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To cite this version:
Isabel Nogueira, Patrícia Almeida Carvalho, José Pereira, Rui Vilar. Complex and superlattice stack- ing faults in D019 Co3W. Philosophical Magazine, Taylor & Francis, 2006, 86 (12), pp.1763-1774.
�10.1080/14786430500501655�. �hal-00514353�
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Complex and superlattice stacking faults in D019 Co3W
Journal: Philosophical Magazine & Philosophical Magazine Letters Manuscript ID: TPHM-05-Aug-0380.R1
Journal Selection: Philosophical Magazine Date Submitted by the
Author: 30-Nov-2005
Complete List of Authors: Nogueira, Isabel; Instituto Superior Técnico, Departamento de Engenharia de Materiais
Carvalho, Patrícia; Instituto Superior Tecnico, Departamento de Engenharia de Materiais
Pereira, José; Instituto Superior Técnico, Departamento de Engenharia de Materiais
Vilar, Rui; Insituto Superior Técnico, Departamento de Engenharia de Materiais
Keywords: transmission electron microscopy, planar defects
Keywords (user supplied): complex stacking faults, antiphase boundaries, superlattice stacking faults
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Complex and superlattice stacking faults in D019 Co3W
I. D. Nogueira†, P. A. Carvalho*‡, J. C. Pereira‡, R. Vilar‡
†Instituto Superior Técnico, Instituto de Ciência de Materiais e Engenharia de Superfícies, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
‡Instituto Superior Técnico, Departamento de Engenharia de Materiais, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Planar defects present in annealed D019 Co3W crystals have been investigated by conventional transmission electron microscopy. Although a predominance of superlattice intrinsic stacking faults was observed, five antiphase boundaries and four complex intrinsic stacking faults were identified. All planar defects were observed in locked configurations or ended at grain boundaries. A comparison of relative defect energies has been carried out with a geometrical model based on pairwise interaction energies. The results suggest that the relative number of defects is not directly related to their expected energy, but rather has origin in locked configurations adopted during crystal growth and annealing.
Keywords: Transmission electron microscopy, planar defects, complex stacking faults;
superlattice stacking faults; Antiphase boundaries.
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1. Introduction
Many non-cubic intermetallic compounds present interesting mechanical properties for high-temperature applications. However, the use of these materials has always been limited by the reduced room temperature ductility associated with complex structures.
As a result, research efforts have focused essentially on structures closely related to cubic ones, namely on the tetragonal D022 (TiAl3, Ni3V), the tetragonal L10 (TiAl) and especially on the hexagonal D019 (Ti3Al, Co3W, Ni3Sn, Fe3Ge, Mg3Cd). In order to understand the mechanical behaviour of this type of compounds it is essential to investigate possible planar defect structures, as these defects are determinant for deformation ability due to their role in slip mechanisms and locked configurations [1].
Namely, the energy of planar defects, such as antiphase boundaries and complex stacking faults, has been shown to critically influence the yield-stress anomaly observed in cubic structures [2], and the same can be expected for ordered close-packed hexagonal structures presenting similar mechanical behaviour [3].
Due to the additional complexity of the ordered D019 structure as compared to the underlying hcp lattice, the number of possible stacking faults is increased and a coherent notation still needs to be established. Close-pack preserving displacements in the D019
structure can originate the following planar defects (for more exhaustive geometric descriptions see Refs. [4-6]):
• 2∆ (or 2∇) superlattice intrinsic stacking faults (SISFs) associated with 1 3 1100 displacements at the basal plane that do not change crystal order. Following the notation adopted by Hirth and Lothe for hcp structures [7], these defects are superlattice intrinsic faults of type I2, i.e., SI2.
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• 2∆ (or 2∇) complex intrinsic stacking faults (CSFs or CISFs) associated with 1 6 01 10 displacements at the basal plane that change crystal order. Following the notation adopted by Hirth and Lothe [7], these defects are complex intrinsic faults of type I2, i.e., CI2.
• 3∆ (or 3∇) extrinsic stacking faults (ESFs) associated with 1 2 0001
[ ]
displacements perpendicular to the basal plane, which result in defects that can be superlattice or complex in nature depending on the order of the extra plane.
Following the notation adopted by Hirth and Lothe [7], these defects are, respectively, of the SE or CE type.
