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Observation of sub-boundary dislocations incorporated in a deformation twin
Scripta METALLURGICA
Vol. 16, pp. 75-78, 1982 Printed in the U.S.A.
OBSERVATION OF INCORPORATED
Department of Hokkaido
Pergamon Press Ltd. All rfghts reserved
SUB-BOUNDARY DISLOCATIONS IN A DEFORMATION TWIN
K.Marukawa and T.Kabutomori* Applied Physics, Faculty University, Sapporo 060,
of Engineering, Japan
(Received October 26, 1981)
Introduction When a growing twin plate encounters crystal defects, such as dislocations, the defects will either be incorporated in the twin, trapped in the twin boundary, or repelled aside. The outcome may depend upon the strength of interaction between them and also upon the speed of their motion. When the incorporation takes place, the defects will suffer the shear deformation of the twin and change their configuration and nature. In some cases, additional defects might be produced by incompatibility of incorporated defects with the twin lattice. The incorporation process of glide dislocations in body-centered cubic crystals has been discussed in detail by Sleeswyk and Verbraak (i). Observation showing such a process, however, has not been reported so far as the present authors are aware, except for the case that dislocations are forced to go into a stationary twin (2). The present paper reports that the incorporation actually occurs at least in the case of dislocation arranged in a sub-boundary. Changes in the configuration and the Burgers vector due to the incorporation have been investigated. The observation was made on a b.c.c, metal, Fe- 3.25wt% Si. Experimental The procedure of specimen preparation and testing are the same as those described in previous papers (3,4). Briefly, specimens machined from a single crystal, which occasionally contained sub-boundaries, were stressed in a tensile testing machine at 77K. They fractured in a brittle manner by the burst of twinning. After thinned, they were observed in an electron microscope at an operating voltage of 650 kV (Hitachi HU-650). Results Figure 1 shows the observed case of incorporation. It may be obvious that a stationary sub-boundary, which is composed of a regular array of dislocations, has been incorporated in a growing twin. The trace of the boundary is sharply bent in accord with the twin shear, while the regularity of the dislocation array is well conserved in the twin. These photographs have been taken in the condition that the matrix is in a good diffracting condition. Incidentally, the twin is also reflecting a beam in Fig.l(a), so that dislocations in the twin as well as in the matrix are visible.
*Now
at
the
Japan
Steel
Works
Ltd.,
Muroran
051,
Japan.
75 0036-9748/82/010075-04503.00/0 Copyright (c) 1982 Pergamon Press Ltd.
76
SUB-BOUNDARY
DISLOCATIONS
Vol.
16
No.
1
FIG.I Incorporation of a subboundary in a deformation twin. Adjoining the twin band, there is a region in which slip has produced almost the same amount of homogeneous shear as the twin. The scale denotes 1 ~m. The reflection vectors are: (a) g= 020 in the matrix and a higher orde~ reflection in the twin, (b) g= 211 m.
The crystallographic elements of the twin and the sub-boundary have been first investigated. The results are summarized in Fig.2. The shear direction of the twin was determined by inspecting the orientations of the matrix and the twin. The twin plane, whose normal was denoted by T, was deduced from the trace of the twin boundary. The system of the observed twin is [iii] (211) in the coordinates of the figure. The direction M of dislocation lines was determined from several photographs taken in different beam directions. To find the vector u, the projected directions of the dislocations were used. Their projected lengths were also utilized for the confirmation. The dislocations are not parallel to any of principal crystallographic axes. The normal n of the sub-boundary plane was obtained from the directions of two lines; one is the dislocation line and the other is the trace of the sub-boundary on the specimen surface. It is to be noted that the vectors S, u , and u÷ are nearly coplanar. The angle between u and u. zs about 15 . The vectors T, n , and n~ are also approxzmately copla~ar. T~e angle between n and n, is 25 . These orientatzon changes of vectors are consistent with the a~sumpt~n that the sub-boundary has suffered the twinning shear without accompanying any other motion of dislocations. (See Discussion). •
-
-
-
~ m
- c
.
Vol.
16,
No.
1
SUB-BOUNDARY
DISLOCATIONS
1010m
77
FIG.2 The direction of dislocation lines ~, arranged in the subboundary shown in Fig.l, whose plane normal is ~. The suffices m and t refer to the matrix and the twin. The normal of the specimen foil is denoted by F. The direction of the twinning shear and the normal of the twin plane is represented by S and T, respectively.
100m As can be seen in Fig.l(b), this sub-boundary is composed of two sets of dislocations which are parallel to each other and arranged alternatingly. The Burgers vector for each set has been identified by the conventional g.b = 0 method. The image feature has also examined and utilized for the identification. For the Burgers vector, the types of ½ and <1007 were assumed. In the reflection ll0m, the dislocation images almost disappeared, although a strong contrast of thlckness fringes appeared along the sub-boundary. In the reflection 211 m (Fig.l(b)), two sets of dislocations presented nearly equal strength of the image intensity. From these and other photographs taken in different reflections, the Burgers vector has been determined as b I = ½[iii] and b~ = [001] for the two sets of dislocations in the matrix. If we take these two seEN for one fictitous set of dislocations which are parallel to the original ones, we obtain =½1113] for the Burgers vector of the composite dislocation. This vector is nearly perpendicular to the dislocation line and also to the sub-boundary surface. Therefore, this sub-boundary is a pure tilt boundary. The axis of the lattice rotation should coincide with the dislocation line. The rotation angle is obtained by m = b / 2D, where D is the spacing of the original dislocation array. With the lattice parameter a= 0.286 nm and the observed spacing D = 22 nm, we obtain w = 0.61 ° . A similar analysis has been made for the sub-boundary in the twin. The sub-boundary has been found again to be composed of two sets of dislocations which are parallel to each other. The images of these dislocations almost disappeared in the reflection II0 . (This reflection is a common reflection between the matrix and the twin).m The two sets of dislocations brought about nearly the same strength of the image intensity in the reflection ~30 . The Burgers vectors for the two sets have been deduced from these and other observations as bn =½[III], and b 4 =½[lli],. In this case, the Burgers vector of the composite-~islocati~n, b~ b_ = (1/3)[114] , is not parallel to the sub-boundary normal n,. Therefore, t~is-~ub-boundary must be accompanied by a long-range stress ~eld. Sub-boundaries which are associated with stresses have been recently observed in annealed NiO (5). Discussion If we assume that the transformation of a lattice vector due to incorporation in a twin is purely geometrical, i.e. if the vector should suffer a homogeneous shear deformation, the transformation can be deduced by a simple consideration (Fig.3). A layer of unit thickness is taken to be parallel to the plane T on which the shear is applied. A vector u I which has its end on the surfac~ of the layer is supposed to be transformed into u 2 by the shear. The vector ~I is not necessarily in the plane of the figure.Obviously, the vector
78
SUB-BOUNDARY
DISLOCATIONS
u~ lies in the plane defined by the vectors S and u I. If T.u.>0, the vector u moves ~owards the ve~to~ S. If T.Ul<0 the direction of motion i~ opposTte. The angle between ~ and S is changed equati~n;fr°m e. to 82, which satisfies the cot
e 2 - cot
81
= ±¥
cos
~,
(i)
Vol.
T[ ,I I
1
~/~
T
i
16, No.
~
where Y is the amount of the shear ~ * ' ' " ' $ strain (Y = I/~-2 for the twin in b.c.c. metals), and a is the angle between the plane of the shear (i.e. the plane FIG.3 Transformation of a lattice defined by S and T) and the plane vector ~ due to a shear deformation containing S and MI" The length of the Y (on the plane T in the direction vector is given by ILl = sec ~ cosec 8. s). Equation (i) may be applied to the direction change of dislocations which is shown in Fig.2. With the measured values for u , ~ = 50 ° and e. = 122 ° , we obtain O~ = 137 ° , which closely agrees with the direction ~t" The length of dislocations m~st have increased by about 24%. The transformation of a lattice plane In this case, the normal of the plane moves T and nl, where n. is the initial posi'tion equation is satisfied; cot
~2
- cot
@i
= ±Y
cos
B,
can be deduced in the plane of the normal.
