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Electron backscattered diffraction study of cleavage fracture in pure iron
Materials Science and Engineering A 417 (2006) 243–248
Electron backscattered diffraction study of cleavage fracture in pure iron R. Ayer, R.R. Mueller, T. Neeraj ∗ Corporate Strategic Research, ExxonMobil Research and Engineering Company, Route 22 East, Annandale, NJ 08801, United States Received in revised form 22 October 2005; accepted 22 October 2005
Abstract EBSD studies were performed to explore the potential of trace analysis to determine the crystallography of cleavage fracture plane and planar defects that form during cryogenic fracture of pure iron. Single- and double-surface trace analysis revealed that cleavage occurred along the cube {1 0 0} planes. In addition, using EBSD we were able to identify the planar defects that formed during fracture to be twins on {1 1 2} planes. The combination of trace analysis and orientation mapping was able to uniquely identify the specific variants of the {1 1 2} planes associated with each set of twins. The twin/matrix interface was mostly scalloped suggesting that twin formation could be the result of twinning on multiple twin planes. © 2005 Elsevier B.V. All rights reserved. Keywords: EBSD; Twin; Cleavage; Fracture and Fe
1. Introduction
2. Experimental procedure
Since the advent of electron backscattered diffraction (EBSD), the method has become increasingly useful in the analysis of grain size and distribution, grain boundary misorientation and texture analysis of materials [1–3]. Recent studies have also extended the capabilities of EBSD to the study of phase transformations [4–6]. Many of the recent advances in electron source and microscope optics (Schottky FE, finer probe size), coupled with advances in EBSD instrumentation, have allowed the characterization of details with sub-micron spatial resolution. The enhanced resolution enables crystallography studies in the scanning electron microscope (SEM) that would be normally performed in transmission electron microscopes (TEM). This ability opens up the potential to perform statistically significant characterization of regions with good spatial resolution. Such analyses can be performed in samples that are not amenable to preparation of thin foils such as plastic zone ahead of crack tips, etc. The present study was performed to determine the crystallography of cleavage planes in pure iron and characterization of planar defects that form in the vicinity of fracture through a combination of trace analysis and orientation mapping.
Ingots from commercially pure iron, 15 cm × 15 cm × 20 cm, were produced by induction melting. They were forged to a thickness of 50 mm at 1473 K following which they were rolled to 10 mm thick plates in a rolling mill at 1300 K. Approximately 10 mm × 10 mm × 40 mm pieces were cut from the plates, annealed at 1273 K for 1 h and furnace cooled to room temperature over a period of 20 h. Five-millimeter notches were cut along one of the 10 mm dimension using a diamond blade and the notched specimens were held in a liquid nitrogen bath for a period of 1 h following which it was removed from the bath and immediately clamped in an anvil and fractured manually. Following initial SEM studies to ensure cleavage fracture, the fractured surfaces were plated with electroless nickel to preserve the fracture edge during subsequent specimen preparation. The plated samples were cut and mechanically polished for metallography and EBSD studies. Two types of specimen configurations were prepared for the present studies as shown in Fig. 1. The figure shows the fracture specimen and the orientation of single- and double-surface metallography sections. As indicated in the figure, the singlesurface specimen was used to image the fracture facets on a single-polished surface, while the double-surface specimen was meant to image the fracture facets from the same grain (at the corner) from two directions. In addition, these samples were
∗
Corresponding author. Tel.: +1 908 730 2462; fax: +1 908 730 3355. E-mail address: [email protected] (T. Neeraj).
0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.10.066
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Fig. 1. Schematic illustration of the fracture specimen showing the orientation of the single- and double-surface samples. The surfaces polished for metallography observation are colored in yellow.
Fig. 2. SEM image of the fracture surface showing cleavage facets.
