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J. Am. Ceram. Soc., 88  2286–2291 (2005) DOI: 10.1111/j.1551-2916.2005.00400.x
Correlation Between Grain-Boundary Segregation and Grain-Boundary Plane Orientation in Nb-Doped TiO2 Ying Pang*,w and Paul Wynblatt* Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890
Nb, and Ga in TiO2, and have studied their segregation to several grain boundaries. Although multiple grain boundaries were studied in the previous work on TiO2, the orientation dependence of segregation was not the primary focus of the observations. This paper describes measurements of segregation by Auger electron spectroscopy (AES) of 83 grain boundaries exposed by inter-granular fracture in samples of 2 mol% Nb-doped TiO2 with the tetragonal rutile structure. Nb51-doped TiO2 metal– oxide system displays moderately strong Nb segregation to grain boundaries. Furthermore, the addition of Nb increases the electrical conductivity of the TiO2, thereby avoiding surface charge build-up, that can lead to difﬁculties in analyzing GB composition by AES. Both sides of the fracture surface were studied, and the matching halves of each grain boundary were identiﬁed, to produce a total of 166 measurements on different GB planes. Various possible factors that may lead to scatter or errors in the measurement of segregation were ﬁrst evaluated, and then the compositions of the two matching GB fracture surfaces of each grain were measured. GB plane normals were determined by a method that combined orientation-imaging microscopy (OIM) with a scanning electron microscope (SEM) stereo-pair technique. The data on composition and orientation were then interrelated to determine the dependence of GB composition on GB plane orientation. Results of an investigation of the change in the GB plane distribution of more than 80,000 boundaries, due to Nb doping, will be reported elsewhere.
Grain-boundary (GB) segregation has been measured in Nbdoped TiO2 (rutile) by Auger electron spectroscopy analyses of the two surfaces exposed by inter-granular fracture. In addition, the orientations of the exposed GB planes on both sides of the fracture surface have been determined. A strong anisotropy of GB composition is found. Measurements on 166 individual GB fracture surfaces show that boundary planes with low and high levels of segregation tend to be clustered along the (110)–(010) and (001)–(011) regions of the stereographic triangle, respectively. The matching halves of GB planes with either high or low segregation also tend to be terminated by planes in the same respective regions of orientation space. High and low levels of segregation occur in regions of GB plane orientation space estimated to correspond to high and low GB energy, respectively. This trend is consistent with qualitative arguments based on Gibbsian adsorption. I. Introduction
or impurity segregation at grain boundaries plays an important role in many materials properties, including sinterability, electrical conductivity, and mechanical strength. As a result, considerable effort has been devoted to the study of grain-boundary (GB) segregation phenomena over the past several years. Although there has been some previous research on GB segregation as a function of GB misorientation by both experimental and computer simulation approaches, only special grain boundaries and limited numbers of general grain boundaries have been examined.1–3 Thus, an adequate picture of the variation of GB segregation over the entire GB orientation space is still lacking. Furthermore, the anisotropy of GB chemistry and its orientation dependence have been less thoroughly probed in ceramics than in metals. These considerations have provided the motivation for the present study of solute segregation at grain boundaries in metal oxides, as a function of GB plane orientation. It should be noted that characterizing the crystallographic orientation of GB planes only provides a determination of four of the ﬁve macroscopic parameters of GB orientation. Nevertheless, this work represents an important ﬁrst step toward the ultimate objective of relating GB composition to the complete set of macroscopic orientation parameters. GB solute segregation phenomena have been previously studied in TiO2 by scanning transmission electron microscopy (STEM). Wang et al.4 have measured the levels of segregation in some 30 grain boundaries in yttrium-doped TiO2, and have compared the results with the predictions of a model that accounts for both electrostatic and elastic driving forces. Ikeda and Chiang5,6 proposed a space charge model for the segregation of various combinations of aliovalent solutes, such as Al, OLUTE
II. Experimental Procedure (1) Sample Preparation TiO2 powderz was doped with 2 mol% niobium, following procedures described by Yan and Rhodes.7 The powder was added to a deionized water solution of niobium ammonium oxalate (NH4[Nb( 5 O)(C2O4)2(H2O)2] 3H2O) to form a slurry. Ammonium hydroxide (NH4OH) solution was added to the slurry to maintain a pH of 11, so as to precipitate Nb as insoluble niobium hydroxides. The slurry was ultrasonically stirred for 1 h to break up possible large TiO2 agglomerates, and then ﬁltered, dried, and calcined at 9001C for 16 h in air. The resulting powder was compacted in a stainless-steel die at about 140 MPa pressure. A scraper was used to remove the surface layers of the compressed pellets to reduce contamination from the die. After this, the pellets were packed in an alumina crucible surrounded by the parent powder and annealed for 24 h at 15701C in air, and then were cooled down at 51C/min to room temperature. The solubility of Nb2O5 in TiO2 is reported to be about 3.5 mol% at the annealing temperature.5 Thin sections of the samples were examined by high-resolution transmission microscopy. The grain boundaries were found to be free of precipitates and of amorphous phase ﬁlms.