in a similar manner. defined by the vectors And the following
(2)
where ~1 and #2 are the angle between T and n before and after the shear deformation, r~spectively, and B is the angle between the plane of the shear and the plane defined by T and ~i" The double sign depends upon the sign of S.n. The observed rotation of the sub-boundary normal closely agrees with this equation. From the results of the identification, it may be obvious that the Burgers vector of one dislocation set has not been affected by the incorporation, i.e. b =b . The transformation of the Burgers vector of the other set, therefore, m~st-~e; [001] ÷½[lli] t. This change obeys equation (i), that is, the transformation ~s purely geometrical. The magnitude of the vector is reduced, and the difference between the vectors must be carried away by a twinning partial. The present case of incorporation may be rather special; dislocations are arranged in an array and the Burgers vectors are such that they are conserved or reduced by the incorporation. This may be the reason why the whole configuration of the sub-boundary is well conserved in the twin. There may, however, be cases in which the change in the Burgers vector does not obey the simple geometric relation (I) and the dislocation configuration is severely changed. To obtain more general feature of incorporation, further study will be necessary, which is now under way. References i. 2. 3. 4. 5.
A.W.Sleeswyk and C.A.Verbraak, Acta Met. 9, 917 (1961). L.L6my, Acta Met. 25, 711 (1977). K.Marukawa, Phil. Mag. 36, 1375 (1977). K.Marukawa and Y.Matsubara, Trans. Japan Inst. Metals 20, 724 (1979). A.Gervais, L.Tertian, J.Desehamps and D.Hokim, Acta Met. 27, 499 (1979).
Vol. 16, pp. 75-78, 1982 Printed in the U.S.A.
OBSERVATION OF INCORPORATED
Department of Hokkaido
Pergamon Press Ltd. All rfghts reserved
SUB-BOUNDARY DISLOCATIONS IN A DEFORMATION TWIN
K.Marukawa and T.Kabutomori* Applied Physics, Faculty University, Sapporo 060,
of Engineering, Japan
(Received October 26, 1981)
Introduction When a growing twin plate encounters crystal defects, such as dislocations, the defects will either be incorporated in the twin, trapped in the twin boundary, or repelled aside. The outcome may depend upon the strength of interaction between them and also upon the speed of their motion. When the incorporation takes place, the defects will suffer the shear deformation of the twin and change their configuration and nature. In some cases, additional defects might be produced by incompatibility of incorporated defects with the twin lattice. The incorporation process of glide dislocations in body-centered cubic crystals has been discussed in detail by Sleeswyk and Verbraak (i). Observation showing such a process, however, has not been reported so far as the present authors are aware, except for the case that dislocations are forced to go into a stationary twin (2). The present paper reports that the incorporation actually occurs at least in the case of dislocation arranged in a sub-boundary. Changes in the configuration and the Burgers vector due to the incorporation have been investigated. The observation was made on a b.c.c, metal, Fe- 3.25wt% Si. Experimental The procedure of specimen preparation and testing are the same as those described in previous papers (3,4). Briefly, specimens machined from a single crystal, which occasionally contained sub-boundaries, were stressed in a tensile testing machine at 77K. They fractured in a brittle manner by the burst of twinning. After thinned, they were observed in an electron microscope at an operating voltage of 650 kV (Hitachi HU-650). Results Figure 1 shows the observed case of incorporation. It may be obvious that a stationary sub-boundary, which is composed of a regular array of dislocations, has been incorporated in a growing twin. The trace of the boundary is sharply bent in accord with the twin shear, while the regularity of the dislocation array is well conserved in the twin. These photographs have been taken in the condition that the matrix is in a good diffracting condition. Incidentally, the twin is also reflecting a beam in Fig.l(a), so that dislocations in the twin as well as in the matrix are visible.
*Now
at
the
Japan
Steel
Works
Ltd.,
Muroran
051,
Japan.
75 0036-9748/82/010075-04503.00/0 Copyright (c) 1982 Pergamon Press Ltd.
76
SUB-BOUNDARY
DISLOCATIONS
Vol.
16
No.
1
FIG.I Incorporation of a subboundary in a deformation twin. Adjoining the twin band, there is a region in which slip has produced almost the same amount of homogeneous shear as the twin. The scale denotes 1 ~m. The reflection vectors are: (a) g= 020 in the matrix and a higher orde~ reflection in the twin, (b) g= 211 m.