also used to study the defects that formed in the vicinity of the fracture. The polished samples were examined in a LEO 1530 FEGSEM fitted with HKL EBSD system and Channel 5 software. EBSD analysis was performed at an accelerating voltage of 15 kV and a tilt angle of 70◦ . 3. Results and discussion 3.1. Trace analysis Fig. 2 shows a secondary electron image of the fracture surface of the sample. The fracture was transgranular with welldefined cleavage facets. Fig. 3A is an optical micrograph of a single-surface sample showing several fracture facets. All of the facets in the image showed straight edges implying that the fracture occurred on specific crystallographic planes. The image also showed several striations (indicted by arrows) within the grains close to the fracture surface; these striations were later identified as deformation twins. Fig. 3B is an EBSD map of the region shown in Fig. 3A. Fig. 3C is the EBSD orientation of a grain (marked by a circle) in Fig. 3B which contained two fracture facets. In this 3-D orientation window, the HKL software provides the orientations of the grain normal as well as orien-
tations of the horizontal and vertical axes1 . The grain normal was indicated to be [1 0 6] and the horizontal and vertical axes ¯ and [5¯ 6 0]. Fig. 3D is a stereogram were indicated to be [6 5 1] of the [1 0 6] orientation rotated to reflect the horizontal and vertical axes referred to above and the traces of the normal to the two facets are plotted on the stereogram. It can be seen that the traces of the two facets pass through the [1¯ 0 0] and the [0 1 0] planes, respectively, suggesting that the cleavage planes could be the cube planes of the bcc lattice. Similar trace analysis were performed on all the facets in Fig. 3B and all the facet normals corresponded to one of the cubic planes, again, suggesting that cleavage occurred on the {1 0 0} planes. Single-surface trace analysis provides the indices of possible planes that would correspond to a surface trace, but it does not provide a unique identification of the specific plane. Unique identification of the plane from traces can only be achieved from the analysis of the same facet in at least two independent orientations by tilting the specimen. This procedure has been practiced in TEM studies for numerous years [7]. Since the sample tilt is fixed in EBSD and rotation of the sample about the specimen axis does not change the orientation of the sample with respect to the electron beam, conventional tilting studies are not possible to obtain unique solutions from plane traces. One approach to obtain unique solutions in the SEM using EBSD is to examine the same facet of interest on two independent surfaces (Sides 1 and 2). In order to achieve a unique solution in trace analysis, it would be helpful to have these surfaces near-orthogonal to each other as possible. When performing two-surface trace analysis, it is necessary to establish a common reference which links the analysis performed independently on both sides. This is illustrated in Fig. 4, which is a SEM image of the specimen showing the fracture facets and the two sides for EBSD analysis. Given that the microscope coordinates are common to the analysis on both surfaces, the edge of the specimen can be used to link the analysis on both sides. EBSD analysis of the double surface was performed on Side 1 by rotating the sample such that the edge of the sample was along the vertical axis on the screen. SEM image was recorded to include the fracture facet and the edge of the specimen. EBSD map was recorded from the corner grain and based on the indexing, the grain normal was determined to be [5 2 5], with the ¯ aligned along the [1¯ 0 1] parallel to the horizontal axis and [1¯ 5 1] vertical axis. Since the edge was aligned along the vertical axis, ¯ the direction along the edge would also correspond to [1¯ 5 1]. The analysis was repeated on Side 2 again with the specimen edge maintained vertical to the screen. As in Side 1, SEM image was recorded with the edge and fracture facet in the field of view followed by the acquisition of EBSD map from the grain closest to the edge (which would correspond to the grain analyzed in Side 1). The grain normal for grain in Side 2 was indicated to ¯ while the x and y axes were indicated to be [5 2 5] be as [1 0 1] ¯ ¯ and [1 4 1], respectively. It should be pointed out that the EBSD software does the indexing of the directions only with respect 1
The orientations are in reference to the microscope stage axis.
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Fig. 3. (A) Optical image of the single-surface sample showing cleavage facets. Striations close to the fracture surface are indicated by arrows. (B) EBSD image of the area in (A) showing Euler coloring. Dotted lines indicate {1 0 0} traces of the fracture facets. (C) 3-D orientation of the region (circle) marked in (A). (D) [1 0 6] Stereogram with traces AB and CD from (B) indicating that they pass through the {1 0 0} poles.
to the microscope stage axes. Therefore, the indices calculated by the software for Side 2 will not be a self consistent set with respect to the orientation measured on Side 1. In the present study, the correct variant of the indices for Side 2 were assigned manually by inspection. For instance, the vertical axis on Side 2 was determined to be [4 1 1] by the HKL software. However, the ¯ based on the vertical axis indexing correct assignment was [1¯ 4 1] of Side 1. In the present analysis, the occluded angle between the two sides measured was 90◦ , as indicated by the indices of both the sides. However, it is quite likely that the occluded angles between the two surfaces may deviate from 90◦ . In such cases, care should be taken to ensure that the indexing would consider small deviations from the normal. Trace analysis was performed based on the orientations of the grain from Sides 1 and 2 and the positions of the facet traces from these two sides. For the trace analysis, the facet traces were transferred to the stereogram similar to what is shown in Fig. 3. A stereogram of the grain normal [5 2 5] oriented with respect to the x and y directions measured from EBSD and the trace from Side 1 are plotted in Fig. 5A The stereogram along with the
Fig. 4. SEM image of the double-surface sample showing Sides 1 and 2. The orientations of the corner grain viewed from Sides 1 and 2 are shown.
