# Fileset

[7c3d-tw8q.pdf](https://mdr.nims.go.jp/filesets/ae7f014c-2c46-4406-9e89-86ad571efda8/download)

## Creator

[Florian Tropper](https://orcid.org/0009-0003-7606-5660), [Takahito Ohmura](https://orcid.org/0000-0001-7528-566X)

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Direct observation of nanoindentation-induced punching-out of prismatic dislocation loops in tungsten](https://mdr.nims.go.jp/datasets/71a62286-b8af-47c2-a7fd-5cc6edad9703)

## Fulltext

PHYSICAL REVIEW MATERIALS 10, L090601 (2026)Letter Editors’ SuggestionDirect observation of nanoindentation-induced punching-out of prismatic dislocationloops in tungstenFlorian Tropper and Takahito Ohmura *Research Center for Structural Materials, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba 305-0047, Japanand Department of Materials Science and Engineering, Graduate School of Engineering, Kyushu University,774 Motooka, Nishi-ku, Fukuoka 819-0395, Japan(Received 26 May 2026; accepted 27 August 2026; published 14 September 2026)While bulk bcc plasticity is traditionally governed by screw dislocation glide, prismatic dislocation loops areproposed as an essential pathway for strain accommodation under severe, local constraints. This experimentalstudy on pure W, as a model bcc system, demonstrates that prismatic dislocation half-loops can develop andpropagate in a triaxial stress field as imposed by nanoindentation. Using electron channeling contrast imaging,the Burgers vector of emitted dislocation half-loops is determined to be 1/2 〈111〉 and the punching-out processis studied during progressive stages of imposed strain. Long arrays of dislocation half-loops are emitted duringthe initial displacement burst (pop-in) and continue to propagate during subsequent loading. Although energeticconsiderations indicate that loop formation alone cannot account for the total plastic deformation energy—implying a concurrent contribution from glide mechanisms—these findings reveal that plastic flow under severehydrostatic stress gradients can be accommodated via non-Schmid loop punching. Crucially, the unique slipsystem multiplicity of the bcc lattice yields highly mobile, circular loop geometries that stand in stark contrastto the faceted loops typical of fcc metals.DOI: 10.1103/7c3d-tw8qThe mechanism of prismatic dislocation loop (PDL)punching, first conceptualized by Seitz [1], represents a funda-mental pathway for crystals to accommodate highly localizedvolume displacement. While PDLs are conventionally asso-ciated with nonconservative processes such as irradiation,they can also form conservatively through complex mechan-ical shear and cross-slip reactions under extreme localizedstress. In face-centered-cubic (fcc) metals, this mechanicalemission of PDLs has been extensively documented bothexperimentally [2–6], via molecular dynamics (MD) [5,7–10] and discrete dislocation dynamics simulations (DDD)[8,11–13]. In contrast, isolating this behavior in body-centered-cubic (bcc) metals remains exceptionally challeng-ing due to their high Peierls barriers and nonplanar dislocationcore structures, which dictate distinct thermally activatedglide kinetics [14]. Consequently, because these intrinsicproperties govern highly dynamic, subsurface defect interac-tions, the exact mechanisms of incipient plasticity and looppunching in bcc systems have largely remained confined tocomputational modeling. MD [15–19] and DDD [20] sim-ulations of nanoindentation have repeatedly predicted thatcomplex stress fields trigger stable PDL emission. Distinctformation pathways, such as local cross slip of shear loops*Contact author: ohmura.takahito@nims.go.jpPublished by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.[17] and twin-induced formation [18] have been found com-putationally. However, direct experimental confirmation hasproven elusive. Although recent nanoindentation studies onpure W observed elongated dislocation configurations, theirexact identity could only be conjectured to be prismatic loops[21,22].In this work, we provide direct experimental evidence ofdeformation-induced PDL formation in bcc metals. Using Was a model bcc material, we demonstrate that the complex,high-stress fields during nanoindentation punch out distinctarrays of PDLs. By systematically utilizing electron channel-ing contrast imaging (ECCI), we clearly resolve the characterand Burgers vectors of these loops in bulk