Boundary plane distribution for Σ13 grain boundaries in magnesium

Andriy Ostapovets a,b,n, Peter Molnár a, Pavel Lejček a

a Institute of Physics of ASCR, Na Slovance 2, 18221 Prague 8, Czech Republicb Central European Institute of Technology, Institute of Physics of Materials, ASCR (CEITEC-IPM), Žižkova 22, 61662 Brno, Czech Republic

a r t i c l e i n f o

Article history:Received 19 August 2014Accepted 29 August 2014Available online 6 September 2014

Keywords:MagnesiumGrain boundariesCSLGrain boundary plane

a b s t r a c t

Grain boundary plane distribution is analyzed for the Σ13 coincident site lattice grain boundaries inmagnesium. These boundaries are relatively frequent in materials with hexagonal structure. It wasshown that the most frequent boundary plane is (0 0 0 1) basal plane. The experimental data obtained bystereological approach are in the agreement with the grain boundary energies obtained by atomisticcalculations.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Magnesium is biodegradable material which is used e.g. forproduction of implants [1]. However, its application is limited dueto very high dissolution rate and thus to production of hydrogen inthe human body. Grain boundary (GB) engineering can be poten-tially considered as a way how to control the dissolution rate. It isoften accepted that presence of some special kinds of grainboundaries improves properties of materials. For instance, presenceof coincident site lattice (CSL) boundaries can improve cracking andcorrosion resistance [2,3], compared to non-coincidence bound-aries. These properties can be useful for the improvement ofmagnesium based materials. Hereby, study of GB properties isactual task of material science. However, the characterization ofthe grain boundary as CSL is based only on the geometricalconsideration and does not take into account any physical aspectof the boundary [4]. The presence of CSL is dependent only on themisorientation between crystals on both sides of the grain bound-ary. However, misorientation represents only three of five macro-scopic parameters characterizing GB. The last two parametersdescribe the orientation of the grain boundary plane.

In hexagonal close packed (hcp) materials, the CSL boundarieswere studied for example in zinc coatings [5] and also in atitanium alloy [6]. Comparatively high numbers of the Σ13 andΣ15 boundaries were reported [7,8] in connection to 301 misor-ientation maximum in deformed magnesium. These studies implythat CSL can have special properties. On the other hand, changes ofthe grain boundary plane at constant misorientation can also

significantly change GB properties [9]. As far as we know, onlylimited number of papers is devoted to investigation of GB planedistributions in hexagonal materials. Five-parameter GB distribu-tions were reported for titanium alloy in [10] and for WC–Cocomposites in [11]. Faceting–roughening transitions of CSL bound-aries in zinc were also studied in [12,13]. However, there is noinformation about GB planes distributions in magnesium.

The aim of the present paper is to report the grain boundaryplane distributions for Σ13 grain boundaries in magnesium todemonstrate GB variability associated with the same Σ value. TheΣ13 boundary was selected due to its “true” CSL nature, which isindependent on c/a ratio of hcp lattice. Besides, Σ13 GB arerelatively frequent because their misorientation (27.81 about[0 0 0 1] axis) lies close to characteristic 301 in misorientationangle distribution in magnesium.

2. Materials and methods

Sample was cut from commercially pure magnesium (99.97wt% of Mg) and was processed by equal channel angular pressing(ECAP) in order to decrease the grain size and increase the amountof grain boundaries. Four ECAP passes were applied to the sampleusing route A at room temperature with back pressure of 350 MPa.Then, the sample was annealed at 200 1C during 30 min in order torelax internal stresses and to get more equilibrium grain bound-aries. The microstructure was strongly inhomogeneous after ECAP.It contained regions with fine grains (grain size �3 μm) as well asregions of larger grains (�33 μm) with high dislocation density. Asignificant amount of twins was also present. The microstructureafter annealing is represented by equiaxed grains with the averagegrain size of about 7 μm. Series of the EBSD maps were collected

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Materials Letters

http://dx.doi.org/10.1016/j.matlet.2014.08.1520167-577X/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author:. Tel.: þ420 266052896; fax: þ420 286890277.E-mail address: ostapov@fzu.cz (A. Ostapovets).

Materials Letters 137 (2014) 102–105

from three mutually perpendicular faces of the sample in order toeliminate texture influence on the boundary plane evaluation.

GB plane distributions were reconstructed by stereologicalmethod described in Ref. [14]. The method does not providedetailed crystallographic information on specific boundary, butprovides statistical information on the distribution of grain bound-ary planes.

3. Results and discussion

Fig. 1 shows EBSD maps from three faces of the sample togetherwith texture, misorientation angle distributions and distribution ofmisorientation axes. The sample has strong basal texture which istypical for magnesium processed by ECAP. The misorientationangle distributions (Fig. 1c) are obtained from identified grains.The experimental distributions significantly differ from the ran-dom one. Both correlated and uncorrelated distributions havecharacteristic maxima for misorientation angles of about 301. Twinmaximum near angles about 861 is low in our data, demonstratingrelatively small number of twin boundaries. Good coincidencebetween correlated and uncorrelated distributions in Fig. 1creveals an important role of observed basal texture in formationof 301 maximum.

