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Triple junction and grain boundary character distributions in metallic materials
Acra rim&- Vol. 45,No. 8,pp. 3459-3461,1997 % 1997 Acta Metallurgica Inc.
Pergamon
Published by Elsevier Science Ltd. Ail rights reserved Prmted in Great Britain
PII: s1359-6454(97)00004-9
1359-6454197 $17.00+ 0.00
TRIPLE JUNCTION AND GRAIN BOUNDARY CHARACTER DISTRIBUTIONS IN METALLIC MATERIALS P. FORTIER, Department
W. A. MILLER and K. T. AUST
of Metallurgy & Materials Science, University of Toronto, Toronto, Ontario, Canada M5S 3E4 (Received 10 September 1996)
Abstract-Triple junction and grain boundary orientations were obtained by electron backscattered diffraction in high purity aluminium and copper, and in copper-bismuth alloys, and were then characterized using the CSL, CAD and I-line (O-lattice) geometrical models. A computer simulation was also performed and compared to the experimental results. Relationships were established between triple junction and grain boundary character distributions using both experimental and computer simulated results. A general trend was observed which shows an increase in special triple junction character density with increasing special grain boundary character content. An increased frequency of low angle and twin boundaries is shown to lead to an increase in the I-line triple junction density. 80 1997 Acta Metallurgicu Inc.
R&sum&Des orientations de jonctions triples et de joints de grain sont obtenues g partir de diffraction d’electrons dans l’aluminium et le cuivre de haute pureti, et dans des alliages de cuivre-bismuth, et elles sont caractCrisCes par les modeles gtomCtriques CSL, CAD et type I. Une simulation par ordinateur est kgalement prBsentte and comparte aux resultats expirimentaux. Une correspondance est etablie entre les distributions de jonctions triples et celles des joints de grain obtenues B partir des r&sultats expCrimentaux et de simulation. Une relation g&&ale est observCe qui montre une augmentation en densit de jonctions triples spkciales quand la proportion de joints de grain specials augmente. La distribution de jonctions triples de type I est dkpendante de la densit de mdcles et de joints de grains de faible disorientation.
1. INTRODUCTION Material properties depend on both the density and type of mircrostructural elements, such as dislocations and interfaces, and they may be improved by the presence of interfaces having appropriate structures [e.g. l-31. Grain boundary design and
control (grain boundary engineering) is a concept introduced by Watanabe [4] who first mentioned the importance of grain boundary character distribution (GBCD) for obtaining improved physical properties. The characterization of grain boundaries is generally carried out using geometrical models (such as the coincidence site lattice (CSL) [S] or the coincident
axial direction (CAD or plane matching) [6] models). Grain boundary engineering involves controlling or optimizing the presence of certain grain boundaries that may enhance materials properties as a result of their intrinsic geometrical characteristics. For instance, twin boundaries, known as C3 in the CSL model, and other low C grain boundaries seem to be more resistant to intergranular degradation than random boundaries [l-3]. Control and optimization of specific and potentially enhancing boundaries may be achieved by thermomechanical processing [2] which varies with the type of material. This control of statistical grain boundary distributions is interesting because it is the first step in designing materials with desired properties.
Nanocrystalline materials have increasingly held the attention of the scientific community recently. The large fraction of grain boundary ant1 triple junction free volume [7, 81 in such materials, due to their extremely small grain size, and the possibility of control of grain boundary character have led to a reconsideration of the properties of both triple junctions and grain boundaries. Specifically, little is known about triple junction character distribution in the presence of a given grain boundary distribution. Studies have confirmed the existence of a correspondence between junction (and boundary) distributions and the texture of the material [9-131 but few detailed relationships have been presented between triple junction and grain boundary distributions [9, 11, 121. Doni et al. [9] obtained the first computer-simulated correlation between grain boundary and triple line character distributions for the case of a CSL description; Kurzydlowski et al. [l 1] and Fortier et al. [12] found relationships between CSL triple junctions and CSL boundary densities, and I-line triple junctions and CSL boundary fractions, respectively, both using computer simulations. Watanabe [14] experimentally found that a relationship exists between the I-line triple junction and CSL boundary fractions. However, no comprehensive and complete investigation is available in the literature that shows
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whether a correspondence exists between the CSL [l 11, CAD [15] and I-line [16] triple junction distributions and the CSL and CAD grain boundary fractions. The present paper proposes to fill this gap, using both experimental and computer-simulated studies. 2. EXPERIMENTAL PROCEDURE High purity (99.999 + %) aluminium and copper were heavily cold rolled by 90% to a thickness of 0.5 mm, mechanically polished using silicon papers of various grades followed by alumina paste, and electropolished in perchloric acid and phosphoric acid solutions, respectively. The specimens were annealed at 0.50, 0.65, 0.80 and 0.95 of the absolute melting point (T,,,) for 24 h. To produce the copper-bismuth alloys, high purity (99.999%) bismuth was evaporated onto a copper surface to obtain a bismuth layer of 3 pm in thickness. The three types of specimen were then annealed for a second time at the same temperature for 24 h. The copper-bismuth samples were gently polished using alumina and all samples were given final electropolishing and etching treatments. Observation by scanning electron microscopy (SEM) of the specimens revealed the microstructure (i.e. grain size, grain boundaries, triple junctions) as well as the presence of bismuth particles at some triple junctions in the copper-bismuth specimens. Electron backscattered diffraction (EBSD) [17] was used to obtain grain orientations with respect to a constant reference frame. Triple junction orientations were collected by obtaining three contiguous grain orientations. Care was taken to make sure that each grain boundary, which is connected to two junctions, was counted only once for the boundary distributions. Triple junctions and grain boundaries were then characterized using the CSL model (junctions [l 11, boundaries [5]), the CAD model (junctions [15], boundaries [6]) and the O-lattice model (junctions [16, 18-211). An average of 104 triple junctions, 269 grain boundaries and 236 grains were assessed per sample (for a total of 1380 junctions, 3622 boundaries and 3213 grains). 3. COMPUTER SIMULATION A computer simulation was performed to determine the relationships between triple junction densities and grain boundary contents, using the Pascal programming language. Fibre textured grain orientations were generated in numbers of 30,000 per texture (60,000 for the randomly oriented material), which correspond to 10,000 junctions and 30,000 boundaries; (loo), ( 110) and (111) fibre textures were computed from Gaussian distributions of the 15”, 8”, 5”, 3” and 1” deviation angles (i.e. from a weak to a sharp texture) [lo]. The characterization of triple junctions and grain boundaries was performed using the CSL framework and the Brandon criterion [22], and the CAD and I-line models. The computer
simulation employed independent sets of three orientations to calculate triple junction classifications, i.e. each triple junction was characterized independently of the others. The method did not utilize a connected spatial model of polycrystals such as Kelvin polyhedra (tetrakaidecahedra) [23]. However, the grain boundary calculations were always performed using the orientation of three grains meeting at a triple junction; thus the grain boundary character distributions presented in this work reflect more closely the real connectivity of boundaries in materials than would be obtained by analyzing sets of independent bicrystals. For every fibre textured material, densities of triple junctions were plotted against grain boundary contents. The texture dependence of relationships between triple junction and grain boundary distributions is usually small [l l] but can be significant in some cases (i.e. I-lines vs CSL boundaries [9, 121). By using the three types of fibre texture ((loo), (110) and (111)) and their associated Gaussian angular deviations, one can establish general relationships between triple junction and grain boundary contents occurring in conventional polycrystalline materials. 4. RESULTS 4.1. CSL triple junctions CSL triple junctions are simply junctions composed of CSL and random boundaries. In this study, CSL boundaries are characterized up to C49-higher C values are considered to be random boundaries. Only four types of junction exist in terms of CSL boundary connectivity: junctions (1) with 3 CSL boundaries, (2) with 2 CSL and 1 random boundary, (3) with 1 CSL and 2 random boundaries and (4) with 3 random boundaries. Figure 1 shows the densities of CSL triple junctions plotted against CSL boundary content, using experimental specimens, computersimulated data and analytically, using probability functions. The computer-simulated fractions of CSL junctions having 3, 2, 1 and 0 CSL boundaries are 0.51 f 0.17%, 6.32 + 0.60%, 35.19 f 1.48% and 57.98 f 1.53% [12], respectively, in a material containing the random content of CSL boundaries (16.5% up to C49 and 12.4% up to ZZ29[24,25]). As the CSL boundary content increases, the densities of 3 and 2 CSL boundary junctions significantly increase [Fig. 1 (a), (b)], whereas the density of junctions composed only of random boundaries drastically decreases [Fig. 1 (d)] while the 1 CSL boundary junction density remains constant for the experimental range considered [ Fig. 1 (c)l. The computer simulation is in good agreement with both the experimental results and the probability analysis. The analytical probability study was performed using probability functions. If g is the CSL grain boundary fraction (i.e. 1 -g is the random grain boundary fraction), the probability of occurrence of 1,2 and 3 CSL grain boundaries at the triple junction
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is g, g? and g”, respectively, and similarly the probability of occurrence of 1, 2 and 3 random boundaries is (1 - g), (1 - g)* and (1 - g)‘, respectively. Therefore the probability of occurrence P of a triple junction having n CSL and 3 - n random boundaries is:
P(n,g)
= ( - n2 + 3n + l)g”(l - g)‘-.”
