crystals

Editorial Crystal Indentation

Ronald W. Armstrong 1,*, Stephen M. Walley 2,† and Wayne L. Elban 3,†

1 Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA 2 Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK; [email protected] 3 Department of Engineering, Loyola University Maryland, Baltimore, MD 21210, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-410-723-4616 † These authors contributed equally to this work.

Academic Editor: Sławomir Grabowski Received: 5 January 2017; Accepted: 6 January 2017; Published: 12 January 2017

Abstract: There is expanded interest in the long-standing subject of the hardness properties of materials. A major part of such interest is due to the advent of hardness testing systems which have made available orders of magnitude increases in load and displacement measuring capabilities achieved in a continuously recorded test procedure. The new results have been smoothly merged with other advances in conventional hardness testing and with parallel developments in improved model descriptions of both elastic and dislocation mechanisms operative in the understanding of crystal plasticity and fracturing behaviors. No crystal is either too soft or too hard to prevent the determination of its elastic, plastic and cracking properties under a suitable probing indenter. A sampling of the wealth of measurements and reported analyses associated with the topic on a wide variety of materials are presented in the current Special Issue.

Keywords: crystal hardness; ; dislocations; contact mechanics; indentation plasticity; plastic anisotropy; stress–strain characterizations; indentation fracture mechanics

1. Introduction The concept of material hardness has been tracked historically by Walley starting from biblical time and proceeding until the 1950s, with pictorial emphasis given to the earliest 19th century design of testing machines and accumulated measurements [1]. Walley’s review leads up to David Tabor setting a new course via science connection with his seminal 1951 book The Hardness of Metals [2] and further leading, for example, to a later 1973 conference proceedings on The Science of Hardness Testing and Its Research Applications [3]. The subject has gained increased importance with the relatively recent advent of orders of magnitude greater force and displacement measuring capabilities available with modern nano-indentation test systems. A review was presented in 2013 of the complete elastic, plastic and, when appropriate, cracking behaviors that can be monitored for crystals, polycrystals, composites and amorphous materials under suitable probing indentation [4]. A substantial reference list was included in the review of conferences and books produced until that time. As will be seen in the current updated collection of research and review articles, no crystal can be too soft or too hard within its environment to escape measurement with a suitable probing indenter applied using appropriate test conditions.

2. Continuous Indentation Testing The original application of the hardness test corresponded to the obtainment of a single reference point for measurement of an applied load and resultant plastic deformation. Much has been made, and continues to be made, of correlating the measurement with some aspect of the same material unidirectional stress–strain behavior beginning from historical association with the ultimate

Crystals 2017, 7, 21; doi:10.3390/cryst7010021 www.mdpi.com/journal/crystals Crystals 2017, 7, 21 2 of 9 Crystals 2017, 7, 21 2 of 9 material unidirectional stress–strain behavior beginning from historical association with the ultimate tensile stress. In like manner, current achievements of continuous indentation load– tensiledeformation stress. measurements, In like manner, particularly current achievements obtained with of nanoindentation continuous indentation test instruments, load–deformation are being measurements,developed to describe particularly the full obtained material with indentation-b nanoindentationased stress–strain test instruments, behavior. are Figure being developed1 provides toan describeexample thein which full material a number indentation-based of measurements stress–strain are compared. behavior. The hardness Figure1 providesstress is load an example divided inby whichcontact a numberarea; and, of the measurements hardness strain are compared.is based on The a spherica hardnessl-tipped stress indenter is load divided and evaluated by contact in area;terms and,of the the surface-projec hardness strainted isindentation based ona diameter, spherical-tipped d, divided indenter by the and actual evaluated or effective in terms ball of thediameter, surface-projected D [5]. The terminal indentation open diameter, circle pointsd, divided on the by dashed the actual and or effective elastic ball loading diameter, linesD are[5]. Thecomputed terminal for open indicated circle pointsD values on the on dashedthe basis and of solid an indentation elastic loading fracture lines aremechanics computed description, for indicated as Dwillvalues be described. on the basis Pathak of an and indentation Kalidindi fracturehave give mechanicsn an updated description, description as will of such be described. nanoindentation Pathak andstress–strain Kalidindi curves have given[6]. Here, an updated a brief descriptionpreview is ofgiven such of nanoindentation information currently stress–strain available curves from [6]. Here,point-by-point a brief preview measurements is given of informationmade conventionally currently available or from from continuous point-by-point load/penetration measurements mademeasurements. conventionally or from continuous load/penetration measurements.

