Hosson, J.Th.M. de

Sleeswyk, A.W.

University of Groningen

   University of GroningenAtomic Configuration of a ½<111>{110} Edge Dislocation in α-FeHosson, J.Th.M. de; Sleeswyk, A.W.Published in:Default journalIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1975Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Hosson, J. T. M. D., & Sleeswyk, A. W. (1975). Atomic Configuration of a ½{110} Edge Dislocation in α-Fe.Default journal.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 12-11-2019Solid State Communications,Vol. 17, pp. 245—248, 1975. Pergamon Press. Printed in Great BritainATOMIC CONFIGURATION OF A ~(111> {l 10) EDGE DISLOCATION IN a-FeJ.Th.M. de Hosson and A.W. Sleeswyk*(Received 23 March 1975 by A.R. Miedema)The atomic arrangement around a ~(111) (11 0} edge dislocation in an a-Fecrystallite embedded in an elastic continuum is calculated, using the Johnson-I interatomic potential. A narrow dislocation without any stacking faultresults, although there is some displacement in the core parallel to thedislocation line.TAKING the lattice parameter as unity, the Burgers The Cartesian coordinates x, y, z are chosen parallelvector of mobile dislocations in b.c.c. crystals is to the Burgers vector ~[111] , perpendicular to the~(111). All planes belonging to the (111) zone appear slip plane and parallel to the dislocation line, respectively;to be active macroscopic slip planes, although (110), v is the Poisson ratio. The initial displacements of the(112 } and (123)predominate.1 In some alloys only atoms are then given by:the most densely packed planes of the (1 10) type are b ( / \ xfound to be active. We have started our investigation, u~= — (arctan ~-) + 2 2 (l)therefore, with the ~(111> edge dislocation on the 2ir \XJ 2(1 — v)(x + y )j(110)plane in a-Fe, for which the Johnson-I potential b 11 — 2v 2 2isknown. Uy = —~ \~4(l—v)1’~+y )A similar calculation was performed by Vitek2 + X2 ~ (2)some while ago on ~<111) (112) dislocations. He found 4(1 — v)(x2 +y2)that although the core structure spreads out widely on = 3the “twinning side” of the dislocation — which is asym- UZmetric in this case — no stacking fault in any sense of While the boundaries are taken to be fixed in thesethe word is formed. positions, the remaining atoms are allowed to move inspace under influence of the effect of the pair-wiseThe predictions from hard-sphere models for interatomic forces resulting from application of the~(111) edge dislocations on (110) planes appear to be potential function developed by Johnson.8 For deter-somewhat more ambiguous35 than those for dis- mining the final result, Gibson’s9 integration procedurelocations on (112) planes.6 is used. Atomic configurations are determined whenthe crystallite upon relaxation reaches minimum poten.The crystallite block of a-Fe chosen for the present tial energy, and the procedure is repeated until theinvestigation — which is a continuation of previous potential energy changes between consecutive stepswork on diffusion paths of interstitial atoms in this are less than 5 x 10 ~ eV.metal7 — contains about 3000 atoms. The dislocation — —is initially introduced in this block by applying to each The stacking sequence: ABCDEFAB . . . of (112)atom the displacement predicted by isotropic elasticity, atomic layers in b.c.c. implies a 6-layer periodicity ofplanes along the dislocation line, and an interplanar~ spacing of 1/sJ6. The crystallite is composed of 14Groningen, The Netherlands. (112) planes in order to be able to embed a multiple245246 4(111> {l 10) EDGE DISLOCATION IN a-Fe Vol. 17, No. 2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000~ [~TiJ000000000000000000 FIG. 2. The projection along the [1101 direction of00000000000000000 thetwo(110)planesbelowtheslipplane andthe two0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 planes above the slip plane in the crystallite whichcontains an edge dislocation with Burgers vector00000000000000000 4[TTl].00000000000000000(ito] centre of the crystallite. These planes were considered00000000000000000 nowasboundary conditionsañd kept fixed duringa(TTi] second relaxation process. Due to this procedure thecrystallite has an effective thickness of 26 planes inFIG. 1. The atomic configuration of one (T1~)plane the z-direction.of the relaxed crystallite containing an edge dislocationwith Burgers vector4 [111].In our previous work7 we observed negligibledifferences between the effects on the core structureof 6 planes in the elastic continuum. During the relax- of a (100> edge dislocation in 7-Fe of isotropic oration process atomic displacements occurred in the z- anisotropic boundary conditions. On account of thisdirection. Therefore, the elastic boundary planes were we estimate that the considerable complication thatreplaced by the relaxed equivalent planes from the anisotropic elasticity would introduce into this moreABOVE SUP PLANE .008 BELOW SUP PLANE 0Q06[1i~] °-00k-086—008‘000DISTANCE X [Us]FIG. 3. The deviation in the [1l~]direction of the atomic positions from the positions in the perfect crystal, foratoms directly above and below the slip plane as a function of the distance in the [TI1] direction. The deviation isgiven with the lattice parameter as unity.Vol. 17, No. 2 4<111> (110)EDGE DISLOCATION iN a-Fe 247ABOVE SLIP