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INTERGRANULAR FRACTURE IN METALSC. Briant

To cite this version:C. Briant. INTERGRANULAR FRACTURE IN METALS. Journal de Physique Colloques, 1988, 49(C5), pp.C5-3-C5-23. <10.1051/jphyscol:1988501>. <jpa-00227998>

JOURNAL DE PHYSIQUE Colloque C5, suppl6rnent au nelO, Torne.49, octobre 1988

INTERGRANULAR FRACTURE I N METALS

C.L. BRIANT

General Electric Company, Corporate Research and Development, PO Box 8. Schenectady, NY 12301, U.S.A.

ABSTRACT

This paper concerns brittle intergranular fracture in metals. It is shown that the primary cause of intergranular fracture is impurity segregation. However, the ability of a given concentration of an embrittling species to cause fracture can be modified by many factors. These include the orientation of the grain boundary with respect to the stress axis, the structure of the grain boundary, the presence of second phase particles, and the general mechanical response of the material. It will be shown that intergranular fracture can be considered as a simple dissociative chemical reaction and models to explain the bond weakening caused by impurities will be discussed.

INTRODUCTION

Intergranular fracture in metals has been studied for many decades. It can occur in many different ways. These include the brittle rapid fracture often observed when impurities have segregated to grain boundaries, failure during creep, failure by liquid metal or solid metal embrittlement, and failure by stress corro- sion cracking. In this paper I will be concerned only with the first of these.

The interest in brittle intergranular fracture arises from the many specific embrittlement problems that can occur in metals. Some examples are listed in Table I. This type of embrittlement causes concern, and hence has stimulated research, because it usually involves a very low energy fracture that proceeds rapidly and leads to a catastrophic failure[l-31. Since it often occurs as a result of a change in the microstructure of the material during service, it can happen unexpectedly. For example, the failure of of the Hinkley Point Power Plant occurred partly because phosphorous segregated to grain boundaries during operation at an elevated tempera- ture and weakened them[3,4]. An example of a brittle intergranular fracture surface is shown in Figure 1.

In this paper I wish to review the work that has been directed at this problem. I will first provide a brief historical perspective. Then I will describe the work which has employed Auger electron spectroscopy to show the importance of impurity segregation in causing this type of failure. However, I also wish to demonstrate that although impurity segregation is often the major cause of intergranular frac- ture, other factors such as the presence of second phase particles, the structure of the grain boundary, the orientation of the grain boundary with respect to the stress axis, and the overall composition of the sample can affect whether or not a grain boundary will separate. Furthermore, there are systems which have now been studied in which no impurity segregation is required to cause intergranular fracture. Next I will describe the results of more fundamental studies of chemical bonding at grain boundaries which have attempted to understand why the presence of the impurities at the boundaries may weaken them. These results will be reconsidered in light of the current ideas of McAdon and Goddard of bonding in metals. Finally, I will relate these studies to current basic studies of grain boundary structure and suggest the appropriate direction that this research should take if it is to address this prob- lem.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988501

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HISTORICAL PERSPECTIVE

Intergranular fracture has been observed for many years, and through much of that time it has been recognized as basically a chemical problem. Work in antimony-doped brass[5], bismuth-containing copper[6,7], and stee1[2.8] clearly showed that the presence of an impurity element, such as bismuth or antimony, was required for grain boundary fracture. Research also showed that the applications of specific heat treatments were required to produce the embrittlement and that dif- ferent heat treatments could remove the embrittlement.

One of the primary concerns of the work between 1940 and 1960 was whether or not the harmful elements were present as precipitates along the grain boundary or whether they were segregated in their elemental form. Since the optical microscope was the primary research tool that was used in these studies, it was a difficult question to answer. However, as a result of studies that employed very careful etching experiments[9,%0] as well as some work with radiography[ll], it was con- cluded that the harmful impurities were probably in their elemental form.

By 1957, Powers[l2] was able to outline many of the basic ideas that are still correct today. He proposed that the impurity elements segregate to grain boundaries during the detrimental heat treatments. He also proposed that the amount of segre- gation was essentially controlled by the solubility of impurities in the alloy. Consequently, the presence of the other elements in the alloy could change this solubility and hence affect segregation. The importance of alloying elements on segregation was further emphasized by Low, et.al.,[l3] in their study of Ni-Cr steels. Figure 2, which is taken from their work, shows that embrittlement was not observed in the high purity material but that the embrittling powers of phosphorous, antimony, silicon, and arsenic could be changed by the presence of nickel and chromium.

Throughout all of this work, however, there was always a certain amount of speculation because it could never be proved that impurities were present in the grain boundaries after the detrimental heat treatments. Once Auger electron spec- troscopy became available, the role of impurity elements was firmly established.

STUDIES THAT EMPLOYED AUGER ELECTRON SPECTROSCOPY

Auger electron spectroscopy was developed by L.A. Harris in 1968[14]. It pro- vides a chemical analysis of the top two to five atomic layers of a metallic surface by using secondary electrons emitted as a result of a primary electron beam. Spec- tra must be taken from a surface that is in an ultra-high vacuum spectrometer so that oxygen and carbon contamination will not affect the Auger signal. For grain boundary studies, it is necessary to fracture the sample along the grain boundaries in the ultra-high vacuum spectrometer. Then one has clean boundaries that can be analyzed by Auger electron spectroscopy.

The early Auger studies of grain boundary embrittlement clearly showed that segregated impurities were a primary cause of this embrittlementrl5-171. Figure 3 shows the results obtained by Stein, et. al.[l5] on embrittled Ni-Cr steel contain- ing antimony. The spectra show that a heat treatment that embrittles grain boun- daries causes antimony to segregate. However, if a de-embrittling heat treatment is used, the amount of antimony in the grain boundaries is decreased.

Since this early work many studies have been performed which have identified the importance of specific impurity elements in this problem. Table I1 summarizes many of these. In the early studies that were performed on easily embrittled Ni-Cr steels, it appeared that there was virtually a perfect correspondence between segre- gation and embrittlement. An example is shown in Figure 4 where it is clear that as the amount of segregation increases, there is an increase in the ductile to brittle transition temperature, which is a measure of embrittlement[46]. However, as these studies have continued and have been carried out on more complex materials, it is clear that the correlations are not so perfect. For example, Figure 5 shows the results obtained on NiCrMoV steels doped with phosphorous or tin[28]. Although there is a general increase in the transition temperature with increasing segrega- tion, it is clear that there is quite a bit of scatter in the data. Furthermore, if one examines the percentage of intergranular fracture across the surface of the test

Table I

Metalhrgical Problems in Which Brittle Intergranular Fracture Plays a Central Role

Temper Embrittlement of Steels Tempered Martensite Embrittlement of Steels Recrystallization Embrittlement of Refractories Burning of Steels Sulfur Cracking of Nickel Hot Shortness of Steels Splitting of Refractory Wires During Drawing Hydrogen Embrittlement

Figure 1 - Brittle intergranular fracture in a low alloy steel.

Figure 2 - The change in the ductile to brittle transition temperature for NiCr, Ni, and Cr steels doped with the indicated impurities. Data from reference 13.

TYPE OF STEEL

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Table I1

Examples of Impurity Induced Grain Boundary Embrittlement

Primary Matrix Embrittering Reference Element Element

dN - dE

0 200 400 600, 800 1000 ELECTRON VOLTS

Figure 3 - Auger spectra. from an antimony-doped steel. The upper spectrum was taken from a non-embrittled (N.E.1 steel. The lower spectrum was taken from an embrittled steel and shows a clearly resolved antimony peak. Data taken from reference 15.

piece, it is found to be quite variable, as shown in Figure 6 and Table 111. These results show that in certain areas of the fracture surface the amount of intergranu- lar fracture can be rather high whereas in others it can be low. These results would suggest that although segregation is the primary cause of intergranular embrittlement, its effect can be modified by other factors. We now wish to describe what these can be.

FACTORS OTHER THAN SEGREGATION THAT AFFECT INTERGRANULAR FRACTURE

The results in the previous section indicated that factors other than grain boundary segregation can affect the ease with which a grain boundary separates. This idea was based primarily on the results which showed that there was some scatter in the correlation between grain boundary segregation and embrittlement. To make this point more clearly, let us examine the results of the following experi- ment. A 4340 type steel was heat treated so that its ductile to brittle transition temperature was near 0°C. A sample of this steel was then cooled to approximately - 150°C in the Auger spectrometer and fractured. Many grain boundaries were exposed and phosphorous was found to be segregated to the grain boundaries. Figure 7 shows a histogram of the phosphorous to iron peak height ratios obtained from the dif- ferent grain boundaries exposed by the fracture. The results show the tmical variability in segregation from grain boundary to grain boundary. A second Auger sample was then cut from the same piece of material but the fracture in the Auger system was performed at approximately 0°C. Only five grain boundary facets were exposed and the amounts of phosphorous segregated to these boundaries are superim- posed on the histograms in Figure 7. The amounts of segregation to these boundaries were not unusually high, so we cannot conclude that these boundaries were opened just because they contained a large amount of segregation. Although the presence of phosphorous was undoubtedly required to produce any grain boundary fracture, factors other than the amount of segregation must determine whether or not a grain boundary will separate.

One factor that has been shown to affect intergranular fracture is the orienta- tion of the grain boundary with respect to the stress axis. This effect has been studied by Hondros and McLean[7] in the Cu-Bi system. Figure 8a shows a micrograph of a sample tested to approximately 90% of its ultimate tensile strength. Most of the cracks have formed on grain boundaries oriented approximately 90' to the stress axis. Figure 8b shows a histogram of grain boundary cracks plotted as a function of the angle of the grain boundary with respect to the stress axis. No cracks were found at angles less that 45" to the axis and most cracks were at 70" or above. These results demonstrate that a boundary with a great amount of segregation which was only a few degrees from the stress axis would be much less likely to fracture than a boundary that has much less segregation but was nearly perpendicular to the stress axis.

The next factor that we wish to consider is that of grain boundary structure. There are a number of qualitative observations that would suggest that grairi boun- dary structure plays some role in determining whether or not a grain boundary will be prone to fracture. Fbr example, micrographs in Figure 9 show that the grain boundaries have only fractured in parts along their length. Close examination of the figure shows that the point where a crack stops or starts can be associated with a change in the lath structure of the matrix. Furthermore, the work of WatanabeI471 has shown a relationship between fracture stress and grain boundary structure.

However, an'under~tandin~ of the true effect of grain boundary structure on fracture is greatly complicated by the fact that structure also affects segregation. Figure 10 shows histograms of the P to Fe or Sb to Fe Auger peak height ratios obtained from grain boundary fracture surfaces in Ni-Cr steels. Each entry corresponds to a value taken from an individual grain boundary. The large variabil- ity in segregation is thought to result from differences in grain boundary struc- ture[48]. Figure 11 shows results obtained by Matanabet471 in which the Sn to Fe and Si to Fe Auger peak height ratios are plotted as a fraction of misorientation for Fe-Sn and Fe-Si bi-crystals. It is clear that as the tilt angle of the bi- crystal increases the amount of segregation increases.

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GRAIN BOUNDARY CONCENTRATION (a/o)

Figure 4 - The shift in the ductile to brittle transi- tion temperature plotted as a function of the grain boundary concentration of phosphorus and antimony. The data were taken from reference 46.

Table I11

The Percentage of Intergranular Fracture Found on the Charpy Fracture Surfaces of a Sn-doped NiCrMov Steel.

Each Enegry Corresponds to Measurements Taken from a Different Photomicrograph at 200X[28].

Aging Test Pct Intergranular Treatment Temperature ("C) Fracture

520°C/500 hours

520°C/1000 hours'

520°C/1500 hours

PIFe AUGER PEAK HEIGHT RATlO

z ' o.& o.& ods 0;s o.io 0 . i ~ 0.;4 0.L

SntFe AUGER PEAK HE16HT RAT10

PlFr W C R PEAK HEPHT RATIO

(c)

Figure 5 - The ductile Figure 6 - A composite micrograph to brittle transition taken from a Charpy fracture temperature plotted as surface of a Sn-doped NiCrMoV a function of the Sn or steel. Taken from reference 28. P to Fe Auger peak height ratios obtained from grain boundaries. Data from reference 28.

10 0)

g 8 i a= C 6

3 IL a 2 3 z

0 0.04 0.08 0.12 0.16 Pf Fe PEAK HEIGHT RATlO

Figure 7 - A histogram of the number of grain boundaries plotted as a function of the P/Fe Auger peak height ratio. The shaded histogram is for a sample that had many grain boundaries exposed. The open entries bounded by a dashed line are for a sample that had only . five boundaries open.