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Fig. 6. EBSD band contrast map of twinned grain showing that the twin/matrix 3 boundaries (highlighted in red). interface consisted of
measurement errors. Therefore, it was concluded that cleavage had occurred along a cube type {1 0 0} plane. 3.2. Analysis of twins
Fig. 5. (A) [5 2 5] Stereogram corresponding to Side 1 with the trace from Side ¯ orientation corresponding to that of Side 1and (B) Stereogram rotated to [1 0 1] 2 with the trace of the fracture facet from Side 2. The traces intersect at the ¯ pole, 2.8◦ from the (0 1¯ 0) pole. [5 100 1]
¯ Following trace was rotated to the grain normal of Side 2 [1 0 1]. ¯ to position the rotation, the stereogram was rotated about [1 0 1] x and y directions as indicated by EBSD on Side 2 (i.e. x = [5 2 5] ¯ as shown in Fig. 5B. The trace of the facet normal and y = [1¯ 4 1]) from Side 2 was transferred to the stereogram and is indicated in Fig. 5B. The intersection of the traces from Sides 1 and 2 should provide a unique solution to the indices of the fracture plane. The intersection of the two traces was determined to be ¯ which was about 2.8◦ from the (0 1¯ 0) pole. This error [5 100 1] is well within the experimental errors of sample positioning and
The second aspect of the study was to determine the nature of striations observed in the optical images close to the fracture surface (see Fig. 3A). Higher magnification analysis suggested that the striations could be platelets forming on specific planes of the matrix. In order to determine the nature of the striations, EBSD maps were recorded at higher resolution with a 0.25 m step size. Fig. 6 shows band contrast (image quality) map of a region with three sets (variants) of the platelets. Interrogation of the nature of the twin/matrix boundaries revealed that they were all of 3 type (Fig. 6). It is well known that matrix/twin interfaces on the {1 1 1} planes in the in face-centered systems and on the {1 1 2}planes in the body-centered cubic systems would consist of 3 boundaries [8]. Therefore, it was speculated that the striations were twins formed during the fracture. Further studies, described below, provided confirmation of this speculation. EBSD provides the unique ability to perform twin variant analysis by combining trace analysis and orientation analysis. Fig. 7A shows the EBSD map with IPF coloring from the same region shown in Fig. 6. The region contained three twin variants, which are marked 1, 2 and 3 in Fig. 6. The orientation of the matrix grain was determined to be [4 1 6] with x and y directions ¯ respectively. The orientadetermined to be [1¯ 4 0] and [6 1 4], tions of the individual twins were determined to be {2 5 10}, {2 5 6} and {1 0 3} type, respectively The twins are color coded (red, blue and green) for easy reference. It should be noted that the indices provided for the twin orientations by the EBSD soft-
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the specific twin orientations and twin planes for the three twin variants shown in Figs. 6 and 7A. Given the matrix orientation of [4 1 6], it should be possible to determine the specific twin planes for the three twins. Fig. 7B shows a [4 1 6] stereogram oriented to correspond to the image (Fig. 7A). The normals to the twin traces are transferred onto the stereogram, as shown in Fig. 7B. All the 12 {1 1 2} twins planes are circled in the stereogram. The {1 1 2} poles that are within ±5◦ from the traces are indicated by solid circles, while the others are indicated by dotted circles. Based on these traces and the proximity criterion, the following possible twin planes can be identified for the three sets of twins. Twin set
Possible twin plane (s)
1 2 3
(1¯ 1 2)/(2¯ 1 1) (2 1¯ 1) ¯ (2 1 1)
Of the three, Twin 1 could be attributed to two possible twin planes while Twins 2 and 3 could be assigned to one twin variant. Having developed a possible list of candidates for the twin planes the next steps in the analysis was to demonstrate that the twin/matrix orientation relationship can be used to uniquely confirm and/or narrow down the twin variant. In the present case, this would refer to narrowing down the variant for Twin 1 and verifying that the variants proposed by the trace analysis for Twins 2 and 3 agree with that predicted by calculations. The 1 1 2 transformation matrix for twinning is as follows [9]:
Fig. 7. (A) Inverse pole figure map of the region shown in this figure. The orientation of the three sets of twins and that of the grain are indicated. (B) Stereogram of the matrix orientation in (A) with the traces from the three set of twins. All the {1 1 2) poles are marked by circles. The poles that met the proximity criterion are marked with solid circles while poles not meeting the criterion are indicated by dotted circle. The {1 1 2} poles that are shaded are specific twin planes for the three twin variants (see text for details).
