Crystal Dislocations - Semantic Scholar
crystals Editorial
Crystal Dislocations Ronald W. Armstrong Received: 28 December 2015; Accepted: 4 January 2016; Published: 6 January 2016 Academic Editor: Helmut Cölfen Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA; [email protected]; Tel.: +1-410-723-4616
Abstract: Crystal dislocations were invisible until the mid-20th century although their presence had been inferred; the atomic and molecular scale dimensions had prevented earlier discovery. Now they are normally known to be just about everywhere, for example, in the softest molecularly-bonded crystals as well as within the hardest covalently-bonded diamonds. The advent of advanced techniques of atomic-scale probing has facilitated modern observations of dislocations in every crystal structure-type, particularly by X-ray diffraction topography and transmission electron microscopy. The present Special Issue provides a flavor of their ubiquitous presences, their characterizations and, especially, their influence on mechanical and electrical properties. Keywords: dislocations; crystals; polycrystals; nanopolycrystals; X-ray topography; transmission electron microscopy; optical microscopy; crystal growth; crystal strength properties; electrical properties
1. Introduction Early interest in dislocations sprang from research investigations into conditions of crystal growth and on subsequent permanent (or plastic) crystal deformation properties, in the latter case, particularly relating to crystal strength and ductility. An important industrial focus on defects in electronic crystals at micro-scale dimensions has led to much ongoing research activity. Cottrell, in 1953, produced a seminal book on dislocations and strength properties based on his teaching at Birmingham [1]. An early conference on dislocation observations, mostly, in metals was held in 1961 [2]. Emphasis was given to observations made via optical and electron microscopy, X-ray diffraction topography, and field ion microscopy. Among a number of subsequent dislocation treatises with broader coverage are books by Nabarro [3] and by Hirth and Lothe [4]. A frequently referenced book is by Hull and Bacon [5]. Nabarro initiated a comprehensive series of Dislocations in Solids volumes, latterly co-edited, first with Duesbury, then with Hirth [6], and later by Hirth, then ending with Hirth and Kubin [7]. In all, 96 chapters were produced over the period from 1980 until 2010 by many experts. The early volumes 1–3 established the elastic theory, lattice relationship and movement properties. Figure 1 shows a schematic view of an edge dislocation with central core and flexible line orientation to circumvent obstacles to migration [8]. 2. Crystal Growth and Dislocation Structures Frank saw first the important advantage in crystal growth of a screw dislocation with displacement (Burgers) vector, b, parallel to line axis, `, and thus providing a consequent never-ending crystal step for atomic attachment [9]. Burton described with Cabrera and Frank the beneficial nature of the trailing spiral ledge [10]. Updated commentary of the crystal growth work by Frank and colleagues and on other work extending until recent time has been given by Woodruff [11]. Figure 2 is a transmission X-ray topograph of a cm-size α-Al2 O3 (sapphire) crystal slice from a larger boule grown by a chemical vapor decomposition technique [12]. The just-visible very finely resolved lines are Crystals 2016, 6, 9; doi:10.3390/cryst6010009
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Crystals 2016, 6, 9 Crystals Crystals2016, 2016,6,6,99
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grown by a chemical vapor decomposition technique [12]. The just-visible very finely resolved lines grown by a chemical vapor decomposition technique [12].shown The just-visible finely resolved lines are individual dislocations. Three “blackened” bunchesare are to emanate emanatevery from individual dislocations. Three “blackened” bunches shown to from individual individualpoints points are individual dislocations. Three “blackened” bunches are shown tothe emanate individual across recognizable upper boundary established when crystalfrom growth had points been across aa recognizable upper boundary tracetrace established when the crystal growth had been temporarily across a recognizable upper boundary trace established when the crystal growth had been temporarily halted. Edge type dislocations with b perpendicular to ℓ, as in the front face of Figure 1, halted. Edge type dislocations with b perpendicular to `, as in the front face of Figure 1, penetrate temporarily halted. Edge type dislocations with b perpendicular to ℓ, as in solutes. the frontOther face of Figure 1, penetrate growth interfaces also, presumably, to incorporate impurities and aspects of growth interfaces also, presumably, to incorporate impurities and solutes. Other aspects of dislocation penetrate growth interfaces also, presumably, tozinc, incorporate impurities and solutes. Other aspects of dislocation arrangements have been reported for and (photovoltaic) silicon arrangements have been reported for zinc, nickel and nickel (photovoltaic) silicon crystals [8].crystals [8]. dislocation arrangements have been reported for zinc, nickel and (photovoltaic) silicon crystals [8].
