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Characteristic orientation relationships in nanoscale Al-Al2Cu Eutectic
Materials Characterization 142 (2018) 170–178
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Materials Characterization journal homepage: www.elsevier.com/locate/matchar
Characteristic orientation relationships in nanoscale Al-Al2Cu Eutectic a
b
S.J. Wang , G. Liu , J. Wang a b
b,⁎
, A. Misra
a,⁎
T
Department of Materials Science and Engineering, College of Engineering, University of Michigan, Ann Arbor, MI 48109-2136, USA Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Al-Al2Cu eutectic Laser surface remelting Orientation relationship Interfaces
A fully lamellar Al-Al2Cu eutectic comprising alternate nano-scale α-Al and θ-Al2Cu phases was synthesized through laser surface remelting of a cast Al-32.7 wt% Cu alloy. The orientation relationship between α-Al and θAl2Cu phases was investigated from Kikuchi patterns obtained using electron backscattered diffraction (EBSD) and t-EBSD techniques. The characteristic orientation relationship (OR), {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al, was observed independent of interlamellar spacing. This OR has two variants where, besides the two parallel planes, the variant I exhibits (001)Al2Cu||{001}Al and the variant II exhibits (001)Al2Cu||{111}Al. Variant I prevails over variant II in laser-processed α-Al and θ-Al2Cu nano-laminates, and atomistic modeling indicates that this is due to the low energy interfaces associated with variant I, i.e., {211}Al2Cu||{111}Al or (001)Al2Cu||{001}Al. A comprehensive understanding of the crystallographic orientation relationships between two phases may help predict or explain the active slip systems in fine-scale Al-Al2Cu eutectic and other cubic-tetragonal two-phase materials.
1. Introduction Al-Al2Cu eutectics comprise alternate lamellae of α-Al and θ-Al2Cu phases. θ-Al2Cu with a C16 body centered tetragonal (bct) structure is brittle at room temperature due to high lattice friction stress associated with dislocations motion. α-Al with a face centered cubic (fcc) structure is ductile because of the easy glide of 1/2〈110〉 dislocation on {111} planes. Under mechanical loading at room temperature, α-Al layers plastically deform via nucleation, propagation and multiplication of dislocations. θ-Al2Cu layers elastically deform corresponding to the brittle nature of Al2Cu phases, acting as strong obstacles for dislocation motion in Al-Al2Cu composites [1–3]. Due to significant difference in elasticity and plasticity between the two phases, α-Al layers are hardened due to back stresses associated with geometric constraint of interfaces. Al2Cu layers are subjected to higher stresses than α-Al due to its higher elastic modulus than Al as well as additional tension or compression stresses caused by the plastic incompatibility across AlAl2Cu interfaces, resulting in failure of Al2Cu layers, such as tensile cracking or compressive instability [4,5]. Experimental and theoretical studies of mechanical behaviors of metallic laminates containing a hard phase suggest that improving mechanical properties of laminated composites could be realized through reducing lamina thickness and/or tailoring interface including orientation relationship, interface structure and interface properties [6–12]. The plasticity in intermetallic or brittle layers is carried over by
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Corresponding authors. E-mail addresses: [email protected] (J. Wang), [email protected] (A. Misra).
https://doi.org/10.1016/j.matchar.2018.05.037 Received 3 April 2018; Received in revised form 22 May 2018; Accepted 23 May 2018 Available online 24 May 2018 1044-5803/ © 2018 Elsevier Inc. All rights reserved.
dislocations that are preferably nucleated from interfaces. Interface ledges/steps act as dislocation sources and slip transmission for dislocations occurs from metal into intermetallic phase [1,13,14]. The interaction force among dislocations in the adjacent interfaces facilitates nucleation and motion of dislocations in intermetallic phase (especially, reducing layer thickness increases the interaction force) [15]. In addition to the layer thickness, these dislocation mechanisms are strongly related to orientation relationships (ORs) between two phases. For example, slip transmission across interface boundary is favored in the orientation relationship with a specific pair of parallel slip systems across the interface, but less favored in systems with significant crystallographic discontinuity in slip systems across the interface [16–19]. It is noted that different interface planes (IPs) can be associated with the same OR [20–22]. Therefore, characterizing ORs and IPs in a laminated composite is essential for understanding and predicting slip systems and mechanical properties of laminated composites. The ORs between α-Al and θ-Al2Cu have been extensively investigated in AleCu alloys [23–38]. In Al-Al2Cu eutectic laminates with the interlamellar spacing above 1 μm, the most commonly observed OR is {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al. This OR was determined according to electron diffraction in transmission electron microscopy (TEM) [28–30], Kikuchi line patterns using either TEM [31] or electron backscattered diffraction (EBSD) technique [32–35], and XRay technique [26,27]. Cantor and Chadwick [31] found that the
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of 23 pA in FEI Helios 650 Nanolab SEM/FIB. The bulk samples for EBSD were mechanically ground and vibration polished. The microstructures of the as-cast and laser treated materials are shown in Fig.1. The phases in the light and dark contrasts are Al2Cu and Al, respectively. The as-cast materials are consisting of primary α-Al dendrites with grains in tens of microns, needle like θ-Al2Cu phase, irregular and regular lamellar Al-Al2Cu eutectics. The average interlamellar spacing of the regular lamellar eutectics in as-cast samples is 1.2 ± 0.2 μm. A cross-sectional view of the laser melted pool perpendicular to the laser scanning direction is illustrated in Fig. 1b. The melted zone is in a half-ellipse shape with a major axis of ~2.6 mm on the surface and a depth of ~0.8 mm from the surface. The pool boundary is marked by the dotted line. The microstructure in the melted region is significantly modified, showing lamellar Al-Al2Cu eutectic colonies with random lamellar directions (Figs. 1 c and d). Each colony contains alternate α-Al and θ-Al2Cu lamina. The eutectic colonies are in columnar shape with a width of ~5–10 μm and a length of ~35–55 μm near the pool boundary (Fig. 1c). Both the size and the aspect ratio of the colonies decrease along the arrows towards the top center (point A) of the pool (Fig. 1b). The eutectics at the pool boundary grow perpendicular to the boundary as observed in Fig. 1c, but the growth direction randomized away from the boundary as shown in Fig. 1d. Furthermore, the average interlamellar spacing decreases along the arrows in Fig. 1b, from ~280 nm at the pool boundary to ~40 nm at the top center of the pool (point A). The reason for the decrease in the average interlamellar spacing is the solidification rate which increases from zero at the pool bottom to a maximum rate close to beam scanning speed at the top surface [43]. The interlamellar spacing scaled with A′(h)-0.25 where h is distance from the pool bottom and A′ is a factor dependent on laser processing conditions [41]. In each colony, the eutectic is nearly single crystal with alternate single crystal of α-Al and θ-Al2Cu lamellae. It was suggested by previous investigations of eutectics [23], each phase of the eutectic maintains an approximately constant crystallographic orientation over distances considerably greater than the interparticle separation. Moreover, the crystallographic OR between the two phases was approximately unchanged in the eutectic compared with as-cast one. For α-Al/θ-Al2Cu lamellar eutectic, there is only a preferred texture in the lamellar region and the orientations of alternate lamellae of each phase may vary continually by up to 2° per lamellae [28]. These small variations in orientation resulted in the presence of low angle sub-boundaries in each colony, shown in Fig. 1d indicated by arrows. The orientations between α-Al and θ-Al2Cu phases within an individual colony were investigated in as-cast and laser treated materials by EBSD and TKD techniques. It is observed that the orientations within each layer and even in alternate layers of each phase vary less than ~2°. Fig. 2a shows a typical inverse pole figure (IPF) map of TKD from four adjacent colonies in laser treated material. The “point to origin” misorientations were inspected along lines 1–3 in Fig. 2a. The black regions are those that are not well indexed in the IPF maps. Lines 1 and 2 are within an individual α-Al/θ-Al2Cu layer along the length direction, respectively. Line 3 is across several α-Al/θ-Al2Cu layers along the width direction. The misorientation angles along the lines 1, 2 and 3 are shown in Figs. 2 b and c, respectively. Fig. 2b (lines 1 and 2) indicates that the misorientations in each single layer are within 2°. Fig. 2c shows that the misorientations of each phase across several layers in the colony are also within 2°. The similar feature in terms of the morphology and orientation characters has been observed in the as-cast lamellar eutectics.
