length scale plasticity: a review from the … · eter, the traditional dislocation multiplication...

21Length scale plasticity: a review from the perspective of dislocation nucleation

© 2018 Advanced Study Center Co. Ltd.

Rev. Adv. Mater. Sci. 56 (2018) 21-61

Corresponding author: M. Bagheripoor, e-mail: [email protected]

LENGTH SCALE PLASTICITY: A REVIEW FROM THEPERSPECTIVE OF DISLOCATION NUCLEATION

Mahdi Bagheripoor and Robert Klassen

Department of Mechanical and Materials Engineering, The University of Western Ontario, London,ON N6A 5B9, Canada

Received: October 30, 2017

Abstract. Sub-micron and nano-size material systems and components are now regularly beingfabricated for use in a wide variety of new applications. These systems exhibit mechanicalproperties that can be drastically different from their macroscopic counterparts and recentlymuch work has focused on the size effects on the mechanical behaviour of materials. Althoughthe size dependent behaviour has been observed in all of the crystal structures, the governingmechanisms have been found to be different. Different theories have been proposed to describethe size dependent behaviour of metallic samples and the governing mechanisms and it is wellknown that the surface plays an important role in the plasticity of small scales. Some of thetheories indicate the importance of surface in nucleating dislocation and some other ones considerthe surface importance as its effect on truncating dislocation loops and activation of internalsources. Moreover, recent studies have revealed that while dislocation based deformation in fccmetals is not very sensitive to temperature, deformation is strongly temperature dependent inbcc metals. The effect of orientation is more clear in the size scale behavior of hcp metals. Thisreview covers recent literature that has focused on uniaxial compression of single crystals at thesub-micron and nanometer scale. The fundamental mechanisms governing the size dependentmechanical behaviour of different crystal structures are described. The effect of fabrication processand current experimental techniques for micro and nano-compression are studied as well.

1. INTRODUCTION

Nano-scale objects often exhibit properties that canbe drastically different from their macroscopic coun-terparts, making them suitable for a wide variety ofnew applications, like micro/nanoelectromechanicalsystems (MEMS/NEMS) or advanced compositematerials. Structural modifications usually occur dueto surface relaxation or reconstruction, which bothmechanisms resulting in surface energy minimiza-tion, while adding an extra contribution to surfacestress [1]. As the sample dimension becomes small,the effect of nucleation at the surface becomes sig-nificant. Surfaces naturally introduce layers of at-oms where their coordination number and the elec-tronic structure are different from that of internal at-

oms [2]. As a result, the physical and chemical prop-erties of materials can be significantly different nearthe surface. The physical change results in a changein the surface energy, residual stress, and vacancydistribution as to facilitate the surface nucleation ofdefects [2,3]. The influence of the surface effect onthe properties of the nano-scale sample is directlyassociated with the surface to volume ratio and ob-viously, the proportion of surface in the total volumeof the sample will become higher when the physicaldimension of the materials becomes smaller, result-ing in increasing significance of the surface nuclea-tion of defects.

Surfaces and interfaces can have a strong effecton the mechanical properties of nanostructures. In

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22 M. Bagheripoor and R. Klassen

the elastic regime, the Young’s modulus can changecompared to their bulk counterparts, due to the sur-face stress, and hence facilitate or hinder the defor-mation of the nanostructure, as a result of decreas-ing or increasing the elasticity coefficients. In theplastic regime, deformation mechanisms can bedifferent in bulk materials and in nanostructures. Forinstance, the dislocation starvation process is oneof the theories that has been proposed to explainthe first stages of plastic deformation innanostructures. Moreover, surface plays more im-portant role in deformation of nanostructures sinceit acts as source of dislocation nucleation and sur-face diffusion could also affect the plasticity at nano-scales [4-6]. However, like bulk materials, bounda-ries between nanograins, are also affecting plastic-ity by emitting or absorbing dislocations or favoringthe deformation by mechanisms like twinning [7,8].

Recently, with the advances of nanotechnologyand fabrication of nano-scale material there has beena great deal of interest in investigating the plasticdeformation of nano-scale materials, such asnanograined, nanotwinned and nanostructured met-als and a huge amount of research has gone intounderstanding dislocation-based plasticity at thenano-scale to achieve fundamental knowledge ofplasticity of this scale, and provide design guide-lines for reliable mechanical devices in the field ofnano- or microelectromechanical systems [8-25].By controlling the size of grains and producingnanocrystalline metals whit grains smaller than 100nm, strength levels can be easily exceed 4–5 timeshigher than those with micron level grain sizes.Recent experiments have also shown that the highdensity of nano-scale growth twins in nanograinedmetals dramatically elevates the strength while pro-viding considerable ductility [9,10,23,26].

In bulk samples, the effect of microstructuralscale on mechanical strength is understood eitherin terms of dislocation pile-up ideas or obstacles todislocation migration [27]. However, these conceptscannot completely describe the behavior as themicrostructural scales reaches dimensions as smallas the average spacing between dislocations [28].One of the major current focus in thenanomechanical community is the investigation ofsingle crystalline strength at reduced dimensionsthrough uniaxial deformation of micro or nano-sizedsamples [29]. At this scale and as metal samplesizes decrease to nano-scale, they are expectedto contain few or no dislocations, and strength iscommonly controlled by dislocations nucleated dur-ing plastic deformation which tend to escape thecrystal by annihilating at a nearby free surface, a

condition known as hardening by dislocation star-vation [30-34]. Such ideas have been used to un-derstand the deformation of nanometer-sized speci-mens [28].

Recent studies on the compression of singlecrystalline micro and nano-sized samples have in-dicated that the strength of crystalline metals, in-dependent of sample size in bulk, increases dra-matically as the sample size decreases to the nano-scale [6,28,31,35-41]. Size scale effects on strengthand plasticity in nano-sized metals can be dividedinto geometry dependent and microstructure de-pendent effects [42] or as some scholars classi-fied, extrinsic and intrinsic size effects. Differentkinds of size effect have been reported in the lastdecade: external geometric size in single crystals,where the attained material strength inversely scaleswith sample dimensions, i.e. thin film thickness ornanopillar diameter due to defect interactions withfree surfaces [43]. One such example is, Greer andNix [6,36] studies on electroplated Au micro/nanopillars which resulted in conclusion that theoverall sample dimensions artificially limit the lengthscale available for plastic processes and therebysignificantly increase the material yield strength.According to Nix et al. [35], below a critical diam-eter, the traditional dislocation multiplication mecha-nisms that control work hardening stop operatingand dislocations freely traverse the sample. In thisdislocation starvation condition, the sample size ismuch smaller than a breeding constant for disloca-tion multiplication and all mobile dislocations willbe annihilated at free surfaces before interacting witheach other, so continuing plastic deformation is onlypossible if the applied stress is large enough tonucleate new dislocations [25,44]. This is also truewhen crystalline materials are indented at thenanometer scale. For this size indentation, the crys-tal volume probed is in fact so small as to be dislo-cation free. As a result the indentation curve is char-acterized by elastic loading followed by discretedisplacement bursts (so called ‘‘pop-ins” [31,45-47]),associated with the dislocation nucleation [32].Therefore, dislocation nucleation, either atnanomaterial surfaces or interiors, plays an impor-tant role in determining nanomaterial strength withinthe “Dislocation Starvation” regime [44]. However,the size effect is not similar for different structuresand as an example while FIB-fabricated bcc Mo andNb nanopillars also show size effects in their flowcurves, the fundamental of this size dependentstrength is quite the opposite and rather than anni-hilating at the free surfaces, dislocations in bccmetals have been found to form intricate networks


as a result of mechanical deformation even in thesmallest pillar size of ~200 nm diameter [48,49].Moreover, strength at the nano-scale depends notonly on specimen size but also on the specimenand loading geometries. The importance of geom-etry was demonstrated in comparisons of indenta-tion results of Al thin films and nanowires, where itwas shown that nanowires are much weaker thanthin films of the same minimum dimension [50].

Till now many research has been done on thesize effect at different crystal structures. Strong sizeeffect has been observed in face-centered cubic[35,51-54], body-centered cubic [48,55-58], hexago-nal closed packed (hcp) [59-66], tetragonal [67-71]and rhombohedral [72] metals with a zero or smallinitial dislocation density that a smaller-is-strongersize effect operates, whereby smaller physical di-mensions are accompanied by a pronounced in-crease in mechanical strength. About the fcc struc-ture, the mechanism of deformation at small scaleis well defined and investigated. However, about thebcc and hcp crystals, the active deformation mecha-nisms appear to be more complicated. Deformationin bulk bcc metals is governed by screw dislocationwhich its behavior and the effect of edge dislocationhave been on the interest in small scales. Due tothe limited slip systems in the hcp crystal structurecompared to cubic metals, deformation may beaccommodated by mechanical twinning, as well asby dislocation plasticity. Moreover, since thecrystallographic texture greatly influences the shearstress necessary to activate slip, the effect of ori-entation in the deformation of bcc and hcp metalshas been on the interest [73]. In this review, themain theories and proposed mechanisms for defor-mation of fcc, bcc and hcp single crystals undercompression loading are studied and compared to-gether. The main focus is on the sub-micron andnano-scales, since the plasticity at the micron-scalehas been documented well [43,74].