Figure Figure1.1.Schematic Schematicdislocation dislocationpicture. picture. Figure 1. Schematic dislocation picture.
Figure2.2.Dislocations Dislocationsin inα-Al α-Al2O crystal. 2O Figure 3 3crystal. Figure 2. Dislocations in α-Al2O3 crystal.
Crystal, Polycrystal,Nanopolycrystal NanopolycrystalDeformations Deformations 3.3.Crystal, Polycrystal, 3. Crystal, Polycrystal, Nanopolycrystal Deformations Dislocationsmove moverelatively relativelyeasy easyininmetal metalcrystals crystalsor orpolycrystals, polycrystals,and andless lessso soininionic, ionic,covalent covalent Dislocations Dislocations moveOne relatively metal crystals or polycrystals, less so in ionic, covalent andmolecular molecular crystals. One mighteasy notein indication Figure of mutual mutualand impediment indicated via and crystals. might note indication ininFigure 11of impediment indicated via and molecular crystals. One might note indication in Figure 1 of mutual impediment indicated via potentialdislocation dislocationintersections, intersections,otherwise otherwise there there are arelattice/solute lattice/soluteinteractions interactionstotobe becontended contendedwith with potential potential dislocation intersections, otherwise there are lattice/solute interactions to be contended with asindicated indicatedininFigure Figure3.3.InInthe thefigure, figure,the thedislocations dislocationsare aredenoted denotedas asrightside-up rightside-upor orinverted invertedT’s T’sand and as as indicated Figure 3. In theby figure, theblack dislocations are denoted as rightside-up or or inverted T’s and various represented the the black dots,dots, eithereither residing individually, or dislocation-associated various soluteinare are represented by residing individually, dislocationvarious solute represented by the black dots, residing or dislocationin three cases: (i) are at individual dislocations, ordislocations, (ii) on the either leftor side ason segregated dislocations arranged associated in three cases: (i) at individual (ii) theindividually, left at side as segregated at associated in three cases: (i) at individual dislocations, or (ii) on the left side as segregated in a verticalarranged subgraininboundary; or (iii) toboundary; greater extent, a (crystal) grain boundary region dislocations a vertical subgrain or (iii)within to greater extent, within a (crystal) grainat dislocations arranged in aadjacent vertical subgrain or (iii)The to greater withinlines a (crystal) between adjacent crystals of different lattice orientations. dottedextent, lines “slip” ofgrain the boundary region between crystals ofboundary; different lattice orientations. The represent dotted represent boundary adjacent crystalsstructure of different lattice orientations. Theindotted lines represent dislocations acrossbetween the subgrain and locally concentrated the grain “slip” of theregion dislocations across theboundary subgrain boundary structure and locally concentrated in boundary the grain “slip” of the dislocations across the subgrain structure locally concentrated in the grain region where thewhere direction-dependent strainsboundary must necessarily beand accommodated. boundary region the direction-dependent strains must necessarily be accommodated. boundary region where the direction-dependent strains must necessarily be accommodated.
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Figure Figure 3. 3. Polycrystal Polycrystal dislocation dislocation slip. slip. Figure 3. Polycrystal dislocation slip.
Figure 4. 4. Nanopolycrystal Nanopolycrystal structure. structure. Figure Figure 4. Nanopolycrystal structure.
The polycrystal strength strength dependence dependenceon onreciprocal reciprocalsquare squareroot rootofofgrain grainsize size was first reported The polycrystal was first reported in The polycrystal strengthofdependence on reciprocal root of grain size was first reported in independent investigations strength properties of square steel materials by Hall Petch independent investigations of thethe strength properties of steel materials by Hall [13] [13] and and Petch [14] [14] and in independent investigations ofsize the strength properties of steel materials by quite Hall [13] and Petch [14] and the same type of size grain dependence was later shown later toquite apply generally to the then then the same type of grain dependence was shown to apply generally to the complete and thenstress-strain the same type of grainofsize dependence was shownnumber later toofapply quite generally to the complete mild steel and to a wider metals [15]. An updated stress-strain behaviorsbehaviors of mild steel and to a wider number of metals [15]. An updated review has complete stress-strain behaviors of mild steel and to a wider number of metals [15]. An updated review has been presented [16]. An analogous relationship to the crack size dependence of the been presented [16]. An analogous relationship to the crack size dependence of the fracture mechanics reviewmechanics has been properties presented of [16]. An analogous relationship tobeen the established crack size dependence of the fracture metals and related materials has [17]. properties of metals and related materials has been established [17]. fracture mechanics properties of metals and related materials has been established [17]. Considerable materials nanotechnology in Considerable research research interest interest is is currently currently being being devoted devoted to to materials nanotechnology in three three Considerable research interest is currently being devoted to materials nanotechnology in three research areas: (1) nano-indentation hardness testing; (2) mechanical testing of specimens with nanoresearch areas: (1) nano-indentation hardness testing; (2) mechanical testing of specimens with research areas: and (1) nano-indentation hardness testing; (2) mechanical testing of specimens with nanoscale structures; testing material specimens of physical nano-scale dimensions. A review has nano-scale structures;(3) and (3) testing material specimens of physical nano-scale dimensions. A review scale structures; and (3) testing material specimens of physical nano-scale dimensions. A review has been reported on crystal/polycrystal nanoindentation hardness testing [18]. Figure 4 is an4 atomic scale has been reported on crystal/polycrystal nanoindentation hardness testing [18]. Figure is an atomic been reported on crystal/polycrystal nanoindentation hardness testing [18]. Figure 4 is an atomic scale simulation of theofdeformation structure within a nickel crystal [19]. [19]. A treatise on the and scale simulation the deformation structure within a nickel crystal A treatise onstructure the structure simulation of the deformation structure within a nickel crystal [19]. A treatise on the structure and properties of nano-scale metals has been by Faester, Hansen, Huang, Juul Jensen and Ralph and properties of nano-scale metals has edited been edited by Faester, Hansen, Huang, Juul Jensen and properties of nano-scale metals has been edited by Faester, Hansen, Huang, Juul Jensen and Ralph [20]. Relating to Figure 3, Hirouchi and Shibutani have reported on slip on transmission across special Ralph [20]. Relating to Figure 3, Hirouchi and Shibutani have reported slip transmission across [20]. Relating to Figure 3, Hirouchi and copper Shibutani have reported on slip transmission across special Σ3 crystal grain boundaries in very small micro-pillars [21]. special Σ3 crystal grain boundaries in very small copper micro-pillars [21]. Σ3 crystal grain boundaries in very small copper micro-pillars [21]. Conflicts of Interest: The authors declare no conflict of interest. Conflicts ofof Interest: The authors declare nono conflict of of interest. Conflicts Interest: The authors declare conflict interest.
References References References 1. 2. 3. 4. 5. 6. 7.
