Deformation Microstructure Developed by Nanoindentation of a MAX Phase Ti2AlC

Yusuke Wada1,+1, Nobuaki Sekido1,+2, Takahito Ohmura2 and Kyosuke Yoshimi1

1Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan2National Institute for Materials Science, Tsukuba 305-0047, Japan

Deformation microstructure that developed during nanoindentation of a MAX phase Ti2AlC was characterized by the scanning probemicroscopy and the transmission electron microscopy. To investigate the plastic anisotropy, nanoindentation measurements were made on grainswith the normal parallel to h33�62i, h0001i, and h11�20i. The basal slip, f0001gh11�20i, was found to be predominant as the deformationmechanism for all the indentation directions. It was also indicated that, upon nanoindentation along h0001i and h11�20i, non-basal slips occurredunderneath the indenter. The slip system of the non-basal dislocations was identified to be ð�12�16Þ½1�211� by analyzing the dislocations.Furthermore, fine-scaled kink-bands were found to form underneath the residual impression. The formation of the kink-band was accompaniedby delamination, i.e., micro-cracking along the basal plane, suggesting that the delamination plays an important role for kink-band formation inTi2AlC. [doi:10.2320/matertrans.MBW201703]

(Received November 6, 2017; Accepted March 2, 2018; Published April 13, 2018)

Keywords: MAX phase, nanoindentation, deformation microstructure, kink band

1. Introduction

MAX phases are ternary compounds that have the formulaof Mn+1AXn, where n is 1 to 3, M is an early transition metal,A is an A-group element, and X is carbon or nitrogen.Recently, MAX phases have attracted a significant researchinterest because they exhibit an apparently contradictorycombination of metallic and ceramic properties.1) Forexample, a MAX phase Ti2AlC exhibits some metallic prop-erties such as high thermal and electrical conductivities2,3)

and good thermal shock resistance,4) as well as some ceramicproperties such as light weight, high stiffness5) and goodoxidation resistance.6) Due to these attracting properties,Ti2AlC is expected as a new type of light-weight, heat-resistant materials.7) Another potential application of Ti2AlCwould be a strengthening phase for TiAl based alloys,8) sinceTi2AlC is in equilibrium with TiAl in the Ti­Al­C ternarysystem.9)

The MAX phase is a hexagonal crystal that consists ofMn+1Xn and A-layers.10) For Ti2AlC, the Ti2C layer and theAl layer are alternatively stacking up along the c-axis. It hasbeen reported that the crystal structure of Ti2AlC is hP8 (P63/mmc: Cr2AlC-type) with the lattice parameters of a =0.3056 nm and c = 1.3623 nm.11) It has been documentedthat the basal slip is predominant as the deformationmechanism in MAX phase compounds, while the other slipsystems, i.e., non-basal slip, are hardly operative at roomtemperature.12,13) Thus, MAX phase alloys in a polycrystal-line form are brittle because the number of operative slipsystems is quite limited.10) However, it has been demonstratedthat ductility and toughness can be improved by texturedevelopments through thermo-mechanical treatments,14) andslip casting in a strong magnetic field.15)

Besides the basal slip, kink-band formation is known asanother deformation mechanism that can operate in MAXphase compounds at room temperature.10) Kink-bandformation is also observed in some hexagonal metals such

as Cd16) and Zn,17) mica,18) and Mg-LPSO phase.19) Althoughseveral models have been proposed to explain the formationof kink-bands, e.g., Hess-Barrett model17) and Frank-Strohmodel,20) the detail of the mechanism still remain unclear.It is well accepted that kink-band formation occurs whenthe basal slip was suppressed under a load applied parallel tothe basal plane.14) On the other hand, Tromas et al. reportedthat, based on the slip lines observed by the atomic forcemicroscopy (AFM), a non-basal slip was indicated to haveoccurred upon nanoindentation of a MAX phase Ti3SnC2 atroom temperature;21) although they did not identify its slipsystem. To take advantage of the plastic anisotropy, theknowledge on the kink formation mechanism and non-basalslip is inevitably necessary.

Recently, nanoindentation has become a common method-ology to characterize the mechanical behavior of smallvolumes.22,23) One advantage of this method is versatility toinvestigate the orientation dependence of plastic deformationbehavior without preparing a single crystal. Therefore inthis study, the anisotropy in the deformation behavior wasinvestigated by nanoindentation of a polycrystalline Ti2AlCalloy. The grain orientation was preliminarily investigatedby the electron backscatter diffraction (EBSD). The detaileddeformation behavior was examined by surface observationwith the scanning probe microscopy (SPM), and bydeformation microstructure observation with the transmissionelectron microscopy (TEM).