D. J. Green—contributing editor
(2) Measurement of GB Chemistry GB composition was determined in a PHI Model 600 Scanning Auger Microprobe (SAM) (Edina, MN) with a base pressure of
Manuscript No. 20136. Received November 23, 2004; approved February 8, 2005. *Member, American Ceramic Society. w Author to whom correspondence should be addressed. e-mail: [email protected]
Analyzed by ﬂame pyrolysis to contain: 13 ppm Al, 40 ppm Si, o 10 ppm Fe.
Correlation between Grain-Boundary Segregation and Grain-Boundary Plane Orientation
Fig. 1. Complementary grain-boundary fracture surfaces on two sides of a 2 mol% Nb-doped sample.
about 1010 Torr. Since it is difﬁcult to examine both fracture surfaces of a sample after in situ fracture in the SAM, a preliminary experiment was conducted to evaluate the effects of fracturing a sample in air, and then introducing both fracture surfaces into the ultrahigh vacuum environment of the SAM. A sample was fractured at room temperature in air, mounted onto a sample holder, and introduced into the SAM as rapidly as possible. A second sample from the same pellet was introduced into the SAM and fractured in situ also at room temperature. The average compositions of the fracture surfaces of both these samples were found to be identical, within experimental error. The only elements present on the fracture surfaces of both these samples were Nb, Ti, O, and C. Although the origin of the C contamination is unclear, it was present in approximately equal amounts on both the air-fractured sample and the in situfractured sample. All the measurements reported below were obtained on air-fractured samples at room temperature. Both halves of fractured specimens were mounted side by side. The fractures obtained were intergranular over about 95% of the fracture area. A typical example of matching fracture surfaces is shown in Fig. 1. Auger analyses were carried out in the SAM at a pressure of B2 1010 Torr, at 3 keV, with a beam current of B50 nA and an analytical spot size of about 0.1 mm. The electron beam was placed at locations on individual grain surfaces, far from edges and pores, to avoid triple-line and free-surface regions. The following Auger transitions were used for analysis: O at 511 eV, Ti at 387 eV, and Nb at 157 eV. Auger data were acquired in the derivative mode, and the peak-to-peak amplitude ratios were used to represent the relative segregation level. A typical Auger spectrum is shown in Fig. 2.
(3) Determination of the GB Plane Orientation on Fracture Surfaces The Miller indices of GB planes on fracture surfaces have been reported infrequently because of the technical challenges involved. In this study, GB plane orientations were ﬁrst obtained in a sample reference frame by the so-called stereo-pair method applied to SEM images of fracture surfaces. This is a wellestablished technique for determining the coordinates of various points on a plane in a microstructure relative to a ﬁxed coordinate system in the microscope.8–11 It involves analyzing micrographs of a given surface taken at two different tilt angles to the microscope axis to obtain the coordinates of various points in space. In this experiment, micrographs of the fracture surface at tilt angles of 01 and 101 were obtained at a magniﬁcation of 500. The coordinates of three points belonging to a given GB fracture plane on the two photomicrographs, Q1, R1, S1 and Q2, R2, S2, as shown in Fig. 3, were measured using Photoshop 6.0 software. The three spatial coordinates of any given point on the surface, (X, Y, Z) are given by12:
GB facet 0° tilt
Q2 GB facet 10° tilt
Fig. 2. Typical Auger spectrum from an Nb-doped TiO2 sample.
Fig. 3. Cartesian coordinate system used in the stereo-pair analysis: x(tilt)-axis parallel to the sample edge, y-axis perpendicular to the x-axis, z(beam)-axis perpendicular to the fracture surface.