where the first term in brackets is the relative probability of occurrence of the junction type. For instance, there is only one occurrence of the 3 and 0 CSL boundary junctions, while there are three occurrences of the 2 and 1 CSL boundary junctions. The probability function P(n,g) is normalized to
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unity, so that
i P(n,g) II
=
”
= i ( - n? + 3n + l)g”(l - g)1-1’ ,/ = 0
= 1 with 0
1.
If the value for a randomly oriented material of 16.5% is taken for g, then P(3,0.165) = 0.45%, P(1,0.165) = 34.51% and P(2,0.165) = 6.82%, P(O,O.165) = 58.22%. These values agree extremely well with those calculated by computer simulation and are within the standard deviations. The match is also good with results from the computer simulation
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Fig. 1. Densities of triple junctions having (a) 3, (b) 2, (c) 1 and (d) 0 CSL boundaries vs CSL boundary content when these are classified up to X49. Experimental points (0) are obtained from aluminium, copper and copper-bismuth specimens using a total of 1380 triple junctions, 3622 grain boundaries and 3213 grains. The computer simulated results ranged from 16.5% (random material) to 65% CSL boundaries. The probability function P, defined in the text, is also displayed, resulting from the dependence of CSL boundaries on their connectivity at triple junctions.
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Q 70 e g 60 .o ti c 60 4 Q, 40 3 E 30 20 10 0 , 0
, 10
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30 40 50 60 70 CSL Boundaries (%)
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90 100
Fig. 2. Densities of triple junctions having 3, 2, 1and 0 CSL boundaries vs CSL boundary content. The symbols represent the results from the computer simulation and the solid lines the results from the probability analysis.
[ 121 for other values of g (Figs 1 and 2): this indicates that the effect of textured grain orientations on the relationship between triple junction distributions and grain boundary distributions is very small. This result was reinforced by Kurzydlowski et al. [l l] who found exactly the same relationships although they used different textured grain orientations. The small discrepancy between simulated and analytical results may be due to the fact that the analytical method does not take into account the Brandon criterion [22] and the geometrical conditions set at triple junctions [26, 271: (1) the maximum allowable deviation angle varies from one boundary to another at the same triple junction (except for the junction composed of three low angle boundaries), therefore the probability of occurrence of n CSL boundaries is slightly different from the value g” and consequently CSL triple junction frequencies differ slightly from the probability function P; (2) it has been noted that the geometrical rule of 3 CSL boundaries at triple junctions [26,27] is not always verified experimentally, owing to non-constant maximum deviations obtained for different X values: a percentage of 18.4% (33 over 179) of experimental 3 X boundary junctions did not satisfy the rule (i.e. we obtained junctions such as z:X + XY = EZ with Z non-divisible by either X or Y). This means that the function P provides only a good approximation of the fractions of CSL boundary junctions in materials and the computer simulation gives more accurate results. The funcion P yields values for g < 16.5%, although this does not physically make sense (the lowest CSL grain boundary content for any material occurs in the random texture) unless a limit beyond which a boundary is random is set lower than C49 (e.g. Z 29, in which case g = 12.4%). If g = 12.4%, then P(3, g) = 0.19%, P(2, g) = 4.04%, P(1, g) = 28.55% and
TRIPLE JUNCTION P(0, g) = 67.22%, which is in excellent agreement with the computer simulation studies of Kurzydlowski et al. [l l] and Garbacz and Grabski [lo], and in fair agreement with the values of Doni et al. [9] who considered a total of only 200 triple junctions. The CSL triple junction density vs the CAD grain boundary content is presented in Fig. 3 (a)-(d). The relationships are similar to those found in Fig. 1: an increase in 3 and 2 CSL boundary junctions and a decrease in 0 CSL boundary junctions are observed with increasing content of CAD grain boundaries. The computer simulated results did not yield a monotonous relationship but rather a domain of existence within which the experimental points are located (indicated as shaded areas in Fig. 3). This results from the fact that different distributions of CAD boundaries can be associated with the same CAD boundary content. For example, consider the two CAD boundary distributions (lT3 = 25%, II4= 5%, rI8 = 5%) and (lI3 = 5%, II4= 5%, lI8 = 25%}, respectively; they have the same CAD boundary fraction classified up to II8, but yield different CSL triple junction densities because the CAD boundary distributions are different. We conclude that the computer simulated results match the experimental results quite well.
4.2. CAD triple junctions CAD triple junction distributions are interesting since the CAD triple junction model [15] is based on a one-dimensional characterization (axis), whereas the ESL model [5, 221 is based on a two-dimensional characterization (angle and axis). The CAD characterization is appropriate for the description of the triple line because triple junctions are line defects. The Il value associated with the CAD model represents the (hkl) common axis of the triple junction, i.e. l-l = h* + k* + l*, and the first n values of the CAD classification are 3, 4, 8, 11, 19, 20 and I 24 with axes corresponding to (11 l), (loo), (1 lo), (311), (331), (210) and (211), respectively [28]. The method for calculating the CAD axis for triple junctions was first given by Palumbo and Aust [15] and is as follows: boundaries are classified by performing the 576 symmetry operations on the misorientation matrices and comparing these to exact CAD axes; if a common l-l value is found to exist for the three boundaries, this determines the II value of the triple junction. The CAD triple junctions were characterized in this way from Il3 up to lT164. A sharp increase in CAD triple junctions was observed with increasing CAD boundary content in Fig. 4, although the experimental points, being clustered, do not show the effect very well. This result was expected since a higher frequency of CAD planes at the three boundaries would increase the chances of obtaining a CAD axis (i.e. the intersection of three lowest index CAD planes). The computer simulation exhibits triple junction fractions slightly higher than the experimental results, but still within the standard
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deviations. Notice that about one third of the experimental triple junctions analyzed in aluminium, copper and copper-bismuth, have a low index CAD axis (low Tl, i.e. (loo), (I 10) and (I 1I)), which may be as important in determining the physical properties of junctions as low C is for the properties of CSL grain boundaries. Figure 5 displays the density of CAD junctions plotted against CSL boundary content. A modest increase in experimental CAD junctions with increasing CSL boundary content is observed but the simulation does not agree well with experimental values (the experimental values are in general much lower than the simulated results). It can be seen that only the first two experimental points up to a 30% CSL boundary content are within the simulated
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(shaded area in Fig. 5). However, the experimental results are in agreement with the conclusion of Palumbo and Aust [ 151, namely I hat the CAD triple junction model is independent of the CSL characterization of adjoining interfaces ,dnd is dependent only upon the continuity of low index crystallographic planes across the three abutting lattices at a triple junction.