PLANE .BELOW SLIP0.300200.10AX[Iii] 0-010-020-030A0-050DISTANCE X [III)FIG. 4. The displacements of the atomic positions in the [1111direction as a function of the distance in the [TI1]direction. The displacements were calculated as the deviations from the positions in the perfect lattice and are pre-sented as fractions of the lattice parameter.intricate case of the 4(111> {l 10) dislocation in a-Fe, above and below the slip plane in the [T1~Jdirectionwould not be worth the effort required. According to are given as a function of the distance in the [TI11Eshelby, Read and Shockley1°the general solution of direction.The asymmetrical structure of the dislocationthe straight dislocation in an anisotropic continuum core is clearly illustrated in Fig. 3. In Fig. 4 the dis-would involve the solution of a 6th-order polynomial placements of the atoms in the two layers above andin p. Because of the twofold rotation axis along the below the slip plane in the [1111direction are given(110> direction and the mirror plane {1 10), this poly- as function of the distance in the [111]direction. Thesenomial can be reduced in the presentproblem to a displacements were calculated as the deviations from3rd-order polynomial in p2. Afurther complication the atomic positions in the perfect lattice. It is obviousis caused by the coefficients D(1) which are involved that nowhere in the core do any of these displacementsin Eshelby’s formulation for the displacements. exhibit a tendency to be a constant, as the presence ofastacking fault would require.One of the central (Il~)planes of the crystalliteis projected in Fig. 1: the atomic positions are those The only effect that has been predicted to someof the fully relaxed lattice. In Fig. 2 the positions of extent by hardsphere models is the displacement ofthe atoms in two planes below the slip plane and the atoms along the direction of the dislocation line. Actwo planes above it are projected along the [1101 cording to Steyn and Brick3~the slip motion over thedirection. Although the appearance of the resulting (110)hardsphere plane in the [111]direction wouldimage might suggest that the dislocation has dis- be composed of a succession of ~[‘ITO]and ~[1T2]sociated in two equal partials with a narrow stacking displacements between saddle point positions. Crussard3fault between them, this is, in fact, an erroneous and Cohen etaL accordingly proposed that the perfectimpression caused by the Moire-effect due to the 4 [ill] dislocation would dissociate into three partials:overlapping images of atoms in successive layers. 4 [111] ~[1101+ ~[TT2] + ~[ITO]. (4)This will be obvious from Fig. 3, where the dis- The displacement component in the [‘Il~]directionplacements of the atoms in the two layers immediately in the two stacking faults would then be 0.102 -248 4(111> {l 10) EDGE DISLOCATION IN a-Fe Vol. 17, No. 2Sleeswyk6 pointed out that the saddle point no indication whatever in Fig. 4 of faulting in thepositions that the earlier authors proposed for faulted narrow 4 [111] dislocation in a-Fe, it is impossible tostacking would be those that would possess lowest either confirm or refute these proposed dissociations.stacking fault energy if the lattice would transforminto f.c.c. Assuming lattice stability prohibiting this In conclusion we can only state that the stackingtype of stacking fault, he proposed a symmetrical dis- fault energy in this material is too high to give rise tosociation instead: any effect that might be associated with the formation4[1T1] -+ &[IT1] + ~[i’I1]. (5) of stacking faults on the {110} plane.The displacement in the stacking fault between the In a subsequent paper we shall discuss the effecttwo partials would then have no component in the of anisotropic boundary conditions on the core struc-[T1~] direction, but the atoms in the cores of the ture and the interaction energy of carbon impuritiestwo partials would probably have been displaced in with lattice sites in the core region.the [11~}direction, in senses opposite in the twonartjals Acknowledgements — The authors wish to thank Mr.D.J. Verel for his stimulating discussion of this work.The research concerning energy and atomic configur-In the present instance the maximum displacement ation of dislocations is sponsored by the Foundationin the [112) direction was about 0.07, but as there is for Research of Matter, F.O.M.REFERENCES1. BARRETT C.S., ANSEL G. and MEHL R.F., Trans. ASM 25, 702 (1937).2. VITEK V., LEJCEK L. and BOWDEN D.K., Interatomic Potentials and Simulation ofLatticeDefects (Editedby GEHLENP.C., BEELER J.R. and JAFFEE R.I.) p.493. Plenum Press, New York (1972).3. CRUSSARD C.R., Compt. Rend. Acad. Sd. Paris 252, 373 (1961).4. COHEN J.B., HINTON R., LAY K. and SASS S.,Acta Met. 10, 894 (1962).5. SLEESWYK A.W., Dislocation Dynamics (Edited by ROSENFIELD A.R., HAHN G.T, BEMENT A.L. andJAFFEE R.I.) p. 507. McGraw-Hill, New York (1968).6. BARREI’T C.S., “Cold Working of Metals”,Amer. Soc. Metals p. 65 (1948).7. DE HOSSON J.T.M. (to be published in Solid State Commun.).8. JOHNSON R.A.,Phys. Rev. 1~4,Al329 (1964).9. GIBSON J.B., GOLAND A.N., MILGRAM M. and VINEYARD G.H.,Phys. Rev. 120, 1229 (1960).10. ESHELBYJ.D., READ W.T. and SHOCKLEYW.,ActaMet. 1,251(1953).11. STEIIN R.P. and BRICK R.M., Trans. ASM46, 1406 (1954).