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L L . . L - ! A

Ingk to Mw oxis

A 0 3 0 . 4 a D x P 0 0 # X ) 0 9 @

b F i g u r e 8 - (a) A m i c r o g r a p h o f a Cu-Bi s a m p l e s h o w i n g t h a t most o f t h e c r a c k s a r e g r o w i n g p e r p e n d i c u l a r t o t h e s t r e s s d i r e c t i o n which i s i n d i c a t e d by t h e a r r o w s . ( b ) A h i s t o g r a m f o r t h e same s y s t e m s h o w i n g t h e a n g u l a r d i s t r i b u t i o n o f g r a i n b o u n d a r i e s w i t h r e s p e c t t o t h e s t r e s s a x i s . Taken f rom r e f e r e n c e 7 .

F i g u r e 9 - M i c r o g r a p h s s h o w i n g t h e t i p s o f i n t e r g r a n u l a r c r a c k s fo rmed i n a p h o s p h o r u s - d o p e d N i C r s t e e l .

Although it is clear that grain boundary structure can affect segregation, it has also been demonstrated that segregation can affect structure. The most obvious cases are those such as tellurium segregation in iron[l6] and bismuth segregation in copper[49], where the segregation causes faceting of the grain boundaries. Also, experiments by Sickafus and Sass[50] that have used X-ray diffraction to monitor atomic positions in bi-crystals of iron have shown that segregation of gold to the grain boundary can alter the atomic positions in the grain boundary. All of these studies suggest that it is difficult to perform experiments that only determine the effect of structure on ease of fracture because of the relationship between segrega- tion and structure.

If such an experiment were to be done, one would either have to use a system where the amount of segregation was constant for all boundaries or a system in which the boundaries were intrinsically weak and would fracture without any segregation. The most complete study of this kind appears to be that of Kurishita, et. a1[45], on grain boundary fracture in molybdenum bi-crystals. They found that the boundaries in molybdenum appear to be intrinsically brittle, and thus they can measure the fracture strength of the crystals as a function of grain boundary misorientation. Figure 12 shows their results. It is clear that there is a peak in the fracture stress and plast5c strain to failure at boundaries with the coincident relationships of 11, 13, and 117. Except for these special boundaries, the fracture energy is rather constant. Therefore, in a standard polycrystalline sample the primary effect of structure may indeed be on the amount of segregation. However, more studies of this type need to be carried out before a complete understanding of the effect of structure on fracture can be obtained.

The next factor that we wish to consider is the role of second phase precipi- tates on grain boundary fracture. To examine this effect one must compare results obtained on samples that have identical amounts of segregation but different amounts of precipitate. An example of this effect can be observed in the problem of tem- pered martensite embrittlement[51]. This type of embrittlement occurs in steels that have been austentized and then quenched to form martensite. The steels are then tempered for short times (usually one or two hours) at temperatures between 150 and 350°C. The fracture energy of samples tempered near 350°C is lower than those obtained for samples tempered at lower temperatures, even though the hardness is higher in the latter samples. An example of this embrittlement is shown in Figure 13. This decrease in fracture energy is usually accompanied by an increase in the amount of intergranular fracture. Studies that have employed Auger electron spec- troscopy to measure the amount of segregation to the grain boundaries have shown that impurity segregation does not increase during tempering at 350°C and below and that all segregation must have occurred during austenitization or during the quench after the austenitization[52,53]. However, what does change is that carbides (Fe3C) precipitate along the grain boundaries as shown in Figure 14. Therefore, it appears that the precipitation of these carbides along grain boundaries that already contain some segregation of embrittling impurities causes the fracture energy to decrease, and we must conclude that as the density of second phase precipitates increases along the grain boundary the ease of intergranular fracture will increase. However, it must be noted that these precipitates alone are not usually sufficient to cause brittle fracture; rather they must be accompanied by some impurity segregation. But with the impurities present on the grain boundaries, they can exacerbate their effect.

The final variable that we wish to consider in this section is how changes in the mechanical response of the sample to stress affects the ease with which grain boundary embrittlement occurs. Research by Mulford, et. a1.[23] has shown that an increase in hardness in a material will allow intergranular fracture to occur at lower amounts of segregation. This effect presumably occurs because with an increase in hardness it becomes more difficult to induce slip across a grain boun- dary and the possibility of nucleating a crack increases. Another example of the effect of a change in mechanical properties causing a change in the ease of inter- granular fracture can be observed in the intermetallic compound Ni3A1. This com- pound is ordinarily very brittle and only with boron segregation to grain boundaries can any ductility be obtained. However, it has been found by several workers that the effe boron is greatly accentuated in compounds that are nickel-rich (e.g. Ni76A124) C54'S51. It was originally thought that this effect might be a result of increased segregation of boron in the nickel-rich compounds[54]. Results in our

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F i g u r e 10 - H i s t o g r a m s s h o w i n g t h e number o f g r a i n h o u n d a r i e s on s a m p l e s o f N i - C r s t e e l s w i t h g i v e n a m o u n t s o f g r a i n b o u n d a r y s e g r e g a t i o n . T h e s t e e l s w e r e d o p e d w i t h S b o r P a n d t h e g r a i n b o u n d a r y c o n c e n t r a t i o n i s e x p r e s s e d a s a P o r S b t o Fe A u g e r p e a k h e i g h t r a t i o . D a t a t a k e n f r o m r e f e r e n c e 4 8 .

,.. o Fe-WUHV)

06- . Fe- Snia~rl A Fe-SI

Tdlt Angle (degl Y

F i g u r e 11 - T h e Sn t o Fe o r I ' i g u r e 1 2 - T h e f r a c t u r e s t r e s s w,, S i t o F e A u g e r p e a k h e i g h t y i e l d s t r e s s .Aj , a n d p l a s t i c s t r a i n r a t i o s p l o t t e d a s a f u n c t i o n t o f a i l u r e p l o t t e d a s a f u n c t i o n o f o f t l l t a n g l e f o r F e - S n a n d t h e misorientation a n g l e 3 f o r (110) F e - S i b i - c r y s t a l s . D a t a b i c r y s t a l s o f Mo. D a t a t a k e n f r o m t a k e n f r o m r e f e r e n c e 4 7 r e f e r e n c e 4 5 .

0 100 200 300 400 500 600 TEMPERING TEMPERATURE ( O C

Figure 13 - The Charpy frqcture energies of 4340 steel samples plotted as a function of tempering temperature. The samples were austenitized at 1 2 0 0 ~ ~ for 3 hours prior to tempering. The temper- ing time was one hour.

Figure 14 - Transmission electron micrographs of carbon extrac- tion replicas taken from 4340 steel samples that were either (a) untempered or (b) tempered at 350'~ for one hour. The precipitates in figure 14b are Fe3C.

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laboratory have shown that this effect can not be explained in this way. For exam- ple, a nickel-rich alloy that had a plastic strain to failure of 20% and failed com- pletely in a transgranular mode had a boron to nickel peak height ratio of 0.03 5- 0.02. A stoichiometric compound that had a plastic strain to failure of zero and failed intergranularly had a boron to nickel Auger peak height ratio of 0.06 5 0.015. Therefore, the amount of intergranular fracture cannot be inversely corre- lated with the amount of boron segregation. What has been found is that the dislo- cation structure and motion in the compounds are very sensitive to the stoichiometry[56]. Thus it would seen likely that as these changes occur, different amounts of boron are required to inhibit intergranular fracture.

FUNDAMENTAL MODELS OF IMPURITY-INDUCED INTERGRANULAR FRACTURE

In the past section we have demonstrated that there are many factors that can contribute to intergranular fracture, and that quite often one cannot make a perfect correlation between segregation of impurities and intergranular fractura. Neverthe- less, there .is no doubt that the primary cause of intergranular fracture in most metals is the presence of impurities on the grain boundaries, and without their segregation no intergranular fracture would be observed. Therefore, if we wish to model this process in any way, we must first start with an understanding of what these impurities will do, and then proceed with other more complicated effects such as the role of second phase particles, the role of structure, or the interaction of dislocations with the impurities.

Let us then begin this section of the paper with a simple premise. We know that when segregation occurs, the grain boundaries, which were previously not the weakest path for fracture in the material, have become the weakest path for frac- ture. Therefore, the chemical bonds that hold the atoms together at the grain boun- daries have been weakened by segregation. To model this process we must try to understand the bonding at grain boundaries and then determine how the segregant weakens these bonds.

Before turning our attention to the specific aspects of a chemical model of intergranular fracture, it is perhaps well to consider a few more general features. The first idea that must be well established is the physical picture that one has of the segregated grain boundary. It is reasonably well established that the grain boundary is composed of various structural units[57]. In simple, well-defined grain boundaries there may be only a few structural units composing the grain boundary. In more complicated, general boundaries, the number of units may be greater. One can probably think of these units as small molecular clusters joined together to make up the boundary. When segregation occurs, a new atom enters the cluster. This new constituent will certainly change the bonding within the cluster and change the bond strengths of the original types of bonds that were present. For example, it is well known that when oxygen or sulfur are adsorbed onto many transition metals, the metal-metal bonds near the surface are greatly changed from the way they were prior to chemisorption[58]. Consequently, we can think of the segregated grain boundary as made up of a new set of molecular clusters which now contain the host metal as well as a segregant. We write this basic idea as the following chemical equation

