Dislocation Reactions in ZrN

P. Li and J. M. Howe

Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904-4745, USA

Abstract

Transmission electron microscopy analysis of an annealed and quenched foil of ZrN revealed that 1/2<110> single dislocations dissociate into two 1/6<112> Shockley partial dislocations bounding an intrinsic stacking-fault (SF). The 1/2<110> single dislocations have a super-jog character and are not coplanar with the dissociated Shockley partials. All dislocations and SF's were found to lie on {111} planes, indicating that a possible slip system is. The dislocation reactions are the same as those observed in usual face-centered cubic metal alloys, although ZrN has an ordered NaCl prototype structure. The stacking fault energy (SFE) of ZrN was calculated based on the separation of the Shockley partial dislocations and had an unusually low value of approximately 4.1 mJ/m². Both the dislocation dissociation reaction and anomalously low SFE can be explained by the large vacancy concentration in ZrN, which was confirmed by the appearance of diffuse intensity maxima in electron diffraction patterns due to short-range ordering of N vacancies.

Keywords: Transmission electron microscopy (TEM); Dislocation; Stacking faults; ZrN

1. Introduction

ZrN has received attention due to its excellent physical and chemical properties [1]. Like many transition-metal carbides and nitrides, such as TiC and ZrC, ZrN has a NaCl-prototype crystal structure. The main slip systems in such structures at high temperature should be {111} according to theoretical analysis [2]. However, various experimental results indicate that other slip systems are active. For example, in TiC, only the {111} slip system was observed at temperatures above the ductile-brittle transition temperature [3-5]. At temperatures below this, either the {111} slip system [3,4], or both the {111} and {110} slip systems were found to operate [3,6]. ZrC differs from TiC regarding the number of active slip planes. Slip has been observed on the {100}, {110} and {111} planes in high-temperature deformed ZrC single crystals [7]. Dislocation reactions in ZrN have not been studied and that was the purpose of the present investigation.

Contrast analysis of dislocations in the transmission electron microscope (TEM) is the usual method for studying slip in alloys. According to theoretical analysis, single dislocation dissociation in TiC and other NaCl-type crystal structures is peculiar as compared to most face-centered cubic (FCC) metals [2]. The presence of interstitial C atoms in the octahedral sites of TiC complicates the process of dislocation dissociation. The most energetically favorable dislocation reaction is for a perfect dislocation to dissociate into two Shockley partials dislocations, and then each of these two partials to further dissociate into two additional Shockley partial dislocations, one on a plane of C atoms and the other on the adjacent plane of Ti atoms. The stacking fault energy (SFE) is generally high in transition-metal carbides and nitrides, due to the bonding in these alloys [8]. This leads to a narrow separation of dissociated dislocations, making it difficult to observe dislocation reactions in carbides and nitrides. Such difficulties have hindered the observation of dislocation dissociation in transition-metal nitrides with NaCl-prototype crystal structure.

The dissociation of perfