Available online at www.sciencedirect.com

www.elsevier.com/locate/actamat

Acta Materialia 60 (2012) 3279–3286

Phase-specific elastic/plastic interface interactions in layeredNiAl–Cr(Mo) structures

R.I. Barabash a,⇑, W. Liu b, J.Z. Tischler a, H. Bei a, J.D. Budai a

a Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USAb Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA

Received 10 February 2012; received in revised form 23 February 2012; accepted 26 February 2012Available online 6 April 2012

Abstract

The depth-dependent, as-grown and deformation-induced strain and dislocations partitioned through the interfaces in a two-phaselayered NiAl–Cr(Mo) structure are directly measured at the mesoscale using 3-D X-ray microdiffraction. It is demonstrated that inthe as-grown, undeformed state, neighboring submicron Cr solid solution and NiAl eutectic lamellae (doped with �3% Mo) form a het-erointerface with 180� rotation around a h11 2i pole. It is shown that the mechanical response to the indentation of a layered compositewith alternating Cr(Mo)–NiAl lamellae is distinct from the response of single-phase materials. In the center of the indent, after the load isreleased, the NiAl lamellae are under compressive forward stresses (with the same sign as the indentation-induced compression) while Crsolid solution lamellae are under tensile back stresses (with opposite sign from the indentation load). The depth-dependent alternation ofcompressive/tensile residual strains in the neighboring Cr solid solution and NiAl lamellae is understood in the framework of the Mugh-rabi’s composite model considering two types of structure elements: harder and softer regions. Under indentation, both kinds of lamellaeare assumed to deform compatibly. After the load is released, residual forward stresses are formed in the harder lamellae, and back stres-ses are formed in the mechanically softer lamellae. Line-broadening analysis of the intensity distribution along the diffraction vectorreveals a 15-times increase in dislocation density in the near-surface zone in the center of the indent. Such a large increase is typicalfor severe deformation.� 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Micromechanics; Deformation; Composites; X-ray synchrotron radiation; Micro-/nanoindentation

1. Introduction

Mesoscale science, encompassing the regime of hun-dreds of nanometers where classical, microscale and nano-scale science meet, is increasingly the focus of currentresearch into the origins of the properties of materials. Inparticular, interfaces play a crucial role in such properties,in part because interfaces themselves possess unique phys-ical properties distinct from the bulk constituent phases[1–5]. In layered composites, the overall interfacial area isvery large. Interfaces between the phases are key elementsresponsible for the unique micromechanisms of plasticity

1359-6454/$36.00 � 2012 Acta Materialia Inc. Published by Elsevier Ltd. All

http://dx.doi.org/10.1016/j.actamat.2012.02.052

⇑ Corresponding author. Tel.: +1 865 2417230; fax: +1 865 5747659.E-mail address: barabashr@ornl.gov (R.I. Barabash).

in composites [1]. Interfaces and boundaries can block dis-location slippage. The discontinuity in chemical composi-tion, elastic moduli, coefficients of thermal expansion,lattice parameters and chemical potential at the interfacesbetween the matrix and the second phase determine theirmechanical performance. NiAl-based composites withchromium as the second phase represent promising alloyssatisfying requirements for prospective energy-conversiontechnologies operating up to 1300 �C in corrosive environ-ments. Superelasticity was observed in a fine-grained NiAl–Cr alloy [6]. Thus, they have great potential for use asstructural components under high thermal and mechanicalloading in energy conversion facilities [7,8]. Huai et al. [9]emphasized that NiAl–Cr(Mo) is “the most logical choiceof the multi-element system examined today because of

rights reserved.

3280 R.I. Barabash et al. / Acta Materialia 60 (2012) 3279–3286

its higher fracture toughness compared to many NiAl-basealloys”. However, the interface structure and its role instrain partitioning between the NiAl-rich and the Cr-richphases are still not completely understood. Cline andWalter [10] and Johnson et al. [11] have shown that Moadditions (up to 6%) in pure NiAl–Cr change the growthdirection to h111i and the microstructure to the lamellarmorphology with a {112} faceted interface. Johnsonet al. [11] found small NiAl precipitates in the Cr-richlamellae in the as-solidified NiAl–28Cr–6Mo eutectic. Inaddition, Chen et al. [12] have found consistent low-energyinterfacial cube-on-cube orientation relationships betweenNiAl and Cr phases for both {111}- and {11 0}-type inter-face planes. Interfacial frictional sliding is an importantcomponent of the response of interlamellae interfaces toexternal force fields [13]. A predictive understanding ofthe interface interactions between the matrix and the Cr-rich solid solution lamellae in the as-grown state and underexternal fields would allow interface engineering to createthe best combination of materials properties [14–18].