where [M ] represents the x metal (M) atoms in the unsegregated grain boundary cluster,X~gks the segregating impurity and [M I] represents the segregated cluster that has now formed at the grain boundary. I$ oE8er for this segregation reaction to occur, there must be a decrease in energy as a result of segregation. This decrease most likely comes from the formation of the M-I bond in the cluster which may be stronger than the M-I bond in the bulk for geomerrical reasons. However, if this reaction is to lead to intergranular fracture, some bonds in the cluster must now be weaker than they were in the Mx cluster.

To consider the breaking of these grain boundary molecular units let us again consider a few simple, more general cases. Hydrogen is a well known embrittler of metals, and its effects on the strength of metal-metal bonds is well documented. Figure 15 shows two chemical reactions where. a metal-metal bond is cleaved as a result of a reaction of a molecule with hydrogen[59]. These two reactions clearly represent very simple, well defined examples of hydrogen embrittlement. However,

one does not have to introduce a new reacting molecule in order to cause breaking of bonds. Many dissociation reactions occur because of the presence of external stimuli such as light, electric fields, and magnetic fields. A common external stimuli in a solid is stress, and when stress is applied to a solid, bonds can break. If we refer again to reaction 1, we would state that the entire process of fracture is now given by

[MxlGB + I * [MxllGB -' [Mx_ylls + fMyIs i2]

where S now refers to the new surface created. If we then view intergranular frac- ture as a dissociative chemical reaction produced by an external stress, the next question is to determine where the bonds would break.

The first work that addressed this issue was that of Losch[60]. He drew on the work of Walch and Goddard[61] to consider embrittlement of nickel by sulfur. He suggested that when segregation occurs, a very strong bond should be formed between the segregant and the metal. He further suggested that fracture would not then occur by breaking of this bond but rather by the breaking of some bond that was weakened by the formation of the strong Ni-S bond. The most likely candidate would be the surrounding Ni-Ni bonds.

This basic idea was extended by the work of Briant and Messmer[62-651. They used full scale quantum mechanical cluster calculations to investigate this problem, and the results were qualitatively similar to those of Losch. They, too, investi- gated the Ni-S system and found that the sulfur, which was electronegative with respect to the nickel, drew electronic charge from the nickel atoms onto itself. This then led to a depletion of electronic charge in the surrounding nickel-nickel bonds. A typical example of their results is shown in Figure 16. Figure 16a shows a ten-atom Archimedian antiprism which was used for this calculation. This particu- lar cluster of atoms is thought to be a basic unit in twist grain boundaries. Fig- ure 16b shows equi-valued contour plots of the total electronic charge density for the Ni cluster and Figure 16c shows the same for Ni S. The plots were taken in a plane '?hat includes the two cap atoms and two of $Re eight equivalent atoms sur- rounding the center of the cluster. In Ni S the sulfur atom which is at the center of the cluster is also included. In the Atl0 cluster one observes that some of the contours surround the entire cluster whereas others are only centered on a single atom. However, one of the contours, which is darkened in the figure, clearly con- tributes to a chemical bond between the cap atom and the atoms in the four-member ring above the cap. In NilOS, this particular contour is changed. Now it no longer contributes to a bond between the nickel atoms. Rather it has been broken into two parts. One part is around the cap atom and the other part is around the Ni atoms and the sulfur. We can see that introducing sulfur into the cluster has formed a bond between the nickel atoms near the center of the cluster and the sulfur and that this bond formation weakens the bonds between the cap atoms and the center nickel atoms. Therefore, we would predict that the fracture would occur between the nickel atoms.

The basic idea presented above held for all cluster geometries that were inves- tigated, although the amount of charge transfer from the nickel atoms to the sulfur depended on the cluster geometry[65]. Also, examination of a number of different impurity atoms showed that the embrittling strength appeared to correlate with the amount of charge transfer that occurred. Consequently, one could state that as the electronegativity of the embrittling species with respect to the host metal increased, one would expect more charge transfer and hence more embrittlement. How- ever, it is important to remember that the simple electronegativity scales such as those developed by Pauling are not reliable for most transition metals and cannot be used to make predictions about the amount of charge transfer in this situation.