values
4.3. I- oritl U-line
triple
junctions
Grain boundaries can be represented as dislocation and their intersection provides arrays special conditions relative to triple line structure. According to Bollmann’s O-lattice model [ 16, 201. there are two distinct ways to accommodate the three grain boundary dislocation networks: either the dislocation 60 ,
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00 40
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60 70 80 CAD Boundaries (%) tc>
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(d)
Fig. 3. Experimental densities of triple junctions having (a) 3, (b) 2. (c) I and (d) 0 CSL grain boundarles (characterized up to X.49) vs CAD grain boundary content when these boundaries are classified up to n8. The shaded area represents the results of the computer simulation. The C.4D boundary content in a random material is 45.9”/“.
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.o 60 ti
S 50-3 $40z 303 2010-
I
I
0 20
30
I ( I , I , I ( I , 1 40
50
60
70
CAD Boundaries
80
90
100
10
20
(%)
Fig. 4. Density of CAD triple junctions vs CAD grain boundary content when characterized up to II8. The experimental and computer simulated results are displayed as symbols and as a shaded area, respectively. The CAD
triple junction percentage found in a random material is 5.0 * 0.5%.
arrays balance at the line, in which case the line is called an I-line, or they do not balance at the line, and it is then called a U-line. Increasing numbers of studies show that triple junctions should be regarded as disclinations [16,20,29-311. Disclinations differ from dislocations in the sense that they are defined by a tensor of rank 3, e.g. a rotation axis and angle, whereas dislocations are defined by a vector [ 161.The first experimental support for Bollmann’s model of triple line classification was due to Clarebrough and Forwood [32]. They analyzed an I-line triple junction (which was also a C3-X9-C27b junction) by transmission electron microscopy (TEM) and
30 40 50 CSL Boundaries (%)
60
Y
Fig. 6. Density of I-line triple junctions vs CSL grain boundary content. The experimental and computer simulated results are displayed as symbols and as a shaded area, respectively. The I-line value found in a random material is 22.2 * 1.5%.
confirmed that a balance of grain boundary dislocation arrays occurred at the triple line. Corrosion studies have also provided support for the I- and U-line characterizations of triple junctions [33]. The I-line densities with respect to the CSL and CAD grain boundary contents are shown in Figs 6 and 7, respectively. The aluminium specimens exhibit an increase in I-lines (i.e. decrease in the U-lines) with increasing CSL boundary percentages, whereas copper and copper-bismuth samples are grouped at about 3040% I-lines and 4&50% CSL boundaries (Fig. 6). It is interesting to note that the computer simulation indicates a wide domain of existence for I-lines for the same CSL boundary density (but not
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Fig. 5. Density of CAD triple junctions vs CSL grain boundary content. The experimental and computer simulated results are displayed as symbols and as a shaded area, respectively.
50
70 60 CAD Boundaries (%)
80
!
Fig. 7. Density of I-line triple junctions vs CAD grain boundary content. The experimental and computer simulated results are displayed as symbols and as a shaded area, respectively.
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may be of importance in increasing the I-line triple junction density. Figure 7 shows the relationship between the I-line density and the CAD grain boundary content. An increase in the experimental fraction of l-lines is observed which seems to be sharper than the computer simulation band. It is noteworthy that most experimental data in Fig. 7 are within a standard deviation of the computer simulation data, except for one point. The experimental match with the simulation is therefore acceptable. Bollmann [20] and Fortier et al. [12] showed that junctions composed of low angle boundaries. i.e. XI. are always l-lines. Other CSL boundaries also contribute to improving the I-line triple junction density, such as twin boundaries, i.e. X3, and more generally twin-related boundaries, i.e. X3”, with 0 < n I 3 [12]. Experimental evidence of the beneficial contribution of 2.1 and X3 boundaries in increasing the I-line density are displayed in Figs 8 and 9. As the Cl content increases, the I-line density increases (Fig. 8). This feature is best shown by the aluminium samples which contain a significant fraction of Cl boundaries (between 5% and 32%). Some of the copper and copper--bismuth samples have higher than predicted I-line densities: this is due to the effect of other CSL boundaries present in the material, such as twin boundaries (between 19% and 31%). On the other hand, the I-line density increases sharply with increasing X3 boundary content, this effect being observed only with the copper and copper-bismuth specimens since very few twin boundaries were present in the aluminium (Fig. 9). It has been shown previously [12] using a computer simulation that the presence of one Cl or Z3 boundary at a triple junction augments its probabilit) of being an I-line. It is possible that the experimental I-line density would further increase for twin and low angle boundaries observed in this study. Experimental and simulated data in Fig. 9 do not agree at all and the simulated data seem to greatly underestimate the experimental twin boundary density (i.e. by a difference of about 20%) since the computer simulation does not take into account the low energy and high occurrence of C3 boundaries in copper. content
0
5
10 15 20 25 30 Low Angle (Cl) Boundaries (%)
35
Fig. X. Density of I-line triple junctions vs low-angle (Xl) grain boundary content in aluminium (a), copper and copper-bismuth (0). The solid line represents the linear relationship found by the computer simulation.
the same CSL boundary distribution), and thus the I-line density may vary greatly. The simulation gives a reasonable approximation of the present experimental results and matches studies of experimental l-line distributions obtained in Ni?Al [ 141 and in high purity nickel [34]. Experimental characterization of triple lines shows 76% (52 out of 68) and 57% (8 out of 14) I-lines in high purity nickel and in Cu-8.5% Al, respectively [33, 351. No CSL boundary distribution was given in these studies although a micrograph in one of these [33] shows more than 50% (24 of 45) CSL boundaries and 70% (17 of 24) of these were X3” boundaries. This suggests that the CSL boundary
I”
0
A
0
Experimental Simulation
,
, Cu +Cu-Bi
f i
0
0
10 20
0
1
0
5. DISCUSSION
1
,1111,1111,1111,111(,IIIJ,IIIJ,IIII 0 5 10 15 20 25 Twin (X.3) Boundaries (%)
30
35
Fig. 9. Density of I-line triple junctions vs twin (C3) grain boundary content. A sharp increase in the I-lines is observed in the copper and copper-bismuth specimens with Increasing twin boundary percentage. The solid line represents the linear regression of the eight copper and copper bismuth experimental points.