specimens, therebybridging the gap between classical geometric predictions andmodern multiscale computational simulations. Furthermore,by tracking the structural evolution of the PDL arrays acrossprogressive indentation loads, we provide key insights into afundamental nanoscale mechanism for strain accommodationin metals.The material used was high-purity (> 99.999 wt%) single-crystalline W having [011] surface normal direction. Thesample was mechanically polished with diamond suspensionsdown to particle sizes of 1 µm and then electrolyticallypolished with an ice-cold aqueous 2 wt% NaOH solution.Nanoindentation was performed on a TI950 TriboIndenter(Bruker, USA) using a blunt diamond Berkovich tip and asharp diamond cube-corner tip. Tip radii were calculated bythe Hertz elastic contact model [23] to be approximately 700and 40 nm, respectively. Indentation using the Berkovich tipwas conducted at a loading rate of 1000 µN/s to peak loads of4500 µN and 10 000 µN at which the load was held constant2475-9953/2026/10(9)/L090601(6) L090601-1 Published by the American Physical Societyhttps://orcid.org/0009-0003-7606-5660https://orcid.org/0000-0001-7528-566Xhttps://ror.org/026v1ze26https://ror.org/00p4k0j84https://crossmark.crossref.org/dialog/?doi=10.1103/7c3d-tw8q&domain=pdf&date_stamp=2026-09-14https://doi.org/10.1103/7c3d-tw8qhttps://creativecommons.org/licenses/by/4.0/FLORIAN TROPPER AND TAKAHITO OHMURA PHYSICAL REVIEW MATERIALS 10, L090601 (2026)brightdarkTriangular indent10 μm500 nm1 μm70.5°(a) (b)(c)11-1-1-1-1 1-1-11-11011-111-11-1FIG. 1. Backscatter electron micrograph of (a) a Berkovich in-dent with emanating streaks of dislocations. The inset shows astereographic projection with black dots representing 〈111〉 direc-tions parallel to the surface and grey dots representing those pointinginto the sample. (b) The tip of the streak marked in (a) in channelingcondition, (c) opposite contrast of dislocation dipoles in a streakduring out of ideal channeling condition and (d) schematic of twodislocation dipoles from (c).for 10 s. Indents with the cube-corner tip were conducted ata loading rate of 1 µN/s to various peak loads ranging from100 to 1000 µN, each with a holding segment of 10 s. Foreach setup, machine compliance and tip area function werecarefully calibrated prior to testing following the Oliver-Pharrmethod on a reference fused silica sample. Crystal orien-tations were determined via electron backscatter diffractionusing an e-FlashHD detector (Bruker Nano GmbH, Germany)in a scanning electron microscope (SEM) Crossbeam 550(Zeiss, Germany) featuring the Gemini II SEM column andapplying a 20 kV acceleration voltage and 10 nA beam cur-rent. ECCI was done under the same current and 30 kV. ForECCI a circular four-quadrant backscatter electron (BSE) de-tector located below the polepiece was used with all quadrantsturned on and gain set to medium. According to the requiredsample tilts a working distance between 5 and 10 mm wasused. Approximate channeling conditions in the SEM wereachieved via controlled ECCI [24] and position fine tuningdone via comparison of observed electron channeling patternswith a simulated dynamical diffraction pattern as described inSec. I of the Supplemental Material [25].Figure 1(a) presents a BSE micrograph of the W (011)surface after Berkovich indentation with a peak load of10 000 µN. The triangular indent is indicated by an arrow,and a stereographic projection showing the crystal orientationof the sample is inserted at the bottom-left corner of theimage. Indentation resulted in X-shaped streaks extendingmore than ten times the indent size from the indent center.The four visible directions of propagation emanating from theindent follow the crystallographic 〈111〉 directions. Measuringthe included angle of the streaks resulted in 70.5 ° ± 0.5 °[Fig. 1(a)], perfectly agreeing with the ideal angle of 70.53 °.Close observation of the tip of the streaks in the areaenclosed by the yellow rectangle in Fig. 1(a) is presented inFig. 