ware are indicated as a family of possible twin orientations. This is because the twin orientations calculated by the EBSD software are not self-consistent with the matrix orientation and the twin transformation. In the following paragraphs trace analysis and the twin transformation analysis is applied to uniquely identify
um
vm
wm
2 1 ⊗ −1 3 2
−1 2 2
2 2 = ut −1
vt
wt
Table 1 Twin plane 1¯ 2¯ 2 2
1 1 1¯ 1
2 1 1 1¯
Possible twina
Calculated twin orientation
Twin 1 Twin 1 Twin 2 Twin 3
3¯ 5¯ 5 1¯
1 2¯ 6¯ 0
Measured twin orientation 0 10 2¯ 3¯
5 5¯ 5 1¯
2 2¯ 6¯ 0
10 10 2¯ 3¯
a Possible twin planes are determined based on the trace analysis shown in Fig. 7B (solid circles).
Fig. 8. (A) Variation in twin coloring in Euler map and (B) inverse pole figure map of twins.
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um vm wm is the orientation of the matrix and where ut vt wt is the orientation of the resultant twin on (h k l) plane. Based on the transformation matrix, twin orientations for the four possible twin planes indicated above were calculated for a matrix orientation of [4 1 6] and the results are listed in Table 1. Also listed in the table are measured orientations (corrected for appropriate variant of the indices. The corresponding twin identification (Twins 1, 2 or 3) that can be assigned to each of the twin planes (two possibilities are assigned for Twin 1) are also indicated. It can be seen from the Table that the calculated and measured orientations for Twins 2 and 3 are in agreement confirming the results indicated by the trace analysis. Of the two possibilities listed for Twin 1, the Table shows that the measured and calculated orientations for the (1¯ 1 2) twin planes do not agree while they agree for the (2¯ 1 1) twin plane, confirming that the latter was the actual twin plane. This analysis demonstrates that it is possible to narrow down the specific twin plane for each of the three twins observed in
Fig. 8A as indicated below: Twin 1: (2¯ 1 1); Twin 2: (2 1¯ 1); ¯ Twin 3: (2 1 1). During the investigation, it was observed that in the Euler maps of the twins showed color variations within a twin. Initially it was hypothesized that this could be result of double twinning (twins within twins). Further analysis revealed that the difference in the Euler color was due to small variations in φ2 close to the Euler space boundary (φ2 < 90◦ ). This is demonstrated in Fig. 8A where the variations in Euler color locally significantly varied due to a small change in φ2 (from 88.2◦ to 2.4◦ ). However, an IPF map of the same region (Fig. 8B) did not show any color variation. Therefore, such local variation in color was disregarded after ensuring that it was due to the definition of Euler space in cubic crystals. A closer examination of the twins showed significant scalloping of the interfaces (Fig. 9). The origin of the scalloped matrix/twin interfaces is not clear. It is possible that the scalloped twins are due to selection different habit planes for a growing twin or it can be that the matrix twinned on more than one {1 1 2} twin plane yielding the same twin orientation. Transmission electron microscopy analysis is currently underway to understand this observation. 4. Conclusions 1. The results of the present study demonstrate that EBSD can be effectively used to determine the crystallographic details of fracture facets and planar defects such as twins. 2. Single- and double-surface trace analysis of the cleavage facets of pure iron fractured at 177 K demonstrated that the cleavage planes were of the {1 0 0} type. 3. EBSD mapping indicated the formation of twins close to the fracture. The combination of trace analysis and orientation mapping was able to uniquely determine the exact variant of the {1 1 2} twin plane for each set of the twins. 4. The twin/matrix interfaces were scalloped suggesting that the twin may have formed on multiple twin planes or have multiple habit planes. References
Fig. 9. SEM images of the twins showing scalloped interfaces: (A) low magnification images of three set of twins and (B) high magnification image showing the irregular, scalloped interface.
[1] V. Randle, O. Engler, Texture Analysis: Microstructure, Microtexture and Orientation Mapping, Gordon and Breach, 2000. [2] A.J. Schwarz, M. Kumar, B.L. Adams, Electron Backscatter Diffraction in Materials Science, Kluwer Academic/Plenum Publishers, 2000. [3] V. Randle, Acta Mater. 52 (2004) 4067–4081. [4] C.G.E. Seward, S. Celotto, D.J. Pryor, J. Wheeler, R.C. Pond, Acta Mater. 52 (2004) 821–832. [5] A.F. Gourges, H.M. Flower, T.C. Lindley, Mater. Sci. Tech. 16 (2000) 26–40. [6] M.V. Kral, G. Spanos, Acta Mater. 51 (2003) 301–311. [7] D.B. Williams, C.B. Carter, Transmission Electron Microscopy, Plenum Press, 1996. [8] P.M. Kelly, Trans. AIME 233 (1965) 264. [9] O. Johari, G. Thomas, Trans. Met. Soc. AIME 230 (1964) 597.
Electron backscattered diffraction study of cleavage fracture in pure iron R. Ayer, R.R. Mueller, T. Neeraj ∗ Corporate Strategic Research, ExxonMobil Research and Engineering Company, Route 22 East, Annandale, NJ 08801, United States Received in revised form 22 October 2005; accepted 22 October 2005
Abstract EBSD studies were performed to explore the potential of trace analysis to determine the crystallography of cleavage fracture plane and planar defects that form during cryogenic fracture of pure iron. Single- and double-surface trace analysis revealed that cleavage occurred along the cube {1 0 0} planes. In addition, using EBSD we were able to identify the planar defects that formed during fracture to be twins on {1 1 2} planes. The combination of trace analysis and orientation mapping was able to uniquely identify the specific variants of the {1 1 2} planes associated with each set of twins. The twin/matrix interface was mostly scalloped suggesting that twin formation could be the result of twinning on multiple twin planes. © 2005 Elsevier B.V. All rights reserved. Keywords: EBSD; Twin; Cleavage; Fracture and Fe
1. Introduction
2. Experimental procedure
Since the advent of electron backscattered diffraction (EBSD), the method has become increasingly useful in the analysis of grain size and distribution, grain boundary misorientation and texture analysis of materials [1–3]. Recent studies have also extended the capabilities of EBSD to the study of phase transformations [4–6]. Many of the recent advances in electron source and microscope optics (Schottky FE, finer probe size), coupled with advances in EBSD instrumentation, have allowed the characterization of details with sub-micron spatial resolution. The enhanced resolution enables crystallography studies in the scanning electron microscope (SEM) that would be normally performed in transmission electron microscopes (TEM). This ability opens up the potential to perform statistically significant characterization of regions with good spatial resolution. Such analyses can be performed in samples that are not amenable to preparation of thin foils such as plastic zone ahead of crack tips, etc. The present study was performed to determine the crystallography of cleavage planes in pure iron and characterization of planar defects that form in the vicinity of fracture through a combination of trace analysis and orientation mapping.
Ingots from commercially pure iron, 15 cm × 15 cm × 20 cm, were produced by induction melting. They were forged to a thickness of 50 mm at 1473 K following which they were rolled to 10 mm thick plates in a rolling mill at 1300 K. Approximately 10 mm × 10 mm × 40 mm pieces were cut from the plates, annealed at 1273 K for 1 h and furnace cooled to room temperature over a period of 20 h. Five-millimeter notches were cut along one of the 10 mm dimension using a diamond blade and the notched specimens were held in a liquid nitrogen bath for a period of 1 h following which it was removed from the bath and immediately clamped in an anvil and fractured manually. Following initial SEM studies to ensure cleavage fracture, the fractured surfaces were plated with electroless nickel to preserve the fracture edge during subsequent specimen preparation. The plated samples were cut and mechanically polished for metallography and EBSD studies. Two types of specimen configurations were prepared for the present studies as shown in Fig. 1. The figure shows the fracture specimen and the orientation of single- and double-surface metallography sections. As indicated in the figure, the singlesurface specimen was used to image the fracture facets on a single-polished surface, while the double-surface specimen was meant to image the fracture facets from the same grain (at the corner) from two directions. In addition, these samples were
∗
Corresponding author. Tel.: +1 908 730 2462; fax: +1 908 730 3355. E-mail address: [email protected] (T. Neeraj).
0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.10.066
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Fig. 1. Schematic illustration of the fracture specimen showing the orientation of the single- and double-surface samples. The surfaces polished for metallography observation are colored in yellow.