Controlling the frequency of occurrence of CSL boundaries is becoming a reality in materials engineering [2] and the optimization of certain CSL boundaries such as 23 (and in general Z3” boundaries, due to geometrical conditions at triple junctions) seems to be useful for controlling the triple junction character. A general trend was observed using both experimental and computational techan increase in CSL and CAD grain niques: boundaries results in an increase in CSL junctions (i.e. junctions composed of 3 and 2 CSL boundaries), CAD junctions and I-line junctions. The lowest
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fractions of CSL, CAD grain boundaries and triple junctions are always obtained from the simulated randomly oriented material (16.5% CSL boundaries up to C49, 45.9% CAD boundaries up to II& 5.0% CAD triple junctions up to II8, 22.2% I-lines). In addition, the I-line density increases with increasing low angle and twin boundary content. Therefore, the study of triple junction distributions and their properties is also related to the study of grain boundary structures and should not be performed independently. For example, preferential corrosion at triple junctions relative to the adjoining grain boundaries in high purity nickel has been found to occur at U-lines but not at I-lines [33]. Thus if one wants to increase corrosion resistance at triple lines, introducing special boundaries, such as low angle and twin boundaries, leads to more I-lines which have a favourable effect on corrosion resistance. Not only are the properties of materials improved by increasing the content of CSL (and possibly CAD) grain boundaries, but also by increasing the content of triple junctions created by these boundaries. Moreover, these junctions have a higher probability of being special, i.e. they may possess all CSL, CAD and I-line characters. Despite the fact that aluminium and copper are chemically distinct and prone to yielding low angle and twin boundaries, respectively, the specimens exhibit similar relationships (Figs 1, 3, 4, 5, 7 and 8) except for the I-line vs CSL boundary and twin boundary contents (Figs 6 and 9), where the latter is due to the low twin boundary fraction in aluminium). The copper and copper-bismuth specimens annealed at the same temperature did not exhibit any significant differences in triple junction and grain boundary character distributions. Thus the effect of bismuth on the boundary and junction distributions in copper is negligible and this is to be expected. The recrystallization and grain growth of the samples in this study occurred during the first heat treatment; bismuth was then evaporated on to the surface and the second heat treatment was then carried out. It is expected that all microstructural characteristics such as CSL, CAD and I-line triple junctions and grain boundaries were determined during the first annealing treatment, and the second annealing treatment produced little change. However, the grain size of the copper-bismuth samples was about 40% larger than that of copper. This suggests that liquid bismuth-induced grain boundary migration [36] occurred during the second anneal. The effect of triple junction structure on the presence or absence of bismuth particles at the junction will be discussed in a forthcoming publication [37]. The general trend of the experimental data was confirmed by the computer simulated results. The match between computer simulated and experimental data is good in six distributions (Figs 1, 3,4, 6, 7 and X), whereas it is not in two distributions (Figs 5 and 9, but the experimental data of Fig. 5 confirm that the
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CAD triple junction model is independent of the CSL character of adjoining interfaces). The limited number of triple junctions investigated experimentally for every sample (about 100) may have been one factor in causing the deviation from the simulated data. Other factors may be, by order of importance, (1) the high occurrence of low energy boundaries such as C3 (or X3”) in copper and 21 in aluminium, which the computer simulation does not take into account and (2) the use of fibre textures in the computer simulation that are unrepresentative of the real materials after cold rolling and annealing. However, the simulated random and fibre textures of various sharpnesses can be used to obtain approximate results for the triple junction distributions plotted against grain boundary distributions in cold rolled and annealed material. A better fit between the experimental and the computer simulated results might be obtained by calculating a simulated texture that produces triple junction and grain boundary distributions resembling closely those in cold rolled and annealed material (i.e. the recrystallization texture) [lo]. In this case, however, it would be difficult to obtain the large variations in CSL or CAD grain boundary contents which are observed for fibre textured materials in order to establish relationships between triple junction and grain boundary distributions. The fibre textures provide an easy way to obtain significant changes in CSL and CAD grain boundary distributions by modifying only the sharpness angle. 6. SUMMARY
AND CONCLUSIONS
The triple junction character distribution is highly dependent on the grain boundary character distribution and on the occurrence of specific CSL grain boundaries such as low angle and twin boundaries. An increase in special triple junctions (composed of 3 or 2 CSL boundaries, or classified in terms of CAD or I-lines) is generally observed with increasing CSL and CAD grain boundary contents, using both experimental and computer simulated techniques. Also, an increase in I-line triple junction density occurs with increasing low angle boundary (Cl) fraction in aluminium, and with increasing twin boundary (X3) content in copper and copper-bismuth. The computer simulation results match well with the experimental results for most distributions although they are based on simulated fibre textured materials. The existence of special triple junctions is closely associated with the presence of adjacent special grain boundaries and as the CSL boundary fraction increases, triple junctions have a higher probability of having combined CAD and I-line characters and having 3 or 2 CSL grain boundaries. Acknowledgements-The authors would like to thank Dr U. Erb (Queen’s University, Kingston), Dr G. Palumbo (Ontario Hydro Technologies), Mr R. Langer (Queen’s University) and Mr P. Lin (University of Toronto) for their
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assistance. We are also grateful for the use of the EBSD system at Queen’s University. Financial support from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. One of the authors (PF) wishes to express his appreciation to the University of Toronto for the award of a graduate fellowship.
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Palumbo. G. and Aust, K. T.. Acta metall. mater. 1990, 38, 2343. Lin, P.. Palumbo, G., Erb, U. and Aust, K. T., Scripta metall. mater., 1995, 33, 1387. Palumbo. G., King, P. J., Aust, K. T., Erb, U. and Lichtenberger, P. C.. Scripta metall. mater., 1991. 25, 1175. Watanabe, T., Res. Mech., 1984, 11, 47. Kronberg, M. L. and Wilson, F. H., Trans. TMSAIME, 1949, 185, 501. Pumphrey, P. H., Scripta metull., 1972, 6, 107. Palumbo, G., Thorpe, S. J. and Aust, K. T., Scripta metall. mater., 1990, 24, 1347. Wang. N., Palumbo, G., Wang, Z., Erb, U. and Aust, K. T., Scripta metall. mater., 1993, 28, 253 Doni, E. G.. Palumbo, G. and Aust. K. T., Scripta metall. mater.. 1990, 24, 2325. Garbacz, A. and Grabski. M. W., Acta metall. mater., 1993, 41, 475. Kurzydlowski, K. J.. Ralph, B. and Garbacz, A., Scripta metall. mater., 1993, 29, 1365. Fortier, P., Aust, K. T. and Miller. W. A., Acta metall. mater.. 1995, 43, 339. Gertsman, V. Y. and Tangri, K., Acta metall. mater., 1995, 43, 2317. Watanabe. T.. Mater. Sci. Engng, 1994, A176, 39.