1(b). The image reveals pairs of visible points that areconnected by lines as can be seen towards the end of thestreak. The fading contrast with increasing depth, the fact thatthese features are invisible to secondary electrons and thatthey vanish under certain directions of observation are clearindicators that these must be dislocation lines. Accordingly,the observed streaks consist of dislocation half-loops.Figure 1(c) shows an ECCI micrograph of an area on thestreak about 20 µm from the indent, where only dots are vis-ible. ECCI reveals dislocation contrast up to ∼100 nm belowthe surface [24], explaining why full lines appeared visible atthe streak ends where the half-loops were shallow and small,while larger loops closer to the indent extended deeper intothe material so that only their near-surface interception pointsremained visible as dots characteristic of dislocation dipoles.Moreover, the crystal could be tilted out of perfect channelingconditions so that dipoles showed opposite bright-dark con-trast as seen in Fig. 1(c), indicating the opposite sign of theline vectors of corresponding threading dislocations.The dislocation half-loops were parallel to each other andperpendicular to the streak direction as shown schematicallyin Fig. 1(d). For the 10 000 µN indent they exhibited a mutualspacing of about 200–500 nm close to the indent and mostly100–200 nm at the streak tip. The loop diameter decreasedfrom roughly the indent size down to 300 nm at the streaktip. These values are highly reproducible. The streaks alsoshow an increased surface elevation on the order of 1 nm,as reported previously [22]. Accordingly, material transportoccurs not only laterally but also vertically to a small extent.Burgers vectors b were evaluated by a transmission elec-tron microscopy (TEM)-style diffraction contrast analysisbased on the invisibility criterion, stating that dislocationsbecome invisible when the condition g · b = 0 is met [26],where g represents the diffraction vector. While TEM offersthe advantage of rotational freedom, accurate alignment totwo-beam conditions and thus clear b determination, it islimited in the sample volume that can be probed, and requiressample preparation via focused ion beam, which might riskthe alteration of surface-near dislocations. Moreover, creatingfree surfaces in the stressed volume around the indent by ma-terial removal may lead to relaxation and annihilation of thedislocation loops. Therefore, an analysis approach via ECCIwas employed, which follows the same physical principles asin TEM and additionally allows for quick analysis of multipleindents.Figures 2(a)–2(d) show four diffraction conditions em-ployed to unequivocally identify b at one end of a dislocationstreak. Due to symmetry considerations the findings applyto all four directions of observed streaks. The dislocationcontrast is clearly visible in Fig. 2(a) for g = (−200) and inFig. 2(b) for g = (01−1). Conversely, dislocations are invis-ible in Fig. 2(c) for g = (−21 − 1) and in Fig. 2(d) for g =(3−21). The expected visibilities of possible b in bcc metalsand the observed visibilities are summarized in Sec. II of theSupplemental Material [25]. It is apparent that only b = 1/2[11–1] satisfies these invisibility conditions. Since this b isL090601-2DIRECT OBSERVATION OF … PHYSICAL REVIEW MATERIALS 10, L090601 (2026)1 μm(a) (b)(c) (d)[11-1]g = (-200) g = (01-1)g = (3-21)g = (-21-1)FIG. 2. Electron channeling contrast micrographs of the samelocation (end of a dislocation streak) for Burgers vector b determina-tion. Dislocations are visible in (a), (b) and invisible in (c), (d). Theyellow arrow shows the direction of b; white arrows represent therespective diffraction vectors g for the set of diffracting planes (hkl).perpendicular to the whole segment of the dislocation line,the observed half-loops can be identified as edge dislocations,which explains why they could propagate far outward fromthe indent. Furthermore, regarding the travel direction parallelto b, the observed loops are almost certainly PDLs. Contrarily,shear loops formed purely by glide would lie within a specificslip plane and would almost inevitably contain mixed andscrew segments. The punching-out of prismatic loops is alsoin agreement with accommodating the volumetric deforma-tion imposed by the indenter.To understand the temporal evolution of the streaks,Berkovich indents were carried out at different peak loads.Figures 3(a) and 3(b) show BSE images of the samplesurface after indentation with peak loads of 10 000 and4500 µN, respectively. Corresponding load-displacementcurves are presented in Fig. 3(c). All indents at these loadsexhibited pronounced pop-in at around 4500 µN. It shouldbe noted that the pop-in event occurred during the holdingsegment at peak load in the case of Fig. 3(b), indicating thatthe