2. Experimental Procedure

Polycrystalline Ti2AlC alloys were prepared by sinteringpure elemental powders with the nominal composition ofTi­25Al­25C (at%). Ti powder (99.9%, <45 µm), Al powder(99.9%, <3 µm) and C powder (99.7%, <5µm) were mixedwith a rocking mill, followed by spark plasma sintering (SPS)at 1400°C for 20min under the pressure of 30MPa undervacuum (<10¹3 Pa). The sintered compacts were wrappedwith Ta foil, and annealed at 1500°C for 24 h under vacuum.

The sample for nanoindentation was prepared bymechanical polishing with SiC grinding papers, followed

+1Graduate Student, Tohoku University+2Corresponding author, E-mail: nobuaki.sekido.b7@tohoku.ac.jp

Materials Transactions, Vol. 59, No. 5 (2018) pp. 771 to 778©2018 The Japan Institute of Metals and Materials

by finishing with diamond and colloidal silica (40 nm)slurries. Nanoindentation measurements were performed bya Hysitron TI950 equipped with a Berkovich indenter. Themeasurements were conducted under the load-controlcondition with the constant loading rate of 50 µN/s to themaximum loads of 3mN and 10mN. The grains with thenormal parallel to h33�62i, h0001i, and h11�20i were foundby EBSD for nanoindentation measurements. The samplesurface topography was imaged by scanning the indenter tipwith the contact load of 1 µN, which is a scanning probemicroscopy (SPM) function equipped with the nanoindenter.The surface images were recorded before and after eachmeasurement.

Deformation microstructure developed by nanoindentationwas observed by the transmission electron microscopy(TEM) operated at 200 kV. TEM samples for the crosssectional observation of the residual impressions wereprepared by a focused ion beam (FIB) system. The originalsurface was protected by carbon deposition before FIBmilling. The foils were lifted out from the sample and fixedon a Cu-grid.

3. Results

Polycrystalline Ti2AlC alloys were successfully synthe-sized by SPS of high purity elemental materials, followed byannealing at 1500°C for 24 h.24) TEM observations revealedthat the dislocation density at the grain interior was as lowas 2 © 1011 (m¹2).24) In the MAX phases, the ð0001Þh11�20ibasal slip is considered as the dominantly operativedeformation mode.12,13) In this study, the crystal orientationwas measured by EBSD, and nanoindentation measurementswere conducted on grains with the normal parallel to h33�62i,h0001i and h11�20i. These indentation orientations areindicated on the standard stereographic triangle in Fig. 1.Figure 2 shows typical load-displacement curves by nano-indentation with the maximum load of 3mN. Several pop-ins,

i.e., discontinuous jumps during loading, have been observedfor all the indentation directions. It has been documentedthat pop-in events correspond to the onset of plasticdeformation within a dislocation-free small volume.25­28)

The present study focuses on the indentation plasticityfollowing the pop-in events. The effect of the indentationdirections on the plastic deformation behavior will bediscussed hereafter in terms of the surface topology and thedeformation microstructure.

3.1 Deformation by nanoindentation along h33�62iFigure 3(a) shows an SPM image around the residual

impression after a nanoindentation measurement with themaximum load of 10mN. In this study, the contrast in theSPM images represents the magnitude of the gradient ofthe surface asperity. The deformation band that consists ofa number of slip lines has developed from the impression.The deformation band extends toward ½1�100�, implying thatdislocation slip has potentially occurred on ð11�2nÞ planes.

Fig. 1 (a) Standard stereographic triangle for Ti2AlC. Solid circlesrepresent the indentation directions. (b) Schematic of the three indentationdirections along with the unit cell.

Fig. 2 Typical load-displacement curves for nanoindentation with themaximum load of 3mN. Pop-in events are indicated by arrows.

Fig. 3 (a) An SPM image around the residual impression after nano-indentation along h33�62i with the maximum load of 10mN, (b) the depthprofile across A­B (residual impression), and (c) the depth profile acrossC­D (deformation band).