Fig. 2. SEM image of the fracture surface showing cleavage facets.
also used to study the defects that formed in the vicinity of the fracture. The polished samples were examined in a LEO 1530 FEGSEM fitted with HKL EBSD system and Channel 5 software. EBSD analysis was performed at an accelerating voltage of 15 kV and a tilt angle of 70◦ . 3. Results and discussion 3.1. Trace analysis Fig. 2 shows a secondary electron image of the fracture surface of the sample. The fracture was transgranular with welldefined cleavage facets. Fig. 3A is an optical micrograph of a single-surface sample showing several fracture facets. All of the facets in the image showed straight edges implying that the fracture occurred on specific crystallographic planes. The image also showed several striations (indicted by arrows) within the grains close to the fracture surface; these striations were later identified as deformation twins. Fig. 3B is an EBSD map of the region shown in Fig. 3A. Fig. 3C is the EBSD orientation of a grain (marked by a circle) in Fig. 3B which contained two fracture facets. In this 3-D orientation window, the HKL software provides the orientations of the grain normal as well as orien-
tations of the horizontal and vertical axes1 . The grain normal was indicated to be [1 0 6] and the horizontal and vertical axes ¯ and [5¯ 6 0]. Fig. 3D is a stereogram were indicated to be [6 5 1] of the [1 0 6] orientation rotated to reflect the horizontal and vertical axes referred to above and the traces of the normal to the two facets are plotted on the stereogram. It can be seen that the traces of the two facets pass through the [1¯ 0 0] and the [0 1 0] planes, respectively, suggesting that the cleavage planes could be the cube planes of the bcc lattice. Similar trace analysis were performed on all the facets in Fig. 3B and all the facet normals corresponded to one of the cubic planes, again, suggesting that cleavage occurred on the {1 0 0} planes. Single-surface trace analysis provides the indices of possible planes that would correspond to a surface trace, but it does not provide a unique identification of the specific plane. Unique identification of the plane from traces can only be achieved from the analysis of the same facet in at least two independent orientations by tilting the specimen. This procedure has been practiced in TEM studies for numerous years [7]. Since the sample tilt is fixed in EBSD and rotation of the sample about the specimen axis does not change the orientation of the sample with respect to the electron beam, conventional tilting studies are not possible to obtain unique solutions from plane traces. One approach to obtain unique solutions in the SEM using EBSD is to examine the same facet of interest on two independent surfaces (Sides 1 and 2). In order to achieve a unique solution in trace analysis, it would be helpful to have these surfaces near-orthogonal to each other as possible. When performing two-surface trace analysis, it is necessary to establish a common reference which links the analysis performed independently on both sides. This is illustrated in Fig. 4, which is a SEM image of the specimen showing the fracture facets and the two sides for EBSD analysis. Given that the microscope coordinates are common to the analysis on both surfaces, the edge of the specimen can be used to link the analysis on both sides. EBSD analysis of the double surface was performed on Side 1 by rotating the sample such that the edge of the sample was along the vertical axis on the screen. SEM image was recorded to include the fracture facet and the edge of the specimen. EBSD map was recorded from the corner grain and based on the indexing, the grain normal was determined to be [5 2 5], with the ¯ aligned along the [1¯ 0 1] parallel to the horizontal axis and [1¯ 5 1] vertical axis. Since the edge was aligned along the vertical axis, ¯ the direction along the edge would also correspond to [1¯ 5 1]. The analysis was repeated on Side 2 again with the specimen edge maintained vertical to the screen. As in Side 1, SEM image was recorded with the edge and fracture facet in the field of view followed by the acquisition of EBSD map from the grain closest to the edge (which would correspond to the grain analyzed in Side 1). The grain normal for grain in Side 2 was indicated to ¯ while the x and y axes were indicated to be [5 2 5] be as [1 0 1] ¯ ¯ and [1 4 1], respectively. It should be pointed out that the EBSD software does the indexing of the directions only with respect 1
The orientations are in reference to the microscope stage axis.
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Fig. 3. (A) Optical image of the single-surface sample showing cleavage facets. Striations close to the fracture surface are indicated by arrows. (B) EBSD image of the area in (A) showing Euler coloring. Dotted lines indicate {1 0 0} traces of the fracture facets. (C) 3-D orientation of the region (circle) marked in (A). (D) [1 0 6] Stereogram with traces AB and CD from (B) indicating that they pass through the {1 0 0} poles.