streaks were formed at pop-in. A comparison of streaklengths for the two different loads and the four observed direc-tions is provided in Fig. 3(d). Indents with the same peak loadfeatured similar streak lengths. While streaks were shorterfor lower peak loads, streaks were still present despite pop-inoccurring during the holding segment. Since the pop-in loadwas naturally the same for different peak loads but the streaklength differed with peak load, subsequent plastic deformationafter pop-in likely dominated the final streak length. There-fore, we suggest that PDLs were instantaneously emitted atpop-in and subsequently traveled during further penetrationof the indenter tip.Moreover, the streak length varied with orientation relativeto the indent geometry. The length was almost double if thestreak was emitted from the side of the indenter [streaks tothe right side on Fig. 3(a)] as compared to emission from a10 μm10 μm(b)10,000 μN(a) 4500 μN11-1-1-11-11-11-11010203040top-left[-11-1]bottom-left[-1-11]top-right[11-1]bottom-right[1-11]Streak length (μm)10,000 μN4500 μN(d)(c)FIG. 3. Berkovich indents at peak load of (a) 10 000 µN and (b)4500 µN. The inset in (a) shows a stereographic projection where redarrows denote the 〈111〉 streak directions. (c) shows the respectiveload-displacement curves; and (d) dislocation streak lengths acrossidentical indents and indents at different peak loads. Error bars de-note standard deviations for 10 measured indents at each load.corner (streaks to the left side). Tests with indents rotated by45 ° confirmed this correlation and corroborated that streakdirection depends solely on crystal orientation (Sec. III of theSupplemental Material [25]).For improved resolution of the PDL emission event, asharper tip was required to enable plasticity at lower loads.BSE images of indents produced by a cube-corner tip atpeak loads of 1000 and 100 µN are displayed in Figs. 4(a)and 4(b), respectively. As the indent dimensions decreased,the streak length, dislocation loop diameter and loop spacingscaled down. The magnified region in Fig. 4(a) highlights thestreak tip, revealing a PDL diameter of approximately 100 nm.Notably, this loop diameter is only a third of that induced bythe blunter Berkovich tip in Fig. 1(b).With decreasing tip radii, the load-displacement curvesof bcc metals typically transition from a single pronouncedpop-in to a staircase behavior, where the intervals betweenthe displacement bursts behave elastically [27]. For the indentshown in Fig. 4(b), between two and nine PDLs are visibledepending on the examined direction.The corresponding staircase-shaped load-displacementcurve, presented in Fig. 4(c), displays nine distinct displace-ment bursts prior to unloading. While it seems plausiblethat each discrete displacement burst may directly correspondto the emission of at least one surface-visible PDL, it isL090601-3FLORIAN TROPPER AND TAKAHITO OHMURA PHYSICAL REVIEW MATERIALS 10, L090601 (2026)2 μm200 nm(a)(b)1000 μN100 μN100 nm(c)WplasticFIG. 4. Backscatter electron micrographs of sharp cube-cornerindents at peak loads of (a) 1000 µN, with the enlarged area indicat-ing the dislocation loop diameter at the streak tip, and (b) 100 µN. (c)Load-displacement curve of the indent in (b), where the shaded arearepresents the integrated plastic deformation energy Wplastic. Pop-insare marked with red arrows.conceivable that the major resistance against deformation maystem from subsurface dislocation nucleation or a dislocationnetwork evolution below the indenter. In this scenario, plasticstrain may be accommodated by the other two potential 1/2[1–1–1] and 1/2 [–1–1–1] Burgers vectors pointing into thedepth directions [see inset in Fig. 1(a)], rendering the emittedsurface PDLs a secondary byproduct.The high reproducibility of even the smaller indentscoupled with sufficient resolution of individual dislocationsallows for an energetic consideration to estimate the contri-bution of the visible dislocations to the total strain. Frombasic dislocation theory the energy of a dislocation loop isthe sum of its self-energy and its interaction energy with otherdislocation loops [14]. Tsuru et al. [28] have derived a relationfor the total energy WD of a line of parallel dislocation loopswith similar spacing dD and loop radius a,WD = nsGb21 − νa{N2(ln8aρ− 1)+ 2π(adD)3 N−1∑α=1N − αα3},(1)where G is the shear modulus, b is the magnitude of