• 1∆ (or 1∇) superlattice intrinsic stacking faults associated with 1 6 2203
displacements that do not change crystal order. These displacements are equivalent to π rotations around [0001] and for that reason have been called π rotation faults (πRFs) [4,8,9]. Following the notation adopted by Hirth and Lothe [7], πRFs are superlattice intrinsic faults of type I1, i.e., SI1.
• 1∆ (or 1∇) complex stacking faults associated with 1 6 01 13 displacements that change crystal order. Following the notation adopted by Hirth and Lothe [7], these defects are complex intrinsic faults of type I1, i.e., CI1, and can be called CI1SFs.
• Antiphase boundaries associated with displacement vectors of the types 1 6 12 10 , 1 2 1010 and 1 6 12 13 .
The notation proposed here for the planar defects listed above is, respectively, SISF, CISF, ESF, πRF, CI1SF and APB. Close-packing preserving displacement vectors at the basal plane are presented in Figure 1 together with a π rotation around [0001].
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[Insert figure 1 about here]
Due to their higher symmetry, superlattice faults are easier to characterize than complex ones. For instance, any of the three displacement vectors of the 1 3 1100 type after a plane B (small atom plane in Figure 1) gives rise to the same SISF configuration (2∆) and can only be differentiated by identification of the bounding dislocations. On the other hand, all three displacement vectors of the 1 3 1100 type after a plane A (large atom plane in Figure 1) originate the same 2∇ superlattice configuration. Furthermore, a similar situation occurs for π rotation faults: any of the six displacements of the 1 6 2203 type after a plane B produces the same superlattice 1∆
configuration and any of the six displacements of the 1 6 2203 type after a plane A results in the same superlattice 1∇ configuration. The first type of displacements corresponds to a π rotation around [0001] at any atomic site of plane A, whereas the latter is equivalent to a π rotation around [0001] at any atomic site of plane B. As for antiphase boundaries associated with displacements at the basal plane, identical defects are generated, for example, by sets of displacements of the 1 6 12 10 and 1 2 1010 types. Conversely, in the case of complex intrinsic faults, displacements of the same type produce crystallographically equivalent but not identical faults.
Research on APBs in D019 structures has been the subject of considerable theoretical [10] and experimental research [11-15]. Early conventional transmission electron microscopy (CTEM) work was carried out on APBs in Mg3Cd [11] and Ti3Al
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[12,13]. More recently, Koizumi et al have investigated APBs in Ti3Al crystals [14,15].
However, research on other type of planar defects has been limited [4,5,8,9]. Fagot et al identified SISFs and APBs in Fe3Ga by CTEM and have reported one fault of complex nature [5]. Carvalho et al using CTEM and high-resolution transmission electron microscopy have identified APBs and πRFs in Co3W precipitates [4,8], and πRFs and SISFs in Ni3Sn precipitates [9].
Stability of the planar defects and their energy are determinant properties when considering mechanical behaviour; however few studies are available for superlattice and complex faults in D019 structures. Umakoshi and Yamaguchi [6] have analysed the stability of faults produced by shear in a generic D019 compound. These authors found that SISFs are always stable, while CISFs and most APBs are not. On the other hand, quantification of fault energy varies substantially with the compound studied. The calculated energy for SISF in a generic D019 structure is 45 mJm-2 [1]; the reported values for CISF range from 84 mJm-2 (generic D019 model [1]) to 320 mJm-2 (Ti3Al [16]); while the energy estimated for APBs can vary from 11 up to 506 mJm-2 depending on their plane and on whether the defect changes first neighbouring order or not (generic D019 model [1], Ti3Al [16] and Ti3Sn [17]). Umakoshi and Yamaguchi have estimated that APB energy in Mg3Cd ranges from 4 to 21 mJm-2 [6]
Due to the fact that D019 Co3W is formed by a peritectoid reaction between Co7W6 and a Co-rich fcc solid solution at 1093 °C [18], production of this intermetallic compound in a monocrystallyne, or even monophasic condition, is not easy to achieve.
This has hindered a direct assessment of its mechanical properties. Nevertheless, there has been extensive research on the formation mechanisms of this phase [4,8,19-22] and interest in the resulting mechanical properties, particularly for structural and wear
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resistance applications [23-27]. Peritectoid Co3W crystals tend to present a high number of planar defects due to stacking change mistakes occurring during crystal growth [8].
