Chapter 4 Imperfections: Point and Line Defects. Dimensional Range for Different Classes of Defects.
-
Upload
theodore-mccarthy -
Category
Documents
-
view
232 -
download
0
Transcript of Chapter 4 Imperfections: Point and Line Defects. Dimensional Range for Different Classes of Defects.
Chapter 4 Imperfections: Point and Line
Defects
Dimensional Range for Different Classes of Defects
Stress Required to Shear a Crystal
Theoretical Shear Strength of Some Materials
Atomic point defects.
Two most common point defects in compounds:Schottky and Frenkel defects.
Point Defects
Interstices in FCC structure. (a) Octahedral void. (b) Tetrahedral void.
Interstices in the BCC structure. (a) Octahedral void. (b) Tetrahedral void.
Interstices in the HCP structure. (a) Octahedral void. (b) Tetrahedral void.
Point Defects
Formation of point defects by the annihilation ofdislocations. (a) Row of vacancies. (b) Row of interstitials.
Formation of Point Defects
Shear stress-versus-strain curves for aluminum single crystals. The crystallographic orientation isshown in the stereographic triangle. (Adapted with permission from A. H. Cottrell, Phil. Mag., 46 (1955) p. 737.)
Shear stress-Shear Strain Curves for Aluminum Single Crystal
Seeger model of damage produced by irradiation. P indicates the position where the first “knock-on” terminates.(Reprinted with permission fromA. Seeger, in Proc. Symp. Radiat.Damage Solids React., Vol. 1,(Vienna, IAEA, 1962) pp. 101, 105.)
Voids formed in nickel irradiated using 400 keV 14N2+ ions to a dose of 40 dpa at 500 ◦C; notice the voids with polyhedral shape; dpa = displacements per atom. (Courtesy of L. J. Chen andA. J. Ardell.)
Radiation Damage
Stress–strain curves for irradiated and unirradiated Zircaloy. (Adapted with permission from 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 fast neutron-induced dilation in stainless steel (Fe–Cr–Ni) as a function 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 a hump.
Line Defects
Arrangement of atoms in an edge dislocation and the Burgers vector b that produces closure of circuit ABCDE.
Edge and Screw Dislocations
Arrangement of atoms in a screw dislocation with “parking garage” setup. Notice car entering garage.
Edge and Screw Dislocations
. (a) Perfect crystal. (b) Edge dislocation. (c) Screw dislocation.
Plastic deformation of a crystal by the movement of a dislocation along a slip plane.
Plastic Deformation
Shear Produced by Dislocation Movement
Mixed dislocation obtained from cut-and-shear operation; notice the anglebetween b and dislocation line.
Mixed Dislocation
(a) Titanium. (Courtesy of B. K. Kad.) (b) Silicon.
Dislocations 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 loop produced by the introduction of a disk into metal. (a) Perspective view. (b) Section AAAA. (c) Section BBBB.
Prismatic Loop
Slip produced by the movement of dislocation. (a) Positive and negative edge dislocations. (b) Positive and negative screw dislocations.
Movement of Dislocation
Expansion of a Dislocation Loop
Stresses due to Dislocations
Screw Dislocation Edge Dislocation
Stress fields around an edge dislocation. (The dislocation line is Ox3), (a) σ11; (b) σ22; (c) σ33; (d) σ12. (Adapted with permission from J. C. M. Li, in Electron Microscopy and Strength of Crystals, eds. G. Thomas and J. Washburn (New York: Interscience Publishers, 1963).)
Stress Fields Around a Edge Dislocation
Schematic representation of an idealized dislocation array (a) in two dimensions (b) in three dimensions; note that dislocations on three perpendicular atomic planes define a volume V.
Dislocation Array
Bending of a Dislocation
Dislocations in an FCC Crystal
Peach-Koehler Equation
Decomposition of a dislocation b1 into two partial dislocations b2 and b3, separated by a distance d0.
Decomposition of Dislocation
Stacking Fault Energies of Some Metals
Short segment of stacking fault in AISI 304 stainless steel overlapping with coherent twin boundary. Differences in the nature of these defects are illustrated by fringe contrast differences.
Stacking Fault and Partial Dislocations
Dislocations in AISI 304 stainless steel splitting into partials bounded by short stacking-fault region. Partials spacing marked as d. (Courtesy of L. E. Murr.)
