Defectsareimperfectionsinthestructure.Theymaybeone-dimensional
pointdefects(Fig.2.6),linedefects(Fig.2.7),two-dimensionalplane
defects(Fig.2.8),orthree-dimensionalvolumedefectssuchasinclusions
orporosity,Fig.1.16(d).Thedifferenttypesofdefectsaredescribedbriefly
in this section.
2.3.1 One-Dimensional Point Defects
One-dimensional point defects [Fig. 2.6) may include vacancies [Fig. 2.6(a)],
interstitials [Figs 2.6(a) and 2.6(b)], solid solution elements [Fig. 2.6(b)], and
pairs or clusters of the foregoing, Fig. 2.6(c). Pairs of ions (Frenkel defects)
or vacancies (Schottky defects) are often required to maintain charge neu-
trality, Fig. 2.6(c). Point defects can diffuse through a lattice, especially at
temperatures above approximately 0.3–0.5 of the absolute melting tempera-
ture. If the movement of point defects produces a net state change, it causes
thermally activated stress-induced deformation, such as creep. The diffusion
of point defects such as vacancies may also lead to the growth of grains in a
polycrystalline material.
2.3.2 Line Defects
Line defects consist primarily of dislocations, typically at the edges of
patches where part of a crystallographic plane has slipped by one lattice
F
IGURE
2.6 Examples of point defects: (a)] vacancy and interstitial elements;
(b) substitutional element and interstitial impurity element; (c) pairs of ions
and vacancies. [(a) and (c) are adapted from Shackleford, 1996—reprinted
with permission from Prentice-Hall; (b) is adapted from Hull and Bacon,
1984. Reprinted with permission from Pergamon Press.]
Copyright © 2003 Marcel Dekker, Inc.
spacing (Fig. 2.7). The two pure types of dislocations are edge and screw,
Figs 2.7(a) and 2.7(b). Edge dislocations have slip (Burgers) vectors perpen-
dicular to the dislocation line [Fig. 2.7a)], while screw dislocations have
translation vectors parallel to the dislocation line, Fig. 2.7(b). In general,

Twinboundariesmayformwithincrystals.Suchboundarieslieacross
deformationtwinplanes,asshowninFig.2.8(d).Notethattheatomson
eithersideofthetwinplanesaremirrorimages.Stackingfaultsmayalsobe
formedwhentheperfectstackinginthecrystallinestackingsequenceis
disturbed,Figs2.8(e)and2.8(f).Thesemaybethoughtofastheabsence
ofaplaneofatoms(intrinsicstackingfaults)ortheinsertionofrowsof
atomsthatdisturbthearrangementofatoms(extrinsicstackingfaults).
IntrinsicandextrinsicstackingfaultsareillustratedschematicallyinFigs
2.8(e)and2.8(f),respectively.NotehowtheperfectABCABCstackingof
atomsisdisturbedbytheinsertionorabsenceofrowsofatoms.
2.3.4VolumeDefects
Volumedefectsareimperfectionssuchasvoids,bubble/gasentrapments,
porosity,inclusions,precipitates,andcracks.Theymaybeintroducedintoa
solidduringprocessingorfabricationprocesses.Anexampleofvolume
defectsispresentedinFig.2.9.ThisshowsMnSinclusionsinanA707
steel.AnotherexampleofavolumedefectispresentedinFig.1.16(d).
This shows evidence of $1–2 vol % of porosity in a molybdenum disilicide
composite. Such pores may concentrate stress during mechanical loading.
Volume defects can grow or coalesce due to applied stresses or temperature
fields. The growth of three-dimensional defects may lead ultimately to cat-
astrophic failure in engineering components and structures.
F
IGURE
2.9 MnS inclusions in an A707 steel. (Courtesy of Jikou Zhou.)
Copyright © 2003 Marcel Dekker, Inc.
2.4THERMALVIBRATIONSAND
MICROSTRUCTURALEVOLUTION
Asdiscussedearlier,atomsinacrystallinesolidarearrangedintounitsthat
arecommonlyreferredtoasgrains.Thegrainsizemaybeaffectedbythe
controlofprocessingandheattreatmentconditions.Grainsmayvaryinsize

À23
JÁatom
À1
K
À1
) and T is the
absolute temperature in degrees Kelvin. The vibrating lattice atoms can only
be excited into particular quantum states, and the energy, q, is given simply
by Planck’s law (q ¼ h). Also, at any given time, the vibrational energy
varies statistically from atom to atom, and the atoms continuously exchange
energy as they collide with each other due to atomic vibrations.
Nevertheless, the average energy of the vibrating atoms in a solid is given
by statistical mechanics to be 3kT at any given time. This may be sufficient
to promote the diffusion of atoms within a lattice.
Copyright © 2003 Marcel Dekker, Inc.