1. Cottrell, A.H. Dislocations and Plastic Flow in Crystals; Oxford University Press: Oxford, UK, 1953. Cottrell, A.H. Dislocations and Plastic Flow inFlow Crystals; OxfordOxford University Press: Press: Oxford, UK, 1953. Cottrell, A.H.Wernick, Dislocations Plastic in Crystals; University Oxford, UK, 1953. 2. 1. Newkirk, J.B., J.H.,and Eds. Direct Observation of Imperfections in Crystals; Interscience Publishers: Newkirk, J.B.; Wernick, J.H. (Eds.) Direct Observation of Imperfections in in Crystals; Interscience Publishers: 2. New Newkirk, J.B., Wernick, J.H., Eds. Direct Observation of Imperfections Crystals; Interscience Publishers: York, NY, USA, 1962. New York, NY, USA, 1962. New York, NY,Theory USA, of 1962. 3. Nabarro, F.R.N. Crystal Dislocations; Clarendon Press: Oxford, UK, 1967. Nabarro, F.R.N. Theory of Crystal Dislocations; Clarendon Press: Oxford, UK, 1967. 3. Nabarro, F.R.N. Theory Dislocations; Clarendon Press: Oxford,New UK, York, 1967. NY, USA, 1968. 4. Hirth, J.P.; Lothe, J. TheoryofofCrystal Dislocations; McGraw-Hill Book Company: Hirth, J.P.; Lothe, J. Theory of Dislocations; McGraw-Hill Book Company: New York, NY, USA, 1968. Hirth, Lothe, Theory of Dislocations; McGraw-Hill Book Company: New York, NY, USA, 1968. 5. 4. Hull, D.;J.P.; Bacon, D.J.J.Introduction to Dislocations, 5th ed.; Butterworth-Heinemann: London, UK, 2011. Hull, D.; Bacon, D.J. Introduction to Dislocations, 5th ed.; Butterworth-Heinemann: London, UK, 2011. 5. Hull, D.; Bacon, D.J. Introduction to Dislocations, 5th ed.; Butterworth-Heinemann: London, UK, 2011. 6. Nabarro, F.R.N., Ed. Dislocations in Solids; Volumes 1–13; Elsevier: Amsterdam, The Netherlands, 1980– Nabarro, F.R.N. (Ed.) Dislocations in Solids; Elsevier: Amsterdam, The Netherlands, 1980–2007; Volumes 1–13. 6. 2007. Nabarro, F.R.N., Ed. Dislocations in Solids; Volumes 1–13; Elsevier: Amsterdam, The Netherlands, 1980– Hirth, J.P.; Kubin, L. (Eds.) Dislocations in Solids; Elsevier: Amsterdam, The Netherlands, 2010; Volume 16. 2007.J.P., Kubin, L., Eds. Dislocations in Solids; Volume 16; Elsevier: Amsterdam, The Netherlands, 7. Hirth, 7. 2010. Hirth, J.P., Kubin, L., Eds. Dislocations in Solids; Volume 16; Elsevier: Amsterdam, The Netherlands, 2010.
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Armstrong, R.W. Symmetry Aspects of Dislocation-Effected Crystal Properties: Material Strength Levels and X-ray Topographic Imaging. Symmetry 2014, 6, 148–163. [CrossRef] Frank, F.C. The influence of dislocations on crystal growth. Disc. Faraday Soc. 1949, 5, 48–54. [CrossRef] Burton, W.K.; Cabrera, N.; Frank, F.C. Role of dislocations in crystal growth. Nature 1949, 163, 398–399. [CrossRef] Woodruff, D.P. How does your crystal grow? A commentary on Burton, Cabrera and Frank (1951) ‘The growth of crystals and the equilibrium structure of their surfaces’. Phil. Trans. R. Soc. A 2015, 373, 20140230. [CrossRef] [PubMed] Armstrong, R.W.; Wu, C.C.; Farabaugh, E.N. Crystal subgrain misorientations via X-ray diffraction microscopy. In Adv. X-ray Anal.; McMurdie, H.F., Barrett, C.S., Newkirk, J.B., Ruud, C.O., Eds.; Plenum Press: New York, NY, USA, 1977; Volume 20, pp. 201–206. Hall, E.O. The deformation and ageing of mild steel; discussion of results. Proc. Phys. Soc. Lond. 1951, B64, 747–753. [CrossRef] Petch, N.J. The cleavage strength of polycrystals. J. Iron Steel Inst. 1953, 174, 25–28. Armstrong, R.W.; Codd, I.; Douthwaite, R.M.; Petch, N.J. The plastic deformation of polycrystalline aggregates. Phil. Mag. 1962, 7, 45–58. [CrossRef] Armstrong, R.W. Plasticity: Grain Size Effects III. In Reference Module in Materials Science and Materials Engineering; Elsevier: Amsterdam, The Netherlands, 2016; pp. 1–23. Armstrong, R.W. Material grain size and crack size influences on cleavage fracture. Philos. Trans. A Math. Phys. Eng. Sci. 2015, 373. [CrossRef] [PubMed] Armstrong, R.W.; Elban, W.L.; Walley, S.M. Elastic, Plastic, Cracking Aspects of the Hardness of Materials. Int. J. Mod. Phys. B. 2013, 27, 1330004. [CrossRef] Weertman, J.R.; Farkas, D.; Hemker, K.; Kung, H.; Mayo, M.; Mitra, R.; Van Swygenhoven, H. Structure and mechanical behavior of bulk nanocrystalline materials. MRS Bull. 1999, 24, 44–50. [CrossRef] Faester, S.; Hansen, N.; Huang, X.; Juul Jensen, D.; Ralph, B.; (Eds.) Nanometals—Status and Perspective: Proceedings of the 33rd Risø International Symposium on Materials Science; Technical University of Denmark: Roskilde, Denmark, 2012; pp. 1–430. Hirouchi, T.; Shibutani, Y. Mechanical Responses of Copper Bicrystalline Micro Pillars with Σ3 Coherent Twin Boundaries by Uniaxial Compression Tests. Mater. Trans. 2014, 55, 52–57. [CrossRef] © 2016 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