Atomic Configuration of a ½&lt;111&gt;{110} Edge Dislocation in α-Fe

University of Groningen Research Database

  
 University of Groningen
Atomic Configuration of a ½<111>{110} Edge Dislocation in α-Fe
De Hosson, J.T.M.; Sleeswyk, A.W.
Published in:
Default journal
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from
it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date:
1975
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Hosson, J. T. M. D., & Sleeswyk, A. W. (1975). Atomic Configuration of a ½{110} Edge Dislocation in α-Fe.
Default journal.
Copyright
Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).
Take-down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the
number of authors shown on this cover page is limited to 10 maximum.
Download date: 11-02-2018
Solid State Communications,Vol. 17, pp. 245—248, 1975. Pergamon Press. Printed in Great Britain
ATOMIC CONFIGURATION OF A ~(111> {l 10) EDGE DISLOCATION IN a-Fe
J.Th.M. de Hosson and A.W. Sleeswyk*
(Received 23 March 1975 by A.R. Miedema)
The atomic arrangement around a ~(111) (11 0} edge dislocation in an a-Fe
crystallite embedded in an elastic continuum is calculated, using the Johnson-
I interatomic potential. A narrow dislocation without any stacking fault
results, although there is some displacement in the core parallel to the
dislocation line.
TAKING the lattice parameter as unity, the Burgers The Cartesian coordinates x, y, z are chosen parallel
vector of mobile dislocations in b.c.c. crystals is to the Burgers vector ~[111] , perpendicular to the
~(111). All planes belonging to the (111) zone appear slip plane and parallel to the dislocation line, respectively;
to be active macroscopic slip planes, although (110), v is the Poisson ratio. The initial displacements of the
(112 } and (123)predominate.1 In some alloys only atoms are then given by:
the most densely packed planes of the (1 10) type are b ( / \ x
found to be active. We have started our investigation, u~= — (arctan ~-) + 2 2 (l)
therefore, with the ~(111> edge dislocation on the 2ir \XJ 2(1 — v)(x + y )j
(110)plane in a-Fe, for which the Johnson-I potential b 11 — 2v 2 2
isknown. Uy = —~ \~4(l—v)1’~+y )
A similar calculation was performed by Vitek2 + X2 ~ (2)
some while ago on ~<111) (112) dislocations. He found 4(1 — v)(x2 +y2)
that although the core structure spreads out widely on = 3
the “twinning side” of the dislocation — which is asym- UZ
metric in this case — no stacking fault in any sense of While the boundaries are taken to be fixed in these
the word is formed. positions, the remaining atoms are allowed to move in
space under influence of the effect of the pair-wise
The predictions from hard-sphere models for interatomic forces resulting from application of the
~(111) edge dislocations on (110) planes appear to be potential function developed by Johnson.8 For deter-
somewhat more ambiguous35 than those for dis- mining the final result, Gibson’s9 integration procedure
locations on (112) planes.6 is used. Atomic configurations are determined when
the crystallite upon relaxation reaches minimum poten.
The crystallite block of a-Fe chosen for the present tial energy, and the procedure is repeated until the
investigation — which is a continuation of previous potential energy changes between consecutive steps
work on diffusion paths of interstitial atoms in this are less than 5 x 10 ~ eV.
metal7 — contains about 3000 atoms. The dislocation — —
is initially introduced in this block by applying to each The stacking sequence: ABCDEFAB . . . of (112)
atom the displacement predicted by isotropic elasticity, atomic layers in b.c.c. implies a 6-layer periodicity of
planes along the dislocation line, and an interplanar
~ spacing of 1/sJ6. The crystallite is composed of 14
Groningen, The Netherlands. (112) planes in order to be able to embed a multiple
245