2. NANO-COMPRESSION TEST

There are many methods used to study the me-chanical properties of materials. For thenanomechanical properties, the possibility of usingall these methods is reduced because of either tech-nical or monetary reasons. The methods that havebeen applied to study nano or small scale mechan-ics are as follows: nanoindentation [75], uniaxialcompression [35], uniaxial tension [76], three/four-point pressing [77], the crack propagation [76], theplane-strain bulge test [78]. All these methods shouldpresumably lead to the same conclusion about a

certain property. However, there are some proper-ties that cannot be studied by all of the mentionedmethods. For example, the yield strength cannotbe determined by nanoindentation. The physicalproperty of the sample is another factor that limitsthe applicable tests, nanoindentation can not beapplied on graphene since there is no thickness forgraphene to be penetrated. Moreover, there is someinaccuracy with experimental condition. For exam-ple, nano-indantation with sharp tips introduces anonuniform distribution of the mechanical strains orstrain gradients within the contact area. The cost ofthe experiments is another factor that limits the avail-able techniques for studying material properties atthe nano-scale. For instance, uniaxial tensile testof nanopillars is very costly and requires more com-plicated procedure in sample fabrication and experi-mental testing [79].

In light of the above factors, the most commontechnique for exploring nano-scale mechanical prop-erties with the fewest limitations and drawbacks –especially that of the presence of strong strain gra-dients –is the uniaxial compressive loading of cylin-drical nanopillars which was first introduced in 2004by Uchic et al. [35] for compression of micro-sizedpillars, and later extended to the nano-scale com-pression in 2005 by Greer et al. [36]. In these test,mimicking the bulk compression experiment, com-pression is applied using a diamond flat punch whichcould be controlled by a nanoindentation pendulumor an AFM tip, and the load displacement curve issimultaneously drawn as the pillar or particle com-presses [28,79]. Experiments can be executed ei-ther under loading rate control or displacement ratecontrol [28]. The most significant difference of thistest than bulk compression test is that the nano-compression samples are not freestanding and theyremain integrally attached to the bulk substrate toeliminate the need for nanomanipulation. In result,the substrate acts as the lower compression platenin this test [74].

2.1. Experimental approaches

Nanoindentation is the most general technique thathas been used for studying nano-scale materialbehavior under compression, due to it’s capabilityof applying force on a specific point with high con-trol accuracy (loading rate control of micro-newtonsper second and displacement rate control ofnanometres per second). Nanoindentation, orinstrumented indentation is a technique, appearedin the early 1980s and consists in measuring theforce and displacement of a hard tip forced into the


material. The load and displacement are measuredthrough a change in capacitance between a refer-ence and a movable electrostatic plate attached tothe tip [80,81]. Oliver and Pharr [82], who have playeda leading role in presenting models for quantitativenanoindentation, have presented a general overviewon the development and recent advances ofnanoindentation techniques [82]. In situnanoindentation was reviewed in 2006 by Schuh [78],in which an excellent overview of in situ techniqueswith particular emphasis on technological advance-ments was provided. Nili et al. [83] traced develop-ments and pinpoints significant recent advances,with emphasis on the applications of in situnanoindentation techniques to materials systems,and highlighting the new insights gained from thesein situ techniques.

Recently and with the advancement of technol-ogy, nanoindentation has been combined with dif-ferent microscopic techniques to make it possibleto observe material behavior during the deformationand investigate active mechanisms while the ex-periment is doing and in situ experimentation hasgained significant attention due to its ability to en-hance material characterization. Performingnanomechanical tests inside of a microscope de-vice with real-time imaging, elucidate the specificdeformation mechanisms that occur, as well as itsoccurrence time, and thus allows us a better under-standing of the material’s properties and overall per-formance [83,84].

Fig. 1. Pictures of the SEMentor (SEM + Nano-indenter) and the inside of chamber. Reprinted with permis-sion from Kim JY, Greer JR. 2009. Tensile and compressive behavior of gold and molybdenum singlecrystals at the nano-scale, Acta Materialia 57 (94), (c) 2009 Elsevier Ltd.

As Ghisleni et al. [85] pointed out, the main ad-vantage of in situ SEM indentation techniques isthe continuous observation of the surface deforma-tion during the application of an external load on thespecimen surface by an indenter. The large field ofview, which helps to locate the feature of interest,and the sub-micron precision positioning allowedby the high magnification available through the SEMare the other advantages of doing nanoindentationin SEM instrument [85]. By performing thenanoindentation experiments in situ with a SEMinstrument, one can observe how the specimendeforms under an applied load, which allows corre-lating the variation in the load-displacement curvesto the variation in the specimen’s topography. Inparticular, the influence of coating failure such asdelamination, crack formation and propagation [86-90], and surface shear band formation [90-93] canbe correlated to a single discontinuity in the load-displacement data. Fig. 1 shows the Greer group’s[94] in situ mechanical tester, SEMentor, in whichthe dynamic contact module (DCM) of thenanoindenter (Agilent Corp., Oak Ridge, TN, USA)inserted into a free port in the SEM (FEI Quanta200, FEI Company, Hillsboro, OR, USA) andequipped with a custom-fabricated conductive dia-mond tension/compression grips. Instrumentationcompanies like Hysitron, has provided PicoIndentersthat could be installed on the SEM and used for insitu mechanical testing. However, even though insitu SEM indentation can observe the deformation


Fig. 2. Schematic diagram of an in-situ nanome-chanical tester integrated with the cryogenic system.Reprinted with permission from Lee SW, Cheng YT, Ryu I, Greer JR. 2014. Cold-temperature deformation ofnano-sized tungsten and niobium as revealed by in-situ nano-mechanical experiments, Science China-Technological Sciences 57: (c) 2014 Springer Nature.

on the surface of the indented specimen, somephysical phenomena that might take place under-neath the surface such as phase transformation, ornucleation and propagation of dislocations are hardlyvisible by SEM observation.

Lee et al. [95,96], developed an in-situ cryogenicnanomechanical testing system by combining thenanomehcanical tester (InSEMTM, Nanomechanic,inc), SEM (Quanta, FEI), and cryogenic systems(Janis Research Company, LLC), to study small-scale mechanical behavior of materials at low tem-peratures. Fig. 2 shows the schematic diagram ofcryogenic system consisting cold finger, Si-diodetemperature sensors, joule heaters, radiationshielded oxygen-free high thermal conductivity cop-per (OFHC) lines, vacuum shielded coolant transferline, the liquid nitrogen dewar, and temperature con-troller [95].

Following early load sensor integration develop-ments, in situ TEM mechanical testing with quanti-tative load measurement including mechanical prob-ing modes such as nanoindentation expanded to-ward commercialization in the last decade [97].These developments are particularly useful for con-ducting size effects experiments, whereby quanti-tative in situ TEM mechanical testing is an idealtool for studying the origin and principles of thematerial deformation through dislocation and twin-

ing observation. Fig. 3 shows some the of involveddeformation mechanisms in size effects which canbe studied by in situ TEM.

Various approaches of mechanical testing insidea TEM exist today. They span from using TEM hold-ers with a simple mechanical actuation to elabo-rated testing units that fit inside the pole pieces.From 2003 to 2005, Hysitron® and Nanofactory In-

Fig. 3. Schematic of various deformation mecha-nisms that can be studied by in situ TEM mechani-cal testing. Reprinted with permission from Yu Q,Legros M, Minor AM. 2015. In situ TEMnanomechanics. Mrs Bulletin 40, [97]: (c) 2015Cambridge University Press.


struments AB® companies further implemented theindenting holders by adjoining them a micro loadcell [98].

In the recent years, nanoindentation, AFM,MEMS-based testing device and scanning tunneling

microscope [99] probe were integrated with the TEMplatform [97,98,100]. In situ mechanical testing viananoindentation, AFM and MEMS device have re-vealed novel deformation phenomena and size de-pendent responses in nano-sized materials[28,59,101-104]. Different holder setups have beendeveloped based on the desired mechanical testand sample geometry (Fig. 4).

For compression tests carried out inside TEM,one of the main concern is always whether the highenergy electron beam (e-beam) affect the measuredmechanical properties or not. The answer is, formaterials with metallic bond, no obvious effect hasbeen observed so far [105]. However, for materialswith covalent and ionic bonds, significant e-beameffect has been confirmed. One typical example isZheng et al. [106] study on amorphous SiO2spheres. As they found during the compression testat room temperature, the flow stress can be de-creased by four times when the e-beam is illumi-nating the sample comparing the condition e-beamis shielded from the sample (Fig. 5) [105].With the advent of the atomic force microscope(AFM) and specialized depth sensing indenters, theprobing of mechanical properties on the micro- andnano-scale under ultra- low loads has become pos-sible [33]. This advancement in technology hasproven useful for understanding the mechanical

Fig. 4. Examples of in situ TEM mechanical testing techniques: (a) Tip of a classical straining holder (b)sketch of the various types of straining configurations used in nanoindentation holders, (c) Push to pulldevice with a Hysitron PI-95 nanoindenter. Reprinted with permission from: Legros M. 2014. In situ me-chanical TEM: Seeing and measuring under stress with electrons. Comptes Rendus Physique 15, [98]: (c)Elsevier Ltd. Carlton CE, Ferreira PJ. 2012. In situ TEM nanoindentation of nanoparticles. Micron 43 [105]:(c) Elsevier Ltd. Kacher J, Yu Q, Chisholm C, Gammer C, Minor AM. 2016. In Situ TEM NanomechanicalTesting. In: Prorok B., Starman L. (eds) MEMS and Nanotechnology, Volume 5. Conference Proceedings ofthe Society for Experimental Mechanics Series [106]: (c) 2014 Springer Nature.

Fig. 5. The effect of E-beam on the mechanicalbehavior of an amorphous silica particle. The con-tact pressure decreased about four times when elec-tron beam was switched from off (black curve) to on(red curve). The inset is a frame from the recordedmovie during compression test. Reprinted withpesrmission from Shan ZW. 2012. In Situ TEM In-vestigation of the Mechanical Behavior ofMicronanoscaled Metal Pillars. Jom 64, [105]: (c)2014 Springer Nature.


