On the fracture path and the intergranular phosphorus distribution in phosphorus-doped FeSi symmetrical bicrystals

Acta metall, mater. Vol. 39, No. 6, pp. 1289-1295, 1991 Printed in Great Britain. All rights reserved

0956-7151/91 $3.00 + 0.00 Copyright © 1991 Pergamon Press plc

O N THE F R A C T U R E PATH A N D THE I N T E R G R A N U L A R P H O S P H O R U S D I S T R I B U T I O N IN P H O S P H O R U S - D O P E D Fe-Si S Y M M E T R I C A L BICRYSTALS M. ME YHARD'~, B. ROTHMAN and C. J. McMAHON Jr Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.

and P. LEJCEK and V. PAIDAR Institute of Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia (Received 24 July 1990) Abstraet--A high-resolution scanning Auger microprobe analysis was carried out on matching fracture surfaces of symmetrical E = 5 (013) bicrystals of Fe-3 wt%Si doped with 270ppm phosphorus which were grown from seeds by floating-zone melting. The phosphorus distribution on some regions of a fracture surface was found to alternate between high and low concentrations; these alternations were often associated with deformation bands, such as mechanical twins. The reverse pattern was found on the matching region on the opposite fracture surface. This confirms a hypothesis made earlier that the inhomogeneous phosphorus concentrations found on fracture surfaces are the result of off-center crack propagation through a laterally extended phosphorus distribution along the grain boundary and the switching of the crack path from one side to the other upon an encounter with a grain-boundary step caused by a deformation band. In the regions of unequal division of the P-enriched region by the fracture, a 2: 1 ratio of phosphorus concentrations was found. The total width of the region was deduced to be about five atomic planes from observations of sputtering rates and an analysis based on simple logic. Rrsumr----On effectue une analyse par spectrom&rie AUGER en balayage 5- haute rrsolution sur des surfaces de rupture correspondantes de bicristaux symrtriques ~ = 5 (013) de Fe-3% en poids Si doprs de 270 ppm de phosphore (ces bicristaux sont 61aborrs 5- partir de germes par la mrthode de la zone flottante). On trouve que la distribution de phosphore sur certaines rrgions de la surface de rupture alterne entre de fortes et de faibles concentrations; ces alternances sont souvent associees 5-des bandes de drformation telles que des macles mrcaniques. On trouve une situation inverse dans la region correspondante, sur la face opposre de la rupture. Ceci confirme l'hypothrse drj5- formulre que les concentrations hrtrrogrnes de phosphore trouvres sur les surfaces de rupture sont le rrsultat de la propagation de fissures qui s'rcartent 5_ travers une distribution de phosphore 6tendue latrralement le long due joint de grains ainsi que du changement du chemin de la fissure d'un crt6 5- l'autre lorsqu'elle recontre une marche du joint de grains due 5- une bande de drformation. Dans les rrgions oti la zone enrichie en phosphore est divisre inrgalement par la rupture, on observe un rapport de concentration en phosphore de 2 1. La largeur totale de cette rrgion est d'environ cinq plans atomiques d'aprrs des observations de vitesse de pulvrrisation et une analyse basre sur la simple logique. Zusammenfassun~-Bruchfl~ichenpaare von symmetrischen E=5/(013)-Bikristallen aus Fe-3 Gew.%Si, die mit 270ppm Phophor dotiert durch Zonenschmelzen yon einem Saatkristall geziichtet worden sind, werden mittels hochauflrsender Raster-Augermikroanalyse untersucht. In einigen Bereichen einer Bruchfl/iche ergab sich, dab die Phosphorverteilung zwischen hoher und niedriger Konzentration schwankte. Diese Schwankungen h/ingen h/iufig mit Verformungsb/inderu, z.B. mechanischen Zwillingen zusammen. Die entgegengesetzte Verteilung findet sich auf der entsprechenden Stelle der passenden Bruchfl/iche. Diese Beobachtung best/itigt eine frfihere Hypothese, dab die inhomogene Phosphorverteilung auf Bruchfl[ichen das Ergebnis einer RiBausbreitung auBerhalb der lateral ausgedehnten Phosphorverteilung an Korngrenzen und des Umschlagens des Risses von eienr Seite zur anderen an Korngrenzstufen, verursacht durch Verformungsb/inder, entsteht. In den vom Bruch ungleich aufgeteilten P-angereicherten Gebieten wird ein Verh/iltnis von 2:1 der Phosphorkonzentrationen gefunden. Die gesamte Breite dieses Bereiches 1/iflt sich aus den Beobachtungen der Sputterraten und einer auf einem einfachen Argument bestehenden Analyse zu etwa 5 Gitterebenen absch/itzen.