Indentation techniques can be used to probe the localinterfacial bond strength in the layered model composite.One of the advantages of the indentation technique is thatit produces information about the elastic/plastic responseof the material in a compact well-defined volume. In orderto obtain spatially resolved structural information aboutlocal interface interactions and strain partitioning betweenboth phases, spatial techniques well suited for mesoscalestudies are used.

The development of X-ray diffraction techniques toprobe materials non-destructively in three dimensions(3-D) at the mesoscale [19–22] has made it possible todetermine non-destructively the as-grown and indenta-tion-induced local strain gradients and interfacial interac-tions near buried interfaces inside mesoscale layeredstructures. For example, 3-D micro-Laue diffraction stud-ies of Mo–NiAl composites containing rod-like Mo sin-gle-crystalline fibers and exhibiting large mismatches incoefficients of thermal expansion and lattice parametersdemonstrated quantitative mapping of large residualstrains and near-surface gradients in both phases of thecomposites [23–27]. In contrast, the present study isfocused on the analysis of micromechanics of the elastic/plastic transition in a model Cr(Mo)–NiAl layered systemwith low misfit of �1% between the cubic Cr and NiAlphases. During deformation, the strain is partitionedthrough the interface between both phases.

When the thickness of the alternating NiAl and Cr solidsolution lamellae is less than a micron, then the input of theinterfaces into the materials behavior becomes very compli-cated and remains poorly understood [1]. In order tounderstand the micromechanisms of plasticity in two-phasematerials, a comprehensive study of heterogeneous disloca-tion distribution and strains in both phases is needed [28].Moreover, Mughrabi and Ungar [28] pointed out that a“rewarding task would be to apply the new diffractiontechniques to study the differences in the deformation

mechanisms and dislocation microstructures prevailing inthe near-surface regions and in the bulk of deformed crys-tals, respectively”. This study is focused on the phase-spe-cific elastic/plastic as-grown and indentation-inducedstrain partitioning across the interfaces between individuallamellae in a layered Cr(Mo)–NiAl structure in the near-surface and in the bulk regions.

2. Materials and experimental procedures

2.1. Growth of Cr(Mo)–NiAl eutectic alloys

The quasi-binary Cr–NiAl phase diagram has a eutecticcomposition at 34 at.% Cr and the related eutectic temper-ature is Teut = 1450 �C. The melting temperature of therefractory body-centered cubic (bcc) Cr metal is Tm =1880 �C. NiAl with an ordered CsCl-type B2 structurebelongs to the high melting point aluminides exhibitingsuperior properties, such as high thermal conductivity of�92 W m�1 K�1, low density of 5.9 g cm�3 and excellentoxidation resistance up to 1300 �C. It has a high meltingpoint of Tsm = 1674 C [7]. As shown in Refs. [10,11], direc-tionally solidified NiAl–Cr have a rod-like microstructurewith Cr rods embedding in NiAl matrix. The rod-likemicrostructure changes to lamellar structure when addi-tional Mo is added. Here we select NiAl–31Cr–3Mo as amodel layered systems because well-aligned lamellar struc-ture can be produced by using directional solidification[10,11].

Cr(Mo)–NiAl eutectic samples were directionally solid-ified in a high-temperature optical floating-zone furnace ata growth rate of 40 mm h–1. Similarly, this method havebeen used to produce other eutectics in both lamellarand rod-like microstructures, e.g. Cr–Cr3Si [29] andNiAl–Mo [30], where details of alloy preparation andeutectic growth can be found. Upon solidification, NiAl–Cr(Mo) alloys organize into well-aligned submicron-sizeCr-rich solid-solution lamellae alternating with NiAllamellae (Fig. 1). The spacing and relative size of thelamellae depend on the growth rate and composition,and under the conditions of this experiment, resulted inapproximately parallel lamellae with approximately equalthickness and a periodicity of �1.2 lm. The sample wascut from a directionally solidified Cr(Mo)–NiAl eutecticrod parallel to the growth lamellae direction (longitudinalsection) and mounted in epoxy as shown at the sketch(Fig. 1a). The orientation of the surface normal in theprobed area was close to the ½�1; �1; 2� direction for bothCr and NiAl lamellae. After grinding with SiC paperthrough 2400 grit, the sample was vibrationally polishedwith a slurry of 0.3 lm Al2O3 and then with a colloidalsuspension of �20 nm SiO2.

2.2. Indentation

Spherical indentation on the polished surface was con-ducted with a Nano Indenter XP equipped with a sapphire

Fig. 1. (a) Sketch of the sample cut with the surface parallel to the growthdirection. The incoming X-ray beam is incident on the cut surface at 45� tothe surface normal and intercepts the Cr and NiAl lamellae perpendicularto their growth direction. (b) SEM image of the indent with alternating Crand NiAl lamellae chosen for PXM and DAXM measurements. Depth-resolved DAXM measurements were performed along the red vertical lineacross the indent. Red arrows show the direction of the beam trajectoriesintercepting the sample surface at 45�. (For interpretation of the referencesto color in this figure legend, the reader is referred to the web version ofthis article.)

