks initiate in sublayers and go up to the may change for a critical temperature (for instance surface by means of GB networks (Fig. 7). Then, 350°C with Au-Ta). Thus, we can conclude that difpropagation can be inter or transcrystalline. fusivity and GB energies have not the same evolution 3. The intermediate silicon alloys (4 wt%) exhibit a vs the lattice concentration. mixed feature (inter and transcrystalline cracks. Figs We cannot explain diffusivity measurements and es8, 9). In fact, grain boundaries appear to be of the pecially the high activation energies only by segregagreatest importance and some observations indicate tion effect of silicon and hence by the GB concenthat cracks accompany a grain boundary at a very tration of silicon (indeed this last value slightly varies short distance (Fig. 10). This feature is to be related to with temperature). We think that we have to consider the problem of the GB width and thus shows all the an increasing evolution of GB structure with lattice importance of a better knowledge of the GB structure. ~ncentration and tempwature, in addition to segre4. At last in 4wt% ferrites quenched from higher gation phenomena. This would lead to an alteration temperatures (950°C) and with coarse grains. cracks initiate in the grain boundary, in the most stressed Of DGB and probably of 6’ (and hence P,,) values. This agrees quite well with Odin’s and Goux’s results zones below the surface. Then, we can observe several and with the large width of segregation (12-16nm) slip planes and especially we notice that one system measured by Watanabe et al. [43 though the profile of seems to appear before the crack at the opposite of distribution of segregation silicon. Usually the conthe other succeeding ones (Fig. 11). Thus, the GB centration profile of segregating species gives width influence upon fatigue properties seems to be related up to 1.5 nm (18), then. it may be possible that the to three fields: A the grain boundary itself, B a thin increase of PGB with s’ilicon content would be a consezone all around GB and at last C the grain unaltered quence of the increase in GB width beyond 4 a?.“/, Si. by any GB- p~enomenom. The B zone, in which
936
D. TREHEUX et al:
SILICON CONTENT OF IRON SILICON ALLOYS
Fig. 6. Feature of cracking for pure iron ferrites.
secondary slips are mainly observed, is mainly noticed for 4 wt% silicon ferrites. For lower silicon contents, the slip bands in “C” region are the main places of cracking. This is probably due to a better accomodation of stresses at GB due to the greater fitness to cross slips of low silicon ferrites (indeed fault energy decreases when silicon decreases). Our fatigue results agree with those of McEvily [ZO] but the influence of fitness to cross slips on intergranular cracking is not yet understood and opposite results can be noticed in b.c.c. or f.c.c. structures [Zl, 22). 6. CONCLUSION In this study, we wanted to get an accurate analysis of grain boundaries in iron-silicon alloys and es-
pecially of the influence of GB segregations. A.E.S. measurements and intergranular fractures that are usually employed for such considerations were not fitted for our alloys, particularly because of their too high carbon content,which increases the GB strength. Thus we chose diffusion measurements using radioactive tracers. This defines the nature of grain boundaries at the very temperature of the segregation process. Furthermore, the mechanical behaviour of grain boundaries was studied through the initiating period of fatigue cracks. The main advantage is that fatigue tests can be performed on the pieces used for diffusion measurements. Experimental results show that diffusivity data cannot be explained only by segregation effect or silicon contents. From fatigue tests, we noticed that inter-
Fig. 7. Superficial cracks observed on Fe 6.5 wt.% Si aPoys.
D. TREHEUX er al:
SILICON CONTENT OF IRON SILICON ALLOYS
931
Fig. 8. Typical feature of cracking for Fe-4 wte< Si alloys. Fig. 9. Typical feature of cracking for Fe 4 wt% Si alloys. granular cracking is strongly favored by high silicon level and that grain boundaries play complex roles. So, we think that grain boundaries structure evolves with both silicon lattice concentrations and temperature. However a better knowledge of grain
Fig. IO
boundaries in iron silicon alloys needs extensive work on carbon effect and especially on the mutual segregation due to silicon, carbon and other minor elements such as oxygen or sulphur. Now, still in relation with
Cracks near a grain boundary
(Fe-4 wtqo Si)
938
D. TREHEUX et al:
SILICON CONTENT OF IRON SILICON ALLOYS 7. P. L. Gruzin, Dokl Akad Nauk SSSR 86,289 (1952). 8. B. Million, Czech. J. Phys. B 27, 928 (1977). 9. H. V. M. Mirani, R. Harthoom, P. J. Zuurendonk, S. J. Herlmerhorst and G. de Vries, Physica status Solidi (a)
29, 115 (1975). 10. R. J. Borg and 0. Y. F. Lai, J. appl. Phys. 41, 5193 (1970). 11. J. Kucera, B. Million, J. Ruzidkova. V. Foldyna and A. Jakobova, Acta metall. 22, 135 (1974). 12. J. Friedberg, L. E. Tomdahl and M. Hillert, Jernkontorets nnn. 153. 263 (1969). in Metals, p. 117. Claren13. D. McLean, G&in b&d&es don Press, Oxford (1957). 14. J. C. Fischer, J. Appl. Phys. 22, 74 (1951). 15. V. T. Borisov, V. M. Golikov and G. V. Schetbedinskiy, Fizikza Metall. 17, 881 (1964). 16. P. Guiraldenq, J. Phys. suppl. 36, C4 201 (1975). 17. D. Gupta and R. Rosenberg, Thin solid Films 25, 171 (1971). 18. E. D. Hondros, J. Phys. suppl. 36. C4 117 (1975). 19. L. Vincent, B. Coquillet and P. Guiraldenq, 1 Vth Bolton Landing-Co&
Grain Boundaries
in Engineering
Materials, p. 410 Claitor’s Pub. Div. (1974). 20. A. J. McEvily and T. L. Johnston, Inc. Con& Fract., Sendai Japan p. 45 (1965). 21. A. W. Thompson and W. A. Backofen. Acta metall. 19. 597 (1971). 22. H. Ishii and J. Weertman, Metal Trans. 2, 3444 (1971).
APPENDIX
Fig. 11. Intergranular cracking for large grain ferrites (Fe-4 wt% Si). the fatigue initiating process, we want to continue this analysis of GB segregation on iron-silicon alloys with a higher purity.
Hondros et al. C2.33 have been working on an iron 3 wt”< silicon alloy that is, xni = 5.7 at.%. Then, they obtain an 18% of segregated monolayer and thus a segregation ratio 9 = 18/5.7 = 3. After McLean. this gives a GE concentration of 0.5 with y = j[lfl. This is obtained as well as A.E.S. as by measuring GB energy. With McLean’s relationship [13],
u
hi XGLW
=
623 (1966). 2. E. D. Hondros and L. E. S. Stuart. Phil. Maa. _ 17. 711 (1968). 3. E. D. Hondros and M. P. Seah. Scripta metall. 6, 1007 (1972). 4. T. Watanabe, T. Murakami and S. Karashima, Scripta metall. 12, 361 (1978). 5. J. Bernardini and G. Martin. Scriota . metall. 10. 833 (1976). 6. P. Gas and J. Bemardini, XIXe Colloque Metallurgie Speciale (edited by C. E. N. Saclay) 459 (1976).
,l
1 + hi ev -
REFERENCES 1. G. Odin and C. Goux, MPm. scient. Rev. M&all 7/8,
exp-- RT
”
RT
we obtain --
rJ RT
=
log
XGSSi %I(1 -
xGBSi*)
For us, U = -2.86RT A.E.S. measurements were made near 1125 K and GB ones near 16OOK. thus we considered a mean value of silicon-GB interaction energy as LI = - 8000 cal/mole.