tPermanent address: Research Institute for Technical Physics of the Hungarian Academy of Sciences, Budapest, Hungary. 1289

1290

MENYHARD et al.:

FRACTURE IN PHOSPHORUS-DOPED Fe-Si BICRYSTALS

INTRODUCTION It was previously reported [1] that a peculiar kind of non-uniform distribution of phosphorus could be observed on the expansive, relatively flat intergranular fracture surfaces of symmetrical X = 5 (013) bicrystals of Fe-3 wt%Si doped with 270 ppm phosphorus, a well-known segregating and embrittling impurity in iron and steels. As can be seen in Fig. 1, the non-uniformities in the phosphorus distribution, as revealed by Auger mapping, are associated with deformation markings, many of which appear to be mechanical twins. The ratio of the phosphorus concentration in regions of high vs low concentration was about 2:1, as shown by Fig. 2. The possibility that the phosphorus distribution was non-uniform in the grain boundary before fracture and that the deformation bands were either causally or fortuitously associated with such non-uniformities was rejected as highly unlikely. Rather, it was suggested that the phosphorus concentration was uniform in the unfractured grain boundary and that the crack propagated off-center along the phosphorusenriched grain boundary. The jumps from high to low

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Fig. 2. Results of Auger analyses of phosphorus concentrations at randomly selected spots in regions of high and low phosphorus [1]. concentration and vice versa were taken to indicate that the crack switched from one side of the boundary region to the other when a grain-boundary step caused by a deformation band was encountered, as indicated schematically by Fig. 3. At the time of these observations, only one side of the fracture could be analyzed, since the opposite side was not retained in the fracture device in the UHV chamber. In order to test the above hypotheses, additional specimens were prepared, and the fracture specimen and holder were modified so that both sides of the fracture could be analyzed. The observation of reversed high/low concentrations on matching sides would confirm the hypotheses. The present report gives the results of the later observations, which have allowed us to make an estimate of the thickness of the phosphorus region along the grain boundary. PROCEDURE

As in the previous work [1], samples with the grain boundary oriented for tensile fracture in bending were cut from one large Fe-Si bicrystal, which had been grown from oriented seeds by the floating-zone technique and which had the composition given in Table 1. P REGION OF P ENRICHMENT ALONG GB

. / CRACK

Fig. 1. (a) Portion of the fracture surface of an Fe-Si bicrystal exhibiting deformation bands due to twinning and slip. (b) Phosphorus Auger map of the same area, showing that the boundaries between regions of high and low phosphorus coincide with the deformation bands [1].

Fig. 3. Schematic representation of a grain boundary offset caused by a deformation twin and the proposed effective switch of the crack path from one side of the phosphorus distribution to the other [1].

MENYHARD et al.: FRACTURE IN PHOSPHORUS-DOPED Fe-Si BICRYSTALS

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Table 1. Alloycompositionwt% Si 2.93

