This document provides an overview of dislocations in face-centered cubic (FCC) metals. It discusses several types of dislocations that can occur in FCC metals including perfect dislocations with 1/2<110> Burgers vectors, Shockley partial dislocations formed by splitting a perfect dislocation, and Frank partial dislocations formed by inserting or removing a close-packed plane. The document also describes how Shockley partial dislocations can cross-slip between planes, the formation of Lomer-Cottrell locks at intersections of partial dislocations, and the nucleation of stacking fault tetrahedra in low stacking fault energy metals.

1. MSE 501
Chapter 5:
Dislocations in FCC Metals
Radwan, Omar
201306050

2. Outline
• Introduction
• Perfect Dislocations
• partial Dislocations
o Shockley Partial Dislocation
• Cross Slip of Partial Dislocations
• Thompson’s Tetrahedron
o Frank Partial Dislocation
• Lomer-Cottrell Locks
• Stacking Fault Tetrahedra

3. Introduction
• Face-centered Cubic: unit cell of cubic
geometry, with atoms located at each of the
corners and the centers of all the cube faces.
• FCC metals: copper, silver, gold, aluminum,
nickel and their alloys
• soft, with critical resolved shear stress
values for single crystals 0.1-1 MNm-2
• ductile but can be hardened considerably by
plastic deformation and alloying
Callister, 1993

4. Introduction
• Each unit cell contains 4 {111}
planes
• Each {111} plane contains 3 <110>
directions
• Thus, there are 12 slip systems in
an FCC unit cell
• For the face-centered crystal
structure, the centers of the third
plane are situated over the C sites
of the first plane. This yields an
ABCABCABC ...stacking sequence;
that is, the atomic alignment
repeats every third plane.
Hull and Bacon, 2011

5. FCC Dislocations
Perfect Dislocations
• Burger vector
– translation vector
– IbI: as small as possible
• No change in crystal
structure before and after
the motion of dislocations
Partial Dislocations
• Burger vector
– not a translation vector
• leaves behind an imperfect
crystal containing a stacking
fault.
Hull and Bacon, 2011

6. Perfect Dislocations
According to Frank’s rule:
Eel=αGb2 : The energy of a dislocation is proportional to
the square of the magnitude of its Burgers vector b2
For FCC
• Shortest lattice vectors (most likely Burgers vectors for
dislocations) in FCC: are of the type ½(110) and (001)
• The energy of ½ <110> dislocations in an isotropic solid will be
only half that of<001>, i.e. 2a2/4 compared with a2. Thus, <001>
dislocations are much less favored energetically and, in fact, are
only rarely observed.

7. Partial Dislocations
Shockley partials
• Formed by splitting a perfect
dislocation
• Glissile dislocation (mobile
dislocation)
Frank Partials
• Formed by inserting or partly
removing a {111} plane
• Sessile dislocation (immobile
dislocation)
Formation of a 1/6[12’1] Shockley partial
dislocation at M due to slip along LM.
Formation of a 1/3[111] Frank partial dislocation by
removal of part of a close-packed layer of atoms.

8. Hull and Bacon, 2011
Shockley Partial Dislocations
According to Frank’s rule:
• A dislocation will decompose into partial
dislocations if the energy state of the sum of
the partials is less than the energy state of
the original dislocation.
• Thus, if
– |b2|2+|b3|2 > |b1|2; b1 will not decompose
– |b2|2+|b3|2 < |b1|2; b1 will decompose
– |b2|2+|b3|2 =|b1|2;will remain in original state
For FCC

9. • First: Before looking at the energetic profile of this reaction, one has to verify
its correctness according to the following steps
Thus, the reaction is proven correct and both sides of Eq. are balanced
• Next: one must check the energetic aspect
– take the absolute values of the indexes of the Burgers vectors
– for the left hand side of Eq., one gets a 2/2 and,
– for the sum of the squares on the right hand side, a2/3.
– Clearly, a2/2>a2/3 and, thus, there is a decrease in energy, thus the splitting of the
dislocation is favored energetically.
Shockley Partial Dislocations

10. Shockley Partial Dislocations

11. Shockley Partial Dislocations

12. Shockley Partial Dislocations

13. Shockley Partial Dislocations
• These two partial dislocations will repel each other to a point where a
balance is reached between the elastic energy decrease, due to the
splitting of the dislocation, and the increase of the stacking-fault energy.
• The combined defect of the partials and the stacking fault is called ‘extended
dislocation’.
• The extended dislocation, consists of Shockley partials and a stacking fault,
which can glide within its own glide plane; therefore, the accepted notation is
glissile dislocation.
• The dissociation of a perfect dislocation is independent of its character (edge,
screw or mixed).

