- Email: [email protected]
Measurement of the stacking fault energy of TiC
Journal of the Less-Common Metals.83 (1982)
L7
L7 - LlO
Letter
Measurement
of the stacking fault energy of TiC
G. DAS Systems Research Laboratories Inc., 2800 Indian Ripple Road, Dayton, OH 45440 (U.S.A.) (Received June 12, 1981)
It is well established [ 1,2 ] that plastic deformation in TiC above the ductile-britt_le transition temperature (approximately 800 “C) takes place on the (lll}(llO) slip system although TiC has the NaCl structure. In transmission electron microscopy (TEM) studies of dislocations in TiC conducted by Hollox and Smallman [2] no evidence of the dissociation of dislocations into partials was found; this led to the speculation that TIC must possess a high stacking fault energy. The weak beam technique [3] has been widely used to determine the stacking fault energy of a number of materials. With this method, crystals are imaged in the dark field using a very large deviation parameter S. Under this condition, very high contrast is produced, and the dislocation images, as narrow peaks typically 15 - 20 a across, can be resolved. Such resolution is not normally possible with the conventional dark field method using a low order reflection with S = 0, where image widths are of the order of 100 i\. High resolution weak beam micrographs of dislocations in slightly deformed TiC were obtained following the procedure of Cockayne et al. [4]. In this note the measurement of the stacking fault energy of TiC from the dissociated width of screw dislocations as resolved by the weak beam technique is presented. Thin foils for TEM observations were prepared from polycrystalline TiC deformed in compression at 1500 “C to about 2% plastic strain by ion thinning using argon ions at 5 kV. A Philips EM300 electron microscope operating at 100 kV was used. The Burgers vector of the dislocations under study was determined using the g.6 criterion, considering the dislocation image intensities in (220) and (111) reflections. Weak beam dark field micrographs were taken in (220)type reflections, with the crystal orientation satisfying the Bragg conditions for (660)-type reflections and no other reflections being strongly excited t51. 0022-5088/82/0000-0000/$02.75
@ Elsevier Sequoia/Printed
in The Netherlands
La
Fig. 1. The dissociation of the screw dislocation A into a pair of partial dislocations in Tic. The dissociated width is about 25 A. The weak 203 diffracted beam was afigned axiafly in the objective lens and the Bragg condition for the GO6 reflection was satisfied (foil normal, (111)).
The dislocations in TiC resulting from deformation at 1500 “C are shown in Fig. 1. Glide dislocations and nodes are observed together with a few elongated loops. The dislocations were found to lie on {ill) planes with a Burgers vector of ia(liO> type [6], which reaffirmed an earlier determination of Hollox and Smallman [ 2 J . In addition, these dislocations were determined to be predominantly screw in character. As can be seen in Fig. 1, some of the dislocations are dissociated while others apparently are not. The dissociated width r of the dislocation A is observed to be about 25 A. By analogy with f.c.c. mater&&, a screw dislocation lying on the (111) plane having a Burgers vector +a[ 1 lo] can dissociate into a pair of Shockley partial dislocations separated by a stacking fault region according to the reaction
It is possible to obtain an anisotropic energy [7] from
elasticity
solution
for the stacking fault
where b is the Burgers vector of the total dislocation and K, and Ke are the effective shear moduli for the screw and edge components respectively given by Hirth and Lothe [7] as
!
K, = CJ4
c
-cl2
l1
2
\
112
i
and
where
2 c 22l = Cl1 f-H
3
and
Using the room temperature elastic constants determined by Chang and Graham [S] for TiC (C,i = 5.145, C,, = 1.06, Ca4 = 1.788, in units of 10” dyn cm-‘) with the lattice parameter a = 4.328 A and r * 25 A, the stacking fault energy y was calculated to be approximately 169 mJ mV2. It is beheved that the partial dislocations become “frozen in” during cooling to room temperature after deformation at elevated temperatures. The above estimation of the stacking fault energy in TiC was based upon room temperature parameters and must be corrected for elevated temperatures. Unfo~unate~y, the temperature dependence of the eIastic constants in TiC is not available nor is that of the increase in lattice parameter due to thermal expansion. It is generally observed that the elastic constants measured at elevated temperatures are lower than those at room temperat~e, Thus, in the absence of information on the temperature dependence of the elastic constants and the increase in the lattice parameter due to thermal expansion, it may be speculated that the stacking fault energy in TiC at room temperature will be lower than that estimated in this study. TiC has the NaCi structure with carbon atoms occupying the octahedral sites in the metal atom substructure. Kelly and Rowdiffe [9] observed that the dissociation of a total dislocation as shown in eqn. (1) in TiC will lead to (1) tetrahedral coordination of carbon atoms if the dissociation takes place on a close-packed sheet of titanium atoms or (2) metal atoms stacking direct-
LlO
ly above one another if the dissociation occurs on a sheet of carbon atoms. In either case, a very high energy configuration will result at the dislocation core. However, these investigators pointed out that tetrahedral coordination of both carbon and metal atoms stacking directly above one another can be avoided if each of the two partial dislocations in eqn. (1) consists of two partial dislocations, one on a sheet of carbon atoms and the other on an adjacent sheet of titanium atoms. In this situation within the stacking fault, the sequence of stacking of the metal atoms corresponds to an intrinsic fault. As for the sequence of stacking of carbon atoms, three layers will lie directly above one another which is expected to produce a high stacking fault energy. Additionally, the two partial dislocations on either side of the fault will have a larger core energy than those in f.c.c. metals. Kelly and Rowcliffe further suggested that some dissociation of the total dislocation should occur with a consequent reduction in energy, even though the stacking fault energy may be large. The observation of dissociation of the total dislocation and the measurement of a high stacking fault energy in TiC in the present study lend credence to these suggestions.
1 W. S. Williams and R. D. Schaal, J. Appl. Phys.. 33 (3) (1962) 955. 2 G. E. Hollox and R. E. Smallman, J. Appl. Phys., 37 (2) (1966) 818. 3 D. J. H. Cockayne, I. L. F. Ray and M. J. Whelan, Philos. Mug., 20 (1969) 1265. 4 D. J. H. Cockayne, M. L. Jenkins and I. L. F. Ray, Philos. dlag., 24 (1971) 1383. 5 D. J. H. Cockayne, Z. Naturforsch.. 24~ (1972) 452. 6 G. Das, K. S. Mazdiyasmi and H. A. Lipsitt, The mechanical properties of polycrystalline Tic, submitted to J. Am. Ceram. Sot. 7 J. P. Hirth and J. Lothe, Theory of Dislocations, McGraw-Hill, New York, 1968. Chap. 13. 8 R. Chang and L. J. Graham, J. Appt. Phys.. 37 (1966) 3778. 9 A. Kelly and D. J. Rowcliffe, Phys. Status Solidi, 24 (1966) K29.
L7
L7 - LlO
Letter
Measurement
of the stacking fault energy of TiC
G. DAS Systems Research Laboratories Inc., 2800 Indian Ripple Road, Dayton, OH 45440 (U.S.A.) (Received June 12, 1981)
It is well established [ 1,2 ] that plastic deformation in TiC above the ductile-britt_le transition temperature (approximately 800 “C) takes place on the (lll}(llO) slip system although TiC has the NaCl structure. In transmission electron microscopy (TEM) studies of dislocations in TiC conducted by Hollox and Smallman [2] no evidence of the dissociation of dislocations into partials was found; this led to the speculation that TIC must possess a high stacking fault energy. The weak beam technique [3] has been widely used to determine the stacking fault energy of a number of materials. With this method, crystals are imaged in the dark field using a very large deviation parameter S. Under this condition, very high contrast is produced, and the dislocation images, as narrow peaks typically 15 - 20 a across, can be resolved. Such resolution is not normally possible with the conventional dark field method using a low order reflection with S = 0, where image widths are of the order of 100 i\. High resolution weak beam micrographs of dislocations in slightly deformed TiC were obtained following the procedure of Cockayne et al. [4]. In this note the measurement of the stacking fault energy of TiC from the dissociated width of screw dislocations as resolved by the weak beam technique is presented. Thin foils for TEM observations were prepared from polycrystalline TiC deformed in compression at 1500 “C to about 2% plastic strain by ion thinning using argon ions at 5 kV. A Philips EM300 electron microscope operating at 100 kV was used. The Burgers vector of the dislocations under study was determined using the g.6 criterion, considering the dislocation image intensities in (220) and (111) reflections. Weak beam dark field micrographs were taken in (220)type reflections, with the crystal orientation satisfying the Bragg conditions for (660)-type reflections and no other reflections being strongly excited t51. 0022-5088/82/0000-0000/$02.75
@ Elsevier Sequoia/Printed
in The Netherlands
La
Fig. 1. The dissociation of the screw dislocation A into a pair of partial dislocations in Tic. The dissociated width is about 25 A. The weak 203 diffracted beam was afigned axiafly in the objective lens and the Bragg condition for the GO6 reflection was satisfied (foil normal, (111)).