R.I. Barabash et al. / Acta Materialia 60 (2012) 3279–3286 3281

tip with radius of 100 lm to a prescribed load of P =650 mN. A 15 � 3 array of indents was patterned on thesample surface with spacing of �150 lm. Load–displace-ment curves were recorded for each indentation. An SEMmicrograph of the indent studied with X-ray microdiffrac-tion is shown in Fig. 1b.

2.3. Depth-resolved X-ray strain microscopy

Polychromatic X-ray microdiffraction was performedwith a focused �0.3 � 0.4 lm beam with an energy-depen-dent penetration depth �30–50 lm [19–22]. The X-raymicrobeam intercepts the sample surface at �45� (Fig. 1aand b). In this measurement mode, depth-integrated Lauediffraction patterns contain overlapping intensity from alllamellae they intercept along the X-ray beam path. In orderto disentangle such diffraction patterns and obtain depth-resolved information about individual phase-specific sub-micron-size lamellae, a special differential-aperture X-raymicroscopy (DAXM) technique was applied [19–21].DAXM measurements using polychromatic radiationallow for measurement of the depth-dependent lattice ori-entation with a spatial resolution of �1 lm. Additionally,DAXM measurements using monochromatic radiationyielding absolute d-spacing measurements were used toprobe the distributions of dilatational lattice strains as afunction of depth. The energy of the beam was scannedover the range 13.43–14.21 keV with a step of 3 eV forthe (�2,�2,4) reflection near the surface normal. The smallX-ray beam size (<0.5 lm) allowed non-destructive mea-surements of lattice rotations and strains in the individualphase-specific mesoscale lamellae at different depths.Details describing applications of the DAXM techniquecan be found in Refs. [19–27].

3. Results and discussion

3.1. Heterointerface between Cr/NiAl lamellae in the

undeformed as-grown state

A scanning electron microscopy (SEM) image of thearea chosen for microdiffraction measurements showsalternating submicron-size Cr(Mo) and NiAl lamellae(Fig. 1b). The combined periodicity of Cr(Mo) and NiAllamellae in the composite is about �1.2 lm. A typicaldepth-integrated Laue pattern (Fig. 1a, upper left) of thesample contained scattering input from all depths up to�50 lm. Even in the undeformed region, it showed charac-teristic streaks of intensity typical for slightly curved lay-ered structures probed with polychromatic X-raymicrobeams. In order to disentangle such complicated pat-terns, polychromatic DAXM measurements separatinginputs coming from different depths were performed. Atypical depth-resolved Laue pattern from the undeformedas-grown region is shown in Fig. 2a. It shows only theinput to the scattering from a particular �1 lm thick vol-ume of sample along the incident X-ray beam path. Asthe individual lamellae thickness is small (�0.6 lm), eachdepth-resolved image contained input from only two neigh-boring NiAl and Cr lamellae. Micro-Laue diffraction anal-ysis of the orientation finds that the growth directionduring directional solidification is along the [11 1] for bothphases which agrees with earlier observations by Clineet al. [10] and Johnson et al. [11]. The normal to the cut sur-face of the sample is close to ½�1; �1; 2�. Moreover, we findthat almost all depth-resolved Laue patterns can beindexed as the superposition of two orientations of a cubiclattice rotated by 180� around the ½�1; �1; 2� pole. Diffractionpeaks in Fig. 2a are labeled with either red or black indicescorresponding to these two 180� rotated orientations. Notethat some reflections (e.g. ½�1; �1; 2�) are common to bothpatterns. In order to determine whether each lattice orien-tation originates from a particular phase, the energy wasscanned through the ½�3; �3; 6�, ½�1; �1; 4� and ½�2; �3; 3� reflec-tions marked by dashed squares in Fig. 2a. For these threereflections, the ½�3; �3; 6� is common to both lattice orienta-tions, while the ½�1; �1; 4� and ½�2; �3; 3� are each unique toone or the other pattern (red and black respectively). Theintensity distributions as a function of the diffraction vec-tor, Q = 2p/d (Q-distribution) were determined for all threereflections. The intensity distribution through the ½�3; �3; 6�reciprocal lattice site shows two intensity maxima corre-sponding to NiAl and Cr lamellae (Fig. 2b). Similar mea-surements for ½�1; �1; 4� and ½�2; �3; 3� reflections show onlyone maximum belonging either to Cr(Mo) or NiAl corre-spondingly (Fig. 2c and d). Thus, the red and black Lauepatterns correspond to the Cr and NiAl phases, respec-tively. We conclude that the two phases are not relatedby the generally reported cube-on-cube orientation [10–12,31], but are instead related by a 180� rotation aboutthe h112i axis lying in the plane of the interface.