Y. Wada, N. Sekido, T. Ohmura and K. Yoshimi772

Note that the basal slip is known as the predominantdeformation mechanism in the MAX phase compounds,and the trace of the basal plane on the surface coincides withthat direction. The depth profiles across the deformation bandare shown in Fig. 3(b) and (c). It is well known that thematerial around the contact area deforms either upward ordownward against the original surface, and the pattern ofsuch upward material flow is called “pile-up”, and the other“sink-in”.29) Figure 3(b) shows a depth profile over theresidual impression, and it clearly exhibits the occurrence of“pile-up” by indentation. In contrast, the depth profile acrossthe deformation band shows that the zone is depressed byseveral nanometers and no pile-up was observed on the edge.

Figure 4 shows bright-field TEM images of the crosssection of the impressions with the maximum loads of (a)3mN and (b) 10mN. The bold arrows represent the areaswhere the indenter was in contact during the measurements.Numerous dislocations have developed on (0001) in bothspecimens, suggesting that the basal slip was predominantas the deformation mechanism for nanoindentation alongh33�62i. Therefore, the deformation band developed on thesurface would be derived from the glide of a large number ofbasal dislocations.

Although no cracking was confirmed in the specimentested with the maximum load of 3mN, a crack along (0001),i.e., delamination, was observed at the point 200 nm beneaththe surface when the maximum load was 10mN as shown inFig. 4(b). A selected-area electron diffraction (SAED) patterntaken from the area around the crack indicates the occurrenceof several degree of in-plane rotation as shown in Fig. 4(c).This lattice rotation would be caused by the arrangement ofa number of basal dislocations, since non-basal dislocationswere not observed in this area. It is therefore speculated thatthe delamination along (0001) is another option to release theaccumulated strain in Ti2AlC.

3.2 Deformation by nanoindentation along h0001iFigure 5(a) shows an SPM image around the residual

impression with the maximum load of 10mN. Contrary toindentation along h33�62i, no slip lines or deformation bandswere observed on the surface around the residual impression.The depth profile across the residual impression is shown inFig. 5(b). The “pile-up” that developed at the edges of the

residual impression appears to be more sharply angulatedthan those of the other indentation directions.

Bright-field TEM images of the cross section of theimpression are shown in Fig. 6. The pile-up was not formedby nanoindentation with the maximum load of 3mN asshown in Fig. 6(a). On the other hand, a large pile-up wasformed by nanoindentation with the maximum load of10mN, accompanying the delamination along (0001) andbuckling, as shown in Fig. 6(b). SAED observations haveconfirmed that a large lattice rotation has developed nearthe buckle. Therefore, the large sized pile-up observed inthis direction was caused by delamination and kink-bandformation near the contact of the indenter. A similar kink-band formation has been observed by indentation of aTi3SiC2 thin film.30)

As shown in Fig. 6(b), dislocations were found to developon (0001). These dislocations are basal dislocations sincethey were out of contrast under the reflection vector ofg = 0008 (Fig. 6(c)). On the other hand, there were severaldislocations that were not on (0001) right beneath the contactof indenter, as indicated by the white arrows in Fig. 6(c).Since they exhibited a strong contrast under g = 0008, theBurgers vector of these non-basal dislocations contains c-axiscomponent.

The line vectors of the non-basal dislocation were analyzedby trace analysis. The trace analysis was done on the imagestaken from three zone axes as shown in Fig. 7: (a) ½2�1�10�,(b) ½8�4�41� and, (c) ½6�3�31�. Since the dislocation analyzed wascurved, we defined the dislocation line vector as the line that

Fig. 4 Bright-field TEM images of the cross sections of the impressions after nanoindentation along h33�62i with the maximum loads of(a) 3mN and (b) 10mN. The TEM images were taken under the reflection vector of g ¼ �1�120, and the bold arrows represent the areaswhere the indenter was in contact. (c) A selected-area electron diffraction (SAED) pattern taken from the area around the crack in (b).

Fig. 5 (a) An SPM image around the residual impression after nano-indentation along h0001i with the maximum load of 10mN. (b) The depthprofile across the residual impression (A­B).

Deformation Microstructure Developed by Nanoindentation of a MAX Phase Ti2AlC 773

connects the two ends of the dislocation. Note that, toenhance the reliability for the trace analysis, these imageswere taken from the exact zone axes (not in two-beamconditions). In addition, the dislocation was nearly edged-onwhen observed from the ½15�6�92� direction, and thisinformation is included in the following analysis. Figure 7(e)represents the result of the line vector analysis on the standardstereographic [0001] projection. Since the dislocation linevector lies on the slip plane of a glide dislocation, the slipplane can be identified by the intersection of the great circlesof the vector parallel to the projected dislocation line on eachimage. The point of intersection is determined as ð�36�320Þ.Considering that the analysis can contain some margin oferrors, the ð�12�16Þ plane, which is deviated by 3° from

ð�36�320Þ, is suggested to be a potential slip plane of thenon-basal dislocations.