P

0.027

C

N

O

S

0.004 0.0007 0.0008 <0.001

The two grains were symmetrically tilted 37° about a (100) rotation axis, and the boundary plane was within 3° of the ~ = 5 (013) orientation. The samples were machined into 3.7 mm dia. cylinders which were fitted with brass extensions, and a circumferential notch was cut at the grain boundary, which was oriented normal to the axis of the cylinder. Three of the samples were fractured in the as-grown and slowly cooled condition, and three were first given an annealing treatment of 750°C in dry hydrogen for 120 hr, followed by slow cooling, before fracture. The samples were fractured in bending at about 140K in a vacuum of about 6 x 10-SPa (5 x 10 -l° torr) in a PHI 600 scanning Auger microprobe. The conditions for analysis were as follows: primary beam voltage = 10 kV, beam diameter = 0.4 pro, detection mode: N ( E ) x E, beam current = < 0.1 #A. In order to be able to retain both halves of the fractured specimens for analysis, a nickel wire was spotwelded to the specimen on either side of the notch, and part of the specimen holder was cut away to accommodate the retained top half of the specimen after it was bent through 180° in the fracture process. Surface compositions are given in terms of atom fractions, as expressed by the system software, which uses the calibration factors given in Ref. [2]. The concentrations of iron, silicon, and phosphorus were taken to add up to 100%; even though small amounts of carbon and oxygen were sometimes present, the error in any case would be small. In the case of phosphorus, a correction factor of 0.6 was applied to the relative sensitivity factor, after [3], to account for the fact that the phosphorus was present in detectable amounts only on the surface. RESULTS A fractured sample is shown in Fig. 4 to illustrate the arrangement by which both halves were retained

Fig. 4. Bicrystalsample after fracture in UHV, showing wire attached to retain both halves for Auger analysis. for analysis. The fracture surface of an as-grown bicrystal is shown at higher magnification in Fig. 5. The fracture is mostly intergranular, but there are many small tongues of cleavage fracture associated with deformation bands. These indicate the tendency of the crack tip to be diverted upon encountering a step in the grain boundary caused by a deformation band. These deformation bands, which appear to be mainly mechanical twins, presumably form ahead of the crack in the high stress field of the approaching crack. Matching portions of the opposite fracture surfaces are shown at still higher magnification, along with the corresponding phosphorus Auger maps, in Fig. 6. It can be seen that the demarcation between the high- and low-phosphorus regions coincides with

(a) (b) Fig. 5. Matching areas from opposite sides of the fracture surface of a bicrystal in the as-grown condition.

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MENYHARD et al.:

FRACTURE IN PHOSPHORUS-DOPED Fe-Si BICRYSTALS

B1 Fig. 6. (a, b) Centralportion ofFigl 5(a)~further magnified, with corresponding phosphorus Auger map. (c, d) Similarly for central (matching) portion of Fig. 5(b).

the prominent twin, indicated by the arrow. The phosphorus concentrations in the high vs low and low vs high concentration regions are shown in Fig. 7. It is apparent that the high concentration on one side of the fracture matches up with a low concentration on the other and that the ratio of the concentrations is about 2:1, as found previously. Other examples of this phenomenon were found on the as-grown sample; the other two as-grown samples failed to fracture along the grain boundary. 11 o o

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Fig. 7. Phosphorus concentrations at several points in the high- and low-phosphorus regions on the matching areas shown in Fig. 6.

The matching halves of one of the fractured samples which had been previously annealed in hydrogen are shown in Fig. 8. The fracture is essentially completely intergranular, and the incidence of deformation bands and cleavage tongues is far less than in the as-grown specimen. The main purpose of the hydrogen anneal was to reduce the carbon content of the alloy and thereby to weaken the grain boundaries, which, as is well known, are greatly strengthened by segregated carbon. This purpose was obviously achieved. Matching areas of the expansive fracture surfaces were analyzed, and two kinds of results were found. One kind is exemplified by Fig. 9, which shows the phosphorus concentrations at twenty points chosen at random from areas which match across the fracture path, within the accuracy of the site location on the scanning electron images. (Note that there is no point-to-point correspondence in the figure). In areas like this, the approximately 2:1 ratio of concentrations was observed, indicating that the crack travelled off-center through the intergranular phosphorus distribution over large distances. Note the absence of overlap between the two sets of measurements. An example of the other kind of area is shown in Fig. 10. Here, the two sets of measurements from

MENYHARD et al.:

FRACTURE IN PHOSPHORUS-DOPED Fe-Si BICRYSTALS 10

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Fig. 8. Matching fracture surfaces of hydrogen-annealed bicrystal.