Fig. 6. Mechanism of the experiment used by Sunet al. [115] to study deformation of nano sized metalcrystals: Graphitic shells encapsulating a metalcrystal (a) are punctured by a focused electron beam(b). Successive electron irradiation of the containerleads to the contraction of the shells and extrusionof the metal crystal (c). The red circles indicate thediameter of the electron beam. Reprinted with per-mission from Sun LT, Krasheninnikov AV, Ahlgren T,Nordlund K, Banhart F. 2008. Plastic Deformationof Single Nanometer-Sized Crystals. Physical Re-view Letters 101, [115]: (c) American Physical So-ciety.

behavior of micro- and nano-scale materials 107-112.As an example, a Hysitron SPM-3800 Atomic ForceMicroscope (AFM) with a pyramidal-shape Berkovichdiamond indenter was used by Gan et al. [113], toperform the nanoindentation measurements of theindividual phases. Wood et al. [114] used AFMnanoindentation to examine the local plasticity andsize dependent hardness of bimetallic Ni–Au NWswith small dimensions attached to chemicallyfunctionalized flat substrates.

In a different method than all the mentioned ex-perimental approaches for nano-compression, Sunet al. [115] designed graphitic cages that contractunder electron irradiation and used them asnanoscopic deformation cells for in situ electronmicroscopy observations of the plastic deformationof individual nanometer-sized Au, Pt, W, and Mocrystals. The principle of their experiment is shownschematically in Fig. 6.

2.2. Sample fabrication and its effect

Similar to the bulk compression test, sample is pre-ferred to be cylindrical in shape, for load displace-ment to stress strain conversion. Moreover, a TEMsample must have a specific geometry, such as afree half-space (Fig. 4b) in front of the electron-trans-parent zone. The use of cylindrical nanopillars witha constant section deformed by flat punch tips isthe easiest way to measure stress from load values[28,35,116].

Experimental techniques such as electron-beamlithography [117-123], scanning tunneling

microscopy [124,125], scratch lithography [126] withatomic force microscopy [127], cluster-beam depo-sition of metallic etch masks [128-130], nanospherelithography [130-138], laser irradiation [139-141] havebeen used to fabricate nano or micropillars. How-ever, not all of them are suitable for the fabricationof nano and micro-compression samples, mainlybecause they don’t make pillars with the uniformcross section along the sample height. Moreover,some of the mentioned techniques are difficult tobe applied for metallic pillar fabrication.

Following the approach of fabricating micropillarsby utilizing focused ion beam (FIB) machining toetch patterns of interest, which was developed byUchic et al. [35] and used by Greer et al. [36], Greerand Nix [6] extended this technique to much smallerpillars in the scale of nano. The fabrication ofnanopillars by FIB is relatively easy, site-specificand can be applied to a wide range of materials.The principles of pillar fabrication with this methodhas been described in [142,143], and [144]. Till now,many scholars have used this method to fabricatesub-micron and nanopillars [6,25,28,40,41,49,94,145-148].

Although FIB milling became a key technologyin small scale mechanics, its side effects raise se-rious concerns about the validity of mechanical data.When the Ga+ ions hit the sample surface duringFIB imaging or milling process, structural defectssuch as point defects and dislocation loops, or evenamorphization are induced into the surface due tothe knock-on displacement and/or Ga+ implantation[149,150], as revealed by transmission electronmicroscopy [28,151-154], X-ray diffraction [155] andatom probe tomography [156]. The FIB effect ondislocation density cannot be ignored when plastic-ity of small scales is studied and is already knownto significantly affect the mechanical properties [25].The thickness of the damaged layer could be around10 to 100 nm, depending on the material and ex-perimental conditions [150,152,156]. Therefore, com-pression tests of sub-micron and nanopillars fabri-cated by FIB milling, may measure the compositemechanical response of a material and its FIB-modi-fied surface rather than measuring the intrinsic prop-erties of a material [146]. According to Lee et al.[157], surface damage induced by FIB irradiation,such as surface roughness or injected dislocationloops, would reduce the yield strength of a defect-free crystal, since facilitates dislocation nucleationat surface. The effect of Ga+ implantation is not lim-ited to mechanical properties, but can also changethe physical properties and the thermodynamic sta-bility [149]. Therefore, compression tests of


nanopillars fabricated by FIB milling, rather thanmeasuring the intrinsic properties of a material, maymeasure the composite mechanical response of amaterial and its FIB-modiûed surface. Moreover, theinûuence of this damaged surface layer increaseswith decreasing specimen size. Hence, character-izing the effects of the FIB damaged layer on me-chanical properties is important in interpreting theresults of nanopillar tests. Remarkably, pillars pre-pared by FIB milling, exhibit a strong size depend-ent strengthening and as the pillar diameter becomessmaller, its flow stress increases as a power law:=d-n, where d is the pillar diameter and n lies be-tween 0.6 and 1 for fcc metals[25,30,31,36,41,51,74,94,145,158-163], 0.22 and0.45 for bcc [30,41,48,55,58,94,160,164-169]. Hex-

agonal close-packed materials also appear to fol-low a power law, but with a lack of data the scalingbehavior is less clear [66,165,170-172] and verydependent to the loading orientation so that Aitkenet al. [170] found n to be 1.11 for AZ31 nanopillarsoriented for basal slip and 0.36 for those compressedalong the c-axis. The mechanical size effect on Au(fcc), Mo (bcc) and Ti (hcp) is shown in Fig. 7, whichillustrates the stress at 5% strain as a function ofdiameter. Because of possible slight misalignmentin the initial stages of deformation, ûow stresses at2.5% to 10% strain and when full contact is estab-lished, have been compared in papers rather thanyield stresses, which cannot be unambiguouslydeûned in the experiments [37].

Shim et al. [173], showed that by doing ion bom-bardment parallel to the surface (glancing inci-dence), the range of penetration of Ga ions into thesurface can decrease significantly, compare millingwith normal incident angle (Fig. 8).

However, it was shown that other mechanismssuch as “mechanical annealing” can remove thision damage [28]. Greer and Nix [6] decreased theGa+ ion concentration by removing the conformalsurface layer by etching the rotating pillar in low-energy Ar+ plasma and annealing. Lee at al. [174],showed that dislocation loops formed by the high-energy Ga+ ion beam impact near the surface ofsub-micron Al pillars can be removed by in-situ TEMannealing at around half of the melting point (T

m).

Burek and Greer [175,176] used Electron BeamLithography coupled with Electroplating techniqueto create isolated, vertically oriented, and virtuallytaper-free metallic nano-scale mechanical testing

Fig. 8. Results of stopping and range of ions in matter (SRIM) calculations for 30 keV Ga ion penetrationinto pure Mo at (a) glancing incidence (1°) and (b) normal incidence (90°). Reprinted with pesrmission fromShim S, Bei H, Miller MK, Pharr GM, George EP. 2009. Effects of focused ion beam milling on the compressivebehavior of directionally solidified micropillars and the nanoindentation response of an electropolished sur-face. Acta Materialia 57: (c) 2009 Elsevier Ltd.

Fig. 7. Size effect on the strength of FIBed pillars(strength is taken as the flow stress at 5% plasticstrain). Adapted from [55] and [60].


specimens with diameters from 750 down to 25 nm.According to Burek and Greer [175], this fabrica-tion method allows control over the pillar microstruc-ture from nanocrystalline to single crystalline. Theprocess had already been used by Greer et al. [6,36]to fabricate micron and nano-scale gold pillars andinvestigate the effect of fabrication process on sizeeffect behavior at these scales. Fabrication methodinvolves lithographic patterning of polymethylmeth-acrylate (PMMA) resist with electron beam, follow-ing by metal electrochemical deposition into theprescribed resist template. Fundamentally, this fab-rication approach is analogous to other template-based syntheses wherein one-dimensionalnanostructures are fabricated by electroplating intothe pores of either polycarbonate or alumina mem-branes. As Burek and Greer [175] claimed, the proc-ess has several advantages over the conventionalFIB milling of nanopillars. At first, by replacing FIBfabrication with a procedure that does not utilize ionbombardment, the metallic nanopillar crystallinestructure is absent of Ga+ ion damage. At secondelectroplating makes it possible to fabricate pillarssmaller than 100 nm, which is difficult using othermethods [52,76,177]. Third, when optimized thisfabrication method greatly reduces pillar taperingrelative to FIB fabrication and virtually eliminates thepresence of any appreciable strain-gradients in thedeformation process. Finally, the FIB fabricationprocess is inherently slow and significantly limits

Fig. 9. Flow stress vs pillar diameter for the FIBed, electroplated, annealed, and Ar plasma-treated pillarscompared with the range of theoretical strength and the yield strength of bulk Au. Reprinted with permissionfrom Greer JR, Nix WD. 2006. Nanoscale gold pillars strengthened through dislocation starvation. PhysicalReview B 73, [6]: ©2006 American Physical Society.

the sample throughput time. Moreover, the processcan be easily applied for the fabrication of morecomplicated geometries like hollow cylindricalnanopillars [69].