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15. Palumbo, G. and Aust, K. T., S@tcl metal/. muter.. 1990, 24, 1771. 16. Bollmann, W., Phil. Mag. A, 1988, 57, 637. 17. Dingley. D. J., Scan. Elect. Micros., 1984, 2, 569. 18. Bollmann, W.. Phil. Mug. A, 1981. 44, 991. 19. Bollmann. W.. Crystal lattices, in Crrsra( Lot/ices. Interfaces,Matrices. privately published, Geneva, 1982. 20. Bollmann, W., Phil. -Msg. k ,‘1984. 49, 73. 21. Bollmann, W., Mater. Sci. Engng. 1989. A113, 129. 22. Brandon, D. G., Acta metall., 1966. 14, 1479. 23. Thompson. W., Phil. Mug., 1987. 24, 53. 24. Garbacz, A. and Grabski. M. W.. Acto metall muter.. 1993, 41, 469. 25. Morawiec, A., Szpunar, J. A. and Hinz. D.C., .4cta metall. mater.. 1993, 41, 2825. 26. Palumbo, G., Aust, K. T., Erb. U.. King, P. J.. Brennenstuhl, A. M. and Lichtenberger, P. C.. Phys. stat. solidi (a), 1992, 131, 425. 27. Randle, V., Acta metall. mater., 1994. 42, 1769. 28. Randle. V. and Ralph, B., J. Mater. Sci.. 1988. 23,934. 29. Kleman, M.. in Dislocations in Solids. Vol. 5. ed. F. R. N. Nabarro. 1980. p. 243. 30. Bollmann. W., J. & Phxsiyue (Colloquc~). 1990, 51, Cl-95. 31. Rybin, V. V., Zisman, A. A. and Zolotorevsky. N. Y.. Acta metall. mater., 1993, 41, 221 I. 32. Clarebrouah. L. M. and Forwood. C. T.. Phil. Map. A. 1987. 55, -17. 33. Palumbo, G. and Aust, K. T.. Mater. Sci. Engng. 1989. A113, 139. 34. Randle, V., Scripta metall. mater.. 1993. 28, 889. 35. Bollmann. W. and Guo, H., Scripta metall.. 1990, 24, 709. W. J.. Ac,tn mrtdl.. 1979, 36. Yoon. D. N. and Huppman. 27, 693. 37. Fortier. P.. Aust, K. T. and Miller, W. A.. submitted to Acta mater.
Pergamon
Published by Elsevier Science Ltd. Ail rights reserved Prmted in Great Britain
PII: s1359-6454(97)00004-9
1359-6454197 $17.00+ 0.00
TRIPLE JUNCTION AND GRAIN BOUNDARY CHARACTER DISTRIBUTIONS IN METALLIC MATERIALS P. FORTIER, Department
W. A. MILLER and K. T. AUST
of Metallurgy & Materials Science, University of Toronto, Toronto, Ontario, Canada M5S 3E4 (Received 10 September 1996)
Abstract-Triple junction and grain boundary orientations were obtained by electron backscattered diffraction in high purity aluminium and copper, and in copper-bismuth alloys, and were then characterized using the CSL, CAD and I-line (O-lattice) geometrical models. A computer simulation was also performed and compared to the experimental results. Relationships were established between triple junction and grain boundary character distributions using both experimental and computer simulated results. A general trend was observed which shows an increase in special triple junction character density with increasing special grain boundary character content. An increased frequency of low angle and twin boundaries is shown to lead to an increase in the I-line triple junction density. 80 1997 Acta Metallurgicu Inc.
R&sum&Des orientations de jonctions triples et de joints de grain sont obtenues g partir de diffraction d’electrons dans l’aluminium et le cuivre de haute pureti, et dans des alliages de cuivre-bismuth, et elles sont caractCrisCes par les modeles gtomCtriques CSL, CAD et type I. Une simulation par ordinateur est kgalement prBsentte and comparte aux resultats expirimentaux. Une correspondance est etablie entre les distributions de jonctions triples et celles des joints de grain obtenues B partir des r&sultats expCrimentaux et de simulation. Une relation g&&ale est observCe qui montre une augmentation en densit de jonctions triples spkciales quand la proportion de joints de grain specials augmente. La distribution de jonctions triples de type I est dkpendante de la densit de mdcles et de joints de grains de faible disorientation.
1. INTRODUCTION Material properties depend on both the density and type of mircrostructural elements, such as dislocations and interfaces, and they may be improved by the presence of interfaces having appropriate structures [e.g. l-31. Grain boundary design and
control (grain boundary engineering) is a concept introduced by Watanabe [4] who first mentioned the importance of grain boundary character distribution (GBCD) for obtaining improved physical properties. The characterization of grain boundaries is generally carried out using geometrical models (such as the coincidence site lattice (CSL) [S] or the coincident
axial direction (CAD or plane matching) [6] models). Grain boundary engineering involves controlling or optimizing the presence of certain grain boundaries that may enhance materials properties as a result of their intrinsic geometrical characteristics. For instance, twin boundaries, known as C3 in the CSL model, and other low C grain boundaries seem to be more resistant to intergranular degradation than random boundaries [l-3]. Control and optimization of specific and potentially enhancing boundaries may be achieved by thermomechanical processing [2] which varies with the type of material. This control of statistical grain boundary distributions is interesting because it is the first step in designing materials with desired properties.
Nanocrystalline materials have increasingly held the attention of the scientific community recently. The large fraction of grain boundary ant1 triple junction free volume [7, 81 in such materials, due to their extremely small grain size, and the possibility of control of grain boundary character have led to a reconsideration of the properties of both triple junctions and grain boundaries. Specifically, little is known about triple junction character distribution in the presence of a given grain boundary distribution. Studies have confirmed the existence of a correspondence between junction (and boundary) distributions and the texture of the material [9-131 but few detailed relationships have been presented between triple junction and grain boundary distributions [9, 11, 121. Doni et al. [9] obtained the first computer-simulated correlation between grain boundary and triple line character distributions for the case of a CSL description; Kurzydlowski et al. [l 1] and Fortier et al. [12] found relationships between CSL triple junctions and CSL boundary densities, and I-line triple junctions and CSL boundary fractions, respectively, both using computer simulations. Watanabe [14] experimentally found that a relationship exists between the I-line triple junction and CSL boundary fractions. However, no comprehensive and complete investigation is available in the literature that shows
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whether a correspondence exists between the CSL [l 11, CAD [15] and I-line [16] triple junction distributions and the CSL and CAD grain boundary fractions. The present paper proposes to fill this gap, using both experimental and computer-simulated studies. 2. EXPERIMENTAL PROCEDURE High purity (99.999 + %) aluminium and copper were heavily cold rolled by 90% to a thickness of 0.5 mm, mechanically polished using silicon papers of various grades followed by alumina paste, and electropolished in perchloric acid and phosphoric acid solutions, respectively. The specimens were annealed at 0.50, 0.65, 0.80 and 0.95 of the absolute melting point (T,,,) for 24 h. To produce the copper-bismuth alloys, high purity (99.999%) bismuth was evaporated onto a copper surface to obtain a bismuth layer of 3 pm in thickness. The three types of specimen were then annealed for a second time at the same temperature for 24 h. The copper-bismuth samples were gently polished using alumina and all samples were given final electropolishing and etching treatments. Observation by scanning electron microscopy (SEM) of the specimens revealed the microstructure (i.e. grain size, grain boundaries, triple junctions) as well as the presence of bismuth particles at some triple junctions in the copper-bismuth specimens. Electron backscattered diffraction (EBSD) [17] was used to obtain grain orientations with respect to a constant reference frame. Triple junction orientations were collected by obtaining three contiguous grain orientations. Care was taken to make sure that each grain boundary, which is connected to two junctions, was counted only once for the boundary distributions. Triple junctions and grain boundaries were then characterized using the CSL model (junctions [l 11, boundaries [5]), the CAD model (junctions [15], boundaries [6]) and the O-lattice model (junctions [16, 18-211). An average of 104 triple junctions, 269 grain boundaries and 236 grains were assessed per sample (for a total of 1380 junctions, 3622 boundaries and 3213 grains). 3. COMPUTER SIMULATION A computer simulation was performed to determine the relationships between triple junction densities and grain boundary contents, using the Pascal programming language. Fibre textured grain orientations were generated in numbers of 30,000 per texture (60,000 for the randomly oriented material), which correspond to 10,000 junctions and 30,000 boundaries; (loo), ( 110) and (111) fibre textures were computed from Gaussian distributions of the 15”, 8”, 5”, 3” and 1” deviation angles (i.e. from a weak to a sharp texture) [lo]. The characterization of triple junctions and grain boundaries was performed using the CSL framework and the Brandon criterion [22], and the CAD and I-line models. The computer
