Revealing the Subsurface Basal 〈a〉 Dislocation Activity in Magnesium Through Lattice Rotation Analysis

A method was proposed in this study to reveal the subsurface basal dislocation activity in Mg-Y alloy and determine the corresponding Burgers vector. This is achieved by correlating the slip directions of dislocations to the lattice rotation represented by the {0001} pole figure. The identified basal slip system by this approach was verified by micro-Laue diffraction. This method can be applied as a complementary method to the conventional slip trace analysis to study the dislocation behavior of Mg alloys.

A method was proposed in this study to reveal the subsurface basal dislocation activity in Mg-Y alloy and determine the corresponding Burgers vector. This is achieved by correlating the slip directions of dislocations to the lattice rotation represented by the {0001} pole figure. The identified basal slip system by this approach was verified by micro-Laue diffraction. This method can be applied as a complementary method to the conventional slip trace analysis to study the dislocation behavior of Mg alloys.
https://doi.org/10.1007/s11661-020-05907-w Ó The Author(s) 2020 It is generally believed that basal hai dislocation slip dominates the deformation of polycrystalline magnesium (Mg) alloys at room temperature as the critical resolved shear stress (CRSS) for basal hai dislocation slip is considerably lower than that for non-basal dislocation slip. [1][2][3][4] The activation of basal hai dislocations in Mg alloys can also trigger other important cross-grain boundary deformation mechanisms like slip transfer, [5] slip-induced twinning, [6] and twin boundary migration. [7] To understand these triggered deformation modes, precise identification of the basal hai dislocation type is important.
Dislocation behavior in Mg alloys can be studied by surface slip trace analysis. [8][9][10][11][12] The activated slip systems in each grain can be identified by the observed slip traces (i.e., intersection of the slip plane and the sample surface) when the grain orientation has been measured by electron back scatter diffraction (EBSD). [8][9][10][11][12][13][14][15][16][17][18] A limitation of the EBSD-based slip trace analysis is that it cannot determine the Burgers vector of the activated basal hai dislocations because three possible basal hai slip systems possess the same surface slip trace. [11,16,17] Recently, a method to determine the Burgers vectors of basal hai dislocations was proposed by Xu et al., [16] where a combination of grain orientation mapping by EBSD and high-resolution digital image correlation (HRDIC) analysis of shear strain was used. Their method relied on visible surface slip traces and powerful data post-processing. However, when basal slip traces are invisible, such as in the circumstance that the corresponding Burgers vectors are almost parallel to the surface with little out-of-plane component, it seems impossible to identify basal slip systems by surface slip trace analysis or Xu's method. [16] This situation is actually very common in the as-rolled or as-extruded Mg alloys, [9,[11][12][13]15] in which the basal plane of most grains is parallel to the rolling direction or the extrusion direction; samples extracted from Mg-rolled sheets and extruded bars often have their surface being parallel to the basal plane of most grains. Even if basal hai dislocations are activated in many grains, basal slip traces are hardly observed. For instance, Boehlert et al. studied a rolled AZ31 (Mg-3Al-1Zn, wt pct) alloy based on surface slip trace analysis and reported more than 50 pct deformed grains did not exhibit any surface slip traces. [11] To characterize subsurface basal hai dislocation activity, it is important to develop an analysis method.
In the present work, we report an experimental method to reveal the subsurface basal hai dislocation activity in Mg and identify the type of the subsurface basal hai dislocation based on the lattice rotation analysis using EBSD data. The validity of this method was confirmed via micro-Laue diffraction.