Through annealing these defects are expected to combine and adopt more stable or locked configurations. In the current work CTEM was used to identify the superlattice or complex nature of growth defects present in annealed Co3W crystals. The aim was to establish the presence of complex faults in this particular D019 structure.
2. Experimental details and procedures
A Co-W alloy (38 wt.%W) was prepared in an arc furnace under a protective Ar atmosphere. The material was subsequently heat-treated in an evacuated quartz tube at 900ºC for 170 h, followed by water quenching. Thin foils for TEM observations were then prepared by grinding, dimpling and further thinning by ion- milling. A Hitachi H- 8100 electron microscope operating at 200 kV was used for CTEM work.
According to the dynamical diffraction theory, under two-beam conditions the phase differences introduced by faults in D019 structures give rise to the following visibility criteria: APBs may show contrast with superlattice reflections but are invisible with the corresponding fundamental reflections. Extrinsic faults are visible for hkil when l is odd and invisible when l is even. Superlattice intrinsic faults present no contrast for reflections with h - k = 3n but are visible with h hl0 . Complex faults are not visible for fundamental reflections with h – k = 3n but are visible for two of the three corresponding superlattice reflections with l even (a visibility table can be found in Ref.
[5]). Experimental bright-field (BF) and dark-field (DF) images have been obtained as close as possible to two-beam conditions. Although the presence of spots belonging to
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the same systematic row was difficult to avoid, special care was taken in minimizing the presence of non-systematic reflections. In some cases, this could only be attained under diffraction conditions close to those of weak-beam images.
3. Results
Figure 2 shows BF and DF images obtained for stacking fault A situated between a grain boundary and the crystal edge. Through tilting experiments it was possible to determine that fault A lies on the basal plane. According to the observed visibility conditions in DF images (invisible with both g=1212 and g=1120 and visible with
=0222
g ), this fault has a superlattice nature.
[Insert figure 2 about here]
Figure 3 exhibits stacking faults B and C, both lying on basal planes. Since the faults are invisible in DF images with both g=1212 and g=1120 and visible with
=0222
g , their nature is again superlattice.
[Insert figure 3 about here]
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Figure 4 presents images obtained during the analysis of faults H and I, which lie on different planes and are joined in the interior of the grain probably representing a locked configuration. Through tilting experiments it was possible to determine that fault H lies on a pyramidal plane and that fault I lies on a plane close to the basal. The visibility conditions for fault H point to a superlattice nature (visible with g=0222 and invisible with both g=1120 and g=2 1 12 in DF images). On the other hand, fault I is a complex defect (visible with g=0222 and g=1120 and invisible with g=2 1 12 in DF images). This fault presents APB contrast when examined with a superlattice reflection (g=1120), and stacking fault contrast when viewed using a fundamental reflection (g=0222), which is in agreement with observations of complex faults in other structures [28]. The observed fringe distortion seems to be induced by the strain- field of a non-identified defect (x).
[Insert figure 4 about here]
The images present in Figure 5 show six planar defects: L, M, N, O, P and Q, in locked configurations. Through tilting experiments it has been determined that fault L is on a basal plane, M is on a prismatic plane and the rest lie on pyramidal planes or present curved configurations. In DF images fault L is visible with g=0222 and invisible with g=1120 and g=2 1 12, indicating a superlattice nature. Fault M, which is visible with g=1120 and g=0222, is complex. Defects N, O, P are APBs with displacement vectors of the R=1 6 12 10 type and Q is an APB with a displacement
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vector of the R=1 6 1123 type. This defect presents residual contrast in the DF image obtained with g=2240 (under these diffraction conditions the dislocations that bound the APBs and the complex fault are also clearly visible). On the other hand, APBs N, O and P present residual contrast with g=0222.
[Insert figure 5 about here]
Figure 6 presents images obtained with faults R and S, which display a locked configuration. Through tilting experiments it was possible to determine that fault R lies on a basal plane and that fault S lies on a pyramidal plane close to
(
1103 . According to)
the visibility conditions, fault R (visible with g=0222 and invisible with both
=1120
g and g=1212 in DF images) has a superlattice nature. Fault S is visible under all the three diffraction conditions in agreement with a complex nature.
[Insert figure 6 about here]
Results similar to the ones presented above have been obtained with other defect structures analysed during the current study. A total of 19 planar defects has been investigated and the results are summarized in Table 1.
