Dislocations in FCC Metals_Radwan

MSE 501

Chapter 5:Dislocations in FCC Metals

Radwan, Omar201306050

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

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

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

FCC DislocationsPerfect 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

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.

Partial DislocationsShockley 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.

Hull and Bacon, 2011

Shockley Partial DislocationsAccording 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

• 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

Shockley Partial Dislocations

Shockley Partial Dislocations

Shockley Partial Dislocations

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).

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.

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.

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

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.

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

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

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

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.

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

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

Frank Partial DislocationNegative 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

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

• 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

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

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

Stacking Fault TetrahedraBy quenching By radiation damage

Stacking-fault tetrahedron in irradiated copper.

Transmission electron micrograph of tetrahedral defects in quenched gold.

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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.