interface plane associated with this OR is close to {211}Al2Cu||{111}Al, varying over an angle of ± 8° according to Kikuchi line patterns in TEM. Davies and Hellawell [28,29] found that the interface plane is tilted 10°-12° away from (211)Al2Cu||(111)Al about [2 11]Al by using electron diffraction. It was noted that (001)Al2Cu plane is closely parallel to (001)Al plane with a deviation angle of 6.25° in this OR [39]. Bonnet and Durand named this OR as “Beta 6”. The other OR (001)Al2Cu||(001)Al and [100]Al2Cu||[130]Al (referred to as “Alpha 4”) was observed in Al2Cu precipitates reinforced aluminum alloys [39] and ternary Al-Cu-Ag alloys by using EBSD [35–38]. Reducing the characteristic dimension of these composites can simultaneously improve their strength and ductility [40,41]. The question is whether nanoscale composites exhibit ORs and IPs same as those observed in microscale eutectics or develop new ORs and IPs during thermo mechanical processing. For example, Cu/Nb metallic laminates show {111}Cu||{110}Nb IP with the Kurdjumov–Sachs (KS) and NishiyamaWassermann (NW) ORs in thin films [20], but {112}Cu||{112}Nb IP with the KS OR in accumulative roll-bonding (ARB) nano-laimates [22]. By tailoring solidification rate and the degree of undercooling [41–44], the interlamellar spacing usually decreases with increasing solidification rate (up to 0.2–0.3 m/s) or undercooling. Ultra-rapid solidification velocity together with high thermal gradient and rapid heating/cooling rate can be achieved by laser surface remelting. This technique has been applied to refine the interlamellar spacing of the Al-Al2Cu eutectics effectively [43,44]. A minimum interlamellar spacing of 17 nm was achieved in AleCu eutectic alloy [43]. In this work, we investigated ORs and IPs in AleCu eutectic alloy with different interlamellar spacing. We synthesized Al-Al2Cu nano-lamellar eutectics with alternate α-Al and θ-Al2Cu laminas (40–280 nm interlamellar spacing) through laser surface remelting treatment of the cast Al-32.7 wt% Cu eutectic alloy with Al-Al2Cu micro-lamellar eutectics (~1–3 μm interlamellar spacing). The morphology of both α-Al and θ-Al2Cu eutectic phases was characterized by using scanning/transmission electron microscopy (S/TEM). The ORs between two phases were determined according to Kikuchi patterns that were obtained by using EBSD and TKD (also called t-EBSD) techniques. TKD technique [45] was proposed which utilizes the transmitted diffraction instead of backscatter diffraction used in the conventional EBSD technique. The main differences of TKD from conventional EBSD are that the sample is electron transparent and the spatial resolution is up to 10 nm. One characteristic orientation relationship, {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al, with two variants was identified in both as-cast and laser melted materials. We further deduced different parallel relationships among low index planes except for the same basic parallel planes from the characteristic orientation relationships. 2. Microstructural Characterization The ingots of Al-32.7 wt% Cu eutectic alloys were produced by Arcast Inc. in an Arc 200 cold copper crucible melter by melting appropriate mixtures of high purity aluminum (99.99%) and copper (99.99%) under protective atmosphere (Ar). The as-cast ingots were cut into several plates with 5 mm thickness. The surface of these specimens was ground with 800 grit SiC emery paper and coated by graphite (Bonderite L-GP G aerosolized graphite lubricant) prior to laser processing. Laser surface remelting experiments were conducted on a solidstate disk laser (TRUMPF Laser HLD 4002) at a wavelength of 1030 nm. Argon shielding gas (flow rate of 9.4 L/min) was also used during the laser remelting process to prevent oxidation. The laser power, spot size and scanning speed were 750 W, 2 mm and 30 mm/s, respectively. Details of synthesis and laser remelting are published elsewhere [46]. Microstructure characterizations were performed on Helios 650 Nanolab SEM and JEOL 3100R05 Double Cs-Corrected TEM. TKD/EBSD analysis of as-cast and laser treated materials were conducted on FEI Helios 650 Nanolab SEM. The thin film samples with a thickness of ~60–100 nm for TKD and TEM experiments were prepared by focused ion beam (FIB) milling with a final voltage of 2.0 KV and beam current
3. Characteristic ORs and IPs 3.1. EBSD/TKD and TEM Analysis The ORs between Al and Al2Cu phases in as-cast and laser treated eutectics were analyzed by EBSD and TKD techniques. It has been reported that EBSD patterns having a confidence index (CI) above 0.1 can correctly index an orientation 95% of the time [47]. In the present work, the 171
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Fig. 1. (a) Microstructures of as-cast material, consisting of primary α-Al dendrites, needle like θ-Al2Cu phase, irregular and lamellar Al-Al2Cu eutectics, (b) a crosssectional view of the laser melted region perpendicular to the laser scanning direction, (c) the Al-Al2Cu eutectic morphology near the laser melted pool boundary, (d) the Al-Al2Cu eutectic morphology away from the pool boundary. The phases in the light and dark contrast are θ-Al2Cu and α-Al phases, respectively.
plane family {hkl}, the parameters of h, k are interchangeable but not with the parameter of l. It can be concluded that the α-Al and θ-Al2Cu eutectics in the 16 colonies have the same parallel relationships {211}Al2Cu||{111}Al and {120}Al2Cu||{110}Al (or 〈120〉Al2Cu||〈110〉Al), indicated by circles in Fig. 3. However, the right pole figure in Fig. 3a reveals that the (100)Al2Cu, (010)Al2Cu and (001)Al2Cu planes are closely parallel to (130)Al, (310)Al and (001)Al (indicated by rectangles), with the deviation angles of ~0–2°, ~1–3.2°, and ~0–2.2°, respectively. Thus, five pairs of planes are nearly parallel in variant I, including {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, {100}Al2Cu||{130}Al, {010}Al2Cu||{310}Al, and {001}Al2Cu||{001}Al. When an OR was described by the three parallel relations {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, and {001}Al2Cu||{001}Al, the OR is same as the wellobserved “Beta 6” OR. When an OR is described by the three parallel relations {100}Al2Cu||{130}Al, {010}Al2Cu||{310}Al, and {001}Al2Cu||{001}Al, the OR is called “Alpha 4”. Thus, the “Beta 6” relationship is close to “Alpha 4” relationship, which is consistent with the previous conclusion [39]. The right pole figure in Fig. 3b reveals that the (100)Al2Cu, (010)Al2Cu and (001)Al2Cu planes are closely parallel to (2 11)Al, (011)Al and (111)Al (indicated by rectangles), with the deviation angles of ~1.6–5.6°, ~3.8–6°, and ~0.9–2.8°, respectively. Correspondingly, five pairs of planes are nearly parallel in variant II, including {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, {100}Al2Cu||{211}Al, {010}Al2Cu||{011}Al, and {001}Al2Cu||{111}Al. When the last three parallel relations are neglected, the variant II is generally confused with variant I. In the sixteen colonies examined in as-cast samples, seven colonies exhibit variant I OR and the other nine colonies exhibit the variant II OR. The ORs in the laser processed materials were analyzed using TKD technique with high spatial resolution (up to 10 nm). Fourteen colonies
average confidence index of the patterns from EBSD/TKD was above 0.5 for each mapping, the points with CI values > 0.2 were selected to establish the pole figures. The OR of α-Al/θ-Al2Cu eutectic was defined by superposing pole figures of α-Al and θ-Al2Cu phases within the same colony. It is well known that the crystal directions or planes are parallel if the corresponding spots from two phases overlap in the superposed pole figures. This allows us to determine the ORs in the eutectics. Regarding the ORs in the as-cast materials, we studied sixteen colonies that exhibit fully lamellar structure. The results were classified into two groups. The corresponding ORs are named as variants I and II. In order to show the difference in ORs clearly, the crystals in each colony were rotated simultaneously to make [001]Al2Cu direction parallel to the normal direction of the sample, [010]Al2Cu direction parallel to the horizontal direction of the sample (denoted by A1), and [100]Al2Cu direction parallel to the vertical direction of the sample (denoted by A2). By doing so, the θ-Al2Cu crystals in the different colonies are in the same orientation, while the orientation of αAl phase relative to adjacent θ-Al2Cu phase in the same colony is unchanged. The left pole figures in Figs. 3 a and b only show spots associated with {211}Al2Cu and {111}Al, the middle pole figures show spots associated with {120}Al2Cu and {110}Al, and the right pole figures show spots associated with {001}Al2Cu, {100}Al2Cu, {001}Al, {130}Al, {111}Al, {101}Al and {121}Al. Here, it is worthwhile to emphasize that only when l is zero, the direction [hk0] is perpendicular to the plane (hk0) in θ-Al2Cu crystal, while in fcc Al crystal, the direction [hkl] is always perpendicular to the plane (hkl). It means in Fig. 3, the spots of θ-Al2Cu phase with l = 0 could indicate both direction [hk0] and plane [hk0]. For example, the spots of {120}Al2Cu and {110}Al planes could represent 〈120〉Al2Cu and 〈110〉Al directions, respectively, in the middle pole figures of Fig. 3. Moreover, in the direction or 172
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Fig. 2. (a) Inverse pole figure (IPF) map of the laser treated material by SEM-TKD. The point to origin misorientation angles along (b) lines 1 and 2 inside Al and Al2Cu lamellae, respectively, (c) line 3 crossing Al and Al2Cu lamellae.