opposing areas overlap extensively, and the means are equivalent. Also, the range of the measurements is less than that found in the areas which showed the 2:1 variation in concentration. Nonetheless, the range is still quite large, and the implication of these results is not that the crack ran along the center of the intergranular phosphorus distribution over large distances, but, rather, than it varied randomly from one side to the other over very short distances. It cannot be determined from this work whether the two kinds of division of the intergranular phosphorus concentration by the fracture process stem from variations in grain boundary structure, although this is certainly a possibility. The grain boundaries in these bicrystals were not absolutely fiat; on the atomic scale the variations in structure were undoubtedly quite large. In the regions in which the phosphorus was unequally distributed on matching areas on either side of the fracture, the 2:1 ratio was found consistently. In order to examine the thickness of the high- and low-phosphorus regions, corresponding fracture surfaces were sputtered with 3 keV Ar + at normal incidence in the scanning mode and intermittently Auger analyzed for phosphorus. The results are given in Fig. 11. Any difference in the thickness of the P-enriched layers in the high- and low-P regions, is too small to be detected by this method.

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Fig. 9. Results of phosphorus Auger analysis at matching spots on opposite sides of the fracture in an area with unequal phosphorus concentrations on either side of the specimen shown in Fig. 8.

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Fig. 11. Results of Ar + sputtering to remove phosphorus from a region of high phosphorus and from one of low phosphorus, showing that the thicknesses of the P-enriched layers are indistinguishable.

MENYHARD et al.: FRACTURE IN PHOSPHORUS-DOPED Fe-Si BICRYSTALS

1294

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Fig. 12. Sputtering profile from an as-fractured grain boundary, compared with the profile obtained when the sputtered surface was reheated to allow phosphorus segregation to the free surface,

To give some idea of the thickness of the segregated layer, the same sputtering procedure removes SiO2 from Si at the rate of 2.8/~/s. Correcting for the difference in density, it would then be expected to sputter iron at about 1/~/s. Hence, an atomic layer would be removed in 2-3 s, depending on the surface involved. The results in Fig. 11 would then indicate that the phosphorus was contained within the first three atomic layers. Several sputtered fracture surfaces were heated in situ in UHV, allowing phosphorus to segregate to the free surface to approximately the same level as had been found on the freshly fractured surface. The rate of phosphorus removal by sputtering was then observed on the re-segregated surface. An example of the comparison of the sputtering rates from the two kinds of surface is shown in Fig. 12. It was consistently found that the phosphorus which segregated to the free surface was removed faster than that on an intergranular fracture surface. The phosphorus on the heated free surface was presumably lying in interstices of the outermost layer of iron atoms. Hence, these results indicate that some of the phosphorus along the fractured grain boundary was situated below, but not far below, the outermost iron layer.

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In order to examine further the possible distribution of phosphorus along the grain boundary, let us use the model of the Y~= 5 (013) boundary in pure iron calculated by Hashimoto et al. [4], as shown in Fig. 13. The central atom layer is designated as layer 0, and the two adjacent layers on either side are called + 1, + 2, respectively. We note that the grain boundary comprises a periodic repetition of the structural unit shown in the figure. Thus, the grain boundary can be considered to comprise the five layers of atoms used to make up the structural units. Any segregation to sites within those five layers, therefore, lies "in the grain boundary." The present results indicate that a sub-monolayer total coverage of phosphorus is distributed over a number of layers. In order to explore the significance of the 2:1 ratio of phosphorus on matching fracture surfaces of unequal concentration, we will start with the simplest possible case, in which the crack is assumed to travel in an absolutely fiat planar path and in which we ignore any attenuation of the phosphorus Auger signal emitted from atoms not on the uppermost atomic layer on the fracture surface. We assume first that the crack travels for a long distance on one or the other side of layer 0 in Fig. 13. That is, it travels between layers 0 and + 1, or 0 and - 1 ; we use the former for this argument. Let the number of phosphorus atoms in each layer be No, Ni ~, N i - , . . • etc. The observed 2:1 ratio means that No + YN~--2. ZN3 Hence

No= Y~N, assuming that N~ = NT. That means that one-third of the phosphorus lies in layer 0, and the rest lies in other layers on either side, If one were to assume, alternatively, that the crack traveled between layers farther from layer 0, then the 2:1 ratio could not be rationalized. For example, if it were assumed to travel between layers + 1 and + 2, then we would write for a five-layer distribution, for example

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which is physically quite unrealistic, since the amount of phosphorus in layers 0 and ± 1 must be larger than in the other layers on one side of the boundary.