Crystal Dislocations Ronald W. Armstrong Received: 28 December 2015; Accepted: 4 January 2016; Published: 6 January 2016 Academic Editor: Helmut Cölfen Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA; [email protected]; Tel.: +1-410-723-4616
Abstract: Crystal dislocations were invisible until the mid-20th century although their presence had been inferred; the atomic and molecular scale dimensions had prevented earlier discovery. Now they are normally known to be just about everywhere, for example, in the softest molecularly-bonded crystals as well as within the hardest covalently-bonded diamonds. The advent of advanced techniques of atomic-scale probing has facilitated modern observations of dislocations in every crystal structure-type, particularly by X-ray diffraction topography and transmission electron microscopy. The present Special Issue provides a flavor of their ubiquitous presences, their characterizations and, especially, their influence on mechanical and electrical properties. Keywords: dislocations; crystals; polycrystals; nanopolycrystals; X-ray topography; transmission electron microscopy; optical microscopy; crystal growth; crystal strength properties; electrical properties
1. Introduction Early interest in dislocations sprang from research investigations into conditions of crystal growth and on subsequent permanent (or plastic) crystal deformation properties, in the latter case, particularly relating to crystal strength and ductility. An important industrial focus on defects in electronic crystals at micro-scale dimensions has led to much ongoing research activity. Cottrell, in 1953, produced a seminal book on dislocations and strength properties based on his teaching at Birmingham [1]. An early conference on dislocation observations, mostly, in metals was held in 1961 [2]. Emphasis was given to observations made via optical and electron microscopy, X-ray diffraction topography, and field ion microscopy. Among a number of subsequent dislocation treatises with broader coverage are books by Nabarro [3] and by Hirth and Lothe [4]. A frequently referenced book is by Hull and Bacon [5]. Nabarro initiated a comprehensive series of Dislocations in Solids volumes, latterly co-edited, first with Duesbury, then with Hirth [6], and later by Hirth, then ending with Hirth and Kubin [7]. In all, 96 chapters were produced over the period from 1980 until 2010 by many experts. The early volumes 1–3 established the elastic theory, lattice relationship and movement properties. Figure 1 shows a schematic view of an edge dislocation with central core and flexible line orientation to circumvent obstacles to migration [8]. 2. Crystal Growth and Dislocation Structures Frank saw first the important advantage in crystal growth of a screw dislocation with displacement (Burgers) vector, b, parallel to line axis, `, and thus providing a consequent never-ending crystal step for atomic attachment [9]. Burton described with Cabrera and Frank the beneficial nature of the trailing spiral ledge [10]. Updated commentary of the crystal growth work by Frank and colleagues and on other work extending until recent time has been given by Woodruff [11]. Figure 2 is a transmission X-ray topograph of a cm-size α-Al2 O3 (sapphire) crystal slice from a larger boule grown by a chemical vapor decomposition technique [12]. The just-visible very finely resolved lines are Crystals 2016, 6, 9; doi:10.3390/cryst6010009
www.mdpi.com/journal/crystals
Crystals 2016, 6, 9 Crystals Crystals2016, 2016,6,6,99
2 of 4