The material used in this study was an extruded Mg-5Y (wt pct) alloy with an average grain size of 96 lm. The processing history (casting and extrusion) of this material has been reported in Reference 19. A tensile sample with nominal gauge dimensions of 18.0 mm 9 3.4 mm 9 1.4 mm (Length 9 Width 9 Thickness) was fabricated by electron discharge machining, with the tensile direction (TD) being parallel to the extrusion direction (ED). The top surface of the sample was ground, polished, and chemo-mechanical-polished in Oxide Polishing Suspension (OPS). Afterwards, the sample was tensioned by a Zwick/Roell Z020 testing machine with initial strain rate of 4.6 9 10 À4 s À1 . When the engineering strain reached 4.5 pct, the sample was unloaded and then scanning electron microscope (SEM, FEI, NOVA NanoSEM 230) was used to image a region of interest in the deformed sample. Orientation data were obtained subsequently by EBSD mapping using operating voltage of 20 kV, step size of 0.4 lm, and spot size of 6. The working distance and sample tilt are 13 mm and 70 deg, respectively.
The micro-Laue diffraction experiment was conducted at the beamline 34-ID-E of the Advanced Photon Source (APS) in the Argonne National Laboratory. A polychromatic X-ray microbeam with a beam size ofF give the angles between the slip directions (Burgers vectors) and the sample surface normal. Evaluation for the visibility of basal slip traces is based on these calculated angles: the larger an angle is, the less possibility the corresponding slip trace can emerge on the sample surface. 0.5 9 0.5 lm 2 was used to scan a 100 lm length on the surface of the deformed sample to obtain a subsurface 2D microstructure map. The sample's ED/TD was oriented at a 45 deg angle to the incoming X-ray and the CCD area detector, which was located approximately 510 mm above the sample to collect Laue diffraction patterns. A data package of the diffraction patterns was obtained by differential aperture X-ray microscopy (DAXM). [20] The methodology to build a correlation between dislocation types and stretched Laue diffraction peaks can be found in References 21 through 23. We used a MATLAB TM script to simulate the streak directions of the collected Laue diffraction peaks. By comparing the streak directions of the experimental Laue diffraction peaks and the simulated streak directions, the type of dislocations in a detected voxel can be identified. Figure 1(a) shows the location of the line scan of Laue diffraction and three neighboring grains labeled as G1, G2, and G3. The inverse pole figure (IPF) map of the box region in Figure 1(a) is shown in Figure 1(b). As can be seen, there are slip traces in G2 and G3. The slip traces in G2 pointed out by black arrows have a good alignment with basal plane. Non-basal slip traces are observed in G3: the slip traces pointed out by red arrows have a good alignment with prismatic ð01 10Þ plane. The corresponding prismatic slip system ð01 10Þ½2 1 10 has a macro Schmid factor (MSF) up to 0.477. Figure 1(c) shows the hexagonal unit cell of each grain. All the possible basal slip systems with the corresponding MSFs were listed as well. G1 and G2 have two and one basal slip systems with MSFs lager than 0.2, respectively. However, all the basal slip systems in G3 have near-zero MSFs. This is consistent with non-basal dislocation activities observed in Figure 1(a). Figure 1(d) provides the angles between the basal hai slip directions and the normal of the ED/TD-WD plane to reflect the visibility of basal slip traces in the grains under SEM. Within G1, the basal slip systems ð0001Þ½2 1 10 (MSF = 0.238) and ð0001Þ½ 12 10 (MSF = 0.220), with the large angles between the Burgers vectors and the sample surface normal (72 and 82 deg, respectively), have the possibilities to be activated, but the corresponding slip traces are invisible on the sample surface.