Figure 1. Hardness-based stress–strain description of indentation test measurements. The hardness Figure 1. Hardness-based stress–strain description of indentation test measurements. The hardness stress is load divided by the projected area of contact; and, the hardness strain is the projected contact stress is load divided by the projected area of contact; and, the hardness strain is the projected contact diameter divided by the actual or effective ball diameter of the indenter tip [5]. The solid experimental diameter divided by the actual or effective ball diameter of the indenter tip [5]. The solid (ball test) and dashed linear dependencies are computed in accordance with a Hertzian description; experimental (ball test) and dashed linear dependencies are computed in accordance with a Hertzian and, the Vickers hardness numbers are plotted on the abscissa scale at a position corresponding to the description; and, the Vickers hardness numbers are plotted on the abscissa scale at a position indenter diagonal, d = 0.375D. corresponding to the indenter diagonal, d = 0.375D.

2.1. Continuous Load–Deformation Measurements 2.1. Continuous Load–Deformation Measurements The NaCl crystal (solid curve) hardness stress–strainstress–strain measurement shown in Figure 11 was was obtained on on indenting indenting an an {001} {001} crystal crystal surface surface wi withth a 6.35 a 6.35 mm mm ball ball in ain standard a standard compression compression test. test.Such Suchmeasurments measurments are made are made much much easier easier with with the the naturally-rounded naturally-rounded tips tips of of nanometer- nanometer- or micrometer-scale indenter tips in nano-test indentationindentation systems. Figure 22 showsshows anan exampleexample elasticelastic loading/unloading behavior behavior recorded recorded for for nanoindenta nanoindentationtion of of a a {0001} {0001} sapphire sapphire crystal crystal surface surface [7]. [7]. The nonlinearnonlinear dependence dependence on on penetration penetration depth, depth,h, mayh, may be employed be employed to determine to determine the effective the effective elastic moduluselastic modulus for a known for a known tip diameter tip diameter in accordance in accordance with the with Hertzian the Hertzian relationship: relationship: CrystalsCrystals 20172017,,7 7,, 2121 33 ofof 99 Crystals 2017, 7, 21 3 of 9

E* = [{(1 − νB)/EB} + {(1 − νS)/ES}]−1 = (3√2/4)(P/D1/2)h−3/2 (1) E* = [{(1 − νB)/EB} + {(1 − νS)/ES}]−1 = (3√2/4)(P/D1/2)h−3/2 (1) −1 √ 1/2 −3/2 In Equation (1),E* ν =B [{(1,EB and− ν Bν)/S,EESB are} + {(1Poisson’s− νS)/ ratioES}] and=(3 Young’s2/4)(P modulus/D )h for ball and specimen,(1) respectively,In Equation P is (1),load, νB and,EB and again, νS, EDS areis (effective) Poisson’s ball ratio diameter. and Young’s As indicated modulus in for Figure ball and2, the specimen, value of In Equation (1), νB, EB and νS, ES are Poisson’s ratio and Young’s modulus for ball and specimen, respectively,E* can be determined P is load, fromand again, fit to theD is indentation (effective) ball loading diameter. curve As if indicatedD for the inrounded Figure indenter2, the value tip ofis respectively, P is load, and again, D is (effective) ball diameter. As indicated in Figure2, the value of Eknown.* can be Dub, determined Brazhkin, from Novikov, fit to the Tolmachovaindentation loadinget al. have curve reported if D for thesimilar rounded measurements indenter tip on is E* can be determined from fit to the indentation loading curve if D for the rounded indenter tip is known.sapphire Dub,and stishoviteBrazhkin, single Novikov, crystals Tolmachova [8]. Elastic moduluset al. have determinations reported similar for aluminum measurements have been on known. Dub, Brazhkin, Novikov, Tolmachova et al. have reported similar measurements on sapphire sapphirereported andfor bothstishovite micro- single and crystalsnano-scale [8]. Elastitest systemsc modulus [9,10]. determinations Solhjoo and for Vakis aluminum have provided have been a and stishovite single crystals [8]. Elastic modulus determinations for aluminum have been reported for reportedmolecular for dynamics both micro- assessment and nano-scale of surface testroughness systems on [9,10]. E* determinations Solhjoo and Vakis[11]. The have initial provided loading a both micro- and nano-scale test systems [9,10]. Solhjoo and Vakis have provided a molecular dynamics molecularmethod compares dynamics with assessment an alternative of surface method roughness of determining on E* determinations E* from an unloading [11]. The curve initial after loading small assessment of surface roughness on E* determinations [11]. The initial loading method compares with methodplastic deformation compares with [12]. an alternative method of determining E* from an unloading curve after small anplastic alternative deformation method [12]. of determining E* from an unloading curve after small plastic deformation [12].