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[Insert Table 1 about here]
4. Discussion
The results summarized in Table 1 point to a predominance of superlattice faults;
nevertheless four complex faults have been identified and five defects displayed APB contrast. Superlattice faults tended to be located at the basal planes. On the other hand, APBs presented essentially curved surfaces suggesting an isotropic energy distribution.
The fact that APBs were not found on basal planes is in agreement with the stability criteria defined by Umakoshi and Yamaguchi [6]. Complex faults were observed on prismatic planes and close to the basal plane, these defects were always associated with either APBs or superlattice faults. Residual contrast could be observed for APBs under fundamental imaging: Q with g=2240; N, O and P with g=0222 (figure 5). Residual contrast associated with APBs has been predicted and observed in L12 [29,30] and D03
structures [31]. The contrast has origin in a shift of the displacement vector deduced from purely geometric considerations due to relaxation of the atomic positions around the defect [30,31]. The extra shift, which is a consequence of the change of order introduced by the defect (or results from the presence of an excess concentration at the boundary [29]) prevents total invisibility to be attained under fundamental conditions.
Umakoshi and Yamaguchi [6] using an ideal hard-sphere D019 model and pairwise interactions up to the eighth-nearest neighbour assessed the energy (γ) associated with shear faults on the basal plane. The experimental departure of the Co3W lattice parameters from the ones corresponding to an ideal hard-sphere model (c/a = 1.633 [32]), leads to splitting at the level of the first, fourth, sixth and seventh nearest-
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neighbours sets. However, this is not sufficient to invert the neighbouring order, and as a result the generic reasoning should be valid for D019 Co3W. Considering that the pairwise interaction energy between kth-neighbouring atoms A and B is given by ϕ , ( )ABk Umakoshi and Yamaguchi [6] have established that:
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
3 3 4 4 5 5
SISF AA BB AA AB AA AB
6 6 7 7 8 8 2
AA BB AA AB AA AB hcp
3 6 6 12 12
9 3 12 12 12 12 3a γ = − ϕ − ϕ + ϕ + ϕ − ϕ − ϕ +
+ ϕ + ϕ + ϕ + ϕ − ϕ − ϕ
and Carvalho et al [8] have determined that:
SESF SISF
γ = γ
Umakoshi and Yamaguchi have derived γCISF by introducing an interaction potential,
( )k =1 2
(
ϕ + ϕ( )AAk kBB)
− ϕkABV , to evaluate the effect of order changes [6]. However, their energy expression does not coincide with the one determined in the course of the present work. The correct expression is:
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
1 2 3 3 3 4 4 4
CISF BB AB BB AB
5 5 5 6 6 6
BB AB BB AB
7 7 7 8 8 8 2
BB AB BB AB hcp
3 6 2 6 16 6 18
24 12 36 12 6 18
30 12 36 24 12 36 3
V V V V
V V
V V a
γ = − − + ϕ − ϕ + − ϕ + ϕ −
− + ϕ − ϕ + − ϕ + ϕ +
+ − ϕ + ϕ − + ϕ − ϕ
Carvalho et al [9] derived an expression for the energy of πRF that also requires correction:
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
3 3 4 4 5 5
RF AA BB AA AB AA AB
6 6 7 7 8 8 2
AA BB AA AB AA AB hcp
3 2 1 2 3 3 6 6
9 2 3 2 6 6 6 6 3a
π
γ = − ϕ − ϕ + ϕ + ϕ − ϕ − ϕ + + ϕ + ϕ + ϕ + ϕ − ϕ − ϕ 3
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The energy associated with ESF and CI1SF is given respectively by:
( )1 ( )2 ( )4 ( )4 ( )6 2
CESF CISF V 3V V 3 AB 3V 3ahcp
γ = γ + − + − ϕ +
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
1
1 2 3 3 3 4 4 4
CI SF BB AB BB AB
5 5 5 6 6 6
BB AB BB AB
7 7 7 8 8 8 2
BB AB BB AB hcp
3 4 3 9 3 9
10 6 18 6 3 9
16 6 18 14 8 20 3
γ = − − + ϕ − ϕ + − ϕ + ϕ −
− + ϕ − ϕ + − ϕ + ϕ +
+ − ϕ + ϕ − + ϕ − ϕ
V V V V
V V
V V a
Although absolute predictions are not possible with this generic reasoning, a comparative study can be carried out. The analysis of the expressions enables establishing the following relations:
RF SISF
2 γ =γ
πCESF CISF CI SF1
γ >γ >γ
Therefore, both superlattice and complex faults of the 1∆ (or 1∇) type are less energetic than the corresponding 2∆ (or 2∇) ones. This approach does not yield a simple energy relation between superlattice defects and APBs or complex faults, however, these latter defects disrupt order at the first and second neighbour level and are expected to be more energetic than superlattice ones.