overlapped pole figures were shown in Fig. 4. It can be concluded that the OR between α-Al and θ-Al2Cu eutectic also has the parallel relationship {211}Al2Cu||{111}Al and {120}Al2Cu||{110}Al (shown inside
from different depth of the melted pool (from the top surface with ~20 nm thick lamella to the bottom boundary with ~100 nm thick lamella in four laser treated samples were examined. A typical set of
Fig. 3. Two unique variants from the basic OR family of {211}Al2Cu||{111}Al and 〈 120〉Al2Cu|| < 110 > Al in the Al-Al2Cu lamellar eutectics of as-cast material. Overlap pole figures from eutectic with (a) variant I and (b) variant II OR. The eutectic colonies were rotated simultaneously to make [001]Al2Cu direction parallel to the normal direction of the sample, [010]Al2Cu direction parallel to the horizontal direction of the sample (denoted by A1), and [100]Al2Cu direction parallel to the vertical direction of the sample (denoted by A2). 173
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Fig. 4. A typical set of overlap pole figures from the nanoscale Al-Al2Cu lamellar eutectics of laser treated material. It reveals variant I OR: (a) (211)Al2Cu||(111)Al, (b) (12 0)Al2Cu||(110)Al and (c) (100)Al2Cu, (010)Al2Cu and (001)Al2Cu planes are closely parallel to (130)Al, (310)Al and (001)Al, with deviations of ~0–1.7°, ~0.7–1.7°, and ~0.8–2.1°, respectively.
3.2. Atomistic Modeling
the circles). Fig. 4c reveals that (100)Al2Cu, (010)Al2Cu and (001)Al2Cu planes are closely parallel to (130)Al, (310)Al and (001)Al (shown inside the rectangles), with deviations of ~0–1.7°, ~0.7–1.7°, and ~0.8–2.1°, respectively. The OR in this colony is the variant I or the “Beta 6”. Among the fourteen colonies with interlamellar spacing from ~40 nm to ~200 nm, the ORs are determined as variant I. Therefore, variant I prevails over variant II in laser processed α-Al/θ-Al2Cu nano-laminates. The interface boundaries in the two variants were determined according to diffraction patterns and the corresponding bright-filed (BF) or high resolution TEM (HRTEM) images. First, lamellar eutectic colonies with variant I or variant II OR were chosen according to EBSD analysis. Secondly, thin foils were lifted out in the direction perpendicular to the interface boundaries from these selected colonies to image the interface boundaries in cross-section in TEM. Thirdly, BF or HRTEM images and the corresponding diffraction patterns were obtained under edge-on interface planes condition (< ~5° sample tilt) from these TEM samples. Finally, according to the relationship between real space (BF and HRTEM images) and reciprocal space (diffraction patterns), the interface planes could be determined by indexing the corresponding diffraction spots (the diffraction spots are perpendicular to their corresponding diffracted planes.). For laminates with variant I OR, we observed two interfaces. Fig. 5a shows a TEM image and Fig. 5b shows the corresponding diffraction pattern (obtained under 2.7° sample tilt) comprising two sets of diffraction spots from two phases. The beam direction is parallel to [100]Al2cu and [130]Al. From the diffraction pattern, it is identified that the interface planes (indicated by the yellow dotted lines) are (002)Al2Cu and (002)Al, and these two planes have a deviation angle of ~2.5°. The interface plane is thus composed of (001)Al2Cu||(001)Al terrace and steps. The other interface plane is identified in Figs. 5 c and d (obtained under 4.9° sample tilt), where the beam direction is parallel to [311]Al2Cu and [112]Al. The overlapped diffraction spots in Fig. 5d are associated with (121)Al2Cu and (111)Al, while the interface plane (indicated by the yellow dotted lines) is deviated ~2–3° from the parallel planes. This suggested that interface plane could be serrated, composing of (121)Al2Cu||(111)Al terrace and steps. In association with variant II OR, the interface boundary plane is identified in Figs. 5 e and f (obtained under 5.6° sample tilt). The diffraction pattern from two phases is obtained along [423]Al2Cu and [111]Al. It is noticed that the interface planes (indicated by the yellow dotted lines) are (24 0)Al2Cu and (22 0)Al, and these two planes are nearly parallel with a deviation angle of ~6°. Thus the interface should comprise (12 0)Al2Cu||(110)Al terrace and steps. HRTEM characterization further confirmed this hypothesis. Fig. 5g shows a terraced (001)Al2Cu||(001)Al interface, and Fig. 5h shows a terraced (12 0)Al2Cu||(110)Al interface.
Corresponding to the crystallography of these interfaces, we constructed atomistic models of these terraces (see Table 2 for model parameters). In the (001)Al2Cu||(001)Al interface of variant I, the misfit strains (εm) are 5.5% in the two orthogonal directions, [100]Al2Cu||[130]Al and [010]Al2Cu||[310]Al directions. Two interfaces are examined with respect to the terminated atomic plane in Al2Cu. Fig. 6a shows two initial structures, the top image shows atomic structure of the interface with Cu terminated plane and the bottom one shows atomic structure of the interface with Al terminated plane. Relaxing interface structures was conducted by molecular statics method [48,49] with the empirical interatomic potentials for Cu, Al, and Al2Cu [50–52]. Atomistic simulations revealed that both interfaces are semicoherent. The interface with the Cu-terminated plane has lower formation energy of 666 mJ/m2. The relaxed interface structure with Cu terminated plane in Al2Cu is shown in Figs. 6 b and c. Atoms in Figs. 6 b and c are colored by their displacement magnitude with respect to the unrelaxed structure. According to atomistically informed Frank-Bilby theory [53], two sets of interface dislocations are identified in the relaxed interface. Their lines are parallel to [120]Al2Cu||[110]Al and [210]Al2Cu||[110]Al, and the average spacing between interface dislocations are measured to be L = 4.05 nm (Fig. 6b). Their Burgers → vectors are then calculated to be bm = ½[110]Al and ½[110]Al according to Frank-Bilby theory [53] where the reference lattice of the interface takes the same lattice as that of {001}Al plane. Fig. 6c shows the relaxed interface structure viewed along the direction of [120]Al2Cu||[110]Al (indicated in Fig. 6b). For the interface plane of (121)Al2Cu and (111)Al, the misfit strains are 0.6% and 2.6% along [111]Al2Cu||[121]Al and [7 19]Al2Cu||[101]Al directions, respectively. Atomistic simulations show that this semi-coherent interface has the interface formation energy, 443 mJ/m2. The (12 0)Al2Cu||(110)Al interface associated with variant II has lattice mismatches of 4.1% and 9.4% along [001]Al2Cu||[111]Al and [210]Al2Cu||[112 ]Al directions, respectively. The interface has high formation energy of 1022 mJ/m2. Thus, the variant selection during laser modification (variant I prevails over variant II in experiments) is ascribed to the low formation energy of the interfaces. Two interfaces associated with variant I have lower formation energy, 443 mJ/m2 for the {211}Al2Cu||{111}Al interface and 666 mJ/m2 for (001) Al2Cu||{001}Al interface, compared with the {120}Al2Cu||{110}Al interface, 1022 mJ/m2, associated with variant II.