simulation employed independent sets of three orientations to calculate triple junction classifications, i.e. each triple junction was characterized independently of the others. The method did not utilize a connected spatial model of polycrystals such as Kelvin polyhedra (tetrakaidecahedra) [23]. However, the grain boundary calculations were always performed using the orientation of three grains meeting at a triple junction; thus the grain boundary character distributions presented in this work reflect more closely the real connectivity of boundaries in materials than would be obtained by analyzing sets of independent bicrystals. For every fibre textured material, densities of triple junctions were plotted against grain boundary contents. The texture dependence of relationships between triple junction and grain boundary distributions is usually small [l l] but can be significant in some cases (i.e. I-lines vs CSL boundaries [9, 121). By using the three types of fibre texture ((loo), (110) and (111)) and their associated Gaussian angular deviations, one can establish general relationships between triple junction and grain boundary contents occurring in conventional polycrystalline materials. 4. RESULTS 4.1. CSL triple junctions CSL triple junctions are simply junctions composed of CSL and random boundaries. In this study, CSL boundaries are characterized up to C49-higher C values are considered to be random boundaries. Only four types of junction exist in terms of CSL boundary connectivity: junctions (1) with 3 CSL boundaries, (2) with 2 CSL and 1 random boundary, (3) with 1 CSL and 2 random boundaries and (4) with 3 random boundaries. Figure 1 shows the densities of CSL triple junctions plotted against CSL boundary content, using experimental specimens, computersimulated data and analytically, using probability functions. The computer-simulated fractions of CSL junctions having 3, 2, 1 and 0 CSL boundaries are 0.51 f 0.17%, 6.32 + 0.60%, 35.19 f 1.48% and 57.98 f 1.53% [12], respectively, in a material containing the random content of CSL boundaries (16.5% up to C49 and 12.4% up to ZZ29[24,25]). As the CSL boundary content increases, the densities of 3 and 2 CSL boundary junctions significantly increase [Fig. 1 (a), (b)], whereas the density of junctions composed only of random boundaries drastically decreases [Fig. 1 (d)] while the 1 CSL boundary junction density remains constant for the experimental range considered [ Fig. 1 (c)l. The computer simulation is in good agreement with both the experimental results and the probability analysis. The analytical probability study was performed using probability functions. If g is the CSL grain boundary fraction (i.e. 1 -g is the random grain boundary fraction), the probability of occurrence of 1,2 and 3 CSL grain boundaries at the triple junction
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is g, g? and g”, respectively, and similarly the probability of occurrence of 1, 2 and 3 random boundaries is (1 - g), (1 - g)* and (1 - g)‘, respectively. Therefore the probability of occurrence P of a triple junction having n CSL and 3 - n random boundaries is:
P(n,g)
= ( - n2 + 3n + l)g”(l - g)‘-.”
where the first term in brackets is the relative probability of occurrence of the junction type. For instance, there is only one occurrence of the 3 and 0 CSL boundary junctions, while there are three occurrences of the 2 and 1 CSL boundary junctions. The probability function P(n,g) is normalized to
TRIPLE
346 1
JUNCTION
unity, so that
i P(n,g) II
=
”
= i ( - n? + 3n + l)g”(l - g)1-1’ ,/ = 0
= 1 with 0
1.
If the value for a randomly oriented material of 16.5% is taken for g, then P(3,0.165) = 0.45%, P(1,0.165) = 34.51% and P(2,0.165) = 6.82%, P(O,O.165) = 58.22%. These values agree extremely well with those calculated by computer simulation and are within the standard deviations. The match is also good with results from the computer simulation
computer simulation probability
if
,
2
probability
I”“I”“TmlIIIIIIIIIIII~
10
20
30 40 50 CSL Boundaries (%)
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20
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(%)
CSL Boundaries
(%)
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Fig. 1. Densities of triple junctions having (a) 3, (b) 2, (c) 1 and (d) 0 CSL boundaries vs CSL boundary content when these are classified up to X49. Experimental points (0) are obtained from aluminium, copper and copper-bismuth specimens using a total of 1380 triple junctions, 3622 grain boundaries and 3213 grains. The computer simulated results ranged from 16.5% (random material) to 65% CSL boundaries. The probability function P, defined in the text, is also displayed, resulting from the dependence of CSL boundaries on their connectivity at triple junctions.
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100 go-
-
0 CSL boundary J junctions
3 CSL boundary junctions\
Q 70 e g 60 .o ti c 60 4 Q, 40 3 E 30 20 10 0 , 0
, 10
I , 20
,
30 40 50 60 70 CSL Boundaries (%)
, I , 80
,
90 100
Fig. 2. Densities of triple junctions having 3, 2, 1and 0 CSL boundaries vs CSL boundary content. The symbols represent the results from the computer simulation and the solid lines the results from the probability analysis.
[ 121 for other values of g (Figs 1 and 2): this indicates that the effect of textured grain orientations on the relationship between triple junction distributions and grain boundary distributions is very small. This result was reinforced by Kurzydlowski et al. [l l] who found exactly the same relationships although they used different textured grain orientations. The small discrepancy between simulated and analytical results may be due to the fact that the analytical method does not take into account the Brandon criterion [22] and the geometrical conditions set at triple junctions [26, 271: (1) the maximum allowable deviation angle varies from one boundary to another at the same triple junction (except for the junction composed of three low angle boundaries), therefore the probability of occurrence of n CSL boundaries is slightly different from the value g” and consequently CSL triple junction frequencies differ slightly from the probability function P; (2) it has been noted that the geometrical rule of 3 CSL boundaries at triple junctions [26,27] is not always verified experimentally, owing to non-constant maximum deviations obtained for different X values: a percentage of 18.4% (33 over 179) of experimental 3 X boundary junctions did not satisfy the rule (i.e. we obtained junctions such as z:X + XY = EZ with Z non-divisible by either X or Y). This means that the function P provides only a good approximation of the fractions of CSL boundary junctions in materials and the computer simulation gives more accurate results. The funcion P yields values for g < 16.5%, although this does not physically make sense (the lowest CSL grain boundary content for any material occurs in the random texture) unless a limit beyond which a boundary is random is set lower than C49 (e.g. Z 29, in which case g = 12.4%). If g = 12.4%, then P(3, g) = 0.19%, P(2, g) = 4.04%, P(1, g) = 28.55% and
TRIPLE JUNCTION P(0, g) = 67.22%, which is in excellent agreement with the computer simulation studies of Kurzydlowski et al. [l l] and Garbacz and Grabski [lo], and in fair agreement with the values of Doni et al. [9] who considered a total of only 200 triple junctions. The CSL triple junction density vs the CAD grain boundary content is presented in Fig. 3 (a)-(d). The relationships are similar to those found in Fig. 1: an increase in 3 and 2 CSL boundary junctions and a decrease in 0 CSL boundary junctions are observed with increasing content of CAD grain boundaries. The computer simulated results did not yield a monotonous relationship but rather a domain of existence within which the experimental points are located (indicated as shaded areas in Fig. 3). This results from the fact that different distributions of CAD boundaries can be associated with the same CAD boundary content. For example, consider the two CAD boundary distributions (lT3 = 25%, II4= 5%, rI8 = 5%) and (lI3 = 5%, II4= 5%, lI8 = 25%}, respectively; they have the same CAD boundary fraction classified up to II8, but yield different CSL triple junction densities because the CAD boundary distributions are different. We conclude that the computer simulated results match the experimental results quite well.