theBurgers vector, ν is the Poisson ratio, ρ is the dislocationcore cut-off radius here taken as ρ = b, ns is the number ofactive slip systems, and N is the number of dislocations in thearray. We take the indent in Fig. 4(b) as proxy for present cal-culation. Four slip systems corresponding to the four streaksare activated (not taking into account the other two 〈111〉directions pointing into the depth from the indent) and anaverage of seven dislocations per slip system. As half-loopsinstead of closed PDLs are present, we estimate the overallenergy of the visible half-loops by taking 50% of WD. Theaverage loop diameter was measured to be about 50 nm with amean PDL spacing of 70 nm. Taking G as 160 GPa, ν as 0.28and b as 0.274 nm, a total energy of 6.9 × 10−14 J is obtained.If using the experimentally determined value for G from 100indents of 124 ± 3 GPa instead, WD results in an even lowervalue of 5.3 × 10−14 J. The discrepancy between theoreticaland measured G most likely stems from an elastic contribu-tion of the sample fixture. The WD can be compared to theoverall plastic deformation energy of the nanoindent Wplastic,by integrating the load P over the displacement h. Hereby, apossible influence from energy dissipation via machine com-pliance is already accounted for owing to the initial indentercalibration procedure. Wplastic is equivalent to the elastic andplastic work done during loading Wloading minus the recoveredelastic energy during unloading Wunloading [Fig. 4(c)] given asWplastic =∫ hmax0P(h)dh = Wloading − Wunloading. (2)The resulting 2.3 × 10−12 ± 0.2 × 10−12 J of total inden-tation work is more than 30 times larger than the energy ofthe observed PDLs. Even if streaks of complete PDLs areformed in a similar manner in the other two 〈111〉 directions,deformation energy cannot be accommodated only by PDLformation. Instead, PDLs appear to contribute to a cascade ofstrain evolution events that collectively require much higherenergy levels than PDL formation alone. Graca et al. ar-rived at an analogous conclusion for PDLs in nanoindentedNi using force-based reasoning [4], which aligns with MDsimulations that show required precursor rearrangement steps,such as shear loop nucleation and cross slip, prior to PDLemission [17].L090601-4DIRECT OBSERVATION OF … PHYSICAL REVIEW MATERIALS 10, L090601 (2026)Combining observations from the present study with find-ings from MD simulations [5,9–11,15,17,29], a plausiblesequence for the emission and propagation of PDL arrays canbe reconstructed. Indentation generates a triaxial stress fieldwith large shear components that induce dislocation nucle-ation and interaction at the first displacement burst, duringwhich a loop with b = 1/2 〈111〉 is produced. Once formed,the PDL experiences a driving force from the indentationstress field that pushes it away from the highly stressed zonevia a classic loop-punching mechanism. The local microstruc-tural configuration at the nucleation site can act as a stablesource, sequentially emitting multiple loops. While the inden-ter stress field drives the initial movement of the PDLs, aftera certain propagation distance, the stress field from adjacentloops dominates, pushing the array further outward [11]. No-tably, the first emitted PDLs along the streaks exhibit smallerdiameters than those emitted later. This trend indicates that theloop diameter at emission increases as the imposed volumet-ric change accumulates. Furthermore, because the dislocationlines are most visible—and thus closest to the surface—at thestreak tips, these early PDLs likely glide outward with negli-gible changes in depth or diameter during propagation. Suchstable, long-distance glide is expected for edge dislocations inhigh-purity single crystals due to their structural inability tochange glide planes and the negligible resistance to climb inW at ambient temperatures.Interestingly, PDLs are punched out along directions wheremacroscopic shear stresses are conventionally considered tobe zero due to a vanishing Schmid factor perpendicular to theloading axis. This apparent violation of Schmid’s law arisesbecause PDLs glide along a three-dimensional cylindricalsurface driven by severe localized hydrostatic stress gradi-ents rather than uniform resolved shear stress on a single flatslip plane. Therefore, their propagation fundamentally eludesdescription by classical Schmid kinetics. Instead, the avail-ability