3.3 Deformation by nanoindentation along h11�20iFigure 8(a) shows an SPM image around the residual

impression with the maximum load of 10mN. Similar to theindentation along h33�62i, the deformation band that extendstoward ½1�100� has developed from the residual impression.The occurrence of “pile-up” was confirmed as shown inFig. 8(b). The deformation band was depressed from theoriginal surface and no protrusion on the edge was observedas shown in Fig. 8(c). Compared to the indentation alongh33�62i, the deformation band was sharp and extended in alonger distance.

Fig. 6 Bright-field TEM images of the cross sections of the impressions after nanoindentation along h0001i with the maximum loads of(a) 3mN and (b) 10mN. The TEM images were taken under the reflection vector of g ¼ 1�100, and the black arrows indicate the basaldislocations. (c) Bright-field TEM image of the impression with the maximum load of 10mN under the reflection vector of g = 0008.The white arrows indicate the non-basal dislocations.

Fig. 7 The results of trace analysis for the slip plane of the non-basal dislocations. The TEM images were taken from the exact zone axes:(a) ½2�1�10�, (b) ½8�4�41� and (c) ½6�3�31�, as well as the corresponding SAED patterns. (d) ATEM micrograph showing the dislocation beingnearly edged-on observed from ½15�6�92�. (e) The summary for the line vector analysis on the standard stereographic [0001] projection.

Y. Wada, N. Sekido, T. Ohmura and K. Yoshimi774

Figure 9 shows TEM images of the cross section of theresidual impression with the maximum load of 3mN. Twodeformation bands denoted by A and B have developed asshown in Fig. 9(a). These deformation bands were fine-scaled; the width of the bands is approximately 200 nm orless. Besides, delamination along (0001) has occurred rightadjacent to the deformation bands. As will be discuss in detaillater, the deformation band A is a kink-band and B is adeformation twin.

Figure 9(b) shows an SAED pattern from the kink-bandand matrix, which indicates that development of thekink-band is accompanied by a lattice rotation of 5.2°.Figures 9(c) and (d) are magnified bright-field TEM imagesof the kink-band under the reflection vectors of g ¼ �1�120

and g ¼ 000�6, respectively. The dislocations forming thewall exhibit a strong contrast under the reflection vector ofg ¼ �1�120, as shown in Fig. 9(c), while they are out ofcontrast under g ¼ 000�6 as shown in Fig. 9(d). Therefore,the dislocation wall would be a kink-boundary composed ofthe basal dislocations. Figure 9(e) shows an HRTEM imageshowing the (0001) lattice fringes in the deformation band B.The rotation angles of the (0001) basal planes at theboundaries are too large to be explained by dislocation array.Therefore the deformation band B is believed to bedeformation twins, although its twinning system could notbe identified in this study.

Figure 10 shows bright-field TEM images of the crosssection of the residual impression with the maximum loadof 10mN. Two TEM samples with the foil normal of ½1�100�and [0001] were prepared by FIB as shown in Fig. 10(a).Figure 10(b) shows a bright-field TEM image under thereflection vector of g ¼ �1�120 from the ½1�100� zone axis.Numerous dislocations were found to develop on (0001),while few kink-bands were observed. That is, for nano-indentation with the maximum load of 10mN, dislocationslip is the predominant deformation mechanism rather thankink-band formation.

Figure 10(c) shows a bright-field TEM image under thereflection vector g ¼ �1�120 from the [0001] zone axis.Several arc-shaped dislocations are observed underneath the

residual impression. Since these dislocations are present on(0001), they were expected to be shear loop dislocations.Besides the shear loop dislocations on (0001), some non-basal dislocations are found to develop as indicated bya circle in Fig. 10(c). The Burgers vector b of thesedislocations was analyzed by the invisibility criterion. Adislocation is out of contrast when the reflection vector gand the Burgers vector of a dislocation b are perpendicular(i.e., g·b = 0). Therefore, if two reflections vectors (g1 andg2) that satisfy the invisible condition are found, the Burgersvector b can be determined by the following equation.

b k g1 � g2: ð1ÞFigures 10(d)­(f ) represent bright-field TEM images taken

under the reflection vectors of (d) g ¼ �1�120, (e) g ¼ 10�10

and (f ) g ¼ �2113. The dislocations show a strong contrastwhen imaged under g ¼ �1�120 as shown in Fig. 10(d), whilethey are out of contrast when imaged under g ¼ 10�10 and�2113, as shown in Fig. 10(e) and (f ). Therefore, the Burgersvector of the non-basal dislocations was identified to be½1�211�.