The basic ideas developed above consider only the electronic interaction between the segregant and the host metal. However, if we continue with our molecu- lar analogue, we must recognize that when a chemical reaction occurs, bond lengths and angles change, and so we would expect there to be some change in the structure of the grain boundary as a result of this segregation. Several examples of this atomic rearrangement have been given above. We now wish to address the question of what the driving forces for this rearrangement might be and how they might affect embrittlement.

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F i g u r e 1 5 - Two c h e m i c a l r e a c t i o n s i n which h y d r o g e n c l e a v e s m e t a l - m e t a l b o n d s . Taken from r e f e r e n c e 5 9 .

F i g u r e 1 6 - ( a ) The t e n a tom A r c h i m e d i a n a n t i p r i s m u s e d f o r t h e c l u s t e r c a l c u l a t i o n s . ( b ) The t o t a l e l e c t r o n i c c h a r g e d e n s i t y f o r N i l ? . - The e q u i v a l u e d c o n t o u r p l o 1s t a k e n i n a p l a n e t h a t i n c l u d e s a t o m s 1 , 2 , 3 , and 4 d e s i g n a t e d i n f i g u r e 1 6 a . ( c ) An e q u i - v a l u e d c o n t o u r p l o t f o r t h e t o t a l e l e c t r o n i c c h a r g e d e n s i t y f o r Ni lOS. The s u l f u r a tom i s a t t h e c e n t e r o f t h e c l u s t e r . Taken f r o m r e f e r e n c e 6 5 .

For this part of our discussion we turn our attention to hydrogen. Cox and Bauschlicher[66] have carried out full scale quantum mechanical calculations of the Ni-H system. They analyzed several cluster geometries and determined the equili- brium distance of the Ni-H bond in each case. This data was analyzed by Messmer and Briant[67] and they pointed out the following correlation. When hydrogen was placed in a tetrahedral or octahedral cluster, the metal atoms relaxed outwards. This relaxation was 8% for the tetrahedron and 1% for the octahedron. When the hydrogen was placed at the center of a capped trigonal prism or an Archimedean anti-prism, the nickel atoms relaxed inwards by 1.7 and 2.8% respectively. When the original interstices of these clusters were analyzed in terms of the Bohr radius of hydrogen, a , it was found that they were 0.50a , 0.89ao, 1.12ao, and 1.38ao for the tgtrahedron, octahedron, capped trigona? prism, and Archimedian antiprism, respec- tively. Therefore, it would appear that hydrogen in each case tried to adjust its metal-hydrogen bond length so that it would have a cavity the size of the Bohr radius. The quantum mechanical relevance of this radius is that it represents the most probable distance of the electron from the nucleus. Thus it would appear that for each segregant there is probably some ideal distance for the metal-segregant bond and that the segregant will try to rearrange the metal atoms to meet this requirement. This rearrangement could put strain on the metal-metal bonds and thus contribute to embrittlement. Furthermore, there may be some preferred angular dis- tribution of the metal atoms about the impurity and some movement may be attempted to adjust for this fact.

In all of the preceeding discussion we have been drawing an analogue to simple molecular chemistry and assuming that chemical bonds are as well defined in metals as they are in simple inorganic molecules. If we are to use these ideas we must be certain that indeed such a description is valid for metals. At first thought it might seem that there is some discrepancy, because the usual picture of metals is one in which the electrons are randomly moving around between the nuclei. However, recent quantum mechanical calculations have suggested that this idea is largely incorrect. Calculations performed by McAdon and Goddard[68] show that the valence electrons are localized in the tetrahedral interstices of the metallic lattice. They can easily move from one tetrahedron to another, but the motion of these inter- stitial electrons is correlated and well-defined. It is also the tetrahedrally localized electrons that provide the one-electron bonds that make a major contribu- tion to the cohesive energy of metals. Furthermore, these electrons could easily allow for bonding across a defect such as a grain boundary.

Let us then consider a simple model of a grain boundary in a face-centered cubic material as shown schematically in Figure 17a. The regions marked T indicate some of the tetrahedral sites in the lattice and according to the rules of McAdon and Goddard these should be the locations of the valence sp electrons. The grain boundary units are in this case capped trigonal prisms, and it can be seen in Figure 17b that the six atom prism is surrounded by truncated tetrahedra, which are desig- nated as T' in the Figure 17a. If one considers the complete analysis of McAdon and Goddard of one, two, and three dimensional systems, then the most logical place for the electrons would be in the caps of these units as shown in Figure 17c. In this way the metal would be bound together across the boundary. Now imagine that an hlectronegative impurity is placed in the center of the capped trigonal prism. It will try to pull the electrons out if their interstices and localize them around itself. The metallic bonding within the interstices is now decreased, and the metallic bonding around the cluster is weakened. This weakening will lead to inter- granular embrittlement.