The dislocations in TiC resulting from deformation at 1500 “C are shown in Fig. 1. Glide dislocations and nodes are observed together with a few elongated loops. The dislocations were found to lie on {ill) planes with a Burgers vector of ia(liO> type [6], which reaffirmed an earlier determination of Hollox and Smallman [ 2 J . In addition, these dislocations were determined to be predominantly screw in character. As can be seen in Fig. 1, some of the dislocations are dissociated while others apparently are not. The dissociated width r of the dislocation A is observed to be about 25 A. By analogy with f.c.c. mater&&, a screw dislocation lying on the (111) plane having a Burgers vector +a[ 1 lo] can dissociate into a pair of Shockley partial dislocations separated by a stacking fault region according to the reaction
It is possible to obtain an anisotropic energy [7] from
elasticity
solution
for the stacking fault
where b is the Burgers vector of the total dislocation and K, and Ke are the effective shear moduli for the screw and edge components respectively given by Hirth and Lothe [7] as
!
K, = CJ4
c
-cl2
l1
2
\
112
i
and
where
2 c 22l = Cl1 f-H
3
and
Using the room temperature elastic constants determined by Chang and Graham [S] for TiC (C,i = 5.145, C,, = 1.06, Ca4 = 1.788, in units of 10” dyn cm-‘) with the lattice parameter a = 4.328 A and r * 25 A, the stacking fault energy y was calculated to be approximately 169 mJ mV2. It is beheved that the partial dislocations become “frozen in” during cooling to room temperature after deformation at elevated temperatures. The above estimation of the stacking fault energy in TiC was based upon room temperature parameters and must be corrected for elevated temperatures. Unfo~unate~y, the temperature dependence of the eIastic constants in TiC is not available nor is that of the increase in lattice parameter due to thermal expansion. It is generally observed that the elastic constants measured at elevated temperatures are lower than those at room temperat~e, Thus, in the absence of information on the temperature dependence of the elastic constants and the increase in the lattice parameter due to thermal expansion, it may be speculated that the stacking fault energy in TiC at room temperature will be lower than that estimated in this study. TiC has the NaCi structure with carbon atoms occupying the octahedral sites in the metal atom substructure. Kelly and Rowdiffe [9] observed that the dissociation of a total dislocation as shown in eqn. (1) in TiC will lead to (1) tetrahedral coordination of carbon atoms if the dissociation takes place on a close-packed sheet of titanium atoms or (2) metal atoms stacking direct-
LlO
ly above one another if the dissociation occurs on a sheet of carbon atoms. In either case, a very high energy configuration will result at the dislocation core. However, these investigators pointed out that tetrahedral coordination of both carbon and metal atoms stacking directly above one another can be avoided if each of the two partial dislocations in eqn. (1) consists of two partial dislocations, one on a sheet of carbon atoms and the other on an adjacent sheet of titanium atoms. In this situation within the stacking fault, the sequence of stacking of the metal atoms corresponds to an intrinsic fault. As for the sequence of stacking of carbon atoms, three layers will lie directly above one another which is expected to produce a high stacking fault energy. Additionally, the two partial dislocations on either side of the fault will have a larger core energy than those in f.c.c. metals. Kelly and Rowcliffe further suggested that some dissociation of the total dislocation should occur with a consequent reduction in energy, even though the stacking fault energy may be large. The observation of dissociation of the total dislocation and the measurement of a high stacking fault energy in TiC in the present study lend credence to these suggestions.
1 W. S. Williams and R. D. Schaal, J. Appl. Phys.. 33 (3) (1962) 955. 2 G. E. Hollox and R. E. Smallman, J. Appl. Phys., 37 (2) (1966) 818. 3 D. J. H. Cockayne, I. L. F. Ray and M. J. Whelan, Philos. Mug., 20 (1969) 1265. 4 D. J. H. Cockayne, M. L. Jenkins and I. L. F. Ray, Philos. dlag., 24 (1971) 1383. 5 D. J. H. Cockayne, Z. Naturforsch.. 24~ (1972) 452. 6 G. Das, K. S. Mazdiyasmi and H. A. Lipsitt, The mechanical properties of polycrystalline Tic, submitted to J. Am. Ceram. Sot. 7 J. P. Hirth and J. Lothe, Theory of Dislocations, McGraw-Hill, New York, 1968. Chap. 13. 8 R. Chang and L. J. Graham, J. Appt. Phys.. 37 (1966) 3778. 9 A. Kelly and D. J. Rowcliffe, Phys. Status Solidi, 24 (1966) K29.