4. Discussion Here we discuss possible ORs with respect to the basic parallel element 174
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Fig. 5. Interface boundaries in Al-Al2Cu eutectic. (a,b) (001)Al2Cu||(001)Al interface boundary in variant I OR and the corresponding diffraction pattern from two phases. (c,d) (121)Al2Cu||(111)Al interface boundary in variant I OR and the corresponding diffraction pattern from two phases. (e,f) (12 0)Al2Cu||(110)Al interface boundary in variant II OR and the corresponding diffraction pattern from two phases. (g) HRTEM image of a terraced (001)Al2Cu||(001)Al interface boundary. (h) HRTEM image of a terraced (12 0)Al2Cu||(110)Al interface boundary.
of {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al. In the basic parallel relationship, the direction of 〈120〉Al2Cu or 〈110〉Al, should be a direction contained in the family of {211}Al2Cu or {111}Al planes, respectively. If we choose [120]Al2Cu||[110]Al, there are four possible parallel pairs between the planes of {211}Al2Cu and {111}Al, which are (211)Al2Cu||(111)Al, (211)Al2Cu||(111)Al, (2 11)Al2Cu||(111)Al and (2 11)Al2Cu||(111)Al. There are four equal 〈120〉 axes in a C16 structure and six equal 〈110〉 axes in an fcc structure. Thus, there are 24 (4 × 6) possible parallel pairs for the relationship of 〈120〉Al2Cu||〈011〉Al, such as [120]Al2Cu||[110]Al or [120]Al2Cu||[110]Al or [210]Al2Cu||[110]Al and so on. Finally, there are 96 (24 × 4) possible pairs for the basic OR of {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al. We examined all the 96 possible pairs and found the three planes in α-Al which are parallel to (100)Al2Cu, (010)Al2Cu and (001)Al2Cu in each pair. The 96 possible pairs of ORs can be equally classified into two groups, one group has relationships of {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, {100}Al2Cu||{130}Al, {010}Al2Cu||{310}Al and (001)Al2Cu||{001}Al, same as the variant I OR observed in Figs. 3a and 4. A representative OR from group one (variant I) is shown in the simulated stereographic projection graph (Fig. 7a). The other group has the relationships of {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, {100}Al2Cu||{211}Al,
{010}Al2Cu||{011}Al and (001)Al2Cu||{111}Al, same as the observation in Fig. 3b. A representative OR from group two (variant II) is shown in Fig. 7b. In Fig. 7, the blue squares and red triangles stand for planes from Al and Al2Cu crystals, respectively. It is noticed that another 12 or 11 pairs planes in variant I or II, respectively, are nearly parallel with the deviation angle < 5°. These parallel pairs are shown in Fig. 7 and are listed in Table 1, which establishes a database for the parallel relationships in the two variants. Therefore, the basic OR can be generally described by {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈011〉Al. A third parallel element (for example (001)Al2Cu||{001}Al) is necessary to precisely define the OR of αAl/θ-Al2Cu eutectic. The difference between two variants was frequently neglected in previous studies because of the common parallel planes and directions in the two variants. The existence of these two variants is due to the lower symmetry of bct structured θ-Al2Cu crystal in comparison with fcc structure of α-Al. In the studies of Davies [29] and Cantor [31], they defined a (001)Al2Cu parallel to (001)Al relationship together with {121}Al2Cu||{111}Al and 〈210〉Al2Cu||〈011〉Al, hence the relationship they observed is variant I. In recent studies using EBSD technique [32–35], although the ORs are claimed as (211)Al2Cu||{111}Al and 175
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Fig. 6. Atomic structure of the {001}Al2Cu||{001}Al interface. (a) Unrelaxed interfaces with different terminates- top one with Cu-terminate and the bottom with Alterminate. (b) Relaxed interface structure of {001}Al||{001}Al2Cu (Cu terminated Al2Cu), and (c) Relaxed interface structure of {001}Al||{001}Al2Cu viewed along the direction of [120]Al2Cu||[110]Al. Atoms in 6b and 6c are colored by their displacements with respect to the unrelaxed structure.
[120]Al2Cu||〈011〉Al or same with “Beta 6”, a third parallel element is always neglected which is necessary to define the real OR. From overlap pole figures of Figs. 3 and 4, it can be seen that in variant I each of the four equal {111}Al planes is always close or parallel to a {211}Al2Cu
plane (shown in Figs. 3a and 4, left pole figures). However, in variant II, there is at least one {111}Al plane that is far away from any {211}Al2Cu plane (shown in Fig. 3b, left pole figures). Therefore, the two variants can be distinguished with the feature of overlap pole figures of
Fig. 7. Stereographic projection of low-index planes from α-Al (blue squares) and θ-Al2Cu (red triangles), showing all the parallel planes (deviations of less than ~10°) in (a) variant I OR and (b) variant II OR. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 176
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Table 1 Derivative parallel planes from two variants in the basic OR family of {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al. Variants
Derivative parallel planes (100), (010), (001) planes of Al2Cu
Variant I [210]Al2Cu||[110]Al (12 1)Al2Cu||(111)Al
Deviations of < 5°
(100)Al2Cu||(13 0)Al
(110)Al2Cu||(210)Al, (111)Al2Cu||(313)Al
(010)Al2Cu||(3 10)Al (~4.5°)
(121)Al2Cu||(33 2)Al, (121)Al2Cu||(201)Al
(001)Al2Cu||(001)Al (~5°)
(211)Al2Cu||(111)Al, (211)Al2Cu||(111)Al (112)Al2Cu||(113 )Al, (3 10)Al2Cu||(010)Al (13 0)Al2Cu||(100)Al, (13 2)Al2Cu||(101)Al (3 21)Al2Cu||(131)Al, (3 12 )Al2Cu||(011)Al
Variant II [210]Al2Cu||[110]Al (121)Al2Cu||(111)Al
(100)Al2Cu||(121)Al (~5°)
(12 0)Al2Cu||(113 )Al, (12 1)Al2Cu||(001)Al
(010)Al2Cu||(15 , 2 ,20)Al
(211)Al2Cu||(131)Al, (211)Al2Cu||(311)Al
(~9° away of (101)Al)
(121)Al2Cu||(301)Al, (112 )Al2Cu||(311)Al
(001)Al2Cu||(3 32 )Al
(111)Al2Cu||(100)Al, (13 0)Al2Cu||(313 )Al
(~10° away of (111)Al)
(321)Al2Cu||(210)Al
electron microscopy was performed at the Michigan Center for Materials Characterization at University of Michigan. Atomistic simulations were conducted at the Holland Computing Center (HCC), which is a high performance computing resource for the University of Nebraska System.
Table 2 Model parameters used in the atomistic model of three semi-coherent α-Al/θAl2Cu interfaces and their formation energy. Variant I - IP I Al2Cu||Al
Variant I - IP II Al2Cu||Al
Variant II Al2Cu||Al
Y-normal to interface
(001) (001)
(121) (111)
[100] [130]
[111] [121]
(12 0) (110) [001] [111]
References
X Z
[010] [310] 666
[7 19 ] [101] 443
[210] [112 ] 1022
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Interface energy (mJ/m2)
{211}Al2Cu and {111}Al. For example, Li et al. [32] showed several overlap pole figures that were displayed from Al-Al2Cu eutectic solidified under various magnetic field intensities. The overlap pole figures of (211)Al2Cu and (111)Al from samples with 0 T, 2 T, 12 T magnetic field have same feature as that of variant I and the overlap pole figures from 6 T sample has same feature as that of variant II (Fig. 4 in Ref. [32]). Although they claimed all the ORs are equal and same as the “Beta 6” OR (variant I), the OR under 6 T magnetic field which belongs to variant II is actually different with “Beta 6”. 5. Conclusions The ORs in as-cast and laser-remelted Al-Al2Cu eutectics appear to be independent of inter-lamellar spacing. The existence of the two variants is due to the low symmetry of bct structured Al2Cu crystal. The characteristic OR is {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al with two variants. Variant I is {211}Al2Cu||{111}Al, 〈120〉Al2Cu||〈110〉Al and (001)Al2Cu||{001}Al. There are two kinds of interface planes associate with variant I, (001)Al2Cu||{001}Al and {211}Al2Cu||{111}Al. Variant 2 is {211}Al2Cu||{111}Al, 〈120〉Al2Cu||〈110〉Al and (001)Al2Cu||{111}Al. The interface plane in variant II is {120}Al2Cu||{110}Al. It is noted that variant I OR is prevailed over variant II as the interlamellar spacing is reduced to nanometers via laser remelting due to the higher formation energy of the interface {120}Al2Cu||{110}Al. A comprehensive analysis, supported by atomistic modeling, of the crystallographic OR between two phases and distribution of OR variants across length scales will be helpful in understanding the active slip systems and stress-strain response of these eutectic composites. Acknowledgements This research is sponsored by DOE, Office of Science, Office of Basic Energy Sciences with the grant number of DE-SC0016808. Authors acknowledge assistance of Q. Lei, B. P. Ramakrishnan, and J. Mazumder at University of Michigan in material synthesis and laser treatment. The 177
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Materials Characterization journal homepage: www.elsevier.com/locate/matchar
Characteristic orientation relationships in nanoscale Al-Al2Cu Eutectic a
b
S.J. Wang , G. Liu , J. Wang a b
b,⁎
, A. Misra
a,⁎
T
Department of Materials Science and Engineering, College of Engineering, University of Michigan, Ann Arbor, MI 48109-2136, USA Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Al-Al2Cu eutectic Laser surface remelting Orientation relationship Interfaces
A fully lamellar Al-Al2Cu eutectic comprising alternate nano-scale α-Al and θ-Al2Cu phases was synthesized through laser surface remelting of a cast Al-32.7 wt% Cu alloy. The orientation relationship between α-Al and θAl2Cu phases was investigated from Kikuchi patterns obtained using electron backscattered diffraction (EBSD) and t-EBSD techniques. The characteristic orientation relationship (OR), {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al, was observed independent of interlamellar spacing. This OR has two variants where, besides the two parallel planes, the variant I exhibits (001)Al2Cu||{001}Al and the variant II exhibits (001)Al2Cu||{111}Al. Variant I prevails over variant II in laser-processed α-Al and θ-Al2Cu nano-laminates, and atomistic modeling indicates that this is due to the low energy interfaces associated with variant I, i.e., {211}Al2Cu||{111}Al or (001)Al2Cu||{001}Al. A comprehensive understanding of the crystallographic orientation relationships between two phases may help predict or explain the active slip systems in fine-scale Al-Al2Cu eutectic and other cubic-tetragonal two-phase materials.