grown by a chemical vapor decomposition technique [12]. The just-visible very finely resolved lines grown by a chemical vapor decomposition technique [12].shown The just-visible finely resolved lines are individual dislocations. Three “blackened” bunchesare are to emanate emanatevery from individual dislocations. Three “blackened” bunches shown to from individual individualpoints points are individual dislocations. Three “blackened” bunches are shown tothe emanate individual across recognizable upper boundary established when crystalfrom growth had points been across aa recognizable upper boundary tracetrace established when the crystal growth had been temporarily across a recognizable upper boundary trace established when the crystal growth had been temporarily halted. Edge type dislocations with b perpendicular to ℓ, as in the front face of Figure 1, halted. Edge type dislocations with b perpendicular to `, as in the front face of Figure 1, penetrate temporarily halted. Edge type dislocations with b perpendicular to ℓ, as in solutes. the frontOther face of Figure 1, penetrate growth interfaces also, presumably, to incorporate impurities and aspects of growth interfaces also, presumably, to incorporate impurities and solutes. Other aspects of dislocation penetrate growth interfaces also, presumably, tozinc, incorporate impurities and solutes. Other aspects of dislocation arrangements have been reported for and (photovoltaic) silicon arrangements have been reported for zinc, nickel and nickel (photovoltaic) silicon crystals [8].crystals [8]. dislocation arrangements have been reported for zinc, nickel and (photovoltaic) silicon crystals [8].
Figure Figure1.1.Schematic Schematicdislocation dislocationpicture. picture. Figure 1. Schematic dislocation picture.
Figure2.2.Dislocations Dislocationsin inα-Al α-Al2O crystal. 2O Figure 3 3crystal. Figure 2. Dislocations in α-Al2O3 crystal.
Crystal, Polycrystal,Nanopolycrystal NanopolycrystalDeformations Deformations 3.3.Crystal, Polycrystal, 3. Crystal, Polycrystal, Nanopolycrystal Deformations Dislocationsmove moverelatively relativelyeasy easyininmetal metalcrystals crystalsor orpolycrystals, polycrystals,and andless lessso soininionic, ionic,covalent covalent Dislocations Dislocations moveOne relatively metal crystals or polycrystals, less so in ionic, covalent andmolecular molecular crystals. One mighteasy notein indication Figure of mutual mutualand impediment indicated via and crystals. might note indication ininFigure 11of impediment indicated via and molecular crystals. One might note indication in Figure 1 of mutual impediment indicated via potentialdislocation dislocationintersections, intersections,otherwise otherwise there there are arelattice/solute lattice/soluteinteractions interactionstotobe becontended contendedwith with potential potential dislocation intersections, otherwise there are lattice/solute interactions to be contended with asindicated indicatedininFigure Figure3.3.InInthe thefigure, figure,the thedislocations dislocationsare aredenoted denotedas asrightside-up rightside-upor orinverted invertedT’s T’sand and as as indicated Figure 3. In theby figure, theblack dislocations are denoted as rightside-up or or inverted T’s and various represented the the black dots,dots, eithereither residing individually, or dislocation-associated various soluteinare are represented by residing individually, dislocationvarious solute represented by the black dots, residing or dislocationin three cases: (i) are at individual dislocations, ordislocations, (ii) on the either leftor side ason segregated dislocations arranged associated in three cases: (i) at individual (ii) theindividually, left at side as segregated at associated in three cases: (i) at individual dislocations, or (ii) on the left side as segregated in a verticalarranged subgraininboundary; or (iii) toboundary; greater extent, a (crystal) grain boundary region dislocations a vertical subgrain or (iii)within to greater extent, within a (crystal) grainat dislocations arranged in aadjacent vertical subgrain or (iii)The to greater withinlines a (crystal) between adjacent crystals of different lattice orientations. dottedextent, lines “slip” ofgrain the boundary region between crystals ofboundary; different lattice orientations. The represent dotted represent boundary adjacent crystalsstructure of different lattice orientations. Theindotted lines represent dislocations acrossbetween the subgrain and locally concentrated the grain “slip” of theregion dislocations across theboundary subgrain boundary structure and locally concentrated in boundary the grain “slip” of the dislocations across the subgrain structure locally concentrated in the grain region where thewhere direction-dependent strainsboundary must necessarily beand accommodated. boundary region the direction-dependent strains must necessarily be accommodated. boundary region where the direction-dependent strains must necessarily be accommodated.