to the microscope stage axes. Therefore, the indices calculated by the software for Side 2 will not be a self consistent set with respect to the orientation measured on Side 1. In the present study, the correct variant of the indices for Side 2 were assigned manually by inspection. For instance, the vertical axis on Side 2 was determined to be [4 1 1] by the HKL software. However, the ¯ based on the vertical axis indexing correct assignment was [1¯ 4 1] of Side 1. In the present analysis, the occluded angle between the two sides measured was 90◦ , as indicated by the indices of both the sides. However, it is quite likely that the occluded angles between the two surfaces may deviate from 90◦ . In such cases, care should be taken to ensure that the indexing would consider small deviations from the normal. Trace analysis was performed based on the orientations of the grain from Sides 1 and 2 and the positions of the facet traces from these two sides. For the trace analysis, the facet traces were transferred to the stereogram similar to what is shown in Fig. 3. A stereogram of the grain normal [5 2 5] oriented with respect to the x and y directions measured from EBSD and the trace from Side 1 are plotted in Fig. 5A The stereogram along with the
Fig. 4. SEM image of the double-surface sample showing Sides 1 and 2. The orientations of the corner grain viewed from Sides 1 and 2 are shown.
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Fig. 6. EBSD band contrast map of twinned grain showing that the twin/matrix 3 boundaries (highlighted in red). interface consisted of
measurement errors. Therefore, it was concluded that cleavage had occurred along a cube type {1 0 0} plane. 3.2. Analysis of twins
Fig. 5. (A) [5 2 5] Stereogram corresponding to Side 1 with the trace from Side ¯ orientation corresponding to that of Side 1and (B) Stereogram rotated to [1 0 1] 2 with the trace of the fracture facet from Side 2. The traces intersect at the ¯ pole, 2.8◦ from the (0 1¯ 0) pole. [5 100 1]
¯ Following trace was rotated to the grain normal of Side 2 [1 0 1]. ¯ to position the rotation, the stereogram was rotated about [1 0 1] x and y directions as indicated by EBSD on Side 2 (i.e. x = [5 2 5] ¯ as shown in Fig. 5B. The trace of the facet normal and y = [1¯ 4 1]) from Side 2 was transferred to the stereogram and is indicated in Fig. 5B. The intersection of the traces from Sides 1 and 2 should provide a unique solution to the indices of the fracture plane. The intersection of the two traces was determined to be ¯ which was about 2.8◦ from the (0 1¯ 0) pole. This error [5 100 1] is well within the experimental errors of sample positioning and
The second aspect of the study was to determine the nature of striations observed in the optical images close to the fracture surface (see Fig. 3A). Higher magnification analysis suggested that the striations could be platelets forming on specific planes of the matrix. In order to determine the nature of the striations, EBSD maps were recorded at higher resolution with a 0.25 m step size. Fig. 6 shows band contrast (image quality) map of a region with three sets (variants) of the platelets. Interrogation of the nature of the twin/matrix boundaries revealed that they were all of 3 type (Fig. 6). It is well known that matrix/twin interfaces on the {1 1 1} planes in the in face-centered systems and on the {1 1 2}planes in the body-centered cubic systems would consist of 3 boundaries [8]. Therefore, it was speculated that the striations were twins formed during the fracture. Further studies, described below, provided confirmation of this speculation. EBSD provides the unique ability to perform twin variant analysis by combining trace analysis and orientation analysis. Fig. 7A shows the EBSD map with IPF coloring from the same region shown in Fig. 6. The region contained three twin variants, which are marked 1, 2 and 3 in Fig. 6. The orientation of the matrix grain was determined to be [4 1 6] with x and y directions ¯ respectively. The orientadetermined to be [1¯ 4 0] and [6 1 4], tions of the individual twins were determined to be {2 5 10}, {2 5 6} and {1 0 3} type, respectively The twins are color coded (red, blue and green) for easy reference. It should be noted that the indices provided for the twin orientations by the EBSD soft-
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the specific twin orientations and twin planes for the three twin variants shown in Figs. 6 and 7A. Given the matrix orientation of [4 1 6], it should be possible to determine the specific twin planes for the three twins. Fig. 7B shows a [4 1 6] stereogram oriented to correspond to the image (Fig. 7A). The normals to the twin traces are transferred onto the stereogram, as shown in Fig. 7B. All the 12 {1 1 2} twins planes are circled in the stereogram. The {1 1 2} poles that are within ±5◦ from the traces are indicated by solid circles, while the others are indicated by dotted circles. Based on these traces and the proximity criterion, the following possible twin planes can be identified for the three sets of twins. Twin set
Possible twin plane (s)
1 2 3
(1¯ 1 2)/(2¯ 1 1) (2 1¯ 1) ¯ (2 1 1)
Of the three, Twin 1 could be attributed to two possible twin planes while Twins 2 and 3 could be assigned to one twin variant. Having developed a possible list of candidates for the twin planes the next steps in the analysis was to demonstrate that the twin/matrix orientation relationship can be used to uniquely confirm and/or narrow down the twin variant. In the present case, this would refer to narrowing down the variant for Twin 1 and verifying that the variants proposed by the trace analysis for Twins 2 and 3 agree with that predicted by calculations. The 1 1 2 transformation matrix for twinning is as follows [9]:
Fig. 7. (A) Inverse pole figure map of the region shown in this figure. The orientation of the three sets of twins and that of the grain are indicated. (B) Stereogram of the matrix orientation in (A) with the traces from the three set of twins. All the {1 1 2) poles are marked by circles. The poles that met the proximity criterion are marked with solid circles while poles not meeting the criterion are indicated by dotted circle. The {1 1 2} poles that are shaded are specific twin planes for the three twin variants (see text for details).