1. Introduction Al-Al2Cu eutectics comprise alternate lamellae of α-Al and θ-Al2Cu phases. θ-Al2Cu with a C16 body centered tetragonal (bct) structure is brittle at room temperature due to high lattice friction stress associated with dislocations motion. α-Al with a face centered cubic (fcc) structure is ductile because of the easy glide of 1/2〈110〉 dislocation on {111} planes. Under mechanical loading at room temperature, α-Al layers plastically deform via nucleation, propagation and multiplication of dislocations. θ-Al2Cu layers elastically deform corresponding to the brittle nature of Al2Cu phases, acting as strong obstacles for dislocation motion in Al-Al2Cu composites [1–3]. Due to significant difference in elasticity and plasticity between the two phases, α-Al layers are hardened due to back stresses associated with geometric constraint of interfaces. Al2Cu layers are subjected to higher stresses than α-Al due to its higher elastic modulus than Al as well as additional tension or compression stresses caused by the plastic incompatibility across AlAl2Cu interfaces, resulting in failure of Al2Cu layers, such as tensile cracking or compressive instability [4,5]. Experimental and theoretical studies of mechanical behaviors of metallic laminates containing a hard phase suggest that improving mechanical properties of laminated composites could be realized through reducing lamina thickness and/or tailoring interface including orientation relationship, interface structure and interface properties [6–12]. The plasticity in intermetallic or brittle layers is carried over by
⁎
Corresponding authors. E-mail addresses: [email protected] (J. Wang), [email protected] (A. Misra).
https://doi.org/10.1016/j.matchar.2018.05.037 Received 3 April 2018; Received in revised form 22 May 2018; Accepted 23 May 2018 Available online 24 May 2018 1044-5803/ © 2018 Elsevier Inc. All rights reserved.
dislocations that are preferably nucleated from interfaces. Interface ledges/steps act as dislocation sources and slip transmission for dislocations occurs from metal into intermetallic phase [1,13,14]. The interaction force among dislocations in the adjacent interfaces facilitates nucleation and motion of dislocations in intermetallic phase (especially, reducing layer thickness increases the interaction force) [15]. In addition to the layer thickness, these dislocation mechanisms are strongly related to orientation relationships (ORs) between two phases. For example, slip transmission across interface boundary is favored in the orientation relationship with a specific pair of parallel slip systems across the interface, but less favored in systems with significant crystallographic discontinuity in slip systems across the interface [16–19]. It is noted that different interface planes (IPs) can be associated with the same OR [20–22]. Therefore, characterizing ORs and IPs in a laminated composite is essential for understanding and predicting slip systems and mechanical properties of laminated composites. The ORs between α-Al and θ-Al2Cu have been extensively investigated in AleCu alloys [23–38]. In Al-Al2Cu eutectic laminates with the interlamellar spacing above 1 μm, the most commonly observed OR is {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al. This OR was determined according to electron diffraction in transmission electron microscopy (TEM) [28–30], Kikuchi line patterns using either TEM [31] or electron backscattered diffraction (EBSD) technique [32–35], and XRay technique [26,27]. Cantor and Chadwick [31] found that the
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of 23 pA in FEI Helios 650 Nanolab SEM/FIB. The bulk samples for EBSD were mechanically ground and vibration polished. The microstructures of the as-cast and laser treated materials are shown in Fig.1. The phases in the light and dark contrasts are Al2Cu and Al, respectively. The as-cast materials are consisting of primary α-Al dendrites with grains in tens of microns, needle like θ-Al2Cu phase, irregular and regular lamellar Al-Al2Cu eutectics. The average interlamellar spacing of the regular lamellar eutectics in as-cast samples is 1.2 ± 0.2 μm. A cross-sectional view of the laser melted pool perpendicular to the laser scanning direction is illustrated in Fig. 1b. The melted zone is in a half-ellipse shape with a major axis of ~2.6 mm on the surface and a depth of ~0.8 mm from the surface. The pool boundary is marked by the dotted line. The microstructure in the melted region is significantly modified, showing lamellar Al-Al2Cu eutectic colonies with random lamellar directions (Figs. 1 c and d). Each colony contains alternate α-Al and θ-Al2Cu lamina. The eutectic colonies are in columnar shape with a width of ~5–10 μm and a length of ~35–55 μm near the pool boundary (Fig. 1c). Both the size and the aspect ratio of the colonies decrease along the arrows towards the top center (point A) of the pool (Fig. 1b). The eutectics at the pool boundary grow perpendicular to the boundary as observed in Fig. 1c, but the growth direction randomized away from the boundary as shown in Fig. 1d. Furthermore, the average interlamellar spacing decreases along the arrows in Fig. 1b, from ~280 nm at the pool boundary to ~40 nm at the top center of the pool (point A). The reason for the decrease in the average interlamellar spacing is the solidification rate which increases from zero at the pool bottom to a maximum rate close to beam scanning speed at the top surface [43]. The interlamellar spacing scaled with A′(h)-0.25 where h is distance from the pool bottom and A′ is a factor dependent on laser processing conditions [41]. In each colony, the eutectic is nearly single crystal with alternate single crystal of α-Al and θ-Al2Cu lamellae. It was suggested by previous investigations of eutectics [23], each phase of the eutectic maintains an approximately constant crystallographic orientation over distances considerably greater than the interparticle separation. Moreover, the crystallographic OR between the two phases was approximately unchanged in the eutectic compared with as-cast one. For α-Al/θ-Al2Cu lamellar eutectic, there is only a preferred texture in the lamellar region and the orientations of alternate lamellae of each phase may vary continually by up to 2° per lamellae [28]. These small variations in orientation resulted in the presence of low angle sub-boundaries in each colony, shown in Fig. 1d indicated by arrows. The orientations between α-Al and θ-Al2Cu phases within an individual colony were investigated in as-cast and laser treated materials by EBSD and TKD techniques. It is observed that the orientations within each layer and even in alternate layers of each phase vary less than ~2°. Fig. 2a shows a typical inverse pole figure (IPF) map of TKD from four adjacent colonies in laser treated material. The “point to origin” misorientations were inspected along lines 1–3 in Fig. 2a. The black regions are those that are not well indexed in the IPF maps. Lines 1 and 2 are within an individual α-Al/θ-Al2Cu layer along the length direction, respectively. Line 3 is across several α-Al/θ-Al2Cu layers along the width direction. The misorientation angles along the lines 1, 2 and 3 are shown in Figs. 2 b and c, respectively. Fig. 2b (lines 1 and 2) indicates that the misorientations in each single layer are within 2°. Fig. 2c shows that the misorientations of each phase across several layers in the colony are also within 2°. The similar feature in terms of the morphology and orientation characters has been observed in the as-cast lamellar eutectics.