According to Greer and Nix [6], the electroplatedpillars, which were never subjected to the Ga+ ions,not only have flow stresses higher than bulk metalbut also exhibit a similar rise in strength as the di-ameter is reduced (Fig. 9). As they observed, theGa+ removal and pretest-annealing resulted in datathat falls on the curve formed by the FIB pillars.Jennings and Greer [52,76] fabricated Cu nanopillarswithout the use of Ga+ and containing several initialdislocations, with electroplating technique and ob-served an identical size effect to the ones fabricatedby FIB (Fig. 10). As Greer and Nix [6] concluded,the observed size effect in small scale is not linkedto a specific fabrication technique. While some mini-mal Ga+ might be present on the surface of the pil-lars, it is not a major contributing factor in the strengthincrease. The same conclusion was reached byDietiker et al. [178], as they compared the behaviorof pillars fabricated by FIB machining andnanoimprinting. However, as Kiener et al. [103]pointed out, length scale depends on the defectcharacteristics in the material. They irradiated ori-ented copper single crystal using a 1.1 MeV protonbeam at near-ambient temperature and subse-quently FIB machined nano-compression samplesand performed quantitative in situ tests in a TEM to


investigate the influence of irradiation defects on thematerial properties (Fig. 11). As they observed, whilethe non-irradiated samples exhibited a size depend-ent behaviour over the entire size ranges, the irradi-ated ones followed this trend only for specimen di-ameters up to ~400 nm. They concluded that thistransition length scale depends on the defect char-acteristics and therefore on the material, irradiationdose and temperature. For the irradiated samples,deformation was observed to be strongly localizeddue to the requirement of forming a large enoughdislocation source in a volume containing denselyspaced irradiation defects.

3. SMALL SCALE DEFORMATIONMECHANISMS

3.1. FCC metals

For typical face-centered cubic (FCC) metals likeAg, Au, Cu, Ni, and Al with various stacking faultenergy values (~22, ~45, ~78, ~128 and ~166 mJ/m2, respectively) [179], it was found that when thesample size is reduced to nano-scale, the mechani-cal properties such as yield strength and plasticitywould both increase [6,35,179,180].

Fig. 12 shows examples of the mechanical prop-erties and flow behavior of sub-micron scale singlecrystalline gold and nickel pillars. The most obvi-

Fig. 10. Flow stress at 10% strain for Cu nanopillarsfabricated by electroplating, presenting a power-lawtrend with n=”0.63, nearly identical to the trend dem-onstrated in FCC metals represented by the solidline. Reprinted with permission from Jennings AT,Burek MJ, Greer JR. 2010. Microstructure versusSize: Mechanical Properties of Electroplated Sin-gle Crystalline Cu Nanopillars. Physical ReviewLetters 104, [52]: ©2010 American Physical Soci-ety.

Fig. 11. Comparison of size dependent behavior ofirradiated and unirradiated copper samples. Whilethe unirradiated copper (open circles) exhibits a sizedependent yield strength over the whole size range,the irradiated samples (red symbols) show this be-haviour only when the size is less than 400 nm.Reprinted with permission from Kiener D, HosemannP, Maloy SA, Minor AM. 2011. In situnanocompression testing of irradiated copper. NatMater 10, [103]: ©2011 Nature Publishing Group.

ous difference between pillars, whiskers, and bulksingle crystals is the observed stress for plastic flow.Bulk single crystals deform at very low strengths,on the order of 10s of MPa. Micro and nanopillarsrange in strength from bulk-levels at large pillar di-ameters to gigapascals at 200 nm, as seen in Fig.12; however, the strengths for the smallest pillarsare still significantly lower than similar size whisk-ers which have near theoretical strengths [181]. Asis seen in Fig. 12, in the larger pillars, the stressstrain curve is continuous and similar to that ob-served in a standard bulk compression tests; while,in smaller pillars with diameters below ~1 m, thedeformation behavior is distinct from bulk tests andis characterized by discrete bursts of plasticity (pop-ins [182]) corresponding to dislocation avalanches.Furthermore, after a dislocation avalanche, the pil-lar loads again until a subsequent dislocation ava-lanche occurs at a similar stress level.

3.1.1. Dislocation starvation andnucleation control

One of the most likely deformation modes that canresult into the observed high strengths is explainedby the concept of dislocation starvation. Accordingto this scenario [6], in small volumes mobile dislo-cations are thought to escape from the crystal atthe nearest free surface before multiplying and in-teracting with other dislocations. Such processes


(a)

(b)

Fig. 12. Stress-strain behavior of (a) oriented FIBed Au and (b) Ni pillars of different diameters,[6,145]. Reprinted with permission from Greer JR, Nix WD. 2006. Nanoscale gold pillars strengthenedthrough dislocation starvation. Physical Review B 73 (6), ©2006 American Physical Society. Reprinted withpermission from Frick CP, Clark BG, Orso S, Schneider AS, Arzt E. 2008. Size effect on strength and strainhardening of small-scale [111] nickel compression pillars. Materials Science and Engineering A 489 (147):(c) 2008 Elsevier Ltd.

lead to a dislocation-starved state, and nucleationof new dislocations in the newly-formed perfect crys-tal is required to accommodate further plastic de-formation. According to Greer et al. [32,36,183,184]description, a dislocation must travel a minimumdistance, (also called breeding distance) before itreplicates itself, and when crystals is smaller thanthis characteristic length, it might behave quite dif-ferently from bulk crystals. When the conditions formultiplication are not met, the dislocations wouldleave the small crystals before having the chance ofmultiplication, leading to dislocation starvation. Oncethe dislocation-starved conditions are reached, veryhigh stresses would be required to nucleate newdislocations, either at surfaces or in the bulk of thecrystal, which could describe the observed near-theoretical-strengths at small scales.

Fig. 13 shows Shan et al. [28] results as theyevaluated the dislocation starvation theory. As theyobserved, the dislocation content of the nanopillarsdropped markedly when deformed in the TEM. Withthis exhaustion, which the authors call ‘mechanicalannealing’, the process controlling strength and plas-ticity changes from dislocation propagation and in-teraction to dislocation nucleation [116].

Jerusalem et al. [185], proposed a continuummodel accounting for dislocation starvation and nu-cleation. As they described, a reference of the aver-age dislocation resistance shear stress for each slipsystem i can be describes as,

i

starv starv0 0,starv 0,nucl 0,nuclmin 1 , ,

(1)


where

abb

a b0

0,starv 0

0

0.5 1.4 ln .4 (1 )

(2)

and starv

considers the plastic strain for which nu-

cleation dislocation is more favorable than disloca-tion starvation, and at which the nucleation criticalresolved shear stresses (CRSS)

0,nucl is reached.

According to Zhu et al. [186] theory, the requiredstress for dislocation nucleation is proportional tothe logarithm of the number equivalent surface nu-cleation sites; N, which is directly affected by thesample geometry. Since nucleation stress is a func-tion of logarithm of N, the size effect arising fromsurface nucleation is expected to be weak, com-pared to that in micropillars showing a power-lawscaling exponent in the range of “0.6 to “0.7[31,36,50,51,145]. As Zhu et al. [186] assumed, atransition in the scaling behavior of yield stress couldbe expected on the sample size in an approximaterange of tens of nanometers, as illustrated byFig. 14.

TEM studies on partial dislocation nucleationhave highlighted the role of various surface defects

Fig. 13. In situ TEM compression of oriented 160 nm Ni pillar. a) Dark-field TEM image of the pillarbefore the test, showing high initial dislocation density, b) Dark-field TEM image of the same pillar after thefirst test which is now free of dislocations, c) Dark-field TEM image of the same pillar after the second test.d) Force versus displacement curve of the first and e) second test. f) Instantaneous stress versus compressivedisplacement for the two tests; the apparent yield stress is similar for both tests. Reprinted with permissionfrom Shan ZW, Mishra RK, Asif SAS, Warren OL, Minor AM. 2008. Mechanical annealing and source-limited deformation in submicrometre-diameter Ni crystals. Nature Materials 7, [28]: ©2008 Nature Publish-ing Group.

in dislocation nucleation. This is most obvious inthe case of thin films where dislocations preferen-tially nucleate at voids as they serve as stress con-centrations sites during tensile experiments[187,188]. The effect of surface steps on decreas-ing the elastic threshold and assisting the nuclea-tion of dislocations [189-197]. As Navarro et al. [197]calculated, the critical stress for dislocation nuclea-tion at the steps is approximately half that on theflat surface.

Large strain bursts were universally observedduring the compression of sub-micron and nano-sized fcc pillars. However, depending sample size,the underlying physical mechanisms are different.As Wang et al. [198] concluded on his studies onAl pillars, for small pillars (with D=80 to 300 nm,group A), the bursts originate from explosive andhighly correlated dislocation nucleation, character-ized by very high ultimate stresses and nearly dis-location-free microstructure after the sample failure.Fig. 15 shows a 165 nm Al pillar as an example ofthis group. The single crystal is loaded along the[2 20] direction and observed under zoneaxis. FIB induced dislocations are clearly seen inthe darkfield image (Fig. 15c). The first burst ob-


Fig. 14. Transition in the scaling behavior of yield stress on the sample size range of tens of nanometers.Reprinted with permission from Zhu T, Li J, Samanta A, Leach A, Gall K. 2008. Temperature and strain-ratedependence of surface dislocation nucleation. Physical Review Letters 100, [186]: (c) American PhysicalSociety.

Fig. 15. Snapshots of the microstructural evolution in 165 nm Al nanopillar compression. (a) Engineeringstress-strain curve (b) The load-time and displacement-time curves. (c) Dark-field images of the pillar beforecompression. (d) Dark-field images of the pillar after collapse (~20% strain). Reprinted with permission fromWang Z-J, Li Q-J, Shan Z-W, Li J, Sun J, Ma E. 2012. Sample size effects on the large strain bursts insubmicron aluminum pillars. Applied Physics Letters 100, [198]: © 2012 AIP Publishing LLC.

served in the stress strain and load time curves (Figs15a and 15b) is caused by the cleaning-up of pre-existing dislocation which were driven out of the pil-lar, in a process known as mechanical annealing

[25,28,101,116,198,199]. Here, the CRSS is equalto the starvation CRSS in equation 1 and then lin-early increases as a function of as the mobiledislocations are moving towards the free surface.