of 〈111〉 directions enables easy glide, that channelsthe plastic flow laterally away from the advancing indentersurface. The PDLs represent the elementary steps of materialcylinders being displaced laterally to accommodate indentervolume. While this volumetric relaxation mechanism appearsto be universally operative across bcc, fcc, and potentially hcpstructures, a distinct crystallographic divergence emerges inthe loop morphology. Whereas fcc loops often feature facetedshapes bounded by less glissile dislocation jogs [6], the bccPDLs observed here are strikingly circular as evidenced bythe gradual fading of dislocation contrast in Fig. 1(b). Thiscircular morphology is driven by line-tension energy mini-mization, facilitated by the high multiplicity of symmetrical,intersecting slip systems available in the bcc lattice. Conse-quently, this isotropic energy landscape likely enhances loopmobility, enabling the formation of the exceptionally long,extended streaks of punched-out PDLs.In conclusion, direct observations demonstrate that me-chanically driven PDL generation and punching are activemechanisms in bcc metals under severe, local constraints.Through ECCI of nanoindented pure W, we tracked the struc-tural evolution of long dislocation streaks along the 〈111〉directions. These defect arrays are generated at the initialpop-in burst and extend during subsequent deformation. De-termining b via ECCI provides clear experimental evidencethat validates prior microstructural conjectures and directlybridges the long-standing gap with atomistic and discretedislocation dynamics simulations. Consistent with these sim-ulations, the circular shape of the PDLs and their ease of glideappear to be characteristic features of the bcc lattice, whilethe mechanically induced punching mechanism is observeduniversally across the major crystal structures. Furthermore,energetic considerations indicate that loop formation alonecannot account for the total plastic deformation energy ofindentation, implying that other mechanisms, such as clas-sical shear loops, contribute concurrently. Ultimately, theseobservations resolve historical ambiguities regarding subsur-face defect transport in bcc systems under highly confineddeformation.This work was partially supported by KAKENHI Grants-in-Aid (Grant No. 24H00389) from the Japan Society for thePromotion of Science (JSPS).Data availability. There are no publicly available researchdata or software supporting this manuscript. Requests for fur-ther information or data should be sent to the authors.[1] F. Seitz, Prismatic dislocations and prismatic punching incrystals, Phys. Rev. 79, 723 (1950).[2] Y. Miura, Punched-out dislocation rosettes in low-dislocation-density copper, J. Appl. Phys. 43, 2917 (1972).[3] Y. Miura, H. Nakamura, and H. Kaieda, Prismatic dislocationloops in copper revealed by X-ray topography, Trans. Jpn. Inst.Met. 17, 793 (1976).[4] S. Graça, P. A. Carvalho, and R. Colaço, Dislocation struc-tures in nanoindented ductile metals—a transmission electronmicroscopy direct observation, J. Phys. D 44, 335402 (2011).[5] S. Lee, A. Vaid, J. Im, B. Kim, A. Prakash, J. Guénolé, D.Kiener, E. Bitzek, and S. H. Oh, In situ observation of theinitiation of plasticity by nucleation of prismatic dislocationloops, Nat. Commun. 11, 2367 (2020).[6] Y. Miura and J. Washburn, Mobility of prismatic dislocationhalf-loops in copper, Cryst. Lattice Defects 2, 197 (1971).[7] T. Tsuru and Y. Shibutani, Atomistic simulations of elasticdeformation and dislocation nucleation in Al under indentation-induced stress distribution, Model. Simul. Mat. Sci. Eng. 14,S55 (2006).[8] T. Tsuru, Y. Shibutani, and Y. Kaji, Nanoscale contact plasticityof crystalline metal: Experiment and analytical investigation viaatomistic and discrete dislocation models, Acta Mater. 58, 3096(2010).[9] M. A. Lodes, A. Hartmaier, M. Göken, and K. Durst, In-fluence of dislocation density on the pop-in behavior andindentation size effect in CaF2 single crystals: Experimentsand molecular dynamics simulations, Acta Mater. 59, 4264(2011).