ANALYSIS OF NEAR-COINCIDENCE SITE LATTICE BOUNDARY FREQUENCY IN AZ31 MAGNESIUM ALLOY. Andriy Ostapovets, Peter Molnár, Aleš Jäger, Pavel Lejček

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1 ANALYSIS OF NEAR-COINCIDENCE SITE LATTICE BOUNDARY FREQUENCY IN AZ31 MAGNESIUM ALLOY Andriy Ostapovets, Peter Molnár, Aleš Jäger, Pavel Lejček Institute of Physics ASCR, Na Slovance 2, Prague, Czech Republic, Abstract The grain boundary misorientation distribution and distribution of coincident site lattice boundaries are reported for the case of magnesium-based AZ31 alloy processed by equal-channel angular pressing. The experimental data were collected by electron backscatter diffraction. It is shown that the most frequent Σ15b and Σ17a coincident site lattice boundaries correspond to twin boundaries. Other frequent coincident site lattice boundaries are Σ15a and Σ13a and correspond to the local maximum around 30 on grain misorientation distribution. Keywords: Equal-channel angular pressing, electron back scattered diffraction, coincident site lattice 1. INTRODUCTION Concept of coincidence site lattice (CSL) is often used for classification of grain boundaries because it allows prediction of boundaries, which potentially have special properties. The CSL model is geometrical construction consisted of coincidence sites of two superimposed lattices [1]. A grain boundary can be characterized by CSL generated from lattices on both sides of boundary. The CSL misorientations are characterized by the parameter Σ, which is equal to the ratio of CSL and crystal unit cell volumes. In comparison with cubic materials, hexagonal ones have some specifics, e.g. the smallest value of Σ is 7 in contrast to 3 in cubic materials, and even Σ values are also possible. The CSL boundaries often have low energy [1]. It is also usually accepted that CSL boundaries can improve properties of materials because they have better cracking and corrosion resistance [2-4] than random boundaries. In the case of materials with hexagonal structure ideal coincidence can only exist for rational values of squared axial ratio (c/a) 2, except for several misorientations obtained by rotation about < 0001> axis. The sets of CSL (Σ) are different for different axial ratios c/a. In practice, near-csl configurations are considered for the case of hexagonal materials i.e. experimental axis ratio is approximated by close rational value [5]. There is no CSL with low Σ and misorientation axis different from < 0001> for magnesium and its alloys with c/a= Hence the near- CSL boundaries are considered which are generated by lattices with close values of c/a. Previously authors reported distribution of CSL boundaries in pure magnesium single crystals processed by equal-channel angular pressing (ECAP) [6]. It was suggested that frequent Σ13a and Σ15a boundaries can correspond to the typically maximum observed around 30 on grain misorientation distribution. The evolution of grain boundary misorientation distribution and CSL boundary distribution during ECAP was modeled in paper [7]. The misorientation scheme was proposed which is based on possible interaction of dislocations belonging to different slip systems. It produces specific grain misorientations depending on relative activity of slip systems. In general the including of misorientation scheme in the visco-plastic self-consistent model improve the model prediction. However the 30 misorientation maximum containing large number of CSL boundaries was not reproduced precisely in [7]. This can be connected with properties of CSL boundaries which were not included in the model. Hence the further study of CSL boundaries and their properties can give new information about material behaviour.

2 The aim of the present work is to report grain boundary misorientation distribution and distribution of CSL boundaries in Mg-based AZ31 alloy processed by ECAP. The frequency of CSL boundaries is discussed. Deviations from CSL are analyzed for the most frequent CSL boundaries which allows to elucidate their prospective special properties. 2. METHODS AND MATERIALS 2.1 Experimental AZ31 alloy with nominal composition Mg-3wt%Al-1wt%Zn was used for our research. Billets with dimensions mm were machined from as-rolled plate. The ECAP die with inner angle of Φ=90 and outer anle Ψ=45 was used. The billets were processed by two ECAP passes at 200 C using route A. The route A does not include rotations about longitudinal axis of the sample. The billets were inserted into pre-heated die and exposed during 3 min in the die before extrusion. The electron backscatter diffraction (EBSD) data was collected by Dual-Beam microscope FEI Quanta 3D FEG. The TSL 5.3 OIM analysis software was used in order to extract data about grain boundary misorientations. Additional analyses were performed in order to obtain CSL boundary frequency and distribution of boundaries near to CSL configurations. 2.2 Methods of analysis The list of CSL and near-csl boundaries for AZ31 alloy is presented in Table 1. Procedure described in [4] is used to obtain frequency of CSL boundaries from experimental data. Due to symmetry each grain boundary misorientation can be described by a set of different axis/angle pairs. In order to avoid ambiguity the only pair of the smallest possible misorientation angle and corresponding axis lying in the main crystallographic triangle is considered. Brandon criterion is used to define possible deviation Δθ from CSL configuration [8]: o Δθ <15 Σ (1) Table 1. CSL and near-csl misorientations for AZ31 (c/a=1.624) axis angle c/a 1 any 0 any any a 27.8 any 13b a b a b c a b any a b c d a b