246 4(111> {l 10) EDGE DISLOCATION IN a-Fe Vol. 17, No. 2
000000000000000000
000000000000000000
000000000000000000
000000000000000000
000000000000000000
~ [~TiJ000000000000000000 FIG. 2. The projection along the [1101 direction of
00000000000000000 thetwo(110)planesbelowtheslipplane andthe two
0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 planes above the slip plane in the crystallite which
contains an edge dislocation with Burgers vector
00000000000000000 4[TTl].
00000000000000000(ito] centre of the crystallite. These planes were considered
00000000000000000 nowasboundary conditionsañd kept fixed duringa
(TTi] second relaxation process. Due to this procedure the
crystallite has an effective thickness of 26 planes in
FIG. 1. The atomic configuration of one (T1~)plane the z-direction.
of the relaxed crystallite containing an edge dislocation
with Burgers vector4 [111].
In our previous work7 we observed negligibledifferences between the effects on the core structure
of 6 planes in the elastic continuum. During the relax- of a (100> edge dislocation in 7-Fe of isotropic or
ation process atomic displacements occurred in the z- anisotropic boundary conditions. On account of this
direction. Therefore, the elastic boundary planes were we estimate that the considerable complication that
replaced by the relaxed equivalent planes from the anisotropic elasticity would introduce into this more
ABOVE SUP PLANE .008 BELOW SUP PLANE 0
Q06
[1i~] °
-00k
-086
—008
‘000
DISTANCE X [Us]
FIG. 3. The deviation in the [1l~]direction of the atomic positions from the positions in the perfect crystal, for
atoms directly above and below the slip plane as a function of the distance in the [TI1] direction. The deviation is
given with the lattice parameter as unity.
Vol. 17, No. 2 4<111> (110)EDGE DISLOCATION iN a-Fe 247
ABOVE SLIP PLANE .
BELOW SLIP
0.30
020
0.10
AX
[Iii] 0
-010
-020
-030
A0
-050
DISTANCE X [III)
FIG. 4. The displacements of the atomic positions in the [1111direction as a function of the distance in the [TI1]
direction. The displacements were calculated as the deviations from the positions in the perfect lattice and are pre-
sented as fractions of the lattice parameter.
intricate case of the 4(111> {l 10) dislocation in a-Fe, above and below the slip plane in the [T1~Jdirection
would not be worth the effort required. According to are given as a function of the distance in the [TI11
Eshelby, Read and Shockley1°the general solution of direction.The asymmetrical structure of the dislocation
the straight dislocation in an anisotropic continuum core is clearly illustrated in Fig. 3. In Fig. 4 the dis-
would involve the solution of a 6th-order polynomial placements of the atoms in the two layers above and
in p. Because of the twofold rotation axis along the below the slip plane in the [1111direction are given
(110> direction and the mirror plane {1 10), this poly- as function of the distance in the [111]direction. These
nomial can be reduced in the presentproblem to a displacements were calculated as the deviations from
3rd-order polynomial in p2. Afurther complication the atomic positions in the perfect lattice. It is obvious
is caused by the coefficients D(1) which are involved that nowhere in the core do any of these displacements
in Eshelby’s formulation for the displacements. exhibit a tendency to be a constant, as the presence of
astacking fault would require.
One of the central (Il~)planes of the crystallite
is projected in Fig. 1: the atomic positions are those The only effect that has been predicted to some
of the fully relaxed lattice. In Fig. 2 the positions of extent by hardsphere models is the displacement of
the atoms in two planes below the slip plane and the atoms along the direction of the dislocation line. Ac
two planes above it are projected along the [1101 cording to Steyn and Brick3~the slip motion over the