MENYHARD et al.: FRACTURE IN PHOSPHORUS-DOPED Fe-Si BICRYSTALS

Fig. 14. Hard-sphere model of the top three atom layers of a {013} surface of a b.c.c, crystal. Hence, in this framework, we would conclude that the crack travels on one side of layer 0 or the other. We note, again, that all five layers can be said to make up the grain boundar3 per se. Thus, atoms lying in layers +__1 or +__2are not to be thought of as being "in the bulk". This calculation could be made more elaborate by considering the escape depth of the 120 eV Auger electron emitted by phosphorus atoms not lying on the topmost layer. However, this would be of questionable value in view of the fact that we are considering only three atomic layers along a {013} fracture surface and that this plane is very loosely packed. The packing density of a {013} plane in a b.c.c, crystal made of hard spheres is only 0.37, compared with the 0.83 packing density of the mostclosely packed ( 110} plane. A hard-sphere representation of three atomic layers of a {013} plane is shown in Fig. 14. This model could represent a fracture surface which relaxed by small atomic shuffles after the crack had passed. If the phosphorus concentration on the surface were around 7at.% , then about 3 of the 48atoms shown would be phosphorus. If a phosphorus atom were to lie in the second layer, the Auger signal attenuation would probably be negligible. The third layer is only 0.73 atom diameters below the top layer and the atoms are partly exposed in the hard-sphere model. Therefore, the Auger signal attenuation from this layer would not be large, either. The sputtering results reported here suggest strongly that essentially all the phosphorus is contained within five atom layers; i.e. two layers on either side of layer zero. This would agree with the state-

1295

ment of Hashimoto et al. [4], based on considerations of the stress fields around phosphorus atoms, that "the impurity atoms easily segregate not only on the boundary p l a n e . . . , but also on the nearest or next-nearest layers." These results point up the fundamental difference between segregation to a grain boundary and to a free surface, on which it is generally found that the segregated atoms lie only in or on the topmost layer. This raises a serious question, for example, about the appropriateness of thermodynamic analyses which attempt to relate the energy of a fractured grain boundary to the energy of a free surface containing the same impurity. CONCLUSIONS The conclusions which can be drawn from this work are that: 1. The path of brittle crack propagation along the present E---5 grain boundaries is often asymmetric with regard to the intergranular phosphorus distribution, sometimes running along one side of the distribution over very large distances. 2. Deformation bands, such as twins, which form ahead of the running crack can serve to deflect the crack front from one side of the distribution to the other. 3. Based on the 2:1 ratio of phosphorus concentration in areas where the fracture path did not divide the P-enriched region symmetrically, on the results of sputtering experiments, and on a simple analysis, it is concluded that the total width of the P-enriched region in these symmetrical tilt boundaries is around five atom layers. Acknowledgements--This work was partly supported by the

National ScienceFoundation through the MRL program at the University of Pennsylvania under Grant No. DMR 88-19885. REFERENCES

1. M. Menyhard, C. J. McMahon Jr, P. Lejcek and V. Paidar, Mater. Res. Soc. Symp. Proc. 122, 255 (1988). 2. L. E. Davis, N. C. McDonald, P. W. Palmberg, G. E. Riach and R. E. Weber, Handbook of Auger Electron Spectroscopy. Physical Electronics, Eden Praire, MN (1978). 3. H. Erhart and H. J. Grabke, Metal Sci. 15, 401 (1981). 4. M. Hashimoto, Y. lshida, R. Yamamoto and M. Doyama, Aeta metall. 32, 1 (1984).