ware are indicated as a family of possible twin orientations. This is because the twin orientations calculated by the EBSD software are not self-consistent with the matrix orientation and the twin transformation. In the following paragraphs trace analysis and the twin transformation analysis is applied to uniquely identify
um
vm
wm
2 1 ⊗ −1 3 2
−1 2 2
2 2 = ut −1
vt
wt
Table 1 Twin plane 1¯ 2¯ 2 2
1 1 1¯ 1
2 1 1 1¯
Possible twina
Calculated twin orientation
Twin 1 Twin 1 Twin 2 Twin 3
3¯ 5¯ 5 1¯
1 2¯ 6¯ 0
Measured twin orientation 0 10 2¯ 3¯
5 5¯ 5 1¯
2 2¯ 6¯ 0
10 10 2¯ 3¯
a Possible twin planes are determined based on the trace analysis shown in Fig. 7B (solid circles).
Fig. 8. (A) Variation in twin coloring in Euler map and (B) inverse pole figure map of twins.
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um vm wm is the orientation of the matrix and where ut vt wt is the orientation of the resultant twin on (h k l) plane. Based on the transformation matrix, twin orientations for the four possible twin planes indicated above were calculated for a matrix orientation of [4 1 6] and the results are listed in Table 1. Also listed in the table are measured orientations (corrected for appropriate variant of the indices. The corresponding twin identification (Twins 1, 2 or 3) that can be assigned to each of the twin planes (two possibilities are assigned for Twin 1) are also indicated. It can be seen from the Table that the calculated and measured orientations for Twins 2 and 3 are in agreement confirming the results indicated by the trace analysis. Of the two possibilities listed for Twin 1, the Table shows that the measured and calculated orientations for the (1¯ 1 2) twin planes do not agree while they agree for the (2¯ 1 1) twin plane, confirming that the latter was the actual twin plane. This analysis demonstrates that it is possible to narrow down the specific twin plane for each of the three twins observed in
Fig. 8A as indicated below: Twin 1: (2¯ 1 1); Twin 2: (2 1¯ 1); ¯ Twin 3: (2 1 1). During the investigation, it was observed that in the Euler maps of the twins showed color variations within a twin. Initially it was hypothesized that this could be result of double twinning (twins within twins). Further analysis revealed that the difference in the Euler color was due to small variations in φ2 close to the Euler space boundary (φ2 < 90◦ ). This is demonstrated in Fig. 8A where the variations in Euler color locally significantly varied due to a small change in φ2 (from 88.2◦ to 2.4◦ ). However, an IPF map of the same region (Fig. 8B) did not show any color variation. Therefore, such local variation in color was disregarded after ensuring that it was due to the definition of Euler space in cubic crystals. A closer examination of the twins showed significant scalloping of the interfaces (Fig. 9). The origin of the scalloped matrix/twin interfaces is not clear. It is possible that the scalloped twins are due to selection different habit planes for a growing twin or it can be that the matrix twinned on more than one {1 1 2} twin plane yielding the same twin orientation. Transmission electron microscopy analysis is currently underway to understand this observation. 4. Conclusions 1. The results of the present study demonstrate that EBSD can be effectively used to determine the crystallographic details of fracture facets and planar defects such as twins. 2. Single- and double-surface trace analysis of the cleavage facets of pure iron fractured at 177 K demonstrated that the cleavage planes were of the {1 0 0} type. 3. EBSD mapping indicated the formation of twins close to the fracture. The combination of trace analysis and orientation mapping was able to uniquely determine the exact variant of the {1 1 2} twin plane for each set of the twins. 4. The twin/matrix interfaces were scalloped suggesting that the twin may have formed on multiple twin planes or have multiple habit planes. References
Fig. 9. SEM images of the twins showing scalloped interfaces: (A) low magnification images of three set of twins and (B) high magnification image showing the irregular, scalloped interface.
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