[10] S. Roy, R. Gatti, B. Devincre, and D. Mordehai, A multiscalestudy of the size-effect in nanoindentation of Au nanoparticles,Comput. Mater. Sci. 162, 47 (2019).L090601-5https://doi.org/10.1103/PhysRev.79.723https://doi.org/10.1063/1.1661628https://doi.org/10.2320/matertrans1960.17.793https://doi.org/10.1088/0022-3727/44/33/335402https://doi.org/10.1038/s41467-020-15775-yhttps://escholarship.org/uc/item/7d86w50hhttps://doi.org/10.1088/0965-0393/14/5/S07https://doi.org/10.1016/j.actamat.2010.01.048https://doi.org/10.1016/j.actamat.2011.03.050https://doi.org/10.1016/j.commatsci.2019.02.013FLORIAN TROPPER AND TAKAHITO OHMURA PHYSICAL REVIEW MATERIALS 10, L090601 (2026)[11] J. Gagel, D. Weygand, and P. Gumbsch, Formation of extendedprismatic dislocation structures under indentation, Acta Mater.111, 399 (2016).[12] L. B. Munday, J. C. Crone, and J. Knap, Prismatic and helicaldislocation loop generation from defects, Acta Mater. 103, 217(2016).[13] C. Erel, G. Po, T. Crosby, and N. Ghoniem, Generation andinteraction mechanisms of prismatic dislocation loops in FCCmetals, Comput. Mater. Sci. 140, 32 (2017).[14] P. Anderson, J. Hirth, and J. Lothe, Theory of Dislocations,3rd ed. (Cambridge University Press, Cambridge, 2017).[15] J. H. A. Hagelaar, E. Bitzek, C. F. J. Flipse, and P. Gumbsch,Atomistic simulations of the formation and destruction ofnanoindentation contacts in tungsten, Phys. Rev. B 73, 045425(2006).[16] I. H. Chen, C. I. Hsiao, R. K. Behera, and W. D.Hsu, Defect formation by pristine indenter at the ini-tial stage of nanoindentation, J. Appl. Phys. 114, 214305(2013).[17] T. P. Remington, C. J. Ruestes, E. M. Bringa, B. A.Remington, C. H. Lu, B. Kad, and M. A. Meyers, Plasticdeformation in nanoindentation of tantalum: A new mech-anism for prismatic loop formation, Acta Mater. 78, 378(2014).[18] F. Zhu, J. Tao, J. Wu, F. Zhou, J. Chen, Y. Pei, L. Song, J. Wu,and D. Wang, Molecular dynamics simulation of the indenta-tion behavior of tungsten with varying crystal orientations andBerkovich indenter orientations, Mater. Today Commun. 41,110738 (2024).[19] N. Zhou, K. I. Elkhodary, X. Huang, S. Tang, and Y. Li,Dislocation structure and dynamics govern pop-in modes ofnanoindentation on single-crystal metals, Philos. Mag. 100,1585 (2020).[20] H. Yu, A. C. F. Cocks, and E. Tarleton, Formation of pris-matic dislocation loops during unloading in nanoindentation,Scr. Mater. 189, 112 (2020).[21] H. Yu, S. Das, H. Yu, P. Karamched, E. Tarleton, and F.Hofmann, Orientation dependence of the nano-indentation be-haviour of pure tungsten, Scr. Mater. 189, 135 (2020).[22] F. Tropper and T. Ohmura, Distinct orientation dependenceof plasticity initiation and subsequent deformation in nanoin-dented tungsten, Int. J. Refract. Met. Hard Mater. 140, 107907(2026).[23] K. L. Johnson, Contact Mechanics (Cambridge UniversityPress, Cambridge, 1985).[24] S. Zaefferer and N. N. Elhami, Theory and application of elec-tron channelling contrast imaging under controlled diffractionconditions, Acta Mater. 75, 20 (2014).[25] See Supplemental Material at http://link.aps.org/supplemental/10.1103/7c3d-tw8q for details on ECCI methodology and addi-tional experimental results.[26] A. Howie and M. J. Whelan, Diffraction contrast of electronmicroscope images of crystal lattice defects. III. Results and ex-perimental confirmation of the dynamical theory of dislocationimage contrast, Proc. R. Soc. A 267, 206 (1962).[27] S. Vadalakonda, R. Banerjee, A. Puthcode, and R. Mirshams,Comparison of incipient plasticity in bcc and fcc metals studiedusing nanoindentation, J. Mater. Sci. Eng. A 426, 208 (2006).[28] T. Tsuru and Y. Shibutani, Theoretical investigation of thedisplacement burst observed in nanoindentation by collectivedislocation loops nucleation model, J. Comput. Sci. Technol. 2,559 (2008).[29] J. Alcalá, R. Dalmau, O. Franke, M. Biener, J. Biener, and A.Hodge, Planar defect nucleation and annihilation mechanismsin nanocontact plasticity of metal surfaces, Phys. Rev. Lett. 109,075502 (2012).L090601-6https://doi.org/10.1016/j.actamat.2016.04.002https://doi.org/10.1016/j.actamat.2015.09.056https://doi.org/10.1016/j.commatsci.2017.07.043https://doi.org/10.1103/PhysRevB.73.045425https://doi.org/10.1063/1.4827175https://doi.org/10.1016/j.actamat.2014.06.058https://doi.org/10.1016/j.mtcomm.2024.110738https://doi.org/10.1080/14786435.2020.1739348https://doi.org/10.1016/j.scriptamat.2020.07.062https://doi.org/10.1016/j.scriptamat.2020.08.014https://doi.org/10.1016/j.ijrmhm.2026.107907https://doi.org/10.1016/j.actamat.2014.04.018http://link.aps.org/supplemental/10.1103/7c3d-tw8qhttps://doi.org/10.1098/rspa.1962.0093https://doi.org/10.1016/j.msea.2006.04.001https://doi.org/10.1299/jcst.2.559https://doi.org/10.1103/PhysRevLett.109.075502