Fig. 2. (a) Indexed depth-resolved Laue pattern from the deformed region in the center of the indent. The Laue pattern can be indexed as two overlappingLaue patterns with indices shown in red and black for Cr and NiAl respectively. The black dashed rectangles mark ½�1; �1; 2�, ½�1; �1; 4� and ½�2; �2; 3� Laue spotschosen to verify the origin of the two lattice orientations. The ð�h; �h; 2hÞ-type Laue spot for both phases was selected for depth-resolved strainmeasurements. (b) Inverse lattice parameter Q336-distribution measured in the energy interval for (336) reflection shows the two maxima belonging toNiAl and Cr lamellae. (c) Inverse lattice parameter Q114-distribution measured in the energy interval for (114) reflection shows the only one intensitymaximum corresponding to Cr lamellae. Dashed vertical line in (b) and (c) show the relaxed lattice parameter for Cr calculated from the measurement ofthe cross-section after etching the NiAl matrix away. (d) Inverse lattice parameter Q233-distribution measured in the energy interval for (233) reflectionshows only one intensity maximum corresponding to NiAl matrix. (For interpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)

3282 R.I. Barabash et al. / Acta Materialia 60 (2012) 3279–3286

The dashed vertical lines in Fig. 2b and c mark the Q

position for relaxed Cr solid-solution phase measured fromexposed Cr lamellae created by etching away the NiAlmatrix to a depth of �7 lm from the surface. Residualas-grown strains caused by the thermal contraction differ-ences between the two lamellae phases measured alongthe ½�1; �1; 2� direction with monochromatic microdiffractionDAXM are about �0.1%. The residual strain therefore iscompressive �0.1% in Cr lamellae along the ½�1; �1; 2� direc-tion and tensile in NiAl lamellae in the same direction. Dueto the unavoidable solubility of Cr in the non-stoichiome-tric NiAl, the experimentally observed Cr/NiAl parametersalways slightly differ from the pure Cr/NiAl ones andshould be determined experimentally for each alloy.

The full width at half maximum (FWHM) for the CrQ336-distribution is almost twice as large as the FWHMfor NiAl (Fig. 2b). The Cr lamellae within the as-grownNiAl/Cr(Mo) composites have been found to be practicallydefect-free [10–12] with the networks of misfit dislocationsadjacent to the interfaces. Thus, the larger FWHM

indicates a larger strain distribution in the Cr comparedto the NiAl lamellae even in the as-grown state. Such inho-mogeneous strain distribution across the Cr lamellae maybe caused by the formation of misfit dislocation networks.

Stereographic projections of the two orientations relatedby a rotation of 180� around the common ½�1; �1; 2� pole areshown in Fig. 3a and b. The average interface plane orien-tation is close to (�110). As described above, the observedtwo orientations are due to the formation of a 180�-rotatedheterointerface between the Cr and NiAl lamellae. Since acube-on-cube orientation was reported earlier [10–12,31],we believe that the heterointerface between the Cr andNiAl lamellae is observed here for the first time. Densityfunctional theory calculations [32] assumes a non-polar(11 0)-type interface because (11 0) is a stable free-surfacefacet for these materials. Calculation of the interfacialenergy within this model shows that (110)-type interfacehas minimal energy for NiAl/Cr phase-separated alloy inagreement with our observations. Thus far, both experi-mental and theoretical studies of the (110) interface

Fig. 3. (a and b) Stereographic projections of the two orientations related by a rotation of 180� around the common (�1�12) pole obtained from thedepth-resolved measurements are consistent with heterointerface between Cr and NiAl lamellae.

R.I. Barabash et al. / Acta Materialia 60 (2012) 3279–3286 3283

[31,32] consider only cube-on-cube orientations, consistentwith most previous experimental descriptions of this low-mismatch composite system. Our observations suggest thattheoretical calculations similar to those reported in Ref.[32] should be expanded to include the possibility of 180�rotation at the (110)-type interface.

Heterotwinned interfaces have been observed in otherphase-separated systems such as Ag–Cu [33–35], (NiCo)precipitates in Ni-base superalloys [36] and Si/CoSi2 [37–39]. A possible explanation for the formation of a heteroin-terface between Cr–NiAl lamellae may be provided bytopological models similar to the ones suggested for theheterotwin interface in the Ag–Cu eutectic system [33–35]. However, these models describe an as-cast Ag–Cusystem, while our Cr(Mo)/NiAl alloy was directionallysolidified. It was pointed out that during directional crys-tallization at constant undercooling, the more rapidlygrowing structure will survive [40]. In the Cr(Mo)/NiAlalloys, a small addition of Mo is known to change therod-like shape of the Cr(Mo) fibers (at 0% Mo) to lamellarones (at 3% Mo in the studied alloys) [10,11]. It is possiblethat the Mo addition changes the Cr(Mo)/NiAl interfacialenergy so that under the specific conditions of directionalsolidification the (110) heterointerface with 180� rotationmay lead to faster lamellar growth.