3 number fraction , Brno, Czech Republic, EU For each Σ there is distribution of grain boundaries, which satisfy Brandon criterion (1). These boundaries are slightly inclined from CSL or near-csl configuration listed in Table 1. It is interesting to study distribution of Δθ for each Σ. One can expect that this distribution is not uniform if considered CSL boundary has special properties. The maximum has to be observed for small Δθ angles if trend exists to set boundary in the exact CSL configuration, for instance due to its low energy. It is necessary to know the random distribution in order to compare it with experimental data. The random distribution around CSL configuration can be found in a similar way as it was done for random misorientation angle distributions [9]. The brief description of the approach is following. It is convenient to perform the analysis in Rodrigues space. In this space rotations are presented by Rodrigues vectors r: r = ntan( ω / 2) (2) where n is rotation axis and ω is rotation angle. The important properties of Rodrigues space is that all points that are at the same angular distance from r as from identity rotation 0 lie on two planes perpendicular to r at the distances from 0 equal to tan(ω/4) and cot(ω/4). For objects with symmetry each orientation is represented by a set of symmetrically equivalent points. A polyhedron filled with points that are closer to 0 than to any other point symmetrically equivalent to 0 is called the fundamental zone. If misorientation distribution is uniform, the number of misorientations with angle ω is proportional to the area part of sphere with radius tan(ω/2) inside fundamental zone. In the case if the CSL structure is taken as reference misorientation, the fundamental zone can be constructed by consideration of rotations r Σ, which correspond to rotation matrix (S i M Σ S j -1 )M Σ 1, where S i is matrix of symmetry operation, M Σ is rotation matrix for CSL configuration. In this stage it is better to use matrix representation for calculation of r Σ in order to avoid uncertainty. It is due to the fact that some of S i represent 180 degrees rotations and it is presented in Rodrigues space by vector of infinite length. 3. RESULTS AND DISCUSSION The diagram on Fig.1 shows misorientation angle distribution for AZ31 alloy after two ECAP passes at 200. The distribution has three maxima. The first one corresponds to low angle grain boundaries with misorientations up to 5, the second maximum is observed at misorientations about 30 and the third maximum occurs at misorientations about 85. The main contribution to the last maximum is from {1012} twin boundaries with misorientation 86 about < 1210 > axis (See Table. 1). 0,10 0,05 0, misorientation angle, deg Fig.1 Misorientation angle distribution in AZ31 alloy after 2 ECAP passes at 200 C.