FigureFigure 2.2. ContinuousContinuous load/unloadload/unload curve for nanoindentat nanoindentationion of a (0001) sapphire crystal surface [[7].7]. Figure 2. Continuous load/unload curve for nanoindentation of a (0001) sapphire crystal surface [7]. 2.2. Crystal Plasticity 2.2.2.2. Crystal Plasticity TheThe omnipresentomnipresent elastic elastic loading loading is eventually is eventually interrupted interrupted moreso moreso sooner sooner than later than by thelater so-called by the so-calledThe omnipresent“pop-in” initiation elastic of loading crystal isplasticity eventually. An interruptedexample is shownmoreso in sooner Figure than3 for laterthe ambient by the “pop-in”so-called initiation“pop-in” ofinitiation crystalplasticity. of crystal Anplasticity example. An is shownexample in is Figure shown3 for in theFigure ambient 3 for temperature the ambient nanoindentationtemperature nanoindentation of several different of several body-centered differen cubict body-centered (bcc) tantalum cubic crystal (bcc) surfaces tantalum [13]. Beyondcrystal temperaturesurfaces [13]. nanoindentationBeyond the higher of hardnessseveral differenof the (001)t body-centered crystal surface, cubic one (bcc) might tantalum note the crystal rapid thesurfaces higher [13]. hardness Beyond of the the higher (001) crystal hardness surface, of the one (001) might crystal note surface, the rapid one hardening might note at the the end rapid of thehardening pop-in displacementat the end of andthe thepop-in indication displacement of greater and strain the indication hardening of within greater the strain hardened hardening (001) hardeningwithin the hardenedat the end (001) of theindentation pop-in displacement region. and the indication of greater strain hardening indentationwithin the hardened region. (001) indentation region.

Figure 3. Nanoindentation load–penetration curves obtained with impressing a (rounded point) Berkovich tri-pyramidal indenter into various tantalum (111), (011) and (001) crystal surfaces [13]. Figure 3. Nanoindentation load–penetration curves obtained with impressing a (rounded point) FigureBerkovich 3. Nanoindentationtri-pyramidal indenter load–penetration into various tantcurvesalum ob (111),tained (011) with and impressing (001) crystal a (rounded surfaces [13].point) Berkovich tri-pyramidal indenter into various tantalum (111), (011) and (001) crystal surfaces [13]. Crystals 2017, 7, 21 4 of 9 Crystals 2017, 7, 21 4 of 9 Such measurements as shown in Figure 3 have provided valuable information for dislocation mechanicsSuch measurementsmodeling of asthe shown crystal in Figuredeformation3 have provided behavior, valuable particularly information in connection for dislocation with determiningmechanics modeling the theoretical of the crystalshear stress deformation required behavior, for dislocation particularly nucleation in connection within witha zone determining below the indentation.the theoretical Ruestes, shear stress Stukowski, required Tang, for dislocationTramontina nucleation et al. have within reported a zone on belowatomic the simulation indentation. of dislocationRuestes, Stukowski, creation Tang, at Tramontinananoindentations et al. have in reportedtantalum on crystals, atomic simulationincluding of the dislocation occurrence creation of deformationat nanoindentations twinning in [14] tantalum. Alhafez, crystals, Ruestes, including Gao and theUrbassek occurrence have investigated of deformation nanoindentations twinning [14]. Alhafez,made in hexagonal Ruestes, Gaoclose-packed and Urbassek (hcp) crystal have surf investigatedaces [15]. A nanoindentations standard (elongated) made Knoop in hexagonal indenter systemclose-packed is often (hcp) employed crystal surfacesto evaluate [15]. the A plasti standardc anisotropy (elongated) of Knoopboth ductile indenter and system brittle iscrystal often materialsemployed [16]. to evaluate the plastic anisotropy of both ductile and brittle crystal materials [16].