3.2. Indentation-induced strain partitioning between

individual lamellae

Thus far, we have described the as-grown microstruc-ture. We now turn to the substructure due to plastic defor-mation as studied using 3-D X-ray microdiffraction usingboth polychromatic (for orientation information) andmonochromatic (for strain information) scattering mea-surements. The indented area was first mapped in 2-D withdepth-integrated white-beam measurements and the regionsof largest deformation were found. Then, depth-resolvedmonochromatic microdiffraction was performed with the

X-ray microbeam positioned along several lines throughthe indented area as schematically shown in Fig. 4a. Asdescribed earlier, the surface normal for the indented areais close to the ½�1; �1; 2� direction which is common to bothphases. The ð�h; �h; 2hÞ Laue spots as observed on theX-ray area detector integrated in depth along the lines 1,2 and 3 are shown in Fig. 4b and appear as streaks due tolattice rotations (mosaic spread) at different depths. Thesedepth-integrated images contain contributions from differ-ent orders of the ð�h; �h; 2hÞ-type reflections. The ð�h; �h; 2hÞLaue reflection was chosen for monochromatic 3-Ddepth-resolved measurements of local strain gradientsthrough the interfaces between Cr and NiAl lamellae. Themeasurement along line 1 is taken in the unaffected areaand used as an as-grown reference. The ð�h; �h; 2hÞ Laue spotalong the line 2 corresponds to the region with the largestplastic deformation in the center of the indent (Fig. 4a).The beam path along line 3 intercepts the sample surface�10 lm away from the indent center and then passes underthe indent.

Depth-resolved information about dilatational straingradients in the indentation area was obtained using mono-chromatic differential aperture microscopy (DAXM) strainmeasurements and results for lines 2 and 3 are shown inFig. 4c and d. The depth-resolved ð�h; �h; 2hÞ d-spacingwas calculated from the measurements of the diffracted-intensity profiles for the (�2,�2,4) and (�3,�3,6) reflec-tions along the three distinct beam paths for both Cr andNiAl submicron-size lamellae. Near-surface lattice param-eters in the undeformed state, including thermal contrac-tion effects, were determined experimentally for bothlamellae phases and used as reference values (horizontaldashed blue lines in Fig. 4c and d). The measured misfitbetween the two phases in the surface normal ½�1; �1; 2� direc-tion was relatively small �1% and the experimental latticeparameters are determined by both composition (thephases are not pure) and by differential contraction. Thisis in contrast to NiAl–Mo and Ni–Mo composites which

Fig. 4. (a) Sketch of the indented area with X-ray beam passing along the three lines: line 1 is far from the indented area and was used as a reference; alongline 2 the beam intercepts the sample surface in the most deformed area; along line 3 the beam intercepts the sample surface further from indented area andpasses under the indent at a distance of 10 lm deeper compared to line 2. (b) Enlarged energy-integrated Laue spots measured along the three linesindicated in Fig. 3a. Depth-dependent ½�1; �1; 2� d112-spacing for Cr and NiAl individual lamellae corresponding to the beam paths along line 2 (c) and line 3(d). Lines 2 and 3 are shown in schematic (a). Every spot in (c) and (d) corresponds to an individual Cr or NiAl lamellae at different depths. Blue dashedhorizontal lines correspond to undeformed Cr and NiAl measured along line 1. Vertical dashed red lines separate different deformation zones in theindented area: in the zone located �10 lm further from the indent center both types of lamellae are under compressive strains; in the center of the indent,NiAl lamellae are under compression and Cr lamellae are under tension. (For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

3284 R.I. Barabash et al. / Acta Materialia 60 (2012) 3279–3286

demonstrated almost an order of magnitude larger misfitbetween the matrix and Mo fibers and large �1% near-sur-face strain gradients [23–27].

Along line 2, the beam intercepts the sample surface inthe area of largest deformation near the center of theindent (Fig. 4a). Depth-dependent d112-spacing measure-ments for Cr solid solution and NiAl lamellae (Fig. 4c)exhibit contrasting strain distributions between these twophases: the NiAl d112-spacing decreases near the surface,revealing that the near-surface deformed NiAl lamellaeare under compression. However at the same location theCr lamellae are under tension. Compressive strains in NiAland tensile strains in the Cr lamellae first increase withdepth and reach their maximal value of �0.5% at a depthof 7–10 lm, then decrease, and at a depth of �20 lm satu-rate at their undeformed bulk values for both lamellaephases. Line 3 (Fig. 4d) is located 10 lm further from theindent center than line 2 and the beam probes the affectedarea 10 lm deeper. Thus, the observed amplitude of com-pressive/tensile strain alternation is less pronounced andoccurs at a greater depth along the incident X-ray beamfor line 3.