To reveal the dislocation activity in G1, its orientation has been closely examined. Figure 2(a) shows the misorientation distribution map of G1. A clear bandshaped zone with distinct misorientation from the rest of the grain can be observed. A misorientation profile across the band is shown in Figure 2(b). A long-range misorientation gradient can be clearly seen, indicating that dislocation slip is activated in G1 and preserved as geometrically necessary dislocations (GNDs). stretching of (0001) pole (see the red arrow from the point 1 to 2), which represents a lattice rotation of G1. The two-dimension (2D) coordinates of point 1 is (À 0.133, À 0.105); the 2D coordinates of point 2 is (À 0.173, À 0.085). By the transfer formula from 2D (X, Y) to 3D coordinates x; y; z ð Þ ¼ 2X 1þX 2 þY 2 ; 2Y 1þX 2 þY 2 ; 1ÀX 2 ÀY 2 1þX 2 þY 2 , the space vectors of points 1 and 2 in Figure 2(c) were calculated as n 1 (À 0.258, À 0.204, 0.944) and n 2 (À 0.333, À 0.164, 0.929) according to the x (-ED/-TD)-y (WD)-z (ND) coordinate system (right-handed Cartesian coordinate system), respectively. The rotation axis (n 1 9 n 2 ) can be calculated as (0.402, 0.866, 0.297), which is very close to the space vector of [ 10 10]: (0.523, 0.809, 0.256). The angle between [ 10 10] and the calculated rotation axis (n 1 9 n 2 ) is 9 deg, which implies that the lattice of G1 may have rotated around [ 10 10] axis. It is well known that basal hai dislocation activities will cause lattice rotation around h10 10i axes where each rotation axis is perpendicular to both the corresponding Burgers vector and basal plane normal. [24][25][26] Thus, the local deformation in G1 is suspected to be caused by the basal hai dislocation activity.
The space vectors of basal hai slip direction ½ 1 120, ½2 1 10, and ½ 12 10 of G1 are calculated as b 1 (0.050, 0.984, 0.170), b 2 (0.867, 0.417, 0.273), and b 3 (0.833, À 0.547, À 0.069), respectively. To examine which basal slip system has caused the lattice rotation of G1, the angles between the rotation axis (n 1 9 n 2 ) and the three Burgers vectors (b 1 , b 2 , and b 3 ) are calculated. The results are b 1^( n 1 9 n 2 ) = 22 deg, b 2^( n 1 9 n 2 ) = 38 deg, and b 3^( n 1 9 n 2 ) = 81 deg, showing that the Burgers vector ½ 12 10(b 3 ) is almost perpendicular to the rotation axis n 1 9 n 2 . Note that the hexagonal lattice was considered during the whole analysis process. It confirms that the rotation of (0001) pole in Figure 2(c) is caused by the activity of the basal slip system with Burgers vector ½ 12 10 (MSF = 0.220, #2 ranked) instead of Burgers vector ½2 1 10 (MSF = 0.238, #1 ranked) in G1. This ''non-Schmid'' activation can also be reflected by Figure 2(c) where the (0001) pole (i.e., the normal vector of the basal plane of G1) has gradually moved away from ND, instead of moving towards ND in the pole figure according to the macro tensile strain. [27] Although this finding is not very surprising as the micro stress status of grains does not always follow the macro stress, it emphasizes that the activated basal slip system cannot be identified solely by the macro Schmid criterion. [16] To verify the identified basal hai dislocation slip in G1, micro-Laue diffraction was used to map the subsurface microstructure. Figure 3(a) shows an orientation map that was extracted from the line scan of Laue diffraction marked in Figure 1(a) as well as two sample Laue patterns from G1 and G2, respectively. As can be seen in the two Laue patterns, the indexed diffraction peaks are stretched, confirming the existence of GNDs. [28,29] The slip systems of the GNDs can be inferred from the streak directions of the diffraction peaks. Figure 3(b) shows an example to identify the GND type in the voxel of G1. The theoretical streak directions for ð2 207Þ, ð1 107Þ, and ð1 108Þ diffraction peaks in G1 were simulated for 24 slip systems (basal slip f0001gh11 20i:1 to 3, prismatic slip f1 100gh11 20i: 4 to 6, pyramidal hai slip f1 101gh11 20i: 7 to 12, and pyramidal hc+ai slip f1 101gh2 1 13i: 13 to 24) in Mg. The simulated streak directions associated with slip system #2 ð0001Þ 12 10 Â Ã matches the observed streak directions for all the three peaks. This indicates that the voxel contains GNDs of basal slip system ð0001Þ 12 10 Â Ã , which is the same as the type that identified by the EBSD analysis method based on lattice rotation mechanism.