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Figure Figure 3. 3. Polycrystal Polycrystal dislocation dislocation slip. slip. Figure 3. Polycrystal dislocation slip.
Figure 4. 4. Nanopolycrystal Nanopolycrystal structure. structure. Figure Figure 4. Nanopolycrystal structure.
The polycrystal strength strength dependence dependenceon onreciprocal reciprocalsquare squareroot rootofofgrain grainsize size was first reported The polycrystal was first reported in The polycrystal strengthofdependence on reciprocal root of grain size was first reported in independent investigations strength properties of square steel materials by Hall Petch independent investigations of thethe strength properties of steel materials by Hall [13] [13] and and Petch [14] [14] and in independent investigations ofsize the strength properties of steel materials by quite Hall [13] and Petch [14] and the same type of size grain dependence was later shown later toquite apply generally to the then then the same type of grain dependence was shown to apply generally to the complete and thenstress-strain the same type of grainofsize dependence was shownnumber later toofapply quite generally to the complete mild steel and to a wider metals [15]. An updated stress-strain behaviorsbehaviors of mild steel and to a wider number of metals [15]. An updated review has complete stress-strain behaviors of mild steel and to a wider number of metals [15]. An updated review has been presented [16]. An analogous relationship to the crack size dependence of the been presented [16]. An analogous relationship to the crack size dependence of the fracture mechanics reviewmechanics has been properties presented of [16]. An analogous relationship tobeen the established crack size dependence of the fracture metals and related materials has [17]. properties of metals and related materials has been established [17]. fracture mechanics properties of metals and related materials has been established [17]. Considerable materials nanotechnology in Considerable research research interest interest is is currently currently being being devoted devoted to to materials nanotechnology in three three Considerable research interest is currently being devoted to materials nanotechnology in three research areas: (1) nano-indentation hardness testing; (2) mechanical testing of specimens with nanoresearch areas: (1) nano-indentation hardness testing; (2) mechanical testing of specimens with research areas: and (1) nano-indentation hardness testing; (2) mechanical testing of specimens with nanoscale structures; testing material specimens of physical nano-scale dimensions. A review has nano-scale structures;(3) and (3) testing material specimens of physical nano-scale dimensions. A review scale structures; and (3) testing material specimens of physical nano-scale dimensions. A review has been reported on crystal/polycrystal nanoindentation hardness testing [18]. Figure 4 is an4 atomic scale has been reported on crystal/polycrystal nanoindentation hardness testing [18]. Figure is an atomic been reported on crystal/polycrystal nanoindentation hardness testing [18]. Figure 4 is an atomic scale simulation of theofdeformation structure within a nickel crystal [19]. [19]. A treatise on the and scale simulation the deformation structure within a nickel crystal A treatise onstructure the structure simulation of the deformation structure within a nickel crystal [19]. A treatise on the structure and properties of nano-scale metals has been by Faester, Hansen, Huang, Juul Jensen and Ralph and properties of nano-scale metals has edited been edited by Faester, Hansen, Huang, Juul Jensen and properties of nano-scale metals has been edited by Faester, Hansen, Huang, Juul Jensen and Ralph [20]. Relating to Figure 3, Hirouchi and Shibutani have reported on slip on transmission across special Ralph [20]. Relating to Figure 3, Hirouchi and Shibutani have reported slip transmission across [20]. Relating to Figure 3, Hirouchi and copper Shibutani have reported on slip transmission across special Σ3 crystal grain boundaries in very small micro-pillars [21]. special Σ3 crystal grain boundaries in very small copper micro-pillars [21]. Σ3 crystal grain boundaries in very small copper micro-pillars [21]. Conflicts of Interest: The authors declare no conflict of interest. Conflicts ofof Interest: The authors declare nono conflict of of interest. Conflicts Interest: The authors declare conflict interest.