4 CSL boundary distribution is shown in Fig2(a). The most frequent Σ15b and Σ17a correspond to {1012}twin boundaries. These CSL are close to the twinning configuration and are misoriented ~0.45 relative to each other. Both are produced by lattices with different c/a ratio, close to that c/a=1.624 of magnesium. The next frequent CSL boundaries are Σ15a, Σ13a, Σ13b, Σ7 and Σ18b. In contrast to the previously reported case of Mg single crystals [6,7] the portion of Σ15a boundaries are larger than Σ13a boundaries. Both Σ15a and Σ13a correspond to the 30 maximum in the misorientation angle distribution and they remarkably contribute to this maximum. The Σ13b boundaries lie inside 85 maximum together with twin boundaries. Relatively high frequency of Σ18b boundaries can be explained if one supposes that they occur from deformed twin boundaries. The twin boundaries always contain large number of defects after course of intensive deformation through ECAP. It can be concluded from EBSD, which show that twin boundaries are not straight-line. Therefore they are often inclined from their ideal orientation. Consequently some of twin boundaries can have relatively large inclination and reach the Σ18b configuration. The frequency of Σ7 boundary is noticeably smaller in polycrystalline AZ31 than in magnesium single crystals. Fig.2 (a) Number fraction of CSL bounaries in AZ31 alloy after 2 ECAP passes at 200 C. The distribution of boundaries inclined from CSL by angle Δθ, which satisfied Brandon criterion. The red and black lines represent uniform random distribution and experimental distribution, respectively for (b) Σ13a (b), (c) Σ15 and (d) Σ17a. The curves are normalized in a way that area under curve is equal to 1. The CSL boundaries often have special properties (e.g. low energy) in comparison with random boundaries. In this case it can be expected that smaller deviation from exact CSL configuration are more probable than higher ones. The Figs. 2(b-d) shows normalized frequency of grain boundary occurrence versus inclination angle Δθ from CSL configuration for several CSL boundaries. The value of Δθ=0 corresponds to the exact CSL configuration. Red curves show the random distribution of inclinations and the black curves correspond to the experimental data. The data are normalized in such a way that area under curves is equal to 1. The trend to reorient boundaries to the CSL position is observed for Σ15a and Σ17a boundaries because experimental curves lie higher than theoretical random curves at small Δθ for these CSL. However the

5 experimental curve practically coincides with curve for random distribution at small Δθ angles in the case of Σ13a boundary. The maximum of black curve is observed at Δθ=2.2 in Fig.2(b). It means that preferable misorientation angle of Σ13a boundaries is different from This is unexpected result because Σ13a has < 0001>misorientation axis and hence belong to the true CSL boundary with coincidence independent on c/a ratio of lattice. 4. CONCLUSIONS The analysis of CSL boundary frequency was performed for AZ31 magnesium alloy processed by ECAP at 200 C by two passes. It was found that the most frequent CSL are Σ15b and Σ17a twin boundaries followed by Σ15a, Σ13a, Σ13b, Σ7 and Σ18b boundaries. The frequency of Σ7 and Σ13a boundaries is lower in comparison with the previously reported case of magnesium single crystals. Frequencies of the Σ17a and Σ15a boundaries are increased with decreasing deviation angle Δθ from exact CSL configuration. However Σ13a has distribution close to the random one without preference of small Δθ angles. ACKNOWLEDGEMENT The financial support of the Academy of Sciences of Czech Republic (KAN ), Czech Science Foundation (P108/12/P054) and Grant Agency of AS CR ( IAA ) is gratefully acknowledged. REFERENCES [1] SUTTON, A.P., BALLUFFI, R.W. On geometric criteria for low interfacial energy. Acta Metallurgica, 1986, vol. 35, pp [2] THOMSON, C.B., RANDLE V. Fine tuning at Σ3n boundaries in nickel. Acta Materialia, 1997, vol. 45, p [3] KOBAYASHI, K., TSUREKAWA, S. WATANABE, T., PALUMBO, G. Grain boundary engineering for control of sulfur segregation-induced embrittlement in ultrafine-grained nickel. Scripta Materialia, 2010, vol. 62, p [4] VINCENT, G., BONASSO, N., LECOMTE, J.S., COLINET, B., GAY, B., ESLING, C. The relationship between the fracture toughness and grain boundary characteristics in hot-dip galvanized zinc coatings. Journal of Materials.Science, 2006, vol. 41, p [5] BONNET, R., COUSINEAU, E.D., WARRINGTON, H. Determination of near-coincident cells for hexagonal crystals. Related DSC lattices. Acta Crystallographica A, 1981, vol. 37, p [6] OSTAPOVETS, A., ŠEDÁ, P., JÄGER, A., LEJČEK, P. Characteristics of coincident site lattice grain boundaries developed during equal channel angular pressing of magnesium single crystals. Scripta Materialia, 2011, vol. 64, p [7] OSTAPOVETS, A., ŠEDÁ, P., JÄGER, A., LEJČEK P. New misorientation scheme for a visco-plastic selfconsistent model: Equal channel angular pressing of magnesium single crystals. International Journal of Plasticity, 2012, vol. 29, p [8] BRANDON, D.G. The structure of high-angle grain boundaries. Acta Metallurgica. 1966, vol. 14, p [9] MORAWIEC, A. Misorientation angle distribution of randomly oriented symmetric objects, Journal of Applied Crystallography, 1995, vol. 28, p