interface plane associated with this OR is close to {211}Al2Cu||{111}Al, varying over an angle of ± 8° according to Kikuchi line patterns in TEM. Davies and Hellawell [28,29] found that the interface plane is tilted 10°-12° away from (211)Al2Cu||(111)Al about [2 11]Al by using electron diffraction. It was noted that (001)Al2Cu plane is closely parallel to (001)Al plane with a deviation angle of 6.25° in this OR [39]. Bonnet and Durand named this OR as “Beta 6”. The other OR (001)Al2Cu||(001)Al and [100]Al2Cu||[130]Al (referred to as “Alpha 4”) was observed in Al2Cu precipitates reinforced aluminum alloys [39] and ternary Al-Cu-Ag alloys by using EBSD [35–38]. Reducing the characteristic dimension of these composites can simultaneously improve their strength and ductility [40,41]. The question is whether nanoscale composites exhibit ORs and IPs same as those observed in microscale eutectics or develop new ORs and IPs during thermo mechanical processing. For example, Cu/Nb metallic laminates show {111}Cu||{110}Nb IP with the Kurdjumov–Sachs (KS) and NishiyamaWassermann (NW) ORs in thin films [20], but {112}Cu||{112}Nb IP with the KS OR in accumulative roll-bonding (ARB) nano-laimates [22]. By tailoring solidification rate and the degree of undercooling [41–44], the interlamellar spacing usually decreases with increasing solidification rate (up to 0.2–0.3 m/s) or undercooling. Ultra-rapid solidification velocity together with high thermal gradient and rapid heating/cooling rate can be achieved by laser surface remelting. This technique has been applied to refine the interlamellar spacing of the Al-Al2Cu eutectics effectively [43,44]. A minimum interlamellar spacing of 17 nm was achieved in AleCu eutectic alloy [43]. In this work, we investigated ORs and IPs in AleCu eutectic alloy with different interlamellar spacing. We synthesized Al-Al2Cu nano-lamellar eutectics with alternate α-Al and θ-Al2Cu laminas (40–280 nm interlamellar spacing) through laser surface remelting treatment of the cast Al-32.7 wt% Cu eutectic alloy with Al-Al2Cu micro-lamellar eutectics (~1–3 μm interlamellar spacing). The morphology of both α-Al and θ-Al2Cu eutectic phases was characterized by using scanning/transmission electron microscopy (S/TEM). The ORs between two phases were determined according to Kikuchi patterns that were obtained by using EBSD and TKD (also called t-EBSD) techniques. TKD technique [45] was proposed which utilizes the transmitted diffraction instead of backscatter diffraction used in the conventional EBSD technique. The main differences of TKD from conventional EBSD are that the sample is electron transparent and the spatial resolution is up to 10 nm. One characteristic orientation relationship, {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al, with two variants was identified in both as-cast and laser melted materials. We further deduced different parallel relationships among low index planes except for the same basic parallel planes from the characteristic orientation relationships. 2. Microstructural Characterization The ingots of Al-32.7 wt% Cu eutectic alloys were produced by Arcast Inc. in an Arc 200 cold copper crucible melter by melting appropriate mixtures of high purity aluminum (99.99%) and copper (99.99%) under protective atmosphere (Ar). The as-cast ingots were cut into several plates with 5 mm thickness. The surface of these specimens was ground with 800 grit SiC emery paper and coated by graphite (Bonderite L-GP G aerosolized graphite lubricant) prior to laser processing. Laser surface remelting experiments were conducted on a solidstate disk laser (TRUMPF Laser HLD 4002) at a wavelength of 1030 nm. Argon shielding gas (flow rate of 9.4 L/min) was also used during the laser remelting process to prevent oxidation. The laser power, spot size and scanning speed were 750 W, 2 mm and 30 mm/s, respectively. Details of synthesis and laser remelting are published elsewhere [46]. Microstructure characterizations were performed on Helios 650 Nanolab SEM and JEOL 3100R05 Double Cs-Corrected TEM. TKD/EBSD analysis of as-cast and laser treated materials were conducted on FEI Helios 650 Nanolab SEM. The thin film samples with a thickness of ~60–100 nm for TKD and TEM experiments were prepared by focused ion beam (FIB) milling with a final voltage of 2.0 KV and beam current
3. Characteristic ORs and IPs 3.1. EBSD/TKD and TEM Analysis The ORs between Al and Al2Cu phases in as-cast and laser treated eutectics were analyzed by EBSD and TKD techniques. It has been reported that EBSD patterns having a confidence index (CI) above 0.1 can correctly index an orientation 95% of the time [47]. In the present work, the 171
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Fig. 1. (a) Microstructures of as-cast material, consisting of primary α-Al dendrites, needle like θ-Al2Cu phase, irregular and lamellar Al-Al2Cu eutectics, (b) a crosssectional view of the laser melted region perpendicular to the laser scanning direction, (c) the Al-Al2Cu eutectic morphology near the laser melted pool boundary, (d) the Al-Al2Cu eutectic morphology away from the pool boundary. The phases in the light and dark contrast are θ-Al2Cu and α-Al phases, respectively.
plane family {hkl}, the parameters of h, k are interchangeable but not with the parameter of l. It can be concluded that the α-Al and θ-Al2Cu eutectics in the 16 colonies have the same parallel relationships {211}Al2Cu||{111}Al and {120}Al2Cu||{110}Al (or 〈120〉Al2Cu||〈110〉Al), indicated by circles in Fig. 3. However, the right pole figure in Fig. 3a reveals that the (100)Al2Cu, (010)Al2Cu and (001)Al2Cu planes are closely parallel to (130)Al, (310)Al and (001)Al (indicated by rectangles), with the deviation angles of ~0–2°, ~1–3.2°, and ~0–2.2°, respectively. Thus, five pairs of planes are nearly parallel in variant I, including {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, {100}Al2Cu||{130}Al, {010}Al2Cu||{310}Al, and {001}Al2Cu||{001}Al. When an OR was described by the three parallel relations {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, and {001}Al2Cu||{001}Al, the OR is same as the wellobserved “Beta 6” OR. When an OR is described by the three parallel relations {100}Al2Cu||{130}Al, {010}Al2Cu||{310}Al, and {001}Al2Cu||{001}Al, the OR is called “Alpha 4”. Thus, the “Beta 6” relationship is close to “Alpha 4” relationship, which is consistent with the previous conclusion [39]. The right pole figure in Fig. 3b reveals that the (100)Al2Cu, (010)Al2Cu and (001)Al2Cu planes are closely parallel to (2 11)Al, (011)Al and (111)Al (indicated by rectangles), with the deviation angles of ~1.6–5.6°, ~3.8–6°, and ~0.9–2.8°, respectively. Correspondingly, five pairs of planes are nearly parallel in variant II, including {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, {100}Al2Cu||{211}Al, {010}Al2Cu||{011}Al, and {001}Al2Cu||{111}Al. When the last three parallel relations are neglected, the variant II is generally confused with variant I. In the sixteen colonies examined in as-cast samples, seven colonies exhibit variant I OR and the other nine colonies exhibit the variant II OR. The ORs in the laser processed materials were analyzed using TKD technique with high spatial resolution (up to 10 nm). Fourteen colonies
average confidence index of the patterns from EBSD/TKD was above 0.5 for each mapping, the points with CI values > 0.2 were selected to establish the pole figures. The OR of α-Al/θ-Al2Cu eutectic was defined by superposing pole figures of α-Al and θ-Al2Cu phases within the same colony. It is well known that the crystal directions or planes are parallel if the corresponding spots from two phases overlap in the superposed pole figures. This allows us to determine the ORs in the eutectics. Regarding the ORs in the as-cast materials, we studied sixteen colonies that exhibit fully lamellar structure. The results were classified into two groups. The corresponding ORs are named as variants I and II. In order to show the difference in ORs clearly, the crystals in each colony were rotated simultaneously to make [001]Al2Cu direction parallel to the normal direction of the sample, [010]Al2Cu direction parallel to the horizontal direction of the sample (denoted by A1), and [100]Al2Cu direction parallel to the vertical direction of the sample (denoted by A2). By doing so, the θ-Al2Cu crystals in the different colonies are in the same orientation, while the orientation of αAl phase relative to adjacent θ-Al2Cu phase in the same colony is unchanged. The left pole figures in Figs. 3 a and b only show spots associated with {211}Al2Cu and {111}Al, the middle pole figures show spots associated with {120}Al2Cu and {110}Al, and the right pole figures show spots associated with {001}Al2Cu, {100}Al2Cu, {001}Al, {130}Al, {111}Al, {101}Al and {121}Al. Here, it is worthwhile to emphasize that only when l is zero, the direction [hk0] is perpendicular to the plane (hk0) in θ-Al2Cu crystal, while in fcc Al crystal, the direction [hkl] is always perpendicular to the plane (hkl). It means in Fig. 3, the spots of θ-Al2Cu phase with l = 0 could indicate both direction [hk0] and plane [hk0]. For example, the spots of {120}Al2Cu and {110}Al planes could represent 〈120〉Al2Cu and 〈110〉Al directions, respectively, in the middle pole figures of Fig. 3. Moreover, in the direction or 172
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Fig. 2. (a) Inverse pole figure (IPF) map of the laser treated material by SEM-TKD. The point to origin misorientation angles along (b) lines 1 and 2 inside Al and Al2Cu lamellae, respectively, (c) line 3 crossing Al and Al2Cu lamellae.