direction. Although the appearance of the resulting (110)hardsphere plane in the [111]direction would
image might suggest that the dislocation has dis- be composed of a succession of ~[‘ITO]and ~[1T2]
sociated in two equal partials with a narrow stacking displacements between saddle point positions. Crussard3
fault between them, this is, in fact, an erroneous and Cohen etaL accordingly proposed that the perfect
impression caused by the Moire-effect due to the 4 [ill] dislocation would dissociate into three partials:
overlapping images of atoms in successive layers. 4 [111] ~[1101+ ~[TT2] + ~[ITO]. (4)
This will be obvious from Fig. 3, where the dis- The displacement component in the [‘Il~]direction
placements of the atoms in the two layers immediately in the two stacking faults would then be 0.102 -
248 4(111> {l 10) EDGE DISLOCATION IN a-Fe Vol. 17, No. 2
Sleeswyk6 pointed out that the saddle point no indication whatever in Fig. 4 of faulting in thepositions that the earlier authors proposed for faulted narrow 4 [111] dislocation in a-Fe, it is impossible to
stacking would be those that would possess lowest either confirm or refute these proposed dissociations.
stacking fault energy if the lattice would transform
into f.c.c. Assuming lattice stability prohibiting this In conclusion we can only state that the stacking
type of stacking fault, he proposed a symmetrical dis- fault energy in this material is too high to give rise to
sociation instead: any effect that might be associated with the formation
4[1T1] -+ &[IT1] + ~[i’I1]. (5) of stacking faults on the {110} plane.
The displacement in the stacking fault between the In a subsequent paper we shall discuss the effect
two partials would then have no component in the of anisotropic boundary conditions on the core struc-
[T1~] direction, but the atoms in the cores of the ture and the interaction energy of carbon impurities
two partials would probably have been displaced in with lattice sites in the core region.
the [11~}direction, in senses opposite in the two
nartjals Acknowledgements — The authors wish to thank Mr.
D.J. Verel for his stimulating discussion of this work.
The research concerning energy and atomic configur-
In the present instance the maximum displacement ation of dislocations is sponsored by the Foundation
in the [112) direction was about 0.07, but as there is for Research of Matter, F.O.M.
REFERENCES
1. BARRETT C.S., ANSEL G. and MEHL R.F., Trans. ASM 25, 702 (1937).
2. VITEK V., LEJCEK L. and BOWDEN D.K., Interatomic Potentials and Simulation ofLatticeDefects (Edited
by GEHLENP.C., BEELER J.R. and JAFFEE R.I.) p.493. Plenum Press, New York (1972).
3. CRUSSARD C.R., Compt. Rend. Acad. Sd. Paris 252, 373 (1961).
4. COHEN J.B., HINTON R., LAY K. and SASS S.,Acta Met. 10, 894 (1962).
5. SLEESWYK A.W., Dislocation Dynamics (Edited by ROSENFIELD A.R., HAHN G.T, BEMENT A.L. and
JAFFEE R.I.) p. 507. McGraw-Hill, New York (1968).
6. BARREI’T C.S., “Cold Working of Metals”,Amer. Soc. Metals p. 65 (1948).
7. DE HOSSON J.T.M. (to be published in Solid State Commun.).
8. JOHNSON R.A.,Phys. Rev. 1~4,Al329 (1964).
9. GIBSON J.B., GOLAND A.N., MILGRAM M. and VINEYARD G.H.,Phys. Rev. 120, 1229 (1960).
10. ESHELBYJ.D., READ W.T. and SHOCKLEYW.,ActaMet. 1,251(1953).
11. STEIIN R.P. and BRICK R.M., Trans. ASM46, 1406 (1954).


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Atomic Configuration of a ½<111>{110} Edge Dislocation in α-Fe

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University of Groningen

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Atomic Configuration of a ½&lt;111&gt;{110} Edge Dislocation in α-Fe

Abstract

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University of Groningen

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Atomic Configuration of a ½<111>{110} Edge Dislocation in α-Fe