Journal of the American Ceramic Society—Pang and Wynblatt B
Euler matrix, g:
n0 ¼ gðf1 ; F; f2 Þ n
Fig. 4. Schematic showing a fractured sample, with arrows indicating the directions for the stereo-pair analysis (A) and for acquisition of electron back-scattered diffraction patterns (B).
X ¼ x1 ¼ x2 ¼ ðx1 þ x2 Þ=2 Y ¼ ðy1 sin y2 y2 sin y1 Þ=sin ðy2 y1 Þ Z ¼ ðx1 cos y2 þ x2 cosy1 Þ= sinðy2 y1 Þ
Vol. 88, No. 8
where (x1, y1) and (x2, y2) are the coordinates of points (e.g. Q1 and Q2) on SEM micrographs obtained at tilt angles of y1 and y2. Two vectors can be deﬁned from the three points on each GB fracture plane. Using the right-hand convention, the normal vector of each boundary fracture plane was obtained from the cross product of the two vectors in the sample reference frame. The crystallographic orientation of the grain containing the boundary fracture plane of interest was then obtained from an electron back-scattered diffraction (EBSD) pattern using an OIM. EBSD patterns were acquired in a Philips XL40FEG SEM (Eindhoven, The Netherlands) at an accelerating voltage of 20 keV. Indexing of the EBSD patterns yielded three Euler angles, f1, F, f2, which relate the crystallographic orientation of the grain to the sample reference frame. Given an average grain size of about 50 mm diameter in the samples used (see Fig. 1), a step size of 2 mm was chosen for the acquisition of EBSD patterns. The key point is that the sample coordinate system must be identical for the EBSD and stereo-pair analysis in order to correctly couple the data obtained from these two techniques. As the OIM technique requires samples that are ﬂat and have two parallel faces, EBSD patterns were acquired from the polished surface adjacent to the fracture surface, rather than on the fracture surface itself. The experimental geometry is illustrated schematically in Fig. 4. Finally, the GB plane normal vectors (n) were transformed to plane normals in the crystal reference frame (n0 ), by means of the
Fig. 5. Five grain-boundary fracture surfaces used for evaluation of experimental scatter.
(1) Reliability of the Auger Measurement Since the purpose of this work was to evaluate the compositional anisotropy of GB fracture planes that originate from grain boundaries with different macroscopic orientation parameters, it is important to know the variability of the Auger measurement on a given GB fracture plane, so as to ensure that no artifacts are present in the measurements. Five typical boundary surfaces (see Fig. 5) inclined at different angles to the electron beam (which corresponds with the SAM axis) were selected to perform the following experiments. 1. A single point on each GB surface plane was measured 10 times. The maximum standard deviation of the Nb/Ti peak ratio was 7% of the mean, as shown in Table I. This provides a baseline of the inherent scatter of the data, and shows that it is acceptable. 2. Auger spectra were acquired at 10 different points on each GB surface plane. The maximum standard deviation of the Nb/Ti peak ratio on the grain boundary is 14% of the mean, as shown in Table I, and in most cases, no different from the underlying experimental scatter of the measurements. This indicates that GB composition is fairly uniform on the scale of the electron beam size (B0.1 mm). The increase in scatter in relation to the inherent measurement error is most likely related to small deviations from boundary planarity (i.e. of GB inclination) from point-to-point on the GB fracture surface. Thus, any point on a given facet could still be used to characterize the whole GB plane. 3. Ten measurements were performed at a single point of a GB fracture plane at different sample tilts, to assess the effects on the measured peak ratio of differences in the angle between the GB fracture plane and the electron beam axis. The mean values of the Nb/Ti peak ratio were found to be essentially independent of tilt over tilt angles from 01 to 451, and the standard deviation of the 10 measurements was still within the 14% scatter mentioned above for multiple point measurements on a given GB plane. This indicates that angular variations from one GB plane to another with respect to the electron beam do not introduce any significant artifacts in the measurements. This independence of the Nb/Ti ratio on tilt angle is most likely because of the use of a cylindrical mirror analyzer (CMA) in our PHI SAM. CMAs are inherently less sensitive to sample tilt, as they naturally average the Auger signal over a range of tilt angles. In summary, the above results show that the standard deviation of compositional measurements over a single boundary does not exceed 14%, and that some of this variation could be real to the extent that it reﬂects small deviations in the inclination of a given grain boundary. (2) Anisotropy of Segregation on Fracture Surfaces Figure 6 displays the distribution of Nb/Ti peak height ratios on both sides of a fracture surface for 83 grain boundaries in 2 mol% Nb-doped TiO2. Four of the supposed GB fracture surfaces, in the original set of 87 grain boundaries, were identiﬁed as transgranular fractures by the OIM measurements, and were therefore excluded from further consideration. As expected, the distributions on both sides are essentially the same. The ﬁgure also establishes that there is a significant anisotropy of GB composition, since there is no overlap of the extreme compositions within the 14% maximum standard deviation that characterizes the data. Figure 7 displays the difference in composition between the two sides of each grain boundary, with the values ordered from the most negative to the most positive difference. This ﬁgure clearly illustrates the result that the compositions of the two sides of a boundary are generally quite different, with many examples showing differences that lie