overlapped pole figures were shown in Fig. 4. It can be concluded that the OR between α-Al and θ-Al2Cu eutectic also has the parallel relationship {211}Al2Cu||{111}Al and {120}Al2Cu||{110}Al (shown inside
from different depth of the melted pool (from the top surface with ~20 nm thick lamella to the bottom boundary with ~100 nm thick lamella in four laser treated samples were examined. A typical set of
Fig. 3. Two unique variants from the basic OR family of {211}Al2Cu||{111}Al and 〈 120〉Al2Cu|| < 110 > Al in the Al-Al2Cu lamellar eutectics of as-cast material. Overlap pole figures from eutectic with (a) variant I and (b) variant II OR. The eutectic colonies were rotated simultaneously to make [001]Al2Cu direction parallel to the normal direction of the sample, [010]Al2Cu direction parallel to the horizontal direction of the sample (denoted by A1), and [100]Al2Cu direction parallel to the vertical direction of the sample (denoted by A2). 173
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Fig. 4. A typical set of overlap pole figures from the nanoscale Al-Al2Cu lamellar eutectics of laser treated material. It reveals variant I OR: (a) (211)Al2Cu||(111)Al, (b) (12 0)Al2Cu||(110)Al and (c) (100)Al2Cu, (010)Al2Cu and (001)Al2Cu planes are closely parallel to (130)Al, (310)Al and (001)Al, with deviations of ~0–1.7°, ~0.7–1.7°, and ~0.8–2.1°, respectively.
3.2. Atomistic Modeling
the circles). Fig. 4c reveals that (100)Al2Cu, (010)Al2Cu and (001)Al2Cu planes are closely parallel to (130)Al, (310)Al and (001)Al (shown inside the rectangles), with deviations of ~0–1.7°, ~0.7–1.7°, and ~0.8–2.1°, respectively. The OR in this colony is the variant I or the “Beta 6”. Among the fourteen colonies with interlamellar spacing from ~40 nm to ~200 nm, the ORs are determined as variant I. Therefore, variant I prevails over variant II in laser processed α-Al/θ-Al2Cu nano-laminates. The interface boundaries in the two variants were determined according to diffraction patterns and the corresponding bright-filed (BF) or high resolution TEM (HRTEM) images. First, lamellar eutectic colonies with variant I or variant II OR were chosen according to EBSD analysis. Secondly, thin foils were lifted out in the direction perpendicular to the interface boundaries from these selected colonies to image the interface boundaries in cross-section in TEM. Thirdly, BF or HRTEM images and the corresponding diffraction patterns were obtained under edge-on interface planes condition (< ~5° sample tilt) from these TEM samples. Finally, according to the relationship between real space (BF and HRTEM images) and reciprocal space (diffraction patterns), the interface planes could be determined by indexing the corresponding diffraction spots (the diffraction spots are perpendicular to their corresponding diffracted planes.). For laminates with variant I OR, we observed two interfaces. Fig. 5a shows a TEM image and Fig. 5b shows the corresponding diffraction pattern (obtained under 2.7° sample tilt) comprising two sets of diffraction spots from two phases. The beam direction is parallel to [100]Al2cu and [130]Al. From the diffraction pattern, it is identified that the interface planes (indicated by the yellow dotted lines) are (002)Al2Cu and (002)Al, and these two planes have a deviation angle of ~2.5°. The interface plane is thus composed of (001)Al2Cu||(001)Al terrace and steps. The other interface plane is identified in Figs. 5 c and d (obtained under 4.9° sample tilt), where the beam direction is parallel to [311]Al2Cu and [112]Al. The overlapped diffraction spots in Fig. 5d are associated with (121)Al2Cu and (111)Al, while the interface plane (indicated by the yellow dotted lines) is deviated ~2–3° from the parallel planes. This suggested that interface plane could be serrated, composing of (121)Al2Cu||(111)Al terrace and steps. In association with variant II OR, the interface boundary plane is identified in Figs. 5 e and f (obtained under 5.6° sample tilt). The diffraction pattern from two phases is obtained along [423]Al2Cu and [111]Al. It is noticed that the interface planes (indicated by the yellow dotted lines) are (24 0)Al2Cu and (22 0)Al, and these two planes are nearly parallel with a deviation angle of ~6°. Thus the interface should comprise (12 0)Al2Cu||(110)Al terrace and steps. HRTEM characterization further confirmed this hypothesis. Fig. 5g shows a terraced (001)Al2Cu||(001)Al interface, and Fig. 5h shows a terraced (12 0)Al2Cu||(110)Al interface.
Corresponding to the crystallography of these interfaces, we constructed atomistic models of these terraces (see Table 2 for model parameters). In the (001)Al2Cu||(001)Al interface of variant I, the misfit strains (εm) are 5.5% in the two orthogonal directions, [100]Al2Cu||[130]Al and [010]Al2Cu||[310]Al directions. Two interfaces are examined with respect to the terminated atomic plane in Al2Cu. Fig. 6a shows two initial structures, the top image shows atomic structure of the interface with Cu terminated plane and the bottom one shows atomic structure of the interface with Al terminated plane. Relaxing interface structures was conducted by molecular statics method [48,49] with the empirical interatomic potentials for Cu, Al, and Al2Cu [50–52]. Atomistic simulations revealed that both interfaces are semicoherent. The interface with the Cu-terminated plane has lower formation energy of 666 mJ/m2. The relaxed interface structure with Cu terminated plane in Al2Cu is shown in Figs. 6 b and c. Atoms in Figs. 6 b and c are colored by their displacement magnitude with respect to the unrelaxed structure. According to atomistically informed Frank-Bilby theory [53], two sets of interface dislocations are identified in the relaxed interface. Their lines are parallel to [120]Al2Cu||[110]Al and [210]Al2Cu||[110]Al, and the average spacing between interface dislocations are measured to be L = 4.05 nm (Fig. 6b). Their Burgers → vectors are then calculated to be bm = ½[110]Al and ½[110]Al according to Frank-Bilby theory [53] where the reference lattice of the interface takes the same lattice as that of {001}Al plane. Fig. 6c shows the relaxed interface structure viewed along the direction of [120]Al2Cu||[110]Al (indicated in Fig. 6b). For the interface plane of (121)Al2Cu and (111)Al, the misfit strains are 0.6% and 2.6% along [111]Al2Cu||[121]Al and [7 19]Al2Cu||[101]Al directions, respectively. Atomistic simulations show that this semi-coherent interface has the interface formation energy, 443 mJ/m2. The (12 0)Al2Cu||(110)Al interface associated with variant II has lattice mismatches of 4.1% and 9.4% along [001]Al2Cu||[111]Al and [210]Al2Cu||[112 ]Al directions, respectively. The interface has high formation energy of 1022 mJ/m2. Thus, the variant selection during laser modification (variant I prevails over variant II in experiments) is ascribed to the low formation energy of the interfaces. Two interfaces associated with variant I have lower formation energy, 443 mJ/m2 for the {211}Al2Cu||{111}Al interface and 666 mJ/m2 for (001) Al2Cu||{001}Al interface, compared with the {120}Al2Cu||{110}Al interface, 1022 mJ/m2, associated with variant II.