Once all mobile dislocations are annihilated, plas-ticity is fully nucleation driven and second drop atstress, marked point 2, happens when new dislo-cations nucleate from the contact interface betweenthe pillar and the indenter. However, since there isno dislocation in the pillar, the new ones movethrough it very fast and escape immediately out ofthe pillar. The drastic strain burst happens in point3, where the structural collapse occurred, in resultof a major shape change within a small fraction of asecond [198]. Post-test, dark-field observation un-der multiple conditions confirmed that this test leftbehind a dislocation-free pillar (Fig. 15d) [28,198].The pronounced decrease in dislocation densityduring the nano-compression tests provides directsupport for the dislocation starvation theory that hasbeen hypothesized based on experiments[6,30,32,36,94] and simulations [38,185,186,200].As Shan et al. [28] pointed out, even the surfaceoxide layer [201] and the FIB damage layer [152],cannot trap dislocations inside the pillar during de-formation [105]. The driving force for the dislocationstarvation within the pillars is a combination of theapplied stress which will activate or nucleate dislo-cations and the image forces from the surface whichwill assist the dislocations in moving towards thefree surfaces of the crystal [28]. The mechanical

Fig. 16. Stress and dislocation density evolution versus strain for a 150 nm diameter Cu pillar. Insets showthe dislocation microstructures at different points along the stress–strain curve. Reprinted with permissionfrom Ryu I, Cai W, Nix WD, Gao H. 2015. Stochastic behaviors in plastic deformation of face-centered cubicmicropillars governed by surface nucleation and truncated source operation. Acta Materialia 95, [202]: (c)2015 Elsevier Ltd.

annealing phenomena is more signiûcant in smallerthe samples [105].

Fig. 16 shows the result of a dislocation dynam-ics (DD) simulation on the behavior of a 150 nm Cupillar in which all dislocations escape the crystalduring the early stages of loading and half loop dis-locations are introduced into the crystal from thesurface, when the stress reaches the critical dislo-cation nucleation stress. If the applied load is notdrop, then these new dislocations will traverse thepillar and subsequently escape and this process isthen repeated with the flow stress reaching a pla-teau without any significant hardening [202].

3.1.2. Single arm dislocation sourcecontrol

Some scholars have proposed a mechanism basedon the operation and stochastic effects of a singlearm dislocation source within a pillar in the scale ofmicrometer, believing that the micropillars containseveral dislocation sources, but only one or two forthe slip plane in the small pillars [153,203]. AsParthasarathy et al. [203] described, in finite sam-ples, where the sample dimensions are of the sameorder of magnitude as the source lengths, all sourcesend up as being single-ended due to interaction with


Fig. 17. (a) A schematic description of changing adouble-pinned Frank–Read sources to single armsources in a small volume. (b) Representation ofsingle arm sources in a finite cylindrical sample incritical configuration, which occur where the distancefrom the pin to the free surface is the shortest. Thelongest arm determines the critical resolved shearstress. Reprinted with permission fromParthasarathy TA, Rao SI, Dimiduk DM, Uchic MD,Trinkle DR. 2007. Contribution to size effect of yieldstrength from the stochastics of dislocation sourcelengths in finite samples. Scripta Materialia 56,[203]: (c) 2015 Elsevier Ltd.

Fig. 18. Single arm source operating in a 750 nmwide Al fiber for a finite time (54 loop emissions in38 s). (a) and (b) are video frames that correspondto the source operating and stopping, respectively.Reprinted with permission from Mompiou F, LegrosM, Sedlmayr A, Gianola DS, Caillard D, Kraft O.2012. Source-based strengthening of sub-microm-eter Al fibers. Acta Materialia 60, [204]: (c) 2012Elsevier Ltd.

the free surface, as in Fig. 17b. Fig. 18 shows oneof single arm sources operating in a 750 nm wide Alfiber [204]. In Fig. 18a, the spiral source is capturedwhile generating dislocation loops in a (111) glideplane by turning clockwise around a fixed arm. Themoving arm propagates to the right, and forms apile-up because of the non-immediate evacuation ofdislocations to the free surfaces. Thick slip traces(noted Tr. in Fig. 18a) are evidence of the slow shearof the native oxide by the dislocations. The sliptraces are erased when the source stops by cross-slipping of the fixed arm, meaning that the disloca-tions have completely escaped the crystal (Fig. 18b).This single arm mechanism has been found accept-able and used in discrete dislocation dynamicsimulations [200,205-212]. Moreover, some physi-cal models have been developed based on thisstochastic effect, such as the single arm source(SAS) model [180,203,206,213,214]. Pan et al.[215], examined the dislocation pile-up mechanismquantitatively and provided a revised SAS model fordescribing the size dependent strength by recon-sidering the back stress and activation stress.

The critical resolved shear stress to activate asingle arm dislocation source is generally computedby summing the friction stress, the elastic interac-tion stress, and the line tension stress. Choosing

Parthasarathy et al. [203] equation and consideringmaterial parameters, Lee and Nix [180] expressedthe required CRSS as,

S

S

k bk b

DCRSS 0 tot

max tot

0.5 ,( , , )

(3)

where CRSS

is the CRSS for the activation of theweakest single arm source,

0is the friction stress,

ks is the anisotropic shear modulus, b is the mag-

nitude of Burgers vector, tot

is the total dislocationdensity, is a constant of the order of unity, and

max is the statistical average length of the weakestsingle arm dislocation source, D is the pillar diam-eter, and is the slip plane orientation. As Lee andNix [180] described, if all of the samples have asimilar dislocation density and slip plane orienta-tion,

max becomes only diameter dependent, which


indicates the capability of SAS theory for describ-ing size scale properties.

The stability of dislocation sources has beenstudied in the literature. Molecular dynamicssimulations have shown that jogs on Lomer–Cottrelldislocations that might form the pinned part of sin-gle arm sources are unstable in the high stress load-ing conditions required to deform Al nanopillars ofdiameter 16–50 nm [216], while 3D discrete dislo-cation plasticity (DDP) simulations approved theimportance of image stresses and cross-slip in con-trolling the lifetime of intermittent sources which tendto be longer lived in larger diameter samples [200].However, TEM observations of deformation of Al fibersof diameter 120 nm confirm that although operatingintermittently, an individual single arm dislocationsource is sufficiently stable to generate large plas-tic strain [217].

Investigating single arm source controlled plas-tic ûow in the micropillars with diameters from 200to 800 nm is extensively investigated by a statisti-cally, Cui et al. [206] noted that the SAS mecha-nism itself is not suitable to explain the hardeningbehavior of very small or very large samples. As thesample size decreases, the image force becomeslarger and together with the external applied stress,the dislocations can be easily driven out of the crys-tal, resulting that available dislocation sources be-come progressively exhausted, even causing dislo-cation starvation. The similar conclusion was madeby Gu et al. [218], pointing out that in fcc singlecrystalline metals, dislocations are generated bythe operation of the single arm dislocation sourcesin micrometer-sized structures and via dislocationnucleation at surfaces in nanometer-sized structures[214,218-220].

Hu et al. [221], studied the behavior 300 to 700nm diameter gold particles and resulted that abun-dant dislocations nucleation and storage exist in-side their 400 and 500 nm particles during the com-pression, while few dislocations nucleate inside thesmaller particles, concluding that the accumulatedemission mechanism controls the collapse of rela-tive larger particles and correlated emission is domi-nant for the smaller ones. As Jennings et al. [52]stated, the same deformation mechanisms governflow behavior of nano-scale samples regardless offabrication methods.

Modifying Jerusalem et al. [185] model (Eq. (1)and considering SAS operation mechanism, Cui etal. [206], developed a more general theoretical modelto quantitatively describe the sub-micron plasticbehavior as follows,

k bb

0star

nucl nuclstar

min 1

, ,

(4)

where is the engineering plastic strain, and star

is

the plastic strain for which dislocation nucleation ismore favorable than SAS operation, and at whichthe CRSS for dislocation nucleation

nucl is reached.

Cui [222] summarized possible mechanisms of FCCsingle crystal plastic deformation in a phase dia-gram shown in Fig 19. As is described, dislocationstarvation is dominant in smaller sample with lowerdislocation density (~1012 m-2). Continuing deforma-tion, dislocations gradually escape from the crys-tal, and surface nucleation controls plasticity. Byincreasing the sample size, it becomes more difûcult

Fig. 19. Plastic deformation mechanisms in FCC single crystal. Reprinted with permission from Y. Cui2017. The Investigation of Plastic Behavior by Discrete Dislocation Dynamics for Single Crystal Pillar atSubmicron Scale, [222]: (c) Springer Singapore.


Fig. 20. Yield stress results of compressing Cu (1 0 0) samples ranging in diameter from 90 nm to 1700 nm.Besides the size eûect, a change in the deformation morphology is shown indicated by differently coloredsymbols. Reprinted with permission from Kiener D, Minor AM. 2011. Source-controlled yield and hardeningof Cu (100) studied by in situ transmission electron microscopy. Acta Materialia 59, [223]: (c) 2011 ElsevierLtd.

to reach the dislocation starvation state and dislo-cation sources emerge because of the interactionbetween internal dislocations. Here, the activationof single arm source plays the main role. If the sam-ple size further increases, classical dislocationmultiplication mechanism controls the deformation.The critical size between different mechanisms de-pends on dislocation density and internal microstruc-ture, as shown schematically in Fig. 19. While thereis still no quantitative expression, it is generallybelieved that the critical size decreases with thedecline of dislocation density [222].

As Kiener and Minor [223] pointed out, the acti-vation of slip planes and changing deformation mor-phology form single slip to alternating slip and mul-tiple slips regimes is dependent to the sample sizeas shown in Fig. 20.