2.3. Crystal Cracking There are twotwo mainmain aspectsaspects of of indentation-induced indentation-induced (cleavage) (cleavage) cracking cracking determinations determinations that that are are of ofinterest: interest: (1) (1) investigation investigation of dislocationof dislocation mechanism(s) mechanism(s) for for crack crack formation; formation; and and (2) specification(2) specification of the of theindentation indentation fracture fracture mechanics mechanics stress stress intensity intensity for crackfor crack propagation. propagation.

2.3.1. Crack Formation Figure 44 provides provides anan exampleexample ofof crackcrack formationformation atat a a crystallographically-aligned crystallographically-aligned diamonddiamond pyramid indentation indentation impressed impressed into into an an ammonium ammonium perchlorate perchlorate (AP) (AP) {210} {210} crystal crystal surface surface [17]. [The17]. Thetop-side top-side cleavage cleavage crack crack has been has beengenerated generated by sessile by sessile dislocations dislocations reacted reacted at the atintersections the intersections of the indicatedof the indicated juxtaposed juxtaposed {111} {111}slip planes, slip planes, in the in thesame same manner manner reported reported for for cracking cracking at at similar indentations putput into into {001} {001} MgO MgO crystal crystal surfaces surfaces and originally and originally proposed proposed for cleavage for crackcleavage formation crack formationin α-iron and in α other-iron bcc and metals other [bcc4]. Closemetals examination [4]. Close examination of the reflected of the optical reflected image optical gives an image indication gives anthat indication the crack hasthat formedthe crack in thehas valleyformed between in the otherwisevalley between raised otherwise surface regions raised on surface either regions side of theon eitherindentation. side of Such the “piling indentation. up” results Such from “piling secondary up” results slip occurring from secondary to accommodate slip occurring the primary to accommodateindentation-forming the primary displacement indentation-forming [4]. displacement [4].

Figure 4. {001} cleavage crack produced by Cottrell-type dislocation reaction at a diamond pyramid indentation impressed into a {210} ammonium perchlorate (AP), NH4ClO4, crystal surface [17]. indentation impressed into a {210} ammonium perchlorate (AP), NH4ClO4, crystal surface [17].

2.3.2. Indentation Fracture Mechanics 2.3.2. Indentation Fracture Mechanics An example of elastic, plastic and cracking hardness measurements spanning load and size An example of elastic, plastic and cracking hardness measurements spanning load and size characterizations for nano- to micro-scale indentations and cracking is shown in Figure 5 [18]. The characterizations for nano- to micro-scale indentations and cracking is shown in Figure5[ 18]. left-side linear solid and dashed line is the computed Hertzian dependence for elastic behavior, The left-side linear solid and dashed line is the computed Hertzian dependence for elastic behavior, following a P ~ d3 dependence. The next broad band containing filled circle, triangle and square Crystals 2017, 7, 21 5 of 9

Crystals 2017, 7, 21 5 of 9 following a P ~d3 dependence. The next broad band containing filled circle, triangle and square points appliespoints applies for the determinationfor the determination of the hardness of the hardness dependence, dependence, with di being with thedi being indentation the indentation diagonal 2 2 lengthdiagonal and length is shown and tois shown approximate, to approximate, at higher atP value,higher to P avalue,P ~di todependence. a P ~ di dependence. The open The symbols open correspondsymbols correspond to the shift to the of the shift load of the and load diagonal and diag measurementsonal measurements to an effective to an effective ball diameter ball diameter result. Theresult. furthest The furthest right-side righ measurementst-side measurements are for anare indentation for an indentation fracture mechanicsfracture mechanics assessment assessment applied 3/2 3/2 toapplied crack extensionsto crack extensions following following a theoretical a theoreticalP ~dC dependence.P ~ dC dependence. The figure The indicates figure thatindicates plasticity that precedesplasticity cracking, precedes incracking, line with in other line with results other shown result ins Figureshown1 inthat Figure also show1 that thatalso crackingshow that requires cracking a higherrequires load a higher at smaller load effectiveat smaller ball effective sizes. Wan,ball sizes. H.; Shen, Wan, Y.; H.; Chen, Shen, Q. Y.; and Chen, Chen, Q. Y.and have Chen, elaborated Y. have onelaborated the plastic on ‘damage’the plastic preceding ‘damage’ such preceding cracking such produced cracking in siliconproduced crystals in silicon with differentcrystals typewith indentersdifferent [type19]. Vodenitcharova,indenters [19]. Vodenitcharova, Borrero-López and Bo Hofffmanrrero-López described and Hofffman the related described cracking the associated related withcracking scratching associated along with different scratching directions along ondifferent {100} silicon directions crystal on wafers{100} silicon [20]. Thecrystal hardness wafers literature [20]. The showshardness such literature Griffith-based shows crack such analyses Griffith-based to be widely crack employedanalyses forto characterizingbe widely employed the cracking for behaviorcharacterizing of brittle the ceramiccracking and behavior glass materials.of brittle ceramic and glass materials.

