6299 chapter 4

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Chapter4

Imperfections: Point and LineDefects



Dimensional Ranges for Different Classes of Defects



Stress Required to Shear a Crystal



Atomic point defects.

Two most commonpoint defects in compounds:Schottky and Frenkel defects.

Point Defects



Interstices in FCCstructure. (a) Octahedral void. (b)Tetrahedral void.

Interstices in the BCCstructure. (a) Octahedral void. (b)Tetrahedral void.

Interstices in the HCPstructure. (a) Octahedral void. (b)Tetrahedral void.

Point Defects



Formation of pointdefects by the annihilation of dislocations. (a) Row of vacancies.(b) Row of interstitials.

Point Defects



Stress-versus-straincurves for aluminum single crystals.The crystallographic orientation isshown in the stereographictriangle. ( Adapted with permissionfrom A. H. Cottrell, Phil. Mag ., 46(1955) p. 737.)

Aluminum Single Crystals



Seeger model of damage produced by irradiation. P indicates the position where thefirst ³knock-on´ terminates.(Reprinted with permission from A. Seeger, in Proc. Symp. Radiat.Damage Solids React ., Vol. 1,(Vienna, I AEA, 1962) pp. 101, 105.)

Voids formed in nickelirradiated using 400 keV 14N2+ions to a dose of 40 dpa at 500 C;notice the voids with polyhedralshape; dpa = displacements per atom. (Courtesy of L. J. Chen and A. J. Ardell.)

Radiation Damage



Stress±strain curvesfor irradiated and unirradiatedZircaloy. ( Adapted with permissionfrom J. T. A. Roberts, IEEE Trans.Nucl. Sci ., NS-22, (1975) 2219.)

Radiation Damage



Stress-free dilation in AISI 316 steel (20% cold worked).( Adapted with permission from J.T. A. Roberts, IEEE Trans. Nucl. Sci .,NS-22, (1975) 2219.)

Dependence of fastneutron-induced dilation instainless steel (Fe±Cr±Ni) as afunction of Ni and Cr amounts.( Adapted with permission from W.B. Hillig, Science, 191 (1976) 733.)

Radiation Damage



(a) Rug with a fold.

Caterpillar with ahump.

Line Defects



(a) Arrangement of atoms in an edge dislocation andthe Burgers vector b thatproduces closure of circuit ABC DE .(b) Arrangement of atoms inscrew dislocation with ³parkinggarage´ setup. (Notice car entering

garage.)

Edge and Screw Dislocations



Geometricalproduction of dislocations. (a)Perfect crystal. (b) Edgedislocation. (c) Screw dislocation.



The plasticdeformation of a crystal by themovement of a dislocation along aslip plane.

Plastic Deformation



Plastic deformation(shear) produced by the movementof (a) edge dislocation and (b)screw dislocation. Note d is thedirection of dislocation motion;is the direction of dislocation line.

Dislocation Movements



Mixed dislocationobtained from cut-and-shear operation; notice the anglebetween b and .

Mixed Dislocation



Dislocations in metals. (a) Titanium. (Courtesy of B. K. Kad.) (b) Silicon.

Dislocation in Metals



Dislocations in (a) Al2O3 and (b) TiC. (Courtesy of J. C. LaSalvia.)

Dislocations in Al2O3 and TiC



Atomic resolution transmission electron micrograph of dislocation inmolybdenum with a Burgers circuit around it. (Courtesy of R. Gronsky.)

Dislocation in Molybdenum



Square Dislocation Loop



Elliptic dislocation loop. (a) Intermediate position. (b) Final (sheared)position. (c) TEM of shear loop in copper (Courtesy of F. Gregori and M. S. Schneider .)

Elliptic Dislocation Loop



Prismatic loopproduced by the introduction of adisk into metal. (a) Perspectiveview. (b) Section AAAA. (c) SectionBBBB.

Prismatic Loop



Slip produced by themovement of dislocation. (a)Positive and negative edgedislocations. (b) Positive andnegative screw dislocations.

Movement of Dislocation



Expansion of a dislocation loop



Simple models for (a)screw and (b) edge dislocations;

the deformation fields can beobtained by cutting a slitlongitudinally along a thick-walledcylinder and displacing the surfaceby b parallel (screw) andperpendicular (edge) to thedislocation line.

Dislocations

Screw Dislocation Edge Dislocation



Stress fields around anedge dislocation. (The dislocationline is Ox 3), (a) 11; (b) 22; (c) 33; (d) 12. ( Adapted withpermission from J. C. M. Li, inE lectron Microscopy and Strength of C rystals, eds. G. Thomas and J.Washburn (New York:Interscience Publishers, 1963).)

Stress Fields Around a Edge Dislocation



Schematicrepresentation of an idealizeddislocation array (a) in twodimensions and (b) in threedimensions; note that dislocationson three perpendicular atomic

planes define a volume V .

Dislocation Array



Curved dislocation



Dislocations in an FCC crystal



Peach-Koehler Equation



Decomposition of a d0dislocation b1 into two partialdislocationsb2 and b3, separatedby a distance d 0.

Decomposition of Dislocations



Short segment of

stacking fault in AISI 304 stainlesssteel overlapping with coherenttwin boundary. Differences in thenature of these defects areillustrated by fringe contrastdifferences. (b) Dislocations in AISI304 stainless steel splitting intopartials bounded by shortstacking-fault region. Partialsspacing marked as d . (Courtesy of L. E. Murr.)