The observation of opposite-sign strain distributions inneighboring Cr and NiAl lamellae does not follow thebehavior of a single-phase material with elastic modulicalculated by a simple rule of mixture. Observed indenta-tion-induced strain partitioning, similar to rotational parti-tioning, [41] probably depends on the ratio between the

elastic moduli of the Cr and NiAl neighboring lamellae.The Young’s modulus, which represents the resistance toelastic strain deformation, is higher in the directionallysolidified NiAl–Cr eutectics compared to either pure Cror NiAl [7]. For h111i-oriented single crystals of pure NiAland pure Cr (which is close to the h112i surface normal inour sample), the bulk elastic moduli are very similar andequal to 277 and 248 GPa, respectively [11]. It is importantto note that deformation in chromium may be complicatedby phase transitions near room temperature. Chromiumexhibits a ductile to brittle transition in the temperaturerange 150–310 K [42]. Moreover, a transition from a para-magnetic to ferromagnetic state at 310 K is believed to beresponsible for observed anomalies in the elastic constantsand coefficients of thermal expansion [43,44].

The contrasting compressive/tensile strains alternatingin individual neighboring lamellae of both phases can beunderstood within the framework of the composite modelproposed by Mughrabi [28,45]. The basic idea of the com-posite model is that under an external load, both phases ofthe composite are assumed to deform compatibly. After theload is released, forward (same sign as compared with theexternal load) internal residual stresses are formed in theharder component, while back (opposite sign) residualstresses are formed in the softer component [28,45–47]. Inthe Cr–NiAl composite, the two phases demonstrate dis-tinct elastic–plastic behavior as a result of load transferthrough the interfaces between the Cr and NiAl lamellae

R.I. Barabash et al. / Acta Materialia 60 (2012) 3279–3286 3285

during constrained deformation. Under load, both phasesinitially compatibly compress both elastically and plasti-cally. After unloading, the material in both lamellae phasestends to spring back in response to the elastic part of thecompression. If the mechanism described by the compositemodel is applicable in this case, then the different elasticmoduli [11] of neighboring lamellae phases along the load-ing ½�1; �1; 2� direction results in compressive residual strainin the NiAl phase and tensile residual strain in the slightlysofter Cr lamellae in the same direction. In the compositesample, the Cr-rich lamellae also contain a small amountof Ni and Al [10,11] impurities and the exact temperatureof the brittle–ductile phase transition is not known. Thetemperature of the phase transition and the anomaly inelastic constants are probably additionally influenced byindentation. Although the micromechanical behavior maybe influenced by impurities and phase transitions, theX-ray measurements clearly show that, in the center ofthe indent, compressively loaded NiAl lamellae are beingconstrained by tensile loaded Cr lamellae.

3.3. Depth-dependent dislocation density in individuallamellae

Plastic deformation in the elastoplastic region shouldalso manifest itself in an increase in dislocation density.The B2-ordered NiAl lamellae have only three independentslip systems, (11 0) h111i, (110) h1 10i and (110) h1 00i,and thus the acting deformation mechanisms are restricted[7,48]. In bcc Cr at room temperatures, dislocation slip hasbeen observed mainly in the {112} and {110} planes witha larger number of dislocation slip systems [7]. In our sam-ple, the linewidth dependence of the radial intensity distri-bution on the total dislocation density [49,50] for specificQ224 and Q336 reflections was used to estimate the depth-dependent dislocation density for individual Cr and NiAllamellae along lines 2 and 3 (Fig. 5). In the most deformednear-surface region, the dislocation density is 15 timeshigher than in the undeformed region in the depth of thesample. Along line 3, which is much less deformed, the dis-location density is an order of magnitude smaller thanalong the line 2. Such pronounced increase of dislocationdensity in the center of indented area is typical for severe

Fig. 5. Depth-dependent dislocation density along line 2 in individual Cr(red circles) and NiAl (blue circles) lamellae decreases into the depth of thesample. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

plastic deformation. Similar increases of dislocation den-sity was observed earlier in the indented Ni-based superal-loys [22]. However, in contrast to the indented superalloys,the dislocation density in the layered phase-separated Cr/NiAl alloys is also inhomogeneous within the individuallamellae.