Fig. 8 (a) An SPM image around the residual impression after nano-indentation along h11�20i with the maximum load of 10mN, (b) the depthprofile across A­B (residual impression), and (c) the depth profile acrossC­D (deformation band).

Fig. 9 (a) Bright-field TEM images of the cross section of the impressionafter nanoindentation along h11�20i under the reflection vectors g ¼ �1�120.(b) An SAED pattern taken from the area around the deformation band Ain (a). Magnified images of the deformation band A (kink-band) imagedunder the reflection vectors of (c) g ¼ �1�120 and (d) g ¼ 000�6. (e) AnHRTEM image showing the (0001) lattice fringes in the deformationband B (deformation twin) taken from zone axis ½1�100�.

Deformation Microstructure Developed by Nanoindentation of a MAX Phase Ti2AlC 775

4. Discussion

4.1 Slip system of non-basal dislocationIt has been demonstrated that basal dislocations can easily

glide and multiply on (0001) in the MAX phases.12) Howeveronly few reports are available for the occurrence of non-basalslips at room temperature; i.e., it has been only indicatedqualitatively by AFM observations around the residualimpression of nanoindentation in Ti3SnC2.21) In this study,non-basal dislocations were observed in the specimensindented along h0001i and h11�20i. It is suggested that theslip plane is ð�12�16Þ from Fig. 7, and the Burgers vector ofthe dislocations is ½1�211� from Fig. 10. Although slip planeanalysis and Burgers vector analysis were performed ondifferent dislocations, the determined Burgers vector of½1�211� lies on ð�12�16Þ. In addition, rough estimation for theslip plane of the dislocation analyzed in Fig. 10 representsa reasonable agreement with the above results. That is,although only rough estimation was possible for the slipplane analysis for these dislocations because the dislocationlines are very short, it is indicated that the trace of theprojection line of the dislocations is roughly parallel to½�4�150� when viewed from [0001], and thus the slip plane canbe deduced from the cross product between ½�4�150� and theBurgers vector of ½1�211� to be ð�23�19Þ, which is only deviatedby 9° from ð�12�16Þ. Therefore, it is reasonable to assume thatthe slip system of the non-basal dislocations observed isð�12�16Þ½1�211� in Ti2AlC.

Figure 11 shows the atomic arrangement of the ð�12�16Þplane for Ti2AlC. There are two kinds of atomic layers for

ð�12�16Þ; (a) Ti­Al mixed layer, and (b) C layer, and theselayers are alternately stacked up as shown in Fig. 11(c).The determined Burgers vector of ½1�211� can be expressedby the summation of the fundamental translation vectors tobe ¹3a + c, which is indicated by the arrow in Fig. 11. Themagnitude of the Burgers vector is 1.6421 nm, which isabout 5 times longer than that of the basal dislocation(0.3056 nm). This means that the non-basal slip hardlyoccurs particularly at room temperature, because crackingcan precede the onset of the non-basal slip for conventionalmechanical tests on polycrystalline samples. On the otherhand, the present study has confirmed that the non-basalslip occurs at room temperature because cracking issuppressed by the presence of the hydrostatic pressureapplied underneath the indenter.

4.2 Kink formation mechanism underneath the indenterIn this study, a fine-scaled kink-band was found to develop

by nanoindentation along h11�20i. The kink-boundary wasformed approximately 130 nm beneath the surface, asshown in Fig. 9(c). Assuming that the kink-boundary wascomposed of an array of the basal dislocations, the followingrelationship is established.31)

b

D¼ 2 sin

ª

2: ð2Þ

Here, b is the magnitude of Burgers vector, D is the meandistance of dislocations, and ª is the lattice rotation angle atthe kink-boundary. The mean distance of the dislocations wasestimated to be 3.6 nm from Fig. 9(c). Using «b« = 0.3056 nm

Fig. 10 (a) An SPM image showing the way of micro-sampling by FIB for TEM foils with the normal parallel to ½1�100� (solid lines), and[0001] (broken lines). Bright-field TEM images of the cross sections of the impressions after nanoindentation along h11�20i under thereflection vectors of g ¼ �1�120 taken from zone axes (b) ½1�100� and (c) [0001]. Bright-field TEM images showing the non-basaldislocations under the reflections vectors of (d) g ¼ �1�120, (e) g ¼ 10�10 and (f ) g ¼ �2113. The non-basal dislocations were indicated byblack circle.