The experimental results show that planar defects present in annealed D019 Co3W crystals either terminate at grain boundaries or are combined in locked configurations.
No isolated extended dislocation could be found, indicating that the energy involved in the planar defects is too high for dislocations to dissociate under equilibrium conditions.
The fact that superlattice faults frequently spanned the crystals and ended at grain boundaries is a result of the crystal growth process, where stacking mistakes are
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preserved at the reaction front during the phase transformation [8]. On the other hand, complex stacking faults were always found in association with either APBs or superlattice faults, suggesting another formation mechanism involving specific dislocation configurations. The moderate number of identifications carried out prevents a statistically accurate analysis. However, the results suggest that the relative presence of the different planar defect types stems from locked configurations into which the faults have evolved during annealing and does not seem to reflect their relative energies.
5. Conclusions
The investigation involved an exhaustive evaluation of growth defects present in annealed Co3W crystals. A predominance of superlattice stacking faults was observed;
nevertheless the presence of complex stacking faults in D019 Co3W could be established.
Antiphase boundaries have also been identified. All the planar defects were either combined in locked configurations or ended at grain boundaries. A comparison of the relative defect energy has been carried out with a geometrical model based on pairwise interaction energies. The results indicate that the relative number of defects is not directly related to the expected energy, and that their presence rather seems to stem from locked configurations.
Acknowledgments
The authors acknowledge Fundação para a Ciência e a Tecnologia, project POCTI/CTM/48617/2002, for financial support.
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Figure 1 – Fault displacement vectors at the basal plane of a X3Y D019 structure. The configuration resulting from a π rotation fault at a plane A is also indicated. The large atoms correspond to planes A and the small atoms to planes B.
Figure 2 – Superlattice stacking fault A on basal plane. A grain boundary (GB) is indicated. (a) BF image where the faults are visible; (b) DF image obtained with
1212
g= ; (c) DF image obtained with g=1120. (d) DF image of fault A obtained with g=0222 at the same region as (c).
Figure 3 – Superlattice stacking faults B, C and D. (a) DF image obtained with 0111
g= ; (b) DF image obtained with g=0222; (c) DF image obtained with 1212
g= (e) DF image obtained with g=1120.
Figure 4 - Superlattice stacking fault H and complex fault I. Fault H is on a pyramidal plane and fault I is close to the basal plane. (a) DF image obtained with g=0222; (b) DF image obtained with g=1120; (d) DF image obtained with g=2 1 12.
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Figure 5 – Superlattice fault L, complex fault M, APBs N, O, P and Q. Fault L lies on a basal plane and M on a prismatic plane. (a) BF image obtained with g=0222; (b) DF image obtained with g=1120. (c) DF image obtained with g=0111; (d) DF image obtained with g=0222; (e) DF image obtained with g=2240; (f) DF image obtained with g=2 1 12. A grain boundary is indicated (GB).
Figure 6 – Superlattice stacking fault R and complex stacking fault S. (a) DF image obtained with g=0222; (b) DF image obtained with g=1212 (c) DF image obtained with g=1120.
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For Peer Review Only
Table 1 – Summary of the planar defect investigation.
Fault Character Plane Notes
A Superlattice Basal Ending at a GB
B,C Superlattice Basal Ending at unidentified defects D Superlattice Basal Ending at unidentified defect E, G Superlattice Basal
F Pure order Prismatic or close Locked configuration H Superlattice Pyramidal
I Complex Close to the basal Locked configuration J Superlattice Basal Ending at a grain boundary L Superlattice Basal
M Complex Prismatic N,O,P Pure order Pyramidal Q Pure order Pyramidal
M locked configuration with L and Q, Q locked configuration
with M and N R Superlattice Basal
S Complex Pyramidal Locked configuration T Complex Pyramidal Locked configuration 3
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For Peer Review Only
3
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For Peer Review Only
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