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
Point Defects
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.
Formation of Point Defects
Formation of point defects by the annihilation of
dislocations. (a) Row of vacancies. (b) Row of
interstitials.
Shear stress-Shear Strain Curves for Aluminum
Single Crystal
Shear stress-versus-strain curves for aluminum
single crystals. The crystallographic orientation is
shown in the stereographic triangle. (Adapted
with permission from A. H. Cottrell, Phil. Mag.,
46 (1955) p. 737.)
Radiation Damage
Seeger model of damage produced by
irradiation. P indicates the position where
the first “knock-on” terminates.
(Reprinted with permission from
A. 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 and
A. J. Ardell.)
Radiation Damage
Stress–strain curves for irradiated and
unirradiated Zircaloy. (Adapted with permission
from J. T. A. Roberts, IEEE Trans. Nucl. Sci., NS22, (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.)
Line Defects
(a) Rug with a fold.
Caterpillar with a hump.
Edge and Screw Dislocations
Arrangement of atoms in an edge dislocation and the Burgers vector b
that produces closure of circuit ABCDE.
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
Plastic deformation of a crystal by the
movement of a dislocation along a slip plane.
Shear Produced by Dislocation Movement
Mixed Dislocation
Mixed dislocation obtained from cutand-shear operation; notice the angle
between b and dislocation line.
Dislocations in Metals
(a) Titanium. (Courtesy of B. K. Kad.)
(b) Silicon.
Dislocations in Al2O3 and TiC
Dislocations in (a) Al2O3 and (b) TiC. (Courtesy of J. C. LaSalvia.)
Dislocation in Molybdenum
Atomic resolution transmission electron micrograph of dislocation in
molybdenum with a Burgers circuit around it. (Courtesy of R. Gronsky.)
Square Dislocation Loop
Elliptic 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.)
Prismatic Loop
Prismatic loop produced by the introduction
of a disk into metal.
(a) Perspective view.
(b) Section AAAA.
(c) Section BBBB.
Movement of Dislocation
Slip produced by the movement of dislocation.
(a) Positive and negative edge dislocations.
(b) Positive and negative screw dislocations.
Expansion of a Dislocation Loop
Stresses due to Dislocations
Screw Dislocation
Edge Dislocation
Stress Fields Around a 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).)
Dislocation Array
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.
Bending of a Dislocation
Dislocations in an FCC Crystal
Peach-Koehler Equation
Decomposition of Dislocation
Decomposition of a dislocation b1 into two partial dislocations b2
and b3, separated by a distance d0.
Stacking Fault Energies of Some Metals
Stacking Fault and Partial Dislocations
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.
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.)
Effects of Stacking-Fault Energy on Dislocation Substructure
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.)
Frank or Sessile Dislocations
Frank or Sessile dislocations.
(a) Intrinsic. (b) Extrinsic.
Cottrell –Lomer and Stairway Dislocations
Cottrell–Lomer lock.
Stairway dislocation.
Important Planes in HCP Structure
Basal, pyramidal, and prism plane in HCP structure.
Temperature for Macroscopic Plasticity in
Some Ceramics
Slip Systems and Burgers Vectors in
Some Ceramics
Expressions for Energy of Dislocation
Screw Dislocation
Edge Dislocation
General Form
Basal Plane in Al2O3
Elastic Energy for Dislocations in Ceramics
Dislocations in Sapphire
(a) Dislocations, dipoles, and loops in sapphire.
(b) Interaction between dislocations in
sapphire. (From K. P. D. Lagerdorf, B. J. Pletka,
T. E. Mitchell, and A. H. Heuer, Radiation
Effects, 74 (1983)).87
Dislocations in Titanium Diboride
Hexagonal array of dislocations in
titanium diboride. (Courtesy of D. A.
Hoke and G. T. Gray.)
Stacking faults in GaP.
(Courtesy of P. Pirouz.)
Homogeneous Nucleation of Dislocations
Grain Boundary as a Source 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.)
Effect of Oxide Layer on the Tensile Properties of Niobium
Effect of oxide layer on the tensile
properties of niobium.
(Reprinted with permission from
V. K. Sethi and R. Gibala, Scripta
Met. 9 (1975) 527.)
Frank-Read Mechanism
Formation of dislocation loop by the Frank–Read mechanism.
Dislocation Source: Cross Slip
Frank–Read source formed by crossslip.
Epitaxial Growth
Epitaxial growth of thin film. (a) Substrate.
(b) Start of epitaxial growth. (c) Formation of
dislocations.
Dislocation Pileups
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 Interactions
(a) Edge dislocation traversing “forest”
dislocation.
(b) Screw dislocation traversing “forest”
dislocations.
Kinks and Jogs in Dislocations
(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.
Orowan’s Equation
  k  b
Peierls-Nabarro Stress
(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.)
Overcoming of Peierls Barrier
Overcoming of Peierls barrier by Seeger kink pair mechanism.
(a) Original straight dislocation.
(b) Dislocation with two kinks.
(c) Kinks moving apart.
Temperature Effect on Young’s Modulus
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: Cambridge
University Press, 1990, p. 143.)
Flow Stress as a Function of Temperature
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).
Dislocations on Film-Substrate Interface
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.)
Critical Film Thickness vs. Atomic Fraction of Ge
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.)
Misfit Dislocation Generation
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.