Chapter 5
Imperfections: Interfacial and
Volumetric Defects
Grains in a Polycrystal
Grains in a crystalline metal or ceramic; the cube depicted in each grain
indicates the crystallographic orientation of the grain in a schematic fashion.
Grain Structure of Tantalum and TiC
Polycrystalline (a) tantalum and (b) TiC.
Low Angle Grain Boudnary
Low-angle grain boundary observed
by high-resolution transmission
electron microscopy. Positions of
individual dislocations are marked
by Burgers circuits. (Courtesy of R.
Gronsky.)
Mean Lineal Intercept
Low-Angle Tilt Boundary
Low-Angle Twist Boundary
Grain-Boundary Energy as a Function of
Misorientation
Variation of grain-boundary energy with misorientation θ. (Adapted with
permission from A. G. Guy,Introduction to Materials Science (New York:
McGraw-Hill, 1972), p. 212.)
Coincidence Lattice Boundary
Coincidence lattice boundary made by every
seventh atom in the two grains, misoriented 22◦
by a rotation around the <111> axis. (Adapted
from M. L. Kronberg and H. F. Wilson, Trans.
AIME, 85 (1949), 501.)
Coincidence Site Boundaries
Interface between Alumina and NiAl2O4
Interface between alumina and NiAl2O4
(spinel). (a) High-resolution TEM. (b)
Representation of individual atomic positions.
(Courtesy of C. B. Carter.)
Grain Size vs. Volume Fraction of Intercrystal Regions
The effect of grain size on calculated
volume fractions of intercrystal regions
and triple junctions, assuming a grain
boundary thickness of 1 nm. (Adapted
from B. Palumbo, S. J. Thorpe, and K. T.
Aust, Scripta Met., 24 (1990) 1347.)
Ledge Formation in Grain Boundary
Models of ledge formation in a grain boundary.
(Reprinted with permission from L. E. Murr,
Interfacial Phenomena in Metals and Alloys
(Reading, MA: Addison Wesley, 1975), p. 255.)
Grain Boundary Ledges
Grain boundary ledges as observed by TEM. (Courtesy of L. E. Murr.)
Tilt Boundary
Image and atomic position model of an approximately 32◦ [110] tilt boundary in gold; note the
arrangement of polygons representing the boundary. (From W. Krakow and D. A. Smith, J. Mater. Res. 22
(1986) 54.)
Twinning
Twinning in FCC Metals
Deformation Twins
Deformation twins in (a) iron-silicon.(Courtesy of O. Vöhringer.)
Deformation Twins in Silicon Nitride
Deformation twins in silicon nitride observed by TEM. (a) Bright field. (b) Dark
field. (c) Electron diffraction pattern showing spots from two twin variants.
(Courtesy of K. S. Vecchio.)
Serrated Stress-Strain Curve Due to Twinning
Serrated stress–strain curve due to twinning in a Cd
single crystal. (Adapted with permission from W.
Boas and E. Schmid, Z. Phys., 54 (1929) 16.)
Twinning in HCP Metals
Stress Required for Twinning and Slip
Effect of temperature on the stress required for twinning and slip (at low
and high strain rates). (Courtesy of G. Thomas.)
Mechanical Effects of Slip and Twinning
(a) Stress–strain curves for copper (which deforms by slip) and 70% Cu–30% Zn brass (which
deforms by slip and twinning). (b) Work-hardening slope dσ/dε as a function of plastic strain; a
plateau occurs for brass at the onset of twinning. (After S. Asgari, E. El-Danaf, S. R. Kalidindi,and
R. D. Doherty, Met. and Mater. Trans., 28A (1997) 1781.)
Effect of Temperature and Stacking-Fault Energy
on Twinning Stress
Effect of temperature on twinning stress for a
number of metals. (From M. A. Meyers, O.
Voehringer, and V. A. Lubarda, Acta
Mater., 49 (2001) 4025.)
Effect of stacking-fault energy on the
twinning stress for several copper alloys.
(From M. A. Meyers, O. Voehringer, and
V. A. Lubarda, Acta Mater., 49 (2001)
4025.)
Temperature-Strain Rate Plots
Temperature–strain rate plots with slip and twinning domains;
(a) effect of grain size in titanium; (b) effect of stacking-fault
energy in copper–zinc alloys. (From M. A. Meyers, O.
Voehringer, and V. A. Lubarda, Acta Mater., 49 (2001) 4025.)
Grain-Size Strengthening
Hall–Petch plot for a number of metals and alloys. Y.S. indicates yield strength.
Hall-Petch Plot
Hall–Petch plot for iron and low-carbon steel
extending from monocrystal to nanocrystal;
notice the change in slope. (After T. R. Smith, R.
W. Armstrong, P. M. Hazzledine, R. A.
Masumura, and C. S. Pande, Matls.
Res. Soc. Symp. Proc., 362 (1995) 31.)
Frank-Read Source
Frank–Read source operating in center
of grain 1 and producing two pileups at
grain boundaries; the Frank–Read
source in grain 2 is activated by stress
concentration.
Dislocation Activity at Grain Boundaries in Stainless Steel
Dislocation activity at grain boundaries in AISI
304 stainless steel deformed at a strain rate of
10−3 s−1. (a) Typical dislocation profiles after a
strain of 0.15 %. (b) Same after a strain of 1.5 %.
(Courtesy of L. E. Murr.)
Meyers-Ashworth Theory
Deformation stages in a polycrystal (a) start of
deformation (b) localized plastic flow in the
grain-boundary regions (microyielding) (c) a
work-hardened grain-boundary layer that
effectively reinforces the microstructure.
Deformation Twins
Deformation twins in shock-loaded nickel (45 GPa
peak pressure; 2 μs pulse duration). Plane of foil
(100); twinning planes (111) making 90◦. (Courtesy
of L. E. Murr.)
Strength of Drawn Wire
Strength of drawn wire after recovery treatment as a function of
transverse lineal-intercept cell size. Recovery temperatures (in ◦C) are
indicated on the curves. (Adapted with permission from H. J. Rack and
M. Cohen, in Frontiers in Materials Science: Distinguished Lectures,
L. E. Murr, ed. (New York: M. Dekker, 1976), p. 365.)
Nanocrystalline Material: Structure
Representation of atomic structure of a nanocrystalline material; white
circles indicate grain-boundary regions. (Courtesy of H. Gleiter.)
Hall-Petch Relationship
Stress–strain curves for conventional (D = 50 μm)
and nanocrystalline (D = 25 μm) copper. (Adapted
from G. W. Nieman, J. R. Weertman, and R. W.
Siegel, Nanostructured Materials, 1 (1992) 185.)
Hall–Petch relationship for nanocrystalline copper. (After
G. W. Nieman, J. R. Weertman, and R. W. Siegel,
Nanostructured Matls., 1 (1992) 185)
Dependence of Yield Strength on
Grain Size
Yield strength as a function of D−0.5 for two
different equations and computational results
assuming a grain-boundary region and grain
interior with different work-hardening curves. As
grain size decreases, grain-boundary region
gradually dominates the deformation process.
(From H.-H. Fu, D. J. Benson, and M. A.
Meyers, Acta Mater., 49 (2001) 2567.)
Voids in Titanium Carbide
Voids (dark regions indicated by arrows) in titanium carbide. The
intergranular phase (light) is nickel, which was added to increase
the toughness of TiC.
Voids
(a) Faceted grain-interior voids in alumina and (b) voids in titanium carbide;
dislocations are pinned by voids. TEM.