3.1.3. Liquid like deformation

As size scales reaches to the order of 10 nm andsmaller, a new regime of behavior emerges and cur-vature and surface stress effects become more im-portant. As an example, the Laplace pressure in anAu cylinder with diameter of 10 nm diameter andisotropic surface is around 0.28 GPa and this largepressure would have significant effects on both elas-tic and plastic properties [224]. Moreover, new irre-versible deformation modes involving structural tran-sitions would occur at these small size scales. Anumber of researches have been done on theses

scales and the effective phenomena[44,104,115,186,225-230].

According to Sun et al. [231] findings, the shapechange of sub-10-nm silver (Ag) nanoparticles atroom temperature is dominated by surface diffusion,causing them deform like liquid drops but with ahighly crystalline core, which is fundamentally dif-ferent from displacive shear plasticity by disloca-tions. They used a set-up where the Ag nanocrystalwas partially bonded to a tungsten tip that approacheda counter ZrO

2 surface. Fig. 21 shows a typical cy-

cle of compression and stretching of a Ag nanocrystalwith a base diameter of 9.8. As the authors observed,when the Ag nanocrystal was compressed againstthe oxide, it continuously flattened (Figs. 21b–21d),and continuously elongated when the tip was re-tracted (Figs. 21e and 21f). Moreover, they observedthat when the nanocrystal detached from the tip itrapidly recovered the original facetted shape. Visu-alization of the lattice planes in the TEM imagesdemonstrated that the nanocrystal remained as aperfect single crystal during the whole process.Importantly, authors demonstrated that thenanocrystal deformed by surface diffusion, as indi-cated by the atomic planes growth on its externalsurface and is fundamentally different from displaciveshear plasticity by dislocations. These results con-firmed by means of molecular dynamics simulations[232].

Although dislocation based plastic deformationis expected to become inactive below a critical par-


ticle size, which has been proposed to be between10 and 30 nanometers according to computersimulations and transmission electron microscopyanalysis [233], on a recent atomistic simulationstudy by Li [234], it is shown that under very highstresses, dislocations can be accelerated to ap-proach the speed of shear wave over a distance asshort as 10 nm and such high speed dislocationsoften react in counter-intuitive manners that are be-yond the descriptions of conventional dislocationbehavior. As they described a high-speed disloca-tion can “rebound” when hitting a free surface ratherthan annihilate. When two high-speed dislocationscollide, they can “penetrate” through each other. Anindividual dislocation can even spontaneously gen-erate multiple dislocations via self-dissociation.These anomalous mechanisms lead to rapid prolif-eration of dislocations that are strongly correlatedboth spatially and temporally, and as such may playa role in high-stress and high-strain-rate plastic de-formation.

Employing a collection of algorithms that assessthe mechanical behavior of two-dimensionalnanopillars (referred as nanoslab), Yan and Sharma[235] carried out a study of the mechanical com-pression behavior of nanoslabs under both low andhigh strain rates (1 and 108 s–1). Their developedmodel was a 116 atom Ni nanoslab with the x–ydimensions of 25 × 70 Å, periodic in the z-direction.According to their results, while high-strain ratedeformation proceeded with the appearance of shear

Fig. 21. Reversible pseudoelastic deformation of the Ag nanoparticles. (a-d) The Ag nanocrystal underwenta compression and (e, f) stretching cycle, almost recovered its initial size (a). Scale bars, 5 nm. The orangearrows indicate the movement direction of the W tip. Reprinted with permission from Henry CR. 2014. Metalnanocrystals deforming like liquid droplets. Nature Materials 13, [232]: ©2014 Nature Publishing Group.

band, the partially rotation of crystal orientation, anda barrel-shaped structure, the slow-strain rate re-sults exhibited a dramatically different behavior anddeformation proceeded with the start ofamorphization from the top and bottom surfaces andwas followed by material extrusion from the freesurfaces. However, the central region of the nanoslabremained crystalline (Fig. 22). As they concludedthe response of nanostructures to slow compres-sion is more “liquid-like” and accompanied by ex-tensive surface reconstructions which is in consist-ent with Sun et al. [233] results.

3.1.4. Effect of pre-strain and aspectratio

Schneider et al. [236] performed micro-compressiontests on pre-strained nickel single crystals to in-vestigate the effect of the initial dislocation arrange-ment on the behavior and size dependence of smallscale metal structures. They studied 5% and 20%pre-strained Ni pillars with different sizes, rangingfrom 200 nm to 5 m. They found that 20% pre-strained pillar’s exhibited similar shapes for thestress–strain curves, with larger and less frequentstrain bursts curves, comparing the 5% pre-strainedpillars. However, the size dependence of the yieldstrength and strain hardening behavior was differentthan those of the 5% pre-strained pillars and for smallpillar diameters the hardening was more pronouncedfor the 5% pre-strained sample (as quantified in Fig.


Fig. 22. Structure evolution of Ni nanoslab under compression at high strain rate (top row) and low strainrate (bottom row). For the case of high strain rate deformation, the structure experiences the appearance ofshear band, the partially rotation of crystal orientation, and a barrel-shaped structure. For the low strain ratedeformation, amorphization starts from the top and bottom surfaces and is followed by material extrusionfrom the free surfaces. Reprinted with permission from Yan X, Sharma P. 2016. Time-Scaling in Atomisticsand the Rate-Dependent Mechanical Behavior of Nanostructures. Nano Letters 16, [235]: © 2016 ACSPublications.

Fig. 23. Strain hardening rate (SHR) versus pillar diameter for pre-strained Ni single crystals. In order totake into account the sample orientations, the SHR was multiplied by Schmid factor square (fs2). Reprintedwith permission from Schneider AS, Kiener D, Yakacki CM, Maier HJ, Gruber PA, et al. 2013. Influence ofbulk pre-straining on the size effect in nickel compression pillars. Materials Science and Engineering: A559, [236]: (c) 2013 Elsevier Ltd.


23). Analysis of TEM images showed that the dislo-cation density remained in the same order of mag-nitude for 5% and 20% pre-strained sample defor-mation, although the cell wall dislocation densitywas higher for the 20% pre-strained specimens. AsSchneider at al. [236] stated, neither dislocationstarvation nor mechanical annealing were explicitlyobserved with increasing dislocation density by pre-straining and as the pillar size decreases from themicron into nano, a size dependent mechanismbegins to dominate, independent of dislocation den-sity. In situ TEM observations showed that disloca-tions were nucleated near the surface for the sub200 nm diameter pillar, regardless of the presenceof dislocations within the pillar.

Milne et al. [237], observed a distinct change inthe deformation mode occurs as the aspect ratio ofthe Al pillar was increased. As they observed, thedominant deformation mode in 2:1 aspect ratio 900nm diameter pillars was collective slip on multipleslip systems. A reduction of the pillar diameter withassociated increased aspect ratio (4:1 for 450 nmdiameter) leaded to significant delocalized deforma-tion and bulging at the apex to relieve stress. Apexwork hardening was followed by slip band formationon a secondary slip system further down the pillar.A transition to a new mode of deformation was ob-served for nanopillars with diameters smaller than250 nm and aspect ratio of 6:1. Axial buckling of ahigh aspect ratio pillar under axial compression,resulted to the lateral shear of the pillar apex andgenerating a bent morphology and a 90° kink withfurther loading.

3.2. BCC metals

Among the common crystal structures of metals,body centered cubic (bcc) structures pose differentconditions for plasticity compared with the fcc ones,due to the higher Peierls stress and easier cross-slip of the slower screw dislocations. The deforma-tion of bcc metals is generally governed by the screwdislocations, whose mobility is signiûcantly lowerthan that of the edge components, and the possibil-ity of cross slip mechanism increases the probabil-ity of forming dislocation networks which results inthe creation of immobile dislocation sources insidethe nanopillar [57].

Although mechanical annealing has been widelyobserved in fcc metals, many scholars believe thatsuch phenomena cannot exist in bcc metals for thefollowing reasons. For the first reason, in a molecu-lar dynamics simulation on Mo nanopillar deforma-tion, Weinberger and Cai [39] found that under com-

bined effects of the image stress and dislocationcore structure, a dislocation nucleated from thesurface of a BCC pillar generates one or more dislo-cations moving in the opposite direction before itexits from the surface. According to their results,the process of self-multiplication is repeatable sothat a single nucleation event is able to produce amuch larger amount of plastic deformation than thatin FCC pillars. As the second reason, bcc metalsare less size dependent at room temperature thanfcc small samples [30,40,41,55,164]. As the thirdreason, postmortem STEM micrographs observa-tion found that deformed, nano-scaled, single crys-tal Iron still have obvious dislocations in the crystal[238]. However, Huang et al. [239] showed that sig-nificant mechanical annealing occurs in BCC Mopillars, when their diameters decrease to hundredsof nanometers.

Therefore, the governing mechanism for defor-mation of bcc nanopillars may be different from thatof fcc nanopillars, and many scholars have tried toexplain the size dependency of BCC nanopillar be-haviour. Recently, pillar compression studies of dif-ferent bcc metals including Mo [30,41,48,55,94,164,240-242], Nb [48,49,55,95], Ta [48,55,58],V [56,243], W [48,55,58,95], and Fe [238,244,245],have been reported.Fig. 24 shows typical compressive stress–strain

curves of [235] oriented Mo, W, and Nb pillars withvarious diameters in compression, showing muchhigher attained flow stresses by the nanopillars withsmaller diameters. It is noteworthy that the shapesof these curves demonstrate that the plastic defor-mation regions for smaller pillars are composed ofdiscrete strain bursts followed by reloading seg-ments. Most of the reloading segments appear tobe elastic as is observed in fcc metals.