Y. Wada, N. Sekido, T. Ohmura and K. Yoshimi776

which is a perfect Burgers vector in Ti2AlC, the rotationangle ª is calculated to be 4.9°. This value is in goodagreement with the value of 5.2° determined experimentallyfrom the SAED pattern in Fig. 9(b). Farber et al. havedemonstrated that the kink-boundary in Ti3SiC2 MAX phasewas composed of parallel alternating mixed perfectdislocations with two different Burgers vectors lying on thebasal plane.32) However the present analysis suggests thatthe kink-boundary is composed of an array of dislocationswith the Burgers vector of b ¼ 1=3½11�20� alone.

According to the model for the kink formation proposed byHess and Barrett,17) kink formation is initiated from elasticbuckling of (0001) planes to nucleate a pair of dislocationswith the opposite sign of the Burgers vectors, which isfollowed by the gliding of these two dislocations towardthe opposite directions. However, elastic buckling is difficultto occur for nanoindentation, since the zone subjected tohigh stress is constrained from the surrounding. Therefore,cracking would be necessary for releasing the constraint toproduce buckling. In fact, a delamination crack was formedright adjacent to the fine-scaled kink-band as shown inFig. 9(c). Furthermore, it is indicated from micropillarcompression tests in Ti3SiC2 MAX phase that thedelamination precedes the formation of kink-bands.33)

Based on these pieces of knowledge, a kink-bandformation mechanism during nanoindentation of Ti2AlC is

proposed as shown schematically in Fig. 12. When theapplied load reached a critical value, a delamination crackwould form underneath the indenter (a). The delaminationcrack releases the constraint from the surroundings, whichleads to elastic buckling (b), and nucleation of the dislocationpairs from the inside and/or the surface (c). Thesedislocations will glide and stop at the depth of the cracktip, by which the kink-boundary forms (d). This is supportedby the experimental fact that the depth of the kink-boundaryis almost the same as that of the delamination crack tip asshown in Fig. 9(c). Namely, delamination is an inevitableprocess for the kink formation, which includes nucleationand glide of the basal dislocations to form the boundary uponnanoindentation.

5. Conclusion

Plastic anisotropy of Ti2AlC was examined by nano-indentation from different orientations. SPM and TEMobservations revealed that the basal slip, ð0001Þh11�20i,was predominant as the deformation mechanism for allthe indentation orientations. It was also indicated that, byindentation along h0001i and h11�20i, non-basal slips hadoccurred underneath the residual impressions of nano-indentation. The slip system of the non-basal slip wasidentified to be ð�12�16Þ½1�211� by analyzing the line vectorand the Burgers vector of the dislocations. Furthermore,fine-scaled kink-bands were found to form underneath theresidual impression. The formation of the kink-band wasaccompanied by delamination, i.e., micro-cracking alongthe basal plane; suggesting that the delamination is thetrigger for the kink-band formation during nanoindentation ofTi2AlC.

Acknowledgements

This research is partially supported by the Advanced LowCarbon Technology Research and Development Programfrom Japan Science and Technology Agency, JST.

Fig. 11 Atomic arrangement for the ð�12�16Þ plane of Ti2AlC. There aretwo kinds of atomic layers for ð�12�16Þ; (a) Ti­Al mixed layer, and (b) Clayer, and these layers are alternately stacked up as shown in (c). Thedetermined Burgers vector of ½1�211� (= ¹3a + c) is represented by thearrow.

Fig. 12 Schematic of the kink-band formation mechanism proposed in thisstudy.

Deformation Microstructure Developed by Nanoindentation of a MAX Phase Ti2AlC 777

REFERENCES

1) M.W. Barsoum and T. El-Raghy: Am. Sci. 89 (2001) 334­343.2) M.W. Barsoum, D. Brodkin and T. El-Raghy: Scr. Mater. 36 (1997)

535­541.3) M.W. Barsoum, I. Salama, T. El-Raghy, J. Golczewski, W.D. Porter, H.