4. Discussion Here we discuss possible ORs with respect to the basic parallel element 174
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Fig. 5. Interface boundaries in Al-Al2Cu eutectic. (a,b) (001)Al2Cu||(001)Al interface boundary in variant I OR and the corresponding diffraction pattern from two phases. (c,d) (121)Al2Cu||(111)Al interface boundary in variant I OR and the corresponding diffraction pattern from two phases. (e,f) (12 0)Al2Cu||(110)Al interface boundary in variant II OR and the corresponding diffraction pattern from two phases. (g) HRTEM image of a terraced (001)Al2Cu||(001)Al interface boundary. (h) HRTEM image of a terraced (12 0)Al2Cu||(110)Al interface boundary.
of {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al. In the basic parallel relationship, the direction of 〈120〉Al2Cu or 〈110〉Al, should be a direction contained in the family of {211}Al2Cu or {111}Al planes, respectively. If we choose [120]Al2Cu||[110]Al, there are four possible parallel pairs between the planes of {211}Al2Cu and {111}Al, which are (211)Al2Cu||(111)Al, (211)Al2Cu||(111)Al, (2 11)Al2Cu||(111)Al and (2 11)Al2Cu||(111)Al. There are four equal 〈120〉 axes in a C16 structure and six equal 〈110〉 axes in an fcc structure. Thus, there are 24 (4 × 6) possible parallel pairs for the relationship of 〈120〉Al2Cu||〈011〉Al, such as [120]Al2Cu||[110]Al or [120]Al2Cu||[110]Al or [210]Al2Cu||[110]Al and so on. Finally, there are 96 (24 × 4) possible pairs for the basic OR of {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al. We examined all the 96 possible pairs and found the three planes in α-Al which are parallel to (100)Al2Cu, (010)Al2Cu and (001)Al2Cu in each pair. The 96 possible pairs of ORs can be equally classified into two groups, one group has relationships of {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, {100}Al2Cu||{130}Al, {010}Al2Cu||{310}Al and (001)Al2Cu||{001}Al, same as the variant I OR observed in Figs. 3a and 4. A representative OR from group one (variant I) is shown in the simulated stereographic projection graph (Fig. 7a). The other group has the relationships of {211}Al2Cu||{111}Al, {120}Al2Cu||{110}Al, {100}Al2Cu||{211}Al,
{010}Al2Cu||{011}Al and (001)Al2Cu||{111}Al, same as the observation in Fig. 3b. A representative OR from group two (variant II) is shown in Fig. 7b. In Fig. 7, the blue squares and red triangles stand for planes from Al and Al2Cu crystals, respectively. It is noticed that another 12 or 11 pairs planes in variant I or II, respectively, are nearly parallel with the deviation angle < 5°. These parallel pairs are shown in Fig. 7 and are listed in Table 1, which establishes a database for the parallel relationships in the two variants. Therefore, the basic OR can be generally described by {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈011〉Al. A third parallel element (for example (001)Al2Cu||{001}Al) is necessary to precisely define the OR of αAl/θ-Al2Cu eutectic. The difference between two variants was frequently neglected in previous studies because of the common parallel planes and directions in the two variants. The existence of these two variants is due to the lower symmetry of bct structured θ-Al2Cu crystal in comparison with fcc structure of α-Al. In the studies of Davies [29] and Cantor [31], they defined a (001)Al2Cu parallel to (001)Al relationship together with {121}Al2Cu||{111}Al and 〈210〉Al2Cu||〈011〉Al, hence the relationship they observed is variant I. In recent studies using EBSD technique [32–35], although the ORs are claimed as (211)Al2Cu||{111}Al and 175
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Fig. 6. Atomic structure of the {001}Al2Cu||{001}Al interface. (a) Unrelaxed interfaces with different terminates- top one with Cu-terminate and the bottom with Alterminate. (b) Relaxed interface structure of {001}Al||{001}Al2Cu (Cu terminated Al2Cu), and (c) Relaxed interface structure of {001}Al||{001}Al2Cu viewed along the direction of [120]Al2Cu||[110]Al. Atoms in 6b and 6c are colored by their displacements with respect to the unrelaxed structure.
[120]Al2Cu||〈011〉Al or same with “Beta 6”, a third parallel element is always neglected which is necessary to define the real OR. From overlap pole figures of Figs. 3 and 4, it can be seen that in variant I each of the four equal {111}Al planes is always close or parallel to a {211}Al2Cu
plane (shown in Figs. 3a and 4, left pole figures). However, in variant II, there is at least one {111}Al plane that is far away from any {211}Al2Cu plane (shown in Fig. 3b, left pole figures). Therefore, the two variants can be distinguished with the feature of overlap pole figures of
Fig. 7. Stereographic projection of low-index planes from α-Al (blue squares) and θ-Al2Cu (red triangles), showing all the parallel planes (deviations of less than ~10°) in (a) variant I OR and (b) variant II OR. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 176
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Table 1 Derivative parallel planes from two variants in the basic OR family of {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al. Variants
Derivative parallel planes (100), (010), (001) planes of Al2Cu
Variant I [210]Al2Cu||[110]Al (12 1)Al2Cu||(111)Al
Deviations of < 5°
(100)Al2Cu||(13 0)Al
(110)Al2Cu||(210)Al, (111)Al2Cu||(313)Al
(010)Al2Cu||(3 10)Al (~4.5°)
(121)Al2Cu||(33 2)Al, (121)Al2Cu||(201)Al
(001)Al2Cu||(001)Al (~5°)
(211)Al2Cu||(111)Al, (211)Al2Cu||(111)Al (112)Al2Cu||(113 )Al, (3 10)Al2Cu||(010)Al (13 0)Al2Cu||(100)Al, (13 2)Al2Cu||(101)Al (3 21)Al2Cu||(131)Al, (3 12 )Al2Cu||(011)Al
Variant II [210]Al2Cu||[110]Al (121)Al2Cu||(111)Al
(100)Al2Cu||(121)Al (~5°)
(12 0)Al2Cu||(113 )Al, (12 1)Al2Cu||(001)Al
(010)Al2Cu||(15 , 2 ,20)Al
(211)Al2Cu||(131)Al, (211)Al2Cu||(311)Al
(~9° away of (101)Al)
(121)Al2Cu||(301)Al, (112 )Al2Cu||(311)Al
(001)Al2Cu||(3 32 )Al
(111)Al2Cu||(100)Al, (13 0)Al2Cu||(313 )Al
(~10° away of (111)Al)
(321)Al2Cu||(210)Al
electron microscopy was performed at the Michigan Center for Materials Characterization at University of Michigan. Atomistic simulations were conducted at the Holland Computing Center (HCC), which is a high performance computing resource for the University of Nebraska System.
Table 2 Model parameters used in the atomistic model of three semi-coherent α-Al/θAl2Cu interfaces and their formation energy. Variant I - IP I Al2Cu||Al
Variant I - IP II Al2Cu||Al
Variant II Al2Cu||Al
Y-normal to interface
(001) (001)
(121) (111)
[100] [130]
[111] [121]
(12 0) (110) [001] [111]
References
X Z
[010] [310] 666
[7 19 ] [101] 443
[210] [112 ] 1022
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Interface energy (mJ/m2)
{211}Al2Cu and {111}Al. For example, Li et al. [32] showed several overlap pole figures that were displayed from Al-Al2Cu eutectic solidified under various magnetic field intensities. The overlap pole figures of (211)Al2Cu and (111)Al from samples with 0 T, 2 T, 12 T magnetic field have same feature as that of variant I and the overlap pole figures from 6 T sample has same feature as that of variant II (Fig. 4 in Ref. [32]). Although they claimed all the ORs are equal and same as the “Beta 6” OR (variant I), the OR under 6 T magnetic field which belongs to variant II is actually different with “Beta 6”. 5. Conclusions The ORs in as-cast and laser-remelted Al-Al2Cu eutectics appear to be independent of inter-lamellar spacing. The existence of the two variants is due to the low symmetry of bct structured Al2Cu crystal. The characteristic OR is {211}Al2Cu||{111}Al and 〈120〉Al2Cu||〈110〉Al with two variants. Variant I is {211}Al2Cu||{111}Al, 〈120〉Al2Cu||〈110〉Al and (001)Al2Cu||{001}Al. There are two kinds of interface planes associate with variant I, (001)Al2Cu||{001}Al and {211}Al2Cu||{111}Al. Variant 2 is {211}Al2Cu||{111}Al, 〈120〉Al2Cu||〈110〉Al and (001)Al2Cu||{111}Al. The interface plane in variant II is {120}Al2Cu||{110}Al. It is noted that variant I OR is prevailed over variant II as the interlamellar spacing is reduced to nanometers via laser remelting due to the higher formation energy of the interface {120}Al2Cu||{110}Al. A comprehensive analysis, supported by atomistic modeling, of the crystallographic OR between two phases and distribution of OR variants across length scales will be helpful in understanding the active slip systems and stress-strain response of these eutectic composites. Acknowledgements This research is sponsored by DOE, Office of Science, Office of Basic Energy Sciences with the grant number of DE-SC0016808. Authors acknowledge assistance of Q. Lei, B. P. Ramakrishnan, and J. Mazumder at University of Michigan in material synthesis and laser treatment. The 177
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