Correlation between Grain-Boundary Segregation and Grain-Boundary Plane Orientation
Table I. Comparison of Single- and Multi-Point Scatter in Measurements of the Nb/Ti Peak Ratio on Five Different Boundaries GB1
(3) Correlation Between GB Composition and Plane Orientation Figure 8 shows orientations of the normals to the GB surface planes, from both sides of the fracture surface (total of 166 measurements), plotted in a standard stereographic triangle for the tetragonal crystal system. Different symbols are used to indicate GB planes with high, moderate, and low values of the Nb/ Ti Auger peak ratio. The ﬁgure illustrates several interesting results. (a) The GB planes are distributed fairly evenly throughout the standard triangle, indicating that the fracture process samples the GB plane texture in a roughly random fashion. The actual GB plane texture, based on OIM measurements of 80 000 boundaries, will be reported elsewhere. (b) The degree of Nb segregation is found to depend on the crystallographic orientation of the boundary plane. Boundaries with high levels of segregation (Nb/Ti peak ratio lying between 0.40 and 0.59 and indicated by solid circles) all lie along the (001)–(011) portion of the lower edge of the triangle, whereas the grain boundaries with a low level of segregation (Nb/Ti peak ratio below 0.05 and indicated by solid lozenges) are clustered close to the (110)–(010) edge of the triangle. Boundaries with intermediate levels of segregation (indicated by crosses) are distributed almost uniformly over the stereographic triangle. It is also interesting to examine the levels of segregation on the matching halves of grain boundaries that display either high or low levels of segregation. Figure 9(a) shows the plane orientations of grain boundaries with high segregation (solid symbols) and the orientations of their corresponding other sides (open symbols). It can be seen that the orientations of the other halves mostly also lie in the same orientation region. A similar trend is shown for grain boundaries with a low level of segregation in Fig. 9(b). IV. Discussion
(1) GB Fracture and Segregation One choice for describing the ﬁve macroscopic parameters of GB orientation is the so-called ‘‘interface plane scheme,’’13 in which the parameters are deﬁned by the terminating crystallographic planes of the two crystals adjacent to the boundary (each plane accounting for two parameters) and a twist angle about the axis perpendicular to the GB plane. If a grain boundary described in this manner is located in a sample that under-
20 15 10
0 0.1 0.2 0.4 0.5 0.6 Nb/ Ti Auger peak ratio
goes inter-granular fracture, then the interpretation of compositional measurements on the two halves of a boundary requires an answer to the following questions. Does the fracture path split the grain boundary so as to produce two fairly perfect surfaces with (hkl) indices corresponding to the crystal planes that terminate the two adjacent crystals? Or, does the fracture path zigzag across the grain boundary such that it samples regions on both sides of the grain boundary? If the grain boundary is split ‘‘perfectly,’’ one would expect to detect some differences in composition between the two halves of the boundary, since the differences in the indices of the terminating surfaces will certainly inﬂuence at least the composition gradients of the segregant in each half, and most likely the actual compositions of the terminating planes.14 Under conditions where the path zigzags, there are two possible outcomes. The compositions on both sides of a grain boundary would tend to be the same, if the periodicity of the zigzag is small compared with the size of the area analyzed by the Auger beam, or, if the zigzag periodicity is much larger than the size of the analyzing beam, there would be patches with significant differences in composition on any given side of the boundary. The results reported in Fig. 7 show that significant differences in the composition are found on opposite sides of a given grain boundary. This implies that the fracture path in the case of Nbdoped TiO2 does not zigzag from one side of the grain boundary to the other. In addition, the fact that only small differences in composition are found on any given side of a GB fracture surface (see Table I) adds further support to this conclusion. It is interesting to note that in the GB fracture of P-doped Fe– Si alloy bicrystals,15 it was shown that the fracture path does indeed zigzag from one side of the grain boundary to the other, thereby splitting a symmetric boundary into two surfaces with patchy compositions. However, in this case, the fracture path was deﬂected from one side of the boundary to the other by the presence of deformation bands impinging on the boundary. Such phenomena are less likely in the grain boundaries of brittle materials such as TiO2.