3.2.1. Dislocation networks formation

Greer et al. [30], compared the deformation behaviorof fcc and bcc single crystals and reported that thedislocation starvation model may not apply to b.c.c.pillars at the diameters considered in their study(300–800 nm). As they described, the dislocationresidence time inside the bcc crystal is relativelylonger than that of fcc pillars, and the image stressesseem to enhance a dislocation’s afûnity for self-rep-lication when approaches a free surface and entan-glement of these dislocation segments inside thepillar can contribute to increased ûow stress, simi-lar to the forest hardening model that describes theplasticity of bulk crystals (Fig. 25).


Fig. 24. Typical compressive stress–strain curves of [235] oriented (a) Mo, (b) W (c) Nb pillars [164,166].Reprinted with permission from Schneider AS, Clark BG, Frick CP, Gruber PA, Arzt E. 2009. Effect oforientation and loading rate on compression behavior of small-scale Mo pillars. Materials Science andEngineering a-Structural Materials Properties Microstructure and Processing 508 [166]: (c) 2009 ElsevierLtd. Reprinted with permission from Schneider AS, Frick CP, Clark BG, Gruber PA, Arzt E. 2011. Influenceof orientation on the size effect in bcc pillars with different critical temperatures. Materials Science andEngineering a-Structural Materials Properties Microstructure and Processing 528 [168]. (c) 2011 ElsevierLtd.

Fig. 25. Dislocation gliding along (0 1) plane in a b.c.c. pillar. The dislocation orients as a screw one andemits additional dislocations promoting strain hardening. Reprinted with permission from Greer JR, WeinbergerCR, Cai W. 2008. Comparing the strength of f.c.c. and b.c.c. sub-micrometer pillars: Compression experi-ments and dislocation dynamics simulations. Materials Science and Engineering a-Structural MaterialsProperties Microstructure and Processing 493, [30]: (c) 2008 Elsevier Ltd.


As Kim et al. [48] pointed out, while FIB-fabri-cated bcc Mo nanopillars show size effects in theflow stress, the underlying foundation for this sizedependent strength is quite the opposite of fcc met-als and rather than annihilating at the free surfaces,dislocations in bcc metals have been found to formintricate networks as a result of mechanical defor-mation even in the smallest pillar size of ~200 nmdiameter [48].

SEM images of niobium (Nb) single crystallinenanopillars before and after uniaxial compressionare shown in Fig. 26. The compressed nanopillarsshowed fine and coarse parallel slip lines at thesurface (Figs. 26b and 26c). The measured anglesbetween most of the slip planes and the load-ing direction, (~43°), shows that many slip planesare likely to be in {110} planes. Generally, disloca-tion motion via cross-slip is prevalent in bcc metalssince the screw dislocations are able to glide indifferent {110} planes or combinations of {110} and{112} planes, often resulting in wavy and ill-definedslip lines [246]. However, Kim et al. [49] deformednanopillar images, revealed that the slip traces atthe surface are not wavy, but rather are elliptical,indicating the preferential confinement of the dislo-

Fig. 26. SEM images of (a) nanopillar before compression, (b and c) severely compressed (up to ~30% truestrain) nanopillars including pronounced crystallographic slip lines [49] d) Wavy lines in (100) surface ofbulk Nb single crystal after 42% shear strain in compression, in which traces of both active slip planes areparallel [247]. Reprinted with permission from Kim JY, Jang DC, Greer JR. 2009. Insight into the deformationbehavior of niobium single crystals under uniaxial compression and tension at the nanoscale. ScriptaMaterialia 61, [49]: (c) 2009 Elsevier Ltd.

cation loops to a single slip plane without cross-slipping. This observation is different from the ob-served wavy slip traces in the single crystalline bulkNb samples after compression (Fig. 26d, [247]),showing that the mean free path of a dislocationloop’s travel prior to cross-slip in Nb is larger thanmicrometer. This is probably due to the non-negligi-ble effects of the image force imposed by the freesurface.

Fig. 27 shows the bright-field TEM images andthe corresponding diffraction patterns of the Nb 100nm diameter pillar before and after compression [49].Besides the small FIB damage dislocation loops,no obvious dislocation lines are present in the pillarand since the dislocation density of a well-annealedmetal is known to be on the order of 108– 1012 m-2, itcould be concluded that there are no or rare dislo-cations in a 100 nm pillar. The deformed image,however, clearly represents the formation of a com-plex dislocation network, display by the numerousblack features present throughout the pillar, whichhave evolved in result of compression. An interest-ing point is that, the dislocation line segments incrystallographic planes are short, parallel to eachanother, and straight, indicating that dislocation ava-


Fig. 27. Bright-field TEM images and corresponding diffraction patterns of 100 nm Nb nanopillar (a) beforeand (b) after compression, in which the true stress–strain curve and representative slip planes are inserted.Reprinted with permission from Kim JY, Jang DC, Greer JR. 2009. Insight into the deformation behavior ofniobium single crystals under uniaxial compression and tension at the nanoscale. Scripta Materialia 61,[49]: (c) 2009 Elsevier Ltd.

lanches probably occurred in parallel planes with-out interacting with one another. Moreover, no pin-ning points or internal Frank–Read sources can beseen in the image, which confirms the lack of dislo-cation cross-slip [49].

3.2.2. Dislocation starvation

Fig. 28a shows the stress–strain curve of bcc sin-gle crystal Fe–3% Si pillar in result of compression[245]. As is observed the pillar undergoes a seriesof pronounced pop-ins which are indicated by num-bers, and the curve is separated into three partsbased on the stress level and dislocation dynam-ics. Figs. 28b-28e show snapshots of the No. 6 pop-in event occurred in part II. An edge dislocation re-mained at the bottom of the pillar before the No. 6pop-in event, and is temporarily sessile, as marked.Fig. 28b shows the moment immediately before thepop-in event. As seen several sets of dislocationsformed and escaped the pillar during the No. 6 pop-in event. Two sets of them are illustrated in Figs.28c and 28d. In Fig. 28e, the formed dislocationNo. 5 remained at the bottom of the pillar, whichmight be associated with the unexpected tapershape of the sample. Pop-in events Nos. 4 and 5are similar to pop-in event No. 6, which is the edgedislocation dominated process. Figs. 28f-28i

presents snapshots of pop-in event No. 9, whichoccurred in zone III. As Zhang et al. [245] described,the pop-in events in zone III are screw dislocationdominated and are completely different from thoseof zone II. The formed dislocations (1-3) graduallymoved toward the pillar surface during the deforma-tion. Even though parts of the newly formed screwdislocations are covered by the carbon layer, it canbe seen that all of the screw dislocations which movein the same direction (from the bottom to the top)do not undergo self-multiplication as described inRefs. [30,39], since self-multiplication involves theformation of a new dislocation moving in the oppo-site direction to the original ones. It is interesting tonote that, the amounts of stress needed to activateedge (part II) and screw dislocations (part III) aredifferent. This might be related to the difference inPeierls barrier stress between edge and screw dis-locations in bcc crystallite which originates from thedislocation core structure [248].

Fig. 29 compares the residual dislocation struc-ture in the deformed 1000 and 200 nm iron pillars[238]. As it is observed in the STEM images, theresidual dislocation structure in the 1000 nm pillarsis quite different from that of 200 nm samples. For1000 nm pillar (Fig. 29a), a high density of disloca-tions was found in the highly deformed zone whileonly a few dislocations are present in other areas.


Fig. 28. (a) resulted stress–strain curve of Fe–3% Si single crystal pillar compression, the numbers indi-cate the pop-in events and the curve is divided into three parts. (b-e) Snapshots of the No. 6 pop-in eventthat occurred in part II; (b) The moment before the pop-in event. A temporarily sessile edge dislocationremained at the bottom of the sample; (c) dislocations 1 and 2 formed at 1 s and escaped the pillar within=0.03 s; (d) another set of dislocations (3–5) formed at 2.2 s; (e) dislocations 3 and 4 escaped the pillar. (f-i) Snapshots of the No. 9 pop-in event that occurred in part III; (f) The moment before the pop-in event. (g-i)The dislocations moved from the lower pillar rim toward the upper pillar rim. Reprinted with permission fromZhang L, Ohmura T, Sekido K, Hara T, Nakajima K, Tsuzaki K. 2012. Dislocation character transition andrelated mechanical response in a body-centered cubic single crystal. Scripta Materialia 67, [245]. (c) 2012Elsevier Ltd.

However, for the 200 nm pillar, only one residualdislocation can be found in the heavily deformedarea, as indicated by the arrows. This is in consist-ent with dislocation escape due to the mechanicalannealing phenomena.

Using in situ TEM compression of Mo nanopillars,Shan [105] demonstrated that with decreasing pil-lar diameter to hundreds of nanometers, significantmechanical annealing does occur in bcc Mo (Fig.30a). In addition, there was a critical size (~200 nmfor Mo at room temperature) below which thestrengthening exponent increased dramatically tothat similar to fcc metals (Fig. 30b). As Shan [105]described, this regime of size effects in bcc con-

verges to that of fcc, revealing deep connection inthe dislocation dynamics of the two systems. Ob-served phenomena were attributed to the diminish-ing importance of lattice friction at high stresses,when the size enhanced flow stress exceeds a sin-gle screw dislocation’s lattice friction.