References References References 1. 2. 3. 4. 5. 6. 7.
1. Cottrell, A.H. Dislocations and Plastic Flow in Crystals; Oxford University Press: Oxford, UK, 1953. Cottrell, A.H. Dislocations and Plastic Flow inFlow Crystals; OxfordOxford University Press: Press: Oxford, UK, 1953. Cottrell, A.H.Wernick, Dislocations Plastic in Crystals; University Oxford, UK, 1953. 2. 1. Newkirk, J.B., J.H.,and Eds. Direct Observation of Imperfections in Crystals; Interscience Publishers: Newkirk, J.B.; Wernick, J.H. (Eds.) Direct Observation of Imperfections in in Crystals; Interscience Publishers: 2. New Newkirk, J.B., Wernick, J.H., Eds. Direct Observation of Imperfections Crystals; Interscience Publishers: York, NY, USA, 1962. New York, NY, USA, 1962. New York, NY,Theory USA, of 1962. 3. Nabarro, F.R.N. Crystal Dislocations; Clarendon Press: Oxford, UK, 1967. Nabarro, F.R.N. Theory of Crystal Dislocations; Clarendon Press: Oxford, UK, 1967. 3. Nabarro, F.R.N. Theory Dislocations; Clarendon Press: Oxford,New UK, York, 1967. NY, USA, 1968. 4. Hirth, J.P.; Lothe, J. TheoryofofCrystal Dislocations; McGraw-Hill Book Company: Hirth, J.P.; Lothe, J. Theory of Dislocations; McGraw-Hill Book Company: New York, NY, USA, 1968. Hirth, Lothe, Theory of Dislocations; McGraw-Hill Book Company: New York, NY, USA, 1968. 5. 4. Hull, D.;J.P.; Bacon, D.J.J.Introduction to Dislocations, 5th ed.; Butterworth-Heinemann: London, UK, 2011. Hull, D.; Bacon, D.J. Introduction to Dislocations, 5th ed.; Butterworth-Heinemann: London, UK, 2011. 5. Hull, D.; Bacon, D.J. Introduction to Dislocations, 5th ed.; Butterworth-Heinemann: London, UK, 2011. 6. Nabarro, F.R.N., Ed. Dislocations in Solids; Volumes 1–13; Elsevier: Amsterdam, The Netherlands, 1980– Nabarro, F.R.N. (Ed.) Dislocations in Solids; Elsevier: Amsterdam, The Netherlands, 1980–2007; Volumes 1–13. 6. 2007. Nabarro, F.R.N., Ed. Dislocations in Solids; Volumes 1–13; Elsevier: Amsterdam, The Netherlands, 1980– Hirth, J.P.; Kubin, L. (Eds.) Dislocations in Solids; Elsevier: Amsterdam, The Netherlands, 2010; Volume 16. 2007.J.P., Kubin, L., Eds. Dislocations in Solids; Volume 16; Elsevier: Amsterdam, The Netherlands, 7. Hirth, 7. 2010. Hirth, J.P., Kubin, L., Eds. Dislocations in Solids; Volume 16; Elsevier: Amsterdam, The Netherlands, 2010.
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