Nb/ Ti Auger peak ratio (right-left)
well outside the 14% maximum standard deviation of the measurement.
− 0.40 0
0.1 0.2 0.4 0.5 0.6 Nb/ Ti Auger peak ratio
Fig. 6. Distributions of Nb/Ti peak height ratio on 83 grain boundaries on each side of the fracture surface.
GB Number Fig. 7. Distribution of compositional differences on matching surfaces of 83 grain boundaries in 2 mol% Nb–TiO2.
Vol. 88, No. 8
Journal of the American Ceramic Society—Pang and Wynblatt (110)
(011) Nb/ Ti<0.05
(010) GB one side 0.40=
Fig. 8. Distribution of grain-boundary planes in the standard stereographic triangle, showing orientations corresponding to high levels (solid circles), low levels (solid lozenges), and moderate levels of segregation (crosses).
(2) Anisotropy of GB Segregation There is ample experimental evidence to support the existence of compositional anisotropy in GB segregation phenomena.16–22 For example, Bi segregation to grain boundaries in Cu shows differences as large as 7100% in Bi concentration from one grain boundary to another.16 There has also been a limited number of studies where the dependence of GB composition on the crystallographic nature of the GB plane has been addressed. Suzuki et al.23 studied P segregation in a-iron polycrystals by an approach similar to the present one. They found that the level of segregation correlated better with the GB plane than with other orientation characteristics such as misorientation or twist angle. A similar conclusion was drawn by Swiatnicki et al.24 in a segregation study of Mg- and Ti-doped alumina containing Si and Ca impurities. The results of both of those studies are also consistent with conclusions drawn from a recent model of the dependence of GB segregation on the ﬁve macroscopic parameters of GB orientation,14 although that model predicts that effects due to twist angle should not be negligible. The present results show (Fig. 8) that there is a strong correlation between GB crystal plane and measured Nb concentration. In addition, when one half of the GB displays either low or high segregation, the orientation of the matching crystal plane also tends to fall in an orientation region where segregation is correspondingly low or high, as shown in Figs. 9(a) and (b). However, this trend is not always obeyed; this implies that there is an interaction between segregated atoms on the two halves of a grain boundary, as expected from the segregation model mentioned above.14 When the solute–solvent phase diagram indicates that the components have a tendency to undergo phase separation (i.e. display a positive heat of mixing), then high solute concentration on one side of the boundary will tend to attract the solute to the other half. This could occur to some extent even if the orientation of the other side does not naturally have a high solute concentration. The results obtained here are consistent with this picture, in the sense that the Nb2O5–TiO2 phase diagram displays a eutectic feature, which implies a positive heat of mixing. (3) GB Energy and Surface Energy There exists a relation between the energy of a grain boundary and the surface energies of the GB planes of the adjoining crystals. This result has emerged from the GB computer simulations of Wolf,25 who showed that GB energy depends linearly on the mean energy of the two surfaces, although it is not proportional to the mean surface energy. For the case of metal oxides, a conceptually similar relationship has been used by Saylor et al.26: gGB ¼ gS1 þ gS2 EB
GB matching side 0.05
(010) GB one side Nb/ Ti<0.05
GB matching side 0.05
(b) Fig. 9. Grain-boundary plane orientations with (a) Nb/Ti peak ratios between 0.40 and 0.59 (solid symbols) and the matching planes on the other sides of those grain boundaries (open symbols) and (b) Nb/Ti peak ratios below 0.05 (solid symbols) and the matching planes on the other sides of those grain boundaries (open symbols).