3.4. Distinct indentation-induced deformation regimes

Forward stresses (enhancing the indentation-inducedcompression) in the NiAl lamellae and back stresses(opposing the indentation-induced load) in the Cr shiftthe d-spacing in the opposite directions, as observed exper-imentally. Along X-ray line 3 (Fig. 4) which is 10 lm fur-ther from the indented area, the beam probes first theregion where both phases are under residual elastic tensilestrains. The elastoplastic region where plastic deformationis observed is surrounded by the region with residual tensilestrain. The X-ray beam passing along the line 3 is probingessentially less-deformed regions compared to line 2 andthe depth-dependent strain changes are less pronounced.

For composites, the following deformation regimes canbe distinguished [51,52]: (I) the elastic regime, in whichboth phases deform elastically; (II) the elastic/plasticregime in which one phase deforms elastically and the sec-ond phase deforms plastically; (III) plastic deformation ofboth phases. The near-surface deformation in the center ofthe indented area corresponds to the second and thirdregimes, and cause the NiAl lamellae and Cr lamellae tobe under compressive and tensile strains, respectively.The second deformation regime is considered to be themost important regime for composites. The stronglydeformed central zone of the indent is surrounded by azone in which both lamellae phases are under residual ten-sile strains. The boundaries between the zones of the resid-ual tensile strains surrounding the zone of plasticdeformation are marked with dashed lines in Fig. 4a. Thegeneral phenomenological description of the above defor-mation regimes has been suggested [51,52] for composites.However, the present study is, to our knowledge, the firstdirect spatially resolved experimental verification of theexistence of alternating tensile/compressive strains formedin the individual neighboring Cr and NiAl lamellae in thenear-surface and bulk indented area. Synchrotron mea-surements with a large 0.1 � 0.1 mm2 beam [53] using a sta-tistically averaging powder-diffraction method showed thatin steel-based metal–matrix composites reinforced withTiB2, the strain was partitioned between both phases ofthe composite in the elastic regime. In contrast to statisti-cally and depth-averaged bulk results obtained with largebeams [53], the spatially resolved information at the submi-cron level allows tracking the depth-dependent near-sur-face lattice rotations, dislocation densities and loadtransfer between the neighboring individual lamellae as aresult of their constrained deformation under the indent.The transition from the elastic to elastoplastic regime andthe composite behavior under the elastoplastic regime is

3286 R.I. Barabash et al. / Acta Materialia 60 (2012) 3279–3286

controlled by the interface interactions, dislocations andload transfer through the interfaces between the Cr andNiAl lamellae.

4. Conclusions

Depth-resolved mesoscale studies of elastic/plastic inter-actions between neighboring submicron Cr and NiAllamellae reveal a {110} heterointerface between the Crand NiAl lamellae with a 180� rotation around the[�1�12] pole in the as-grown state.

Indentation-induced strain partitioning between theindividual lamellae results in alternating tensile/compres-sive strains in the submicron-size Cr and NiAl lamellae.The indentation-induced opposite-sign strain distributionsin the neighboring Cr and NiAl lamellae is understoodwithin the framework of Mughrabi’s composite model asa result of the compatibly constrained lamellae deforma-tion and load partitioning through the interfaces betweenthe harder and softer parts of the composite. After unload-ing, the harder NiAl lamellae are under forward compres-sive stresses, while less hard Cr lamellae are under backtensile stresses. In contrast to depth-averaged informationusually obtained with large beams, the spatially resolvedsubmicron-beam study reveals depth-dependent alternatingstrain gradients between individual phase-specific lamellae.The dislocation density is 15 times higher within �20 lmnear the surface of the indent, decreases with depth andsaturates at the undeformed level at a depth of �25 lm.

Acknowledgements

This research was supported by the US Department ofEnergy, Office of Basic Energy Sciences, Materials Sciencesand Engineering Division. The use of the APS was sup-ported by the US Department of Energy, Office of BasicEnergy Sciences, the Scientific Users Facilities Division.

References

[1] Wang J, Hoagland RG, Liu XY, Misra A. Acta Mater 2011;59:3164.[2] Puri S, Acharya A, Rollett AD. Metall Mater Trans A 2011;42A:669.[3] Van der Giessen E, Needleman A. Interf Sci 2003;11:291.[4] Liu P, Cheng L, Zhang YW. Acta Mater 2001;49:817.[5] Elizalde MR, Sanchez JM, Martinez-Esnaola JM, Scherban T, Sun B,

Xu G. Acta Mater 2003;51:4295.[6] Frommeyer G, Kowalski W, Rablbauer R. Metall Mater Trans A

2006;37A:3511.[7] Frommeyer G, Rablbauer R. Steel Res Int 2008;79:507.[8] Frommeyer G, Rablbauer R, Schafer HJ. Intermetallics 2010;18:299.[9] Huai K, Guo J, Ren Z, Gao Q, Yang RJ. Mater Sci Technol

2006;22:164–8.[10] Cline HE, Walter JH. Metall Trans 1970;1:2907.[11] Johnson DR, Chen XF, Oliver BF, Noebe RD, Whittenberger JD.