FigureFigure 5.5.The The load, load,P ,P versus, versus elastic, elastic,d, plastic,d, plastic,di, or di crack, or crack extent, extent,dc, dependence dc, dependence for cracking for cracking of silicon of crystalsilicon surfacescrystal surfaces indented indented with various with various sharp indenters sharp indenters [18]. [18].

3.3. Applications ParticularParticular attention was was given given to to example example hardness hardness aspects aspects of ofsurface surface films films and and coatings coatings in the in theprevious previous review review [4]. [ 4Here,]. Here, we we mention, mention, first, first, an an important important hardness hardness co connectionnnection with materialmaterial compactioncompaction behaviorsbehaviors thatthat arisearise forfor softersofter organicorganic crystalscrystals relatingrelating toto pharmaceuticalpharmaceutical tabletingtableting [[21]21] andand formulatedformulated energetic energetic material material processing processing [5]. [5]. Research Research effort effort on the on former the former topic hastopic been has carried been oncarried to investigating on to investigating temperature temperature [22] and [22] strain and rate strain [23] influencesrate [23] influences on molecular on molecular crystal hardness. crystal Inhardness. the latter In energetic the latter crystal energetic case, crystal a recent case, report a onrecent hardness report and on molecularhardness and dynamics molecular aspects dynamics of RDX (cyclotrimethylenetrinitramine)aspects of RDX (cyclotrimethylenetrinitramine) crystals has dealt crystals with concern has dealt for with their concern mechanical for their and tribologicalmechanical propertiesand tribological [24]. properties [24]. Beyond the referenced-above consideration of hardness-determined elastic deformation behavior of sapphire, its hardness properties have been investigated to relate with abrasive wear resistance [25]. Tribological concern has been with chemomechanical aspects of sapphire crystal, Crystals 2017, 7, 21 6 of 9

Beyond the referenced-above consideration of hardness-determined elastic deformation behavior of sapphire, its hardness properties have been investigated to relate with abrasive wear resistance [25]. Tribological concern has been with chemomechanical aspects of sapphire crystal, polycrystal ZnO coating and other ceramic material hardness properties [26]. In addition, there are interesting optical (cathodoluminescence) properties associated with dislocation zones at nanoindentations in ZnO crystalsCrystals [27 ].2017, 7, 21 6 of 9