4.2. CAD triple junctions CAD triple junction distributions are interesting since the CAD triple junction model [15] is based on a one-dimensional characterization (axis), whereas the ESL model [5, 221 is based on a two-dimensional characterization (angle and axis). The CAD characterization is appropriate for the description of the triple line because triple junctions are line defects. The Il value associated with the CAD model represents the (hkl) common axis of the triple junction, i.e. l-l = h* + k* + l*, and the first n values of the CAD classification are 3, 4, 8, 11, 19, 20 and I 24 with axes corresponding to (11 l), (loo), (1 lo), (311), (331), (210) and (211), respectively [28]. The method for calculating the CAD axis for triple junctions was first given by Palumbo and Aust [15] and is as follows: boundaries are classified by performing the 576 symmetry operations on the misorientation matrices and comparing these to exact CAD axes; if a common l-l value is found to exist for the three boundaries, this determines the II value of the triple junction. The CAD triple junctions were characterized in this way from Il3 up to lT164. A sharp increase in CAD triple junctions was observed with increasing CAD boundary content in Fig. 4, although the experimental points, being clustered, do not show the effect very well. This result was expected since a higher frequency of CAD planes at the three boundaries would increase the chances of obtaining a CAD axis (i.e. the intersection of three lowest index CAD planes). The computer simulation exhibits triple junction fractions slightly higher than the experimental results, but still within the standard
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deviations. Notice that about one third of the experimental triple junctions analyzed in aluminium, copper and copper-bismuth, have a low index CAD axis (low Tl, i.e. (loo), (I 10) and (I 1I)), which may be as important in determining the physical properties of junctions as low C is for the properties of CSL grain boundaries. Figure 5 displays the density of CAD junctions plotted against CSL boundary content. A modest increase in experimental CAD junctions with increasing CSL boundary content is observed but the simulation does not agree well with experimental values (the experimental values are in general much lower than the simulated results). It can be seen that only the first two experimental points up to a 30% CSL boundary content are within the simulated
TRIPLE
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(shaded area in Fig. 5). However, the experimental results are in agreement with the conclusion of Palumbo and Aust [ 151, namely I hat the CAD triple junction model is independent of the CSL characterization of adjoining interfaces ,dnd is dependent only upon the continuity of low index crystallographic planes across the three abutting lattices at a triple junction.
values
4.3. I- oritl U-line
triple
junctions
Grain boundaries can be represented as dislocation and their intersection provides arrays special conditions relative to triple line structure. According to Bollmann’s O-lattice model [ 16, 201. there are two distinct ways to accommodate the three grain boundary dislocation networks: either the dislocation 60 ,
T
50
60
70
CAD Boundaries
80
90
100
00 40
50
(%)
60
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70
CAD Boundaries
(a>
80
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(%)
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60
60 ,
g 50 E .o 40 5 5 g30 z S m”20 z _ 10
00 40
50
60 70 80 CAD Boundaries (%) tc>
90
1
50
60 70 60 CAD Boundaries (%)
90
(d)
Fig. 3. Experimental densities of triple junctions having (a) 3, (b) 2. (c) I and (d) 0 CSL grain boundarles (characterized up to X.49) vs CAD grain boundary content when these boundaries are classified up to n8. The shaded area represents the results of the computer simulation. The C.4D boundary content in a random material is 45.9”/“.
100
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80 -
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.o 60 ti
S 50-3 $40z 303 2010-
I
I
0 20
30
I ( I , I , I ( I , 1 40
50
60
70
CAD Boundaries
80
90
100
10
20
(%)
Fig. 4. Density of CAD triple junctions vs CAD grain boundary content when characterized up to II8. The experimental and computer simulated results are displayed as symbols and as a shaded area, respectively. The CAD
triple junction percentage found in a random material is 5.0 * 0.5%.
arrays balance at the line, in which case the line is called an I-line, or they do not balance at the line, and it is then called a U-line. Increasing numbers of studies show that triple junctions should be regarded as disclinations [16,20,29-311. Disclinations differ from dislocations in the sense that they are defined by a tensor of rank 3, e.g. a rotation axis and angle, whereas dislocations are defined by a vector [ 161.The first experimental support for Bollmann’s model of triple line classification was due to Clarebrough and Forwood [32]. They analyzed an I-line triple junction (which was also a C3-X9-C27b junction) by transmission electron microscopy (TEM) and
30 40 50 CSL Boundaries (%)
60
Y
Fig. 6. Density of I-line triple junctions vs CSL grain boundary content. The experimental and computer simulated results are displayed as symbols and as a shaded area, respectively. The I-line value found in a random material is 22.2 * 1.5%.
confirmed that a balance of grain boundary dislocation arrays occurred at the triple line. Corrosion studies have also provided support for the I- and U-line characterizations of triple junctions [33]. The I-line densities with respect to the CSL and CAD grain boundary contents are shown in Figs 6 and 7, respectively. The aluminium specimens exhibit an increase in I-lines (i.e. decrease in the U-lines) with increasing CSL boundary percentages, whereas copper and copper-bismuth samples are grouped at about 3040% I-lines and 4&50% CSL boundaries (Fig. 6). It is interesting to note that the computer simulation indicates a wide domain of existence for I-lines for the same CSL boundary density (but not
go-
80870E .g 60$ 50$40L _ ; 30$ 20-
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Fig. 5. Density of CAD triple junctions vs CSL grain boundary content. The experimental and computer simulated results are displayed as symbols and as a shaded area, respectively.
50
70 60 CAD Boundaries (%)
80
!
Fig. 7. Density of I-line triple junctions vs CAD grain boundary content. The experimental and computer simulated results are displayed as symbols and as a shaded area, respectively.
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may be of importance in increasing the I-line triple junction density. Figure 7 shows the relationship between the I-line density and the CAD grain boundary content. An increase in the experimental fraction of l-lines is observed which seems to be sharper than the computer simulation band. It is noteworthy that most experimental data in Fig. 7 are within a standard deviation of the computer simulation data, except for one point. The experimental match with the simulation is therefore acceptable. Bollmann [20] and Fortier et al. [12] showed that junctions composed of low angle boundaries. i.e. XI. are always l-lines. Other CSL boundaries also contribute to improving the I-line triple junction density, such as twin boundaries, i.e. X3, and more generally twin-related boundaries, i.e. X3”, with 0 < n I 3 [12]. Experimental evidence of the beneficial contribution of 2.1 and X3 boundaries in increasing the I-line density are displayed in Figs 8 and 9. As the Cl content increases, the I-line density increases (Fig. 8). This feature is best shown by the aluminium samples which contain a significant fraction of Cl boundaries (between 5% and 32%). Some of the copper and copper--bismuth samples have higher than predicted I-line densities: this is due to the effect of other CSL boundaries present in the material, such as twin boundaries (between 19% and 31%). On the other hand, the I-line density increases sharply with increasing X3 boundary content, this effect being observed only with the copper and copper-bismuth specimens since very few twin boundaries were present in the aluminium (Fig. 9). It has been shown previously [12] using a computer simulation that the presence of one Cl or Z3 boundary at a triple junction augments its probabilit) of being an I-line. It is possible that the experimental I-line density would further increase for twin and low angle boundaries observed in this study. Experimental and simulated data in Fig. 9 do not agree at all and the simulated data seem to greatly underestimate the experimental twin boundary density (i.e. by a difference of about 20%) since the computer simulation does not take into account the low energy and high occurrence of C3 boundaries in copper. content
0
5
10 15 20 25 30 Low Angle (Cl) Boundaries (%)
35
Fig. X. Density of I-line triple junctions vs low-angle (Xl) grain boundary content in aluminium (a), copper and copper-bismuth (0). The solid line represents the linear relationship found by the computer simulation.