We mentioned in a previous section that there are some reported cases where impurities do not appear to be required to cause embrittlement. These are for the intermetallic compounds Ni3A1[69] and PCuAlNi[70] and for the metals molybdenum[45] and iridium[71]. If we follow the reasoning above, it would seem logical that impurities would not be required if all of the bonding between the atoms was very directional and there were very few interstitial electrons. When all the electrons are in these directional bonds then the lattice is electronically more rigid and the boundary becomes a greater perturbation.

Of the three cases, the embrittlement of the intermetallic compounds seem to be the best documented. The Auger spectra for these compounds have no overlapping matrix peaks with any of the .common embrittling impurities such as sulfur and

JOURNAL DE PHYSIQUE

Figure 17 - (a) A schematic of a tilt grain boundary showing the locations of tetrahedra (T) in the matrix and truncated tetrahedra (T') in the grain boundary. (b) A capped trigonal prism. ( c ) An end-on view of a capped trigonal prism showing the electrons located in the truncated tetrahedra. They are

C designated as e .

phosphorus and the results have been duplicated in several laboratories. This result can also be rationalized by a simple consideration of what ordering might mean in terms of the types of chemical bonds that could be formed. Ordering comes about because a certain configuration of the atoms involved in the alloy becomes the lowest energy state. This configuration is very specific in that the nearest neigh- bors are defined in terms of both position and atomic species. Such an arrangement must come about because a preferred set of chemical bonds can be formed in this way. It seems logical to assume that these bonds may be more directional than in the nor- mal solid solution alloy because of the specificity of nearest neighbor types. Therefore, one could rationalize that the brittleness of these compounds comes about because of this directional bonding.

The case for molybdenum or iridium is harder to rationalize, because it seems unlikely that the s electrons would not be interstitial. One might argue that for some reason the d-bonding in these metals is more important than in some other metals, but our knowledge of bonding in these metals is not sufficient for this to be anything other than a suggestion. Another issue is whether or not Auger electron spectroscopy can be reliably used to detect small concentrations of impurities such as S and P in these metals. An examination of the Auger spectra for these metal shows that they have peaks close enough to the peaks of one or both of these impur- ity elements so that the impurity peaks could not be independently resolved. Conse- quently, small concentrations of these impurities, which should be sufficient to cause embrittlement, could go undetected.

SUMMARY

In this paper I have attempted to give an overview of the research that has been carried out on intergranular fracture. In doing so, I hope that I have pointed out a number of the variables that can contribute to this .type of fracture. In most systems, segregation of embrittling impurities is required to cause failure, but the effect of impurities can be modified by a number of other variables. Consequently, whether or not a given grain boundary will fracture will depend on more than just the amount of segregation. I have also tried to present our understanding of why these impurities cause embrittlement. This aspect will be developed more in the 'future as our understanding of chemical bonding in metals becomes more sophisti- cated.

It appears that if we want to develop a more complete understanding of this problem the work needs to be aimed more at an understanding of the chemical bonding at grain boundaries rather than at purely structural studies. Although the struc- tural data that can be obtained by the X-ray diffraction measurements of segregated boundaries is very interesting, it will not have its full impact until these struc- tural changes can be explained in terms of the new sets of chemical bonds formed as a result of this segregation. Although it might be possible to use some experimen- tal probes of the grain boundaries such as Mossbauer spectroscopy[72], it seems that at present the best approach would be to combine structural studies with theory. The next obvious question is what type of theory is required. Certainly, pair potentials are completely meaningless in any problem where chemical bonds are involved. However, the force field approach as described by McAdon and Goddard[68] seems to be much better. This method involves taking the results of full-scale quantum mechanical calculations and expressing them as analytical expressions that can be applied to other systems. Their initial work on lithium showed that in order to provide correct force fields, they needed to consider electron-nuclear terms as well as three body terms such as atom-electron-atom bend and atom-electron-atom asymmetric stretch. Although obtaining these force fields may still be some years away, it would appear that research aimed at trying to achieve them will eventually make a valuable contribution to this problem.

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