3.2.3. Cross-split of edge dislocations

Kositski et al. [107], proposed a rapid conservativeathermal dislocation mechanism by which edge dis-locations overcome obstacles and change their glideplane by splitting (Fig. 31). This mechanism is acollective process by which edge dislocation splits


Fig. 29. Postmortem bright-field STEM images of the Fe pillars after compression tests. (a) 1000 nm; (b)magnified image of the area framed in (a); (c) 200 nm; (d) magnified image of the area indicated by the twowhite arrows in (c). The dislocation line marked by the black arrows. Reprinted with permission from HuangR, Li QJ, Wang ZJ, Huang L, Li J, et al. 2015. Flow Stress in Submicron BCC Iron Single Crystals: Sample-size-dependent Strain-rate Sensitivity and Rate-dependent Size Strengthening. Materials Research Letters3, [238]: Copyright © 2015 Informa UK Limited.

Fig. 30. (a) The typical engineering stress-strain curve for a 142 nm FIBed Mo single crystal. The insets arebright-ûeld TEM images taken before and after the dramatic strain burst. The scale bar represents 100 nm.(b) Maximum ûow stress plotted as a double-log function of pillar diameter D, representing two differentstrengthening exponent values, 1.0 and 0.29 for red and blue lines, respectively. Reprinted with permissionfrom Shan ZW. 2012. In Situ TEM Investigation of the Mechanical Behavior of Micronanoscaled MetalPillars. JOM 64, [105]: © 2012 Springer International Publishing AG.

into two edge dislocations which are not arrestedby the obstacle. They performed MD simulations togain insight into deformation of Fe nanoparticles.The simulations revealed that plasticity starts by

nucleating dislocations at two opposite top verticesof the nanoparticle. Once nucleated, dislocationsare curved with two ends on the facets of thenanoparticle, obtaining mixed characteristics at ends


and an edge characteristic at its center. As the ap-plied stress increased, the dislocations move in theinward directions towards the substrate, and bothends traveled along the edges and the facets of thenanoparticles, straightening the overall dislocationline towards the edge character. In this mechanism,the dislocation line is finally arrested close to thesubstrate, where it gained an edge character alongits entire line. If the particle is sufficiently wide, theslip planes of the dislocations nucleated at verticesA and B reach the substrate without interacting withone another. Since these dislocations are preventedfrom gliding by the interface, further deformation takeplace by additional nucleation events at the two ver-tices and inward propagation. These nucleationevents do not produce catastrophic or substantialstrain bursts as was observed in FCC nanoparticles[50] after each nucleation event and consecutivenucleation events require higher stress in order toovercome the back-stress from the growing pile up,

Fig. 31. MD simulation of a 20.8nm high Fe nanoparticle under compression. (a) The two top verticesmarked with “A” and “B” are the points where dislocations nucleate. (b) A three-dislocation pile-up formed atB is shown (all the atoms were removed except those in the dislocation cores) (c) A view from the bottom onthe dislocation pile-up shown in (b) slightly after the front 1/2[1 1 1] dislocation in the pile-up splits into[001] and 1/2[1 11] dislocations. (d) A bottom view into the particle after cross-split. The color representheight with red being the height of the top facet and blue the bottom. Reprinted with permission fromKositski R, Kovalenko O, Lee SW, Greer JR, Rabkin E, Mordehai D. 2016. Cross-Split of Dislocations: AnAthermal and Rapid Plasticity Mechanism. Scientific Reports 6, [107]. © 2016 Springer Nature.

which manifests itself in hardening of thenanoparticle as it is compressed [107].

3.2.4. Effect of temperature

Schneider et al. [166] proposed that the mobility ofthe screw dislocation controls the size effect of thebcc pillars and with decreasing T

c (critical tempera-

ture; the temperature above which the flow stressbecomes relatively insensitive to temperature andstrain rate) or pillar diameter, the effect of relativescrew dislocation immobility becomes less impor-tant and the strength of fcc and bcc pillars are de-termined by similar dislocation processes. Possi-ble explanations for this behavior include kinetic pile-ups of screw dislocations [164] and kink nucleationat the pillar surface [39].

Generally, for bcc metals, when the tempera-ture is at or above the T

c, the screw dislocations

would glide much easier or the Peierls stress for


bcc metals becomes effectively very small [249].As Han et al. [57] pointed out, the size effects onthe strength of bcc nanopillars are dependent onthe T

cand, equivalently, the Peierls stress (sp).

When the testing temperature is higher than thecritical temperature of a bcc metal, peierls stresscan be neglected, and the strengthening mecha-nism is similar to that for fcc metals with the sizeeffect exponent n in the range of 0.8–1.0. When T <T

c, the effect of sp cannot be neglected, and n would

decrease with increasing sp. A clear reduction inthe dislocation density has been observed after de-formation of V nanopillars, suggesting a low sp forV at room temperature, as expected [57]. Thus somebcc metals like V, display dislocation starvationmechanism due to their low Tc and low sp that fa-cilitated dislocation motion and easier removal fromthe body of the nanopillar, although the rate of dislo-cation removal is slightly slower than that for fccnanopillars [57].

Franke et al. [46] showed that there is a signifi-cant change in the plasticity of a high-melting pointBCC material once the critical temperature is sur-passed. As they described, the mean pop-in loadincreases from (111) to (110) and (100) which showsthe highest resistance against localized yielding.The differences in the pop-in load of the differentorientations was explained by the hydrostatic pres-sure presents in each orientation which aids nucle-ating defects such as twins and stacking fault (SF).

Abad et al. [58] studies on Ta and W micropillarsshowed that the strain hardening behavior is not onlysize dependent but, more importantly, test tempera-

ture dependent and lower SHRs are observed athigher temperatures. This behavior is opposed tobulk BCC metals, where the easier mobility of screwdislocations at higher temperatures increases dis-location forest hardening and could be explained bythe easier activation of dislocation sources near thesurface and better dislocation mobility at higher tem-peratures.

3.3. HCP metals

Compared to bcc and fcc structures, metals with ahexagonal closed-packed (hcp) crystalline structurehave smaller number of slip systems, which makestheir plastic deformation more difûcult. For instance,both tension/compression twinning [250,251] andvarious kinds of pyramidal slips [252] havebeen observed in bulk single or poly crystal hcpmaterials because of the limited number of slipsactivated on the basal and prismatic planes. Espe-cially for micro-compression under c-axis, twinningand pyramidal slips have been found to bethe main sources of deformation [61,62,253]. Ac-cording to Yu et al. [59] studies on titanium allysingle crystal, the stress required for deformationtwinning increases drastically with decreasing sam-ple size until the sample size is reduced to onemicrometer, below which the deformation twinningis entirely replaced by less correlated, ordinary dis-location plasticity. Meanwhile, compression resultsof pure magnesium single micro crystals showedno twinning in samples from approximately 2–10µm in diameter, and the pyramidal slips were foundto dominate the plasticity [61,62].

Fig. 32. Size effect in the flow stress of Ti pillars. (a) Engineering stress–strain curves of compressing Tisamples with different diameters; (b) The flow stress at 5% plastic strain vs the effective diameter (theequivalent circular pillar diameter of the square pillar;

effecrived S4 / ). Reprinted with permission from

Sun QY, Guo Q, Yao X, Xiao L, Greer JR, Sun J. 2011. Size effects in strength and plasticity of single-crystalline titanium micropillars with prismatic slip orientation. Scripta Materialia 65, [60]: © 2011 Elsevier.


Jin et al. [73] characterized the mechanicalbehaviors of electroplated sub-micron cadmium pil-lars by uniaxial compression techniques. Their re-sults revealed that the mechanical strength of sub-micron cadmium structures is sensitive to strain rateand size dependent. As they observed while thestrength of 0.5 and 1.1 m diameter specimens wereslightly higher than bulk, the flow stresses of 130nm diameter ones approached to the theoreticalstrength of cadmium. Representative compressivestress–strain curves of Ti pillars are shown in Fig.32a [60]. Clearly, the higher flow stress is observed

Fig. 33. Example of extension twinning in a 200 nm pure Mg pillar. (a) Dark-field image of the pillar beforethe test. (b) Dark-field image of the pillar after the test, showing that the pillar now has a different orientationfrom the base of the pillar. Inset shows the diffraction pattern of the twinned pillar, revealing that the basalplane is now roughly perpendicular to the loading axis. (c) Engineering stress- displacement curve of thepillar compression. The large load drop seen at 75 nm displacement is a result of a large dislocation burstthrough the pillar. (d-f) frames from the in situ video, corresponding to marked points in (c). At point (d) thepillar is relatively defect free (d) after the large burst of dislocations. At point (e) a twin is nucleated, with theboundary shown in (e). At point (f) the twin boundary has moved through the pillar and is seen in (f). The finalresult is a completely twinned pillar (b). Reprinted with permission from Ye J, Mishra RK, Sachdev AK,Minor AM. 2011. In situ TEM compression testing of Mg and Mg-0.2 wt.% Ce single crystals. ScriptaMaterialia 64, [63]. © 2011 Elsevier.

in smaller samples, and the deformation is charac-terized by a single, large strain burst subsequent toyielding. Fig. 32b shows the size effect on the flowstress at 5% plastic strain (

f), indicating Ti follows

the power law rule (Section 3) with the exponent of-0.5.

3.3.1. Twining

Ye et al. [63] performed in situ TEM nano-compres-sion tests on around 200 nm diameter single crys-tal pure Mg and Mg-0.2.wt.% Ce pillars. They fo-


cused on the two major deformation mechanismsin Mg, i.e. basal plane sliding and twinning. A clearsize effect was found for both deformation mecha-nisms, by measuring the critical stress for nuclea-tion of either basal sliding or extension twinning.They also reported a significant reduction of twiningcritical stress in result of alloying with Ce. Fig. 33shows formation of extension twinning in compres-sion of a pure Mg single crystal

length scale plasticity: a review from the … · eter, the traditional dislocation multiplication...

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