3.1. Polycrystals,polycrystal ZnO Polyphases coating and and Amorphous other ceramic Phases material hardness properties [26]. In addition, there are interesting optical (cathodoluminescence) properties associated with dislocation zones at Particularnanoindentations attention in ZnO was crystals also directed [27]. in [4] to relating hardness properties between individual crystals and their polycrystalline counterparts. The connection was reasonably shown to be well-established3.1. Polycrystals, in the Polyphases so-called and Hall–Petch Amorphous Phases (H–P) relationship for hardness: Particular attention was also directed in [4] to relating hardness properties between individual −1/2 crystals and their polycrystalline counterpartsH = H0 +. kTheH` connection was reasonably shown to be (2) well-established in the so-called Hall–Petch (H–P) relationship for hardness: 2 In Equation (2), H is Meyers hardness, P/(πd /4); H0 is the single crystal hardness; kH is a H = H0 + kHℓ−1/2 (2) microstructural stress intensity; and ` is average (crystal) grain diameter, generally measured on a line intercept basis.In Equation Other (2), hardness H is Meyers values hardness, are easily P related/(πd2/4); to H the0 is Meyerthe single hardness. crystal hardness; kH is a Equationmicrostructural (2) is stress related intensity; to the and same ℓ is type average equation (crystal) for grain the diameter, true compressive generally measured (or tensile) on stressa line intercept basis. Other hardness values are easily related to the Meyer hardness. (σε)–true strain (ε) behavior for which kH ≈ 3kε. Recent estimations have been reported for H–P k Equation (2) is related to the same type equation for the true compressive (or tensile) stress (σε)– values determined for steel materials through nanoindentation measurements [28]. In line with the true strain (ε) behavior for which kH ≈ 3kε. Recent estimations have been reported for H–P k values H–P modeldetermined description, for steel materials the obstacle through presented nanoindent to slipation penetrations measurements by [28]. grain In boundariesline with the hasH–P been investigatedmodel description, in the bcc metalsthe obstacle case bypresented Soer, Aifantis to slip and penetrations De Hosson by [29grain] and boundaries more recently has been in (hcp) α-titaniuminvestigated via high in the resolution bcc metals X-ray case by and Soer, electron Aifantis microscope and De Hosson methods [29] and [30 more]. Related recently hardness in (hcp) and grainα size-titanium dependent via high scratch resolution results X-ray have and been electron reported microscope for polycrystalline methods [30]. copper Related [31 hardness]. The influence and of H–Pgrain strengthening size dependent of polycrystalline scratch results diamondhave been has reported been describedfor polycrystalline [32] and copper also for [31]. cubic The boron nitrideinfluence via nanotwinned of H–P strengthening (boundary) of strengthening polycrystalline [ 33diamond]. has been described [32] and also for Ancubic important boron nitride crystal via size-dependentnanotwinned (boundary) connection strengthening has been made[33]. with composite WC–Co cermet material forAn which important indentations crystal size-dependent made on the connection individual has components been made with were composite known WC–Co to follow cermet separate material for which indentations made on the individual components were known to follow separate H–P dependencies [34]. A recent report on the system has been made by Roa, Jimenez–Pique, Verge, H–P dependencies [34]. A recent report on the system has been made by Roa, Jimenez–Pique, Verge, Tarragó et al. [35]; see Figure6. In related work, Roa et al. have determined an intermediate k for the Tarragό et al. [35]; see Figure 6. In related work, Roa et al. have determined an intermediate kH for combinedthe combined deformation deformation of phases of [phases36]. Zhang, [36]. Zhang, Wang Wang and Dai and have Dai employedhave employed nanoindentation nanoindentation testing to investigatetesting to theinvestigate rate dependence the rate dependence of plastic of flow plastic in metallicflow in metallic glass materials glass materials [37]. [37].

FigureFigure 6. Berkovich 6. Berkovich nanoindentations nanoindentations made made withinwithin the WC WC particle particle and and Co Co binder binder phases phases of the of the composite cermet material [35]. composite cermet material [35]. 3.2. Hardness as a Test Probe 3.2. Hardness as a Test Probe In this concluding section, we return to reference [3] in which Gilman pointed to the important Inuse this of concludinglocal hardness section, testing we as a return strength to referencemicroprobe [3 ][38] in whichand was Gilman able to pointedcorrelate to hardness the important with a use of localnumber hardness of material testing asproperties a strength such microprobe as strength, [38] and elastic was ablemodu tolus, correlate glide activation hardness energy with a and number energy gap density for a variety of crystals. The advent of nanoindentation testing has given greater meaning to such probe capability. Emphasis was given previously in [4] to connection with probe aspects of atomic force microscopy for which a new tip fabrication procedure has recently been reported [39]. Another recent application has been to investigate the strain hardening surrounding Crystals 2017, 7, 21 7 of 9 of material properties such as yield strength, elastic modulus, glide activation energy and energy gap density for a variety of crystals. The advent of nanoindentation testing has given greater meaning to such probe capability. Emphasis was given previously in [4] to connection with probe aspects of atomic force microscopy for which a new tip fabrication procedure has recently been reported [39]. Another recent application has been to investigate the strain hardening surrounding larger Rockwell indentations made in electrodeposited nanocrystalline nickel material with different grain sizes [40]. Additional examples include (1) investigating shear banding in metallic glass materials [41]; and, nano-probing of diffusion-controlled deformation on a copper crystal surface [42] and on different surfaces of ZnO crystals [43].

4. Summary An editorial introduction to the Special Issue on crystal indentation hardness has been presented by the authors while building upon their previous review entitled Elastic, Plastic and Cracking Aspects of the Hardness of Materials [4]. The wide variation in currently referenced journals gives an indication of the broad interest in the subject. Hopefully, the more recent referenced reports will be viewed as indicating an expanded interest in the topic of crystal hardness testing, particularly as provided in this sampling of important measurements and analyses stemming from current attention being given to all aspects of nanoindentation hardness testing.

Conflicts of Interest: The authors declare no conflict of interest.

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