Wang, H.J. Seifert and F. Aldinger: Metall. Mater. Trans. A 33 (2002)2775­2779.

4) V. Adamaki, T. Minster, T. Thomas, G. Fourlaris and C.R. Bowen:Mater. Sci. Eng. A 667 (2016) 9­15.

5) M. Radovic, M.W. Barsoum, A. Ganguly, T. Zhen, P. Finkel, S.R.Kalidindi and E. Lara-Curzio: Acta Mater. 54 (2006) 2757­2767.

6) X.H. Wang and Y.C. Zhou: Oxid. Met. 59 (2003) 303­320.7) X.H. Wang and Y.C. Zhou: J. Mater. Sci. Technol. 26 (2010) 385­416.8) R. Ramaseshan, A. Kakitsuji, S.K. Seshadri, N.G. Nair, H. Mabuchi, H.

Tsuda, T. Matsui and K. Morii: Intermetallics 7 (1999) 571­577.9) M.A. Pietzka and J.C. Schuster: J. Phase Equilibria 15 (1994) 392­400.10) M.W. Barsoum and M. Radovic: Annu. Rev. Mater. Res. 41 (2011)

195­227.11) S. Sridharan and H. Nowotny: Int. J. Mater. Res. 74 (1983) 468­472.12) M.W. Barsoum, L. Farber and T. El-Raghy: Metall. Mater. Trans. A 30

(1999) 1727­1738.13) A. Guitton, A. Joulain, L. Thilly and C. Tromas: Philos. Mag. 92

(2012) 4536­4546.14) M.W. Barsoum and T. El-Raghy: Metall. Mater. Trans. A 30 (1999)

363­369.15) C. Hu, Y. Sakka, T. Nishimura, S. Guo, S. Grasso and H. Tanaka: Sci.

Technol. Adv. Mater. 12 (2011) 044603.16) E. Orowan: Nature 149 (1942) 643­644.17) J.B. Hess and C.S. Barrett: Metall. Trans. 185 (1949) 599­606.

18) S. Basu, A. Zhou and M.W. Barsoum: J. Struct. Geol. 31 (2009) 791­801.

19) K. Hagihara, N. Yokotani and Y. Umakoshi: Intermetallics 18 (2010)267­276.

20) F.C. Frank and A.N. Stroh: Proc. Phys. Soc. London, Sect. B 65 (1952)811­821.

21) C. Tromas, P. Villechaise, V. Gauthier-Brunet and S. Dubois: Philos.Mag. 91 (2011) 1265­1275.

22) M.F. Doerner and W.D. Nix: J. Mater. Res. 1 (1986) 601­609.23) W.C. Oliver and G.M. Pharr: J. Mater. Res. 7 (1992) 1564­1583.24) Y. Wada, N. Sekido, T. Ohmura and K. Yoshimi: J. Japan Inst. Met.

Mater., in press.25) K. Sekido, T. Ohmura, L. Zhang, T. Hara and K. Tsuzaki: Mater. Sci.

Eng. A 530 (2011) 396­401.26) T. Ohmura and K. Tsuzaki: J. Mater. Sci. 42 (2007) 1728­1732.27) A.M. Minor, S.A. Syed Asif, Z. Shan, E.A. Stach, E. Cyrankowski, T.J.

Wyrobek and O.L. Warren: Nat. Mater. 5 (2006) 697­702.28) L. Zhang and T. Ohmura: Phys. Rev. Lett. 112 (2014) 145504.29) A.C. Fischer-Cripps: Nanoindentation Third Edition, (Springer, New

York, 2011) pp. 88­91.30) J.M. Molina-Aldareguia, J. Emmerlich, J.P. Palmquist, U. Jansson and

L. Hultman: Scr. Mater. 49 (2003) 155­160.31) J. Weertman and J.R. Weertman: Elementary Dislocation Theory, (The

Macmillan Company, The United States of America, 1964) pp. 187­189.

32) L. Farber, I. Levin and M.W. Barsoum: Philos. Mag. Lett. 79 (1999)163­170.

33) K. Kishida, M. Higashi, S. Momono, N. Okamoto and H. Inui:Collected Abstracts of the 2017 Autumn Meeting of the Japan Inst.Metals (2017) p. 29.

Y. Wada, N. Sekido, T. Ohmura and K. Yoshimi778