14. Shockley Partial Dislocations
• If the spacing of the partials is d, the repulsive force per unit
length between the partials of either pure edge or pure screw
perfect dislocations is:
• The widths predicted by equations are rather greater than
these for edge dislocations and less for screws.

15. Shockley Partial Dislocations
• Stacking-fault energy varies widely from metal to metal,
depending on the width of the fault.
– Thus, the width of the stacking fault in Cu is about 10 atomic spacings,
whereas, in Al, it is only 2 atomic separations.
– This means that the stacking-fault energy of Cu is low ( 80) compared to
that of Al ( 200 mJ/m2)
• The width of a stacking fault is the consequence of the balance
between:
– the repulsive force between the two partial dislocations
– the attractive force due to the stacking fault.
• When the stacking-fault energy is:
– high, the splitting of the perfect dislocation into two partials is unlikely
and glide in the material occurs only as a result of perfect dislocation
glide.
– Low, stacking-fault energy will promote the formation of wider stacking
faults.

16. Shockley Partial Dislocations
• During glide under stress, a dissociated
dislocation moves as a pair of partials
bounding the fault ribbon, the leading
partial creating the fault and the trailing
one removing it: the total slip vector is
b1=1/2<110>.
• Figure shows sets of extended
dislocations lying in parallel slip planes.
The stacking fault ribbon between two
partials appears as a parallel fringe
pattern.
Hull and Bacon, 2011

17. Cross Slip of Partial Dislocations
• It was stated that, in edge dislocations, the slip direction and the
dislocation line define the slip system; however, in screw
dislocations, the Burgers vector is parallel to the dislocation line
and, thus, it may cross slip into planes belonging to the same
form. The situation is different in cases of extended
dislocations, where stacking fault influences cross slip.
• An edge dislocation with its partials is able to move within its
glide plane along with its faulted region-the extended
dislocation-but it will not be able to move into another
octahedral plane unless it climbs. A screw dislocation or a screw
component will not have such a problem as long as the direction
of slip and the Burgers vector are common to both {111} planes.
However, cross slip can occur only if a ‘constriction’ (i.e., a
joining of the partials) forms.

18. Cross Slip of Partial Dislocations
• Cross Slip of Partial Dislocations can occur only if a
‘constriction’ (i.e., a joining of the partials) forms.
• Formation of a constriction can be assisted by:
– thermal activation and hence the ease of cross slip decreases
with decreasing temperature.
– stress acting on the edge component of the two partials so as
to push them together.
Hull and Bacon, 2011

19. Cross Slip of Partial Dislocations
• sequence of events envisaged during the cross-slip process is
illustrated in Fig:
• Four stages in the cross slip of a dissociated dislocation (a) by the
formation of a constricted screw segment (b). The screw has
dissociated in the cross-slip plane at (c).
Hull and Bacon, 2011

20. Thompson’s Tetrahedron
• provides a convenient notation for describing all the important
dislocations and dislocation reactions in face-centered cubic
metals.
• arose from the appreciation that the four different sets of {111}
planes lie parallel to the four faces of a regular tetrahedron and
the edges of the tetrahedron are parallel to the {110} slip
directions
Hull and Bacon, 2011

21. Thompson’s Tetrahedron
• The corners of the tetrahedron are denoted by A, B, C, D, and the mid-
points of the opposite faces by α, β, γ, δ. The Burgers vectors of
dislocations are specified by their two end points on the tetrahedron.
– the Burgers vectors of the perfect dislocations are defined both in magnitude
and direction by the edges of the tetrahedron and are AB, BC, etc
– Burgers vectors of Shockley partial can be represented by the line from the
corner to the center of a face, such as Aβ, Aγ, etc.