the same CSL boundary distribution), and thus the I-line density may vary greatly. The simulation gives a reasonable approximation of the present experimental results and matches studies of experimental l-line distributions obtained in Ni?Al [ 141 and in high purity nickel [34]. Experimental characterization of triple lines shows 76% (52 out of 68) and 57% (8 out of 14) I-lines in high purity nickel and in Cu-8.5% Al, respectively [33, 351. No CSL boundary distribution was given in these studies although a micrograph in one of these [33] shows more than 50% (24 of 45) CSL boundaries and 70% (17 of 24) of these were X3” boundaries. This suggests that the CSL boundary
I”
0
A
0
Experimental Simulation
,
, Cu +Cu-Bi
f i
0
0
10 20
0
1
0
5. DISCUSSION
1
,1111,1111,1111,111(,IIIJ,IIIJ,IIII 0 5 10 15 20 25 Twin (X.3) Boundaries (%)
30
35
Fig. 9. Density of I-line triple junctions vs twin (C3) grain boundary content. A sharp increase in the I-lines is observed in the copper and copper-bismuth specimens with Increasing twin boundary percentage. The solid line represents the linear regression of the eight copper and copper bismuth experimental points.
Controlling the frequency of occurrence of CSL boundaries is becoming a reality in materials engineering [2] and the optimization of certain CSL boundaries such as 23 (and in general Z3” boundaries, due to geometrical conditions at triple junctions) seems to be useful for controlling the triple junction character. A general trend was observed using both experimental and computational techan increase in CSL and CAD grain niques: boundaries results in an increase in CSL junctions (i.e. junctions composed of 3 and 2 CSL boundaries), CAD junctions and I-line junctions. The lowest
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fractions of CSL, CAD grain boundaries and triple junctions are always obtained from the simulated randomly oriented material (16.5% CSL boundaries up to C49, 45.9% CAD boundaries up to II& 5.0% CAD triple junctions up to II8, 22.2% I-lines). In addition, the I-line density increases with increasing low angle and twin boundary content. Therefore, the study of triple junction distributions and their properties is also related to the study of grain boundary structures and should not be performed independently. For example, preferential corrosion at triple junctions relative to the adjoining grain boundaries in high purity nickel has been found to occur at U-lines but not at I-lines [33]. Thus if one wants to increase corrosion resistance at triple lines, introducing special boundaries, such as low angle and twin boundaries, leads to more I-lines which have a favourable effect on corrosion resistance. Not only are the properties of materials improved by increasing the content of CSL (and possibly CAD) grain boundaries, but also by increasing the content of triple junctions created by these boundaries. Moreover, these junctions have a higher probability of being special, i.e. they may possess all CSL, CAD and I-line characters. Despite the fact that aluminium and copper are chemically distinct and prone to yielding low angle and twin boundaries, respectively, the specimens exhibit similar relationships (Figs 1, 3, 4, 5, 7 and 8) except for the I-line vs CSL boundary and twin boundary contents (Figs 6 and 9), where the latter is due to the low twin boundary fraction in aluminium). The copper and copper-bismuth specimens annealed at the same temperature did not exhibit any significant differences in triple junction and grain boundary character distributions. Thus the effect of bismuth on the boundary and junction distributions in copper is negligible and this is to be expected. The recrystallization and grain growth of the samples in this study occurred during the first heat treatment; bismuth was then evaporated on to the surface and the second heat treatment was then carried out. It is expected that all microstructural characteristics such as CSL, CAD and I-line triple junctions and grain boundaries were determined during the first annealing treatment, and the second annealing treatment produced little change. However, the grain size of the copper-bismuth samples was about 40% larger than that of copper. This suggests that liquid bismuth-induced grain boundary migration [36] occurred during the second anneal. The effect of triple junction structure on the presence or absence of bismuth particles at the junction will be discussed in a forthcoming publication [37]. The general trend of the experimental data was confirmed by the computer simulated results. The match between computer simulated and experimental data is good in six distributions (Figs 1, 3,4, 6, 7 and X), whereas it is not in two distributions (Figs 5 and 9, but the experimental data of Fig. 5 confirm that the
TRIPLE
JUNCTION
CAD triple junction model is independent of the CSL character of adjoining interfaces). The limited number of triple junctions investigated experimentally for every sample (about 100) may have been one factor in causing the deviation from the simulated data. Other factors may be, by order of importance, (1) the high occurrence of low energy boundaries such as C3 (or X3”) in copper and 21 in aluminium, which the computer simulation does not take into account and (2) the use of fibre textures in the computer simulation that are unrepresentative of the real materials after cold rolling and annealing. However, the simulated random and fibre textures of various sharpnesses can be used to obtain approximate results for the triple junction distributions plotted against grain boundary distributions in cold rolled and annealed material. A better fit between the experimental and the computer simulated results might be obtained by calculating a simulated texture that produces triple junction and grain boundary distributions resembling closely those in cold rolled and annealed material (i.e. the recrystallization texture) [lo]. In this case, however, it would be difficult to obtain the large variations in CSL or CAD grain boundary contents which are observed for fibre textured materials in order to establish relationships between triple junction and grain boundary distributions. The fibre textures provide an easy way to obtain significant changes in CSL and CAD grain boundary distributions by modifying only the sharpness angle. 6. SUMMARY
AND CONCLUSIONS
The triple junction character distribution is highly dependent on the grain boundary character distribution and on the occurrence of specific CSL grain boundaries such as low angle and twin boundaries. An increase in special triple junctions (composed of 3 or 2 CSL boundaries, or classified in terms of CAD or I-lines) is generally observed with increasing CSL and CAD grain boundary contents, using both experimental and computer simulated techniques. Also, an increase in I-line triple junction density occurs with increasing low angle boundary (Cl) fraction in aluminium, and with increasing twin boundary (X3) content in copper and copper-bismuth. The computer simulation results match well with the experimental results for most distributions although they are based on simulated fibre textured materials. The existence of special triple junctions is closely associated with the presence of adjacent special grain boundaries and as the CSL boundary fraction increases, triple junctions have a higher probability of having combined CAD and I-line characters and having 3 or 2 CSL grain boundaries. Acknowledgements-The authors would like to thank Dr U. Erb (Queen’s University, Kingston), Dr G. Palumbo (Ontario Hydro Technologies), Mr R. Langer (Queen’s University) and Mr P. Lin (University of Toronto) for their
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assistance. We are also grateful for the use of the EBSD system at Queen’s University. Financial support from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. One of the authors (PF) wishes to express his appreciation to the University of Toronto for the award of a graduate fellowship.
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