Stacking Fault



Effect of stacking-faultenergy on dislocationsubstructure. (a)

High-stacking-fault-energy material(pure copper); (b)lower-stacking-fault-energymaterial (copper±2 wt%aluminium). Both materials werelaser-shock compressed with aninitial pressure of 40 GPa andpulse duration of 3 ns. (Courtesyof M. S. Schneider.)

Effects of Stacking-Fault Energy on Dislocation Substructure



Frank or Sessiledislocations. (a) Intrinsic. (b)Extrinsic.

Frank or Sessile Dislocations



Cottrell±Lomer lock.

Stairway dislocation.

Dislocations



Basal, pyramidal, andprism plane in HCP structure.

Planes in HCP Structure



Screw Dislocation

Edge Dislocation

General Form



Basal plane in Al2O3



(a) Dislocations,dipoles, and loops in sapphire. (b)Interaction between dislocations insapphire. (From K. P. D. Lagerdorf,B. J. Pletka, T. E. Mitchell, and A. H.Heuer, Radiation E ffects, 74 (1983)87.)

Dislocations in Sapphire



Hexagonal array of dislocations in titanium diboride.(Courtesy of D. A. Hoke and G. T.Gray.)

Stacking faults in GaP.(Courtesy of P. Pirouz.)

Dislocations in Titanium Diboride



Homogeneousnucleation of dislocation inconventional deformation.

Homogeneous Nucleation of Dislocations



Emission of dislocations from ledges in grainboundary, as observed intransmission electron microscopyduring heating by electron beam.(Courtesy of L. E. Murr.)

Grain Boundary Dislocations



Effect of oxide layer onthe tensile properties of niobium.(Reprinted with permission fromV. K. Sethi and R. Gibala, ScriptaMet . 9 (1975) 527.)

Effect of Oxide Layer on the Tensile Properties of Niobium



Sequence of theformation of dislocation loop bythe Frank±Read mechanism.

Frank-Read Mechanism



Frank±Read sourceformed by cross-slip.

Epitaxial growth of thinfilm. (a) Substrate. (b) Start of epitaxial growth. (c) Formation of dislocations.

Cross Slip



Pileup of dislocationsagainst a barrier.

Pileup of dislocationsagainst grain boundaries (or dislocations being emitted fromgrain-boundary sources?) incopper observed by etch pitting.

Pileup Dislocations



(a) Edge dislocationtraversing ³forest´dislocation. (b)Screw dislocationtraversing³forest´ dislocations.

Dislocation Movements



(a) Kink and jog inedge dislocation. (b) Kink and jogin screw dislocation.

Loop being pinchedout when jog is left behind bydislocation motion.

Intersection of Dislocation



Orowan¶s Equation

k bK V R!



(a) Movement of dislocation away from itsequilibrium position. (b) Variationof Peierls±Nabarro stress withdistance. (Reprinted withpermission from H. Conrad, J .Metals, 16 (1964), 583.)

Peierls-Nabarro Stress



Overcoming of Peierlsbarrier by Seeger kink pair mechanism. (a) Original straightdislocation. (b) Dislocation withtwo kinks. (c) Kinks moving apartat velocity vk .

Seeger Kink Pair Mechanism



Effect of temperatureon Young¶s modulus. ( Adaptedfrom J. B.Wachtman Jr.,W. E. Tefft,D. G. Lam, Jr., and C. S. Apstein, J .

Res. Natl. Bur. Stand ., 64 A (1960)213; and J. Lemartre and J. L.Chaboche, Mechanics of Solid Materials, Cambridge: CambridgeUniversity Press, 1990, p. 143.)

Temperature Effect on Young¶s Modulus



Flow stress as a

function of temperature for (a) anidealized material, (b) BCC metals,and (c) FCC metals. Notice thegreater temperature dependencefor Ta and Fe (BCC).

Flow Stress as a Function of Temperature



Stresses anddislocations generated atfilm-substrate interface; (a) filmand substrate with different latticeparameters; (b) elastic (coherent)accommodation of strains by film;(c) elastic + dislocation(semi-coherent) accommodationof strains at a film thicknessgreater than hc .( Adapted from W.D. Nix, Met. Trans., 20 A (1989)2217.)

Dislocations on Film-Substrate Interface



Critical film thicknessas a function of misfit strain for Ge x Si1- x film grown on Sisubstrate; the greater fraction Ge x ,the greater the misfit stain and the

smaller hc . Predictions from vander Merwe Matthews theory;measurements from J. C. Bean, L.C. Feldman, A. T. Fiory, S.Nakahara, and I. K. Robinson,J .V ac. Sci. Technol. A, 2 (1984) 436.( Adapted from W. D. Nix., Met.Trans., 20 A (1989) 2216.)

Critical Film Thickness vs. Atomic Fraction of Ge



Mechanisms of misfitdislocation generation; (a) Freundmechanism in which a ³threading´dislocation preexisting in substratelays over interface creating misfitdislocation; (b) Nix mechanism, bywhich surface source createshalf-loops that move toward

interface.

Misfit Dislocation Generation

6299 chapter 4

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