22. Frank Partial Dislocation
• Formed by inserting or removing one close-packed {111}
layer of atoms.
– Removal of a layer results in the intrinsic fault with stacking
sequence ABCACABC...
– insertion produces the extrinsic fault with ABCABACAB...(
Hull and Bacon, 2011

23. Frank Partial Dislocation
• The sequence of the stacking of the {111} planes is modified at the region
where the fault exists from the FCC to a hexagonal close-packed (HCP)
structure.
• The Burgers vectors are normal to the {111} planes and are not the slip
direction in FCC crystals.
• The Frank partial is an edge dislocation and since the Burgers vector is not
contained in one of the {111} planes, it cannot glide and move
conservatively under the action of an applied stress. Such a dislocation is
said to be sessile, unlike the glissile Shockley partial. However, it can move
by climb.
Hull and Bacon, 2011

24. Frank Partial Dislocation
Negative Frank dislocation
• the collapse of a platelet of vacancies
• local supersaturation of vacancies
produced by rapid quenching
• displacement cascades formed by
irradiation with energetic atomic
particles
Positive Frank dislocation
• the precipitation of a close-packed
platelet of interstitial atoms
• irradiation damage
Sólyom, 2007

25. Lomer-Cottrell Locks
• Dislocation gliding on intersecting {111} planes can form a series
of obstacles known as ‘Lomer-Cottrell barriers’, preventing further
glide.
• Before interaction: Figures show stacking faults, bounded by
partial dislocations, are gliding on intersecting {111} planes.
Pelleg, 2013

26. • After interaction: The leading partial dislocations on the intersecting planes
have formed a new partial dislocation with Burgers vector a/6[11’0] according
to:
This reaction is correct, as can be seen by checking the components of the
Burgers vectors, and it is also favorable energetically. The consequence of the
above reaction is the formation of a sessile dislocation, beyond which the
trailing dislocations pile up. The Burgers vector of the newly formed partial
dislocation, i.e. a/6<110>, as shown in the above reaction, is not the vector of
the FCC lattice (but rather a/2<110>) located in plane {001}, which is not a slip
plane in the FCC structure, so it cannot glide.
Lomer-Cottrell Locks
Pelleg, 2013

27. Lomer-Cottrell Locks
• It impedes slip and is
therefore called a “lock.”
• It was initially proposed
by “Lomer”.
• “Cottrell” later showed
that the same reasoning
could be applied to partial
dislocations (also known
as Shockley partials)
• By analogy with carpet on
a stair, it is called a “stair-
rod dislocation”.
Hull and Bacon, 2011

28. Stacking Fault Tetrahedra
• dislocation arrangement has been
observed in metals and alloys of low
stacking-fault energy following treatment
that produces a supersaturation of
vacancies.
• consists of a tetrahedron of intrinsic
stacking faults on {111} planes with 1/6
<110> type stair-rod dislocations along the
edges of the tetrahedron.
• induced by different treatments, such as
irradiation, ageing after quenching and
deformation
• Once nucleated, they can grow in a
supersaturation of vacancies by the climb
of ledges (‘jog lines’) on the {111} faces
due to vacancy absorption
Hull and Bacon, 2011

29. Stacking Fault Tetrahedra
By quenching By radiation damage
Stacking-fault tetrahedron in
irradiated copper.
Transmission electron micrograph of
tetrahedral defects in quenched gold.

30. REFERENCES
• Hull, D., Bacon, D.J., 2011. Chapter 5 - Dislocations in Face-
centered Cubic Metals, in: Introduction to Dislocations (Fifth
Edition). Butterworth-Heinemann, Oxford, pp. 85–107.
• Pelleg, J., 2013. Introduction to Dislocations, in: Mechanical
Properties of Materials, Solid Mechanics and Its
Applications. Springer Netherlands, pp. 85–146.
• Sólyom, J., 2007. The Structure of Real Crystals, in:
Fundamentals of the Physics of Solids. Springer Berlin
Heidelberg, pp. 273–302.
• Callister, J.W.D., 1993. Materials Science and Engineering: An
Introduction, 3 edition. ed. Wiley, New York.
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