Effect of stacking-fault energy on dislocation substructure. (a) High-stacking-fault-energy material (pure copper); (b) Low-stacking-fault-energy material (copper–2 wt% aluminum).
Both materials were laser-shock compressed with an initial pressure of 40 GPa and pulse duration of 3 ns. (Courtesy of M. S. Schneider.)
Effects of Stacking-Fault Energy on Dislocation Substructure
Frank or Sessile dislocations. (a) Intrinsic. (b) Extrinsic.
Frank or Sessile Dislocations
Cottrell–Lomer lock.
Stairway dislocation.
Cottrell –Lomer and Stairway Dislocations
Basal, pyramidal, and prism plane in HCP structure.
Important Planes in HCP Structure
Temperature for Macroscopic Plasticity in Some Ceramics
Slip Systems and Burgers Vectors in Some Ceramics
Screw Dislocation
Edge Dislocation
General Form
Expressions for Energy of Dislocation
Basal Plane in Al2O3
Elastic Energy for Dislocations in Ceramics
(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 Effects, 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
Homogeneous Nucleation of Dislocations
Emission of dislocations from ledges in grain boundary, as observed in transmission electron microscopy during heating by electron beam. (Courtesy of L. E. Murr.)
Grain Boundary as a Source of Dislocations
Effect of oxide layer on the 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
Formation of dislocation loop by the Frank–Read mechanism.
Frank-Read Mechanism
Frank–Read source formed by cross-slip.
Dislocation Source: Cross Slip
Epitaxial growth of thin film. (a) Substrate. (b) Start of epitaxial growth. (c) Formation ofdislocations.
Epitaxial Growth
Pileup of dislocations against a barrier.
Pileup of dislocations against grain boundaries (or dislocations being emitted from grain boundary sources?) in copper observed by etch pitting.
Dislocation Pileups
(a) Edge dislocation traversing “forest” dislocation. (b) Screw dislocation traversing “forest” dislocations.
Dislocation Interactions
(a) Kink and jog in edge dislocation. (b) Kink and jog in screw dislocation.
Loop being pinched out when jog is left behind by dislocation motion.
Kinks and Jogs in Dislocations
Orowan’s Equation
k b
(a) Movement of dislocation away from its equilibrium position. (b) Variation of Peierls–Nabarro stress with distance. (Reprinted with permission from H. Conrad, J. Metals, 16 (1964), 583.)
Peierls-Nabarro Stress
Overcoming of Peierls barrier by Seeger kink pair mechanism. (a) Original straight dislocation. (b) Dislocation with two kinks. (c) Kinks moving apart.
Overcoming of Peierls Barrier
Effect of temperature on Young’s modulus. (Adapted from J. B. Wachtman Jr.,W. E. Tefft, D. G. Lam, Jr., and C. S. Apstein, J. Res. Natl. Bur. Stand., 64A (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) an idealized material, (b) BCC metals, and (c) FCC metals. Notice the greater temperature dependence for Ta and Fe (BCC).
Flow Stress as a Function of Temperature
Stresses and dislocations generated at film-substrate interface; (a) Film and substrate with different lattice parameters; (b) elastic (coherent) accommodation of strains by film;(c) elastic + dislocation (semi-coherent) accommodation of strains at a film thickness greater than hc.(Adapted from W. D. Nix, Met. Trans., 20A (1989) 2217.)
Dislocations on Film-Substrate Interface
Critical film thickness as a function of misfit strain; the greater fraction Ge, the greater the misfit stain and the smaller hc. Predictions from van der Merwe Matthews theory; measurements from J. C. Bean, L. C. Feldman, A. T. Fiory, S. Nakahara, and I. K. Robinson, J. Vac. Sci. Technol. A, 2 (1984) 436.(Adapted from W. D. Nix., Met. Trans., 20A (1989) 2216.)
Critical Film Thickness vs. Atomic Fraction of Ge
Mechanisms of misfit dislocation generation; (a) Freund mechanism in which a “threading”dislocation preexisting in substrate lays over interface creating misfit dislocation; (b) Nix mechanism, in which a surface source creates
half-loops that move toward interface.
Misfit Dislocation Generation