The above peak streak analysis was performed for all voxels in G1 and G2, and the identified dislocation slip systems are shown in Figure 4 where voxels are colored according to the GND types: light blue for basal hai slip  Figure 4 as well. Note that if a voxel has diffraction peaks without apparent stretching, it is colored in gray. The GND distribution map obtained by Laue diffraction indicates that there is a large fraction of basal hai dislocations with Burgers vector 12 10 Â Ã in G1, which is consistent with the type determined by the EBSD-based misorientation analysis method (see Figure 2). In G2, the major dislocation slip is prismatic hai, which is consistent with the type determined by the conventional slip trace analysis (see Figure 1(a)).
The basal dislocation activities of other ten grains in this alloy were also revealed by the EBSD-based lattice rotation analysis. To further validate the present method, the slip systems determined by lattice rotation axis analysis have been compared to the slip line traces. The results are consistent. An example is included in Appendix A. It has to be noted the positioning for the starting point and the end point of the stretched (0001) pole (e.g., points 1 and 2 in Figure 2(c)) will, to some extent, change the rotation axis determined by the present approach. For example, the variation angle about the averaged rotation axis is in the range of ± 5 deg. However, this uncertainty in angle is much smaller than the angles between the rotation axes of basal dislocation slip, 60 deg. It will not reduce the certainty for determining the subsurface basal slip type. However, it should be mentioned that this EBSD method for determination of dislocation slip is based on the same lattice rotation analysis approach which was originally developed for X-ray diffraction analysis of dislocation slip behavior of zirconium (Zr) single crystals. [30] Such an approach was later applied by Chun et al. for statistical analysis of in-grain misorientation axis (IGMA) based on EBSD images to determine the active slip modes in cold-rolled pure titanium (Ti) samples. [26] The difference between the present approach and the IGMA method is that their application fields are different. Due to the limited angular resolution of EBSD, even for the fully annealed Ti sample, 95 pct of the misorientation angles of neighboring scanning-grid pairs were found to be in the range of 0.5 to 0.97 deg. [26] So the lower cutoff misorientation angle included in IGMA analysis was taken as 1.2 deg. Accordingly, the lowest density of GND necessary to be detected by IGMA method can be roughly estimated by using the equation q = h/bd, where q is dislocation density, h misorientation angle within a distance of d, and b magnitude of Burgers vector. [31] With the 1.2 deg cutoff angle and the step size of EBSD scanning (0.5 lm in Reference 26), it can be calculated that only when the local density of GND is larger than 1.3 9 10 14 m À2 , the dislocation slip can be distinguished. It means that IGMA method is only valid for metals subjected to high deformation strains or even severe plastic deformations. In contrast, the present method is based on the asterism of {0001} poles which provides the longrange lattice rotation information of local regions in grains and is less sensitive to the dislocation density. It is therefore able to reveal the dislocation activity of samples subjected to low deformation strains. Moreover, the specific Burgers vector of the activated basal hai dislocation can be identified. Thus it can be considered as a complementary to the IGMA method as well. Application of such a method can be expected to bring deeper insights into the basal hai dislocation behavior and the mechanisms related to basal hai dislocations in Mg alloys.
In conclusion, the subsurface dislocation behavior of a deformed Mg-Y alloy was studied. One main achievement in this study is that a method based on local lattice rotation analysis using EBSD was proposed to identify the Burgers vector of basal hai dislocations, especially for those not showing slip traces at grain surface. Its validity has been confirmed by the Laue diffraction technique. This method can serve as a complementary method to the conventional slip trace analysis and the IGMA method to determine the real basal hai slip directions in grains.

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