The crystallographic elements of the twin and the sub-boundary have been first investigated. The results are summarized in Fig.2. The shear direction of the twin was determined by inspecting the orientations of the matrix and the twin. The twin plane, whose normal was denoted by T, was deduced from the trace of the twin boundary. The system of the observed twin is [iii] (211) in the coordinates of the figure. The direction M of dislocation lines was determined from several photographs taken in different beam directions. To find the vector u, the projected directions of the dislocations were used. Their projected lengths were also utilized for the confirmation. The dislocations are not parallel to any of principal crystallographic axes. The normal n of the sub-boundary plane was obtained from the directions of two lines; one is the dislocation line and the other is the trace of the sub-boundary on the specimen surface. It is to be noted that the vectors S, u , and u÷ are nearly coplanar. The angle between u and u. zs about 15 . The vectors T, n , and n~ are also approxzmately copla~ar. T~e angle between n and n, is 25 . These orientatzon changes of vectors are consistent with the a~sumpt~n that the sub-boundary has suffered the twinning shear without accompanying any other motion of dislocations. (See Discussion). •
-
-
-
~ m
- c
.
Vol.
16,
No.
1
SUB-BOUNDARY
DISLOCATIONS
1010m
77
FIG.2 The direction of dislocation lines ~, arranged in the subboundary shown in Fig.l, whose plane normal is ~. The suffices m and t refer to the matrix and the twin. The normal of the specimen foil is denoted by F. The direction of the twinning shear and the normal of the twin plane is represented by S and T, respectively.
100m As can be seen in Fig.l(b), this sub-boundary is composed of two sets of dislocations which are parallel to each other and arranged alternatingly. The Burgers vector for each set has been identified by the conventional g.b = 0 method. The image feature has also examined and utilized for the identification. For the Burgers vector, the types of ½
78
SUB-BOUNDARY
DISLOCATIONS
u~ lies in the plane defined by the vectors S and u I. If T.u.>0, the vector u moves ~owards the ve~to~ S. If T.Ul<0 the direction of motion i~ opposTte. The angle between ~ and S is changed equati~n;fr°m e. to 82, which satisfies the cot
e 2 - cot
81
= ±¥
cos
~,
(i)
Vol.
T[ ,I I
1
~/~
T
i
16, No.
~
where Y is the amount of the shear ~ * ' ' " ' $ strain (Y = I/~-2 for the twin in b.c.c. metals), and a is the angle between the plane of the shear (i.e. the plane FIG.3 Transformation of a lattice defined by S and T) and the plane vector ~ due to a shear deformation containing S and MI" The length of the Y (on the plane T in the direction vector is given by ILl = sec ~ cosec 8. s). Equation (i) may be applied to the direction change of dislocations which is shown in Fig.2. With the measured values for u , ~ = 50 ° and e. = 122 ° , we obtain O~ = 137 ° , which closely agrees with the direction ~t" The length of dislocations m~st have increased by about 24%. The transformation of a lattice plane In this case, the normal of the plane moves T and nl, where n. is the initial posi'tion equation is satisfied; cot
~2
- cot
@i
= ±Y
cos
B,
can be deduced in the plane of the normal.
in a similar manner. defined by the vectors And the following
(2)
where ~1 and #2 are the angle between T and n before and after the shear deformation, r~spectively, and B is the angle between the plane of the shear and the plane defined by T and ~i" The double sign depends upon the sign of S.n. The observed rotation of the sub-boundary normal closely agrees with this equation. From the results of the identification, it may be obvious that the Burgers vector of one dislocation set has not been affected by the incorporation, i.e. b =b . The transformation of the Burgers vector of the other set, therefore, m~st-~e; [001] ÷½[lli] t. This change obeys equation (i), that is, the transformation ~s purely geometrical. The magnitude of the vector is reduced, and the difference between the vectors must be carried away by a twinning partial. The present case of incorporation may be rather special; dislocations are arranged in an array and the Burgers vectors are such that they are conserved or reduced by the incorporation. This may be the reason why the whole configuration of the sub-boundary is well conserved in the twin. There may, however, be cases in which the change in the Burgers vector does not obey the simple geometric relation (I) and the dislocation configuration is severely changed. To obtain more general feature of incorporation, further study will be necessary, which is now under way. References i. 2. 3. 4. 5.
A.W.Sleeswyk and C.A.Verbraak, Acta Met. 9, 917 (1961). L.L6my, Acta Met. 25, 711 (1977). K.Marukawa, Phil. Mag. 36, 1375 (1977). K.Marukawa and Y.Matsubara, Trans. Japan Inst. Metals 20, 724 (1979). A.Gervais, L.Tertian, J.Desehamps and D.Hokim, Acta Met. 27, 499 (1979).