Intermetallics 1995;3:99.[12] Chen YX, Cui CY, He LL, Guo JT, Li DX. Mater Lett 2000;44:186.

[13] Needleman A, Borders TL, Brinson LC, Flores VM, Schadler LS.Compos Sci Technol 2010;70:2207.

[14] Needleman A. Acta Mater 2000;48:105.[15] Wei Y, Hutchinson JW. J Mech Phys Solids 1997;45:1253.[16] Zacharopoulos N, Srolovitz DJ, LeSar R. Acta Mater 1997;45:3745.[17] Su C, Wei YJ, Anand L. Int J Plast 2004;20:2063.[18] Ostergaard RC, Sorensen BF, Brondsted P. J Sandwich Struct Mater

2007;9:445.[19] Larson BC, Yang W, Ice GE, Budai JD, Tischler JZ. Nature

2002;415:887.[20] Ice G, Barabash R, Walker F. Compos B Eng 2005;36:271.[21] Yang W, Larson BC, Ice GE, Tischler JZ, Budai JD, Chung KS. Appl

Phys Lett 2003;82:3856.[22] Barabash OM, Santella M, Barabash RI, Ice GE, Tischler J. JOM

2010;62:29.[23] Bei H, Barabash RI, Ice GE, Liu W, Tischler J, George EP. Appl

Phys Lett 2008;93:071904.[24] Barabash RI, Bei H, Gao YF, Ice GE, George EP. JMR 2010;25:2.[25] Barabash RI, Bei H, Gao YF, Ice GE. Acta Mater 2010;58:6784.[26] Barabash RI, Bei H, Gao YF, Ice GE. Scripta Mater 2011;64:900.[27] Barabash RI, Bei H, Ice GE, Gao YF, Barabash OM. J Met

2011;63:30.[28] Mughrabi H, Ungar T. Nat Mater 2006;5:601.[29] Bei H, George EP, Kenik EA, Pharr GM. Acta Mater 2003;51:6241.[30] Bei H, George EP. Acta Mater 2005;53:69.[31] Chen YX, Cui CY, He LL, Guo JT, Li DX. J Mater Sci Lett

2000;19:519.[32] Liu W, Li JC, Zheng WT, Jiang Q. Phys Rev B 2006;73:205421.[33] Rao G, Howe JM, Wynblan P. Scripta Metall Mater 1994;30:731.[34] Han K, Hirth JP, Embury JD. Acta Mater 2001;49:1537.[35] Liu JB, Zeng YW, Meng L. J Alloys Compd 2008;464:168.[36] Loubradou M, Penisson JM, Bonnet R. Ultramicroscopy

1993;51:270.[37] Bulle-Lieuwma CWT, Van Ommen AH, Hornstra J. In: Sinclair R,

Smith DJ, Dahmen U, editors. MRS symp proc on high resolutionelectron microscopy of defects in materials, vol. 102. Pittsburgh (PA);1988. p. 377.

[38] Bouzaner A, Verger-Gaugry JL, Bonnet R. Scripta Metall Mater1992;26:1107.

[39] Gibson JM, Bean JC, Poate JM, Tung RT. Thin Solid Films1982;93:99.

[40] Li S, Chen XC, Barabash OM, Barabash RI, Egorov BV. Met PhysAdv Technol 1997;16:359.

[41] Wang J, Hirth JP, Pond RC, Howe JM. Acta Mater 2011;59:241.[42] Chan KC, Harada Y, Liang J, Yoshida F. J Mater Proc Technol

2002;122:272.[43] Bolef DI, De Klerk J. Phys Rev 1963;129:1063.[44] Muir WC, Perz JM, Fawcett E. J Phys F: Met Phys 1987;17:243.[45] Mughrabi H. Acta Metall 1983;31:1367.[46] Levine LE, Larson BC, Yang W, Kassner ME, Tischler JZ, Delos-

Reyes MA, et al. Nat Mater 2006;5:619.[47] Jakobsen B, Poulsen HF, Lienert U, Almer J, Shastri SD, Sorensen

HO, et al. Science 2006;312:889.[48] Miracle DB. Acta Metall Mater 1993;41:649.[49] Barabash RI. Mater Sci Eng A 2001;320:49.[50] Krivoglaz MA. X-ray and neutron diffraction in non-ideal crys-

tals. New York: Springer Verlag; 1996.[51] McDaniel DL, Jech RW, Weeton JW. Trans TMS-AIME

1965;233:636.[52] Metcalfe AG. In: Broutman Lawrence J, Krock, Richard H, editors.

Interfaces in metal matrix composites. New York: Academic Press;1974.

[53] Bacon DH, Edwards L, Moffatt JE, Fitzpatrick ME. Acta Mater2011;59:3373.