where gGB is the GB energy, gS1 and gS2 are the surface energies corresponding to the two adjacent GB planes, and EB is an orientation-dependent binding energy that accounts for the bonding that results when two half-crystals terminated by free surfaces are joined to form a boundary. Saylor measured the anisotropy of both the surface energy and GB energy in MgO, and concluded that in the case of high-angle boundaries, the term EB is, to a ﬁrst approximation, constant. In order to assess the effects of GB energy anisotropy on the segregation behavior observed here, it would be useful to consider the implications of Eq. (3) on our results. For this purpose, it is necessary to have access to data on the surface energy anisotropy of TiO2. Although no experimental information is available, we will use the results of some 0 K calculations by Ramamoorthy et al.27 in order to infer certain general trends. The results of Ramamoorthy et al. are displayed in the form of an equilibrium crystal shape in Fig. 10(a), and as a stereographic projection in Fig. 10(b). The ﬁgure shows that the surfaces with highest energies occur between (001) and (011), which corresponds to the edge of the stereographic triangle along which high levels of segregation are observed for boundaries terminated with those planes in Figs. 8 and 9(a). Thus, high-energy grain boundaries (i.e. those terminated on one or both sides by planes of high surface energy) are also those that display high segregation. This result is satisfying in the sense that there is a greater potential for reduction of the total interfacial energy of a polycrystal if Gibbsian adsorption (or segregation) occurs most strongly on highenergy grain boundaries. Conversely, if Fig. 10 is compared with Figs. 8 and 9(b), we see that low surface energies occur at the orientations where GB planes of low segregation are found. Whereas the above arguments are mainly qualitative, they do
Correlation between Grain-Boundary Segregation and Grain-Boundary Plane Orientation
(001) (110) (011)
(001) (011) (010)
regions of the stereographic triangle, respectively. The matching halves of grain boundaries with either very high or very low segregation also tend to be terminated by planes in the same respective regions of orientation space. Furthermore, high levels of segregation occur along regions of GB plane orientation space estimated to correspond to high GB energy, while low levels of segregation occur along regions corresponding to low GB energy. This trend appears to be consistent with qualitative arguments based on considerations of Gibbsian adsorption.
Fig. 10. Surface energy anisotropy of TiO2 displayed (a) in the form of the equilibrium crystal shape, after the calculations of Ramamoorthy et al.27 and (b) in a stereographic projection, with the poles corresponding to surface planes in (a) shaded in order of increasing relative surface energy.
appear to provide useful insights for the interpretation of the pattern of segregation in the orientation space of GB planes.
(4) Electrostatic Effects Electrostatic effects in interfacial segregation can be important in metal oxide systems, and have been shown to play a role in the segregation of Nb and other aliovalent solutes in TiO2 grain boundaries.4–6 The presence of a space charge region extending (from a few to possibly tens of nanometers) into the bulk away from a grain boundary, and the related potential difference between the bulk and the boundary, can contribute to the compositional differences between the boundary region and the bulk. The interfacial composition measurements performed here by AES cannot probe deeply enough below the fracture surface to detect evidence of deviations from bulk composition associated with the space charge region, and are therefore limited to evaluating the composition of the GB core. Nevertheless, even the core composition could be affected by the presence of a potential difference between the boundary and the bulk. Different boundaries with different structures will exhibit different abilities to accommodate charged defects and/or impurity ions, and will therefore display different potential differences with the bulk. For the qualitative interpretation of the differences among boundaries, and hence their capacity to accommodate solute on either a structural or an electrostatic basis, we have chosen to use GB energy as a metric. The results of this approach seem to be promising. V. Summary Auger measurements of the composition of individual GB fracture surfaces have been performed on both matching sides of 83 boundaries. It has been shown that small but significant differences in composition can occur over a given boundary surface. These differences have been attributed to deviations from planarity, which correspond to small changes in local GB inclination. When the compositions of all the boundaries are compared, there is a large anisotropy in the segregation. In addition, large differences in composition have been found between the two matching fracture surfaces of a given grain boundary. This indicates that the fracture path does not zigzag, but tends to split grain boundaries in a manner that produces two fairly distinct surfaces with (hkl) indices that correspond to the terminating crystal planes of the adjacent crystals. The dependence of segregation level on GB plane orientation has been determined. High and low levels of segregation occur for GB planes that lie along the (001)–(011) and the (010)–(110)
The authors wish to acknowledge the support of this research by the MRSEC Program of the National Science Foundation under award number DMR0079996.
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