6299 Chapter 4

transcript

5/13/2018 6299 Chapter 4 - slidepdf.com

http://slidepdf.com/reader/full/6299-chapter-4 1/61

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

Documents