Totally, about 69 thousands grain boundary segments are presentin all collected maps. Brandon criterion [15] in the formΔθo151=

ffiffiffiffiΣ

p

was used for selection of Σ13 boundaries from experimental dataset.Here, Δθ is the minimal angle between actual misorientation andexact CSL misorientation. There are 400 segments of the Σ13 grainboundaries (0.6% of total population) in the investigated boundary set.The fraction of Σ13 is much lower than the height of 301 maximumindicating that lot of the boundaries is outside of Brandon criterion.The misorientation axes distribution is shown in Fig. 1d for misor-ientation angles near 301. There is much more uniform distribution ofmisorientation axes in our annealed sample in contrast to thedistribution reported in [7] for ECAPed single crystal. However, weakgrouping of misorientation is still present around the [0 0 0 1] axis(near Σ13 misorientation) as well as around the ½2 1 1 0� axis (nearΣ15 misorientation).

Fig. 2a presents the grain boundary plane distribution for Σ13boundaries reconstructed by stereological method. The maximumof distribution is observed for (0 0 0 1) plane (point A in Fig. 2a).Lower maxima are also observed for 7 5 2 0

� �planes (point B).

Fig. 2b shows positions of special symmetry types of Σ13 grainboundaries. The diagram was generated in GBToolbox [16]. Thecomparison of Fig. 2a and b leads to conclusion that twist boundariesare the most frequent ones. The GBs with 7 5 2 0

� �planes are

symmetric tilt boundaries. The AB line in Fig. 3a contains so-calledimproper quasi-symmetric GB’s [17,18]. These GBs have symmetricallyequivalent planes on both sides of the boundary. However, the grainboundary plane is not the mirror plane in this case, in contrast toproper symmetrical GB.

Fig. 1. (a) Typical EBSD maps obtained from ND, ED and TD faces of the annealed sample. The Σ13 grain boundaries are designated by thick black lines; (b) (0 0 0 1) and1 0 1 0

� �pole figures for texture obtained from ND, ED and TD faces; (c) correlated, uncorrelated and random misorientation distributions for studied sample;

(d) distribution of misorientation axes for the grain boundaries with misorientations 301751 in equal area projection.

A. Ostapovets et al. / Materials Letters 137 (2014) 102–105 103

The stereological method does not allow to perform reliablequantitative analysis for low statistics. However, it can be used forqualitative description and for indicating of pronounced maximaon the GB plane distribution. This possibility is supported bydistribution of twin boundary planes (Fig. 2c). The main maximumis observed around 1 0 1 2

n oplane in agreement with expecta-

tion, despite the very low statistics (only 76 twin boundaries wereanalyzed).

In general, development of the GB plane distributions duringannealing is related to GB energy. However, some features ofdistribution can be also determined by the thrust of the system toincrease the rate of the Gibbs energy reduction [12]. Fig. 3 showsvariation of energy for the Σ13 grain boundaries with GB planeslocated along AB line in Fig. 2a and b. The energies were obtainedfrom atomistic calculations in LAMMPS [19] using the Sun EAMpotential [20] for magnesium. The lowest minimum correspondsto (0 0 0 1) twist boundary; the 7 5 2 0

� �boundaries are located

in higher energy minimum. The frequencies of GB planes (Fig. 2a)vary inversely to GB energy, similarly to results reported in [9,21]for other materials. Such behavior can serve as indirect confirma-tion that reconstructed GB plane distribution is realistic and thatGBs are equilibrated during annealing. Fig. 3 demonstrates that GBenergies vary about 2.5 times relatively to (0 0 0 1) grain boundarydepending on the grain boundary plane. Let us emphasize that thisvariation exists for constant misorientation and thus, constant Σvalue. Consequently, the CSL GB with the same Σ, but different GBplanes can possess different properties. This fact makes difficult

the straightforward relationship between frequency of CSL bound-aries in the sample and their properties and demonstrates neces-sity to consider all five macroscopic GB parameters.

4. Conclusions

Grain boundary plane distribution was examined for the Σ13grain boundaries in magnesium by stereological method. It wasshown that the most frequent boundaries are twist ones on the(0 0 0 1) plane. Symmetric grain boundaries with the f7 5 2 0gplane are less frequent; however, they are also present in thedistribution.

The grain boundary plane frequencies are inversely correlatedwith the grain boundary energy. The grain boundary with mini-mum energy is the most frequent (0 0 0 1) grain boundary.

Energy of the Σ13 grain boundaries varies significantly depend-ing on the grain boundary plane. The pronounced dependencedemonstrates insufficiency of the grain boundary characterizationby the Σ value only.

Acknowledgements

The work was supported by Czech Science Foundation (P108/12/P054). AO also acknowledges the support of the Ministry ofEducation, Youth and Sports of the Czech Republic, project no.CZ.1.07/2.3.00/30.0063. PL acknowledges the Czech Science Foun-dation (Grant P108/12/G043).

We are also grateful to Dr. Adam Morawiec and KrzysztofGlowinski for useful discussion.

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Fig. 3. Variation of GB energy with GB plane for grain boundaries located along lineAB (Fig. 2a). The GB in point A is twist boundary, the GB in point B is propersymmetrical tilt boundary, the boundaries between them are improper quasi-symmetric boundaries.

Fig. 2. (a) Stereographic projection of GB planes distribution for Σ13 (27.81 [0 0 0 1]) grain boundaries. The intensities are in multiples of random distribution (MRD);(b) Stereographic projection with special kinds of Σ13 grain boundaries: blue—tilt GBs, black—symmetric tilt GBs, red—twist GBs, green—improper quasi-symmetric GBs;(c) GB plane distribution for tensile twin boundaries (86.31 [0 0 0 1]), magenta points indicate positions of the f1 0 1 2g planes. (For interpretation of the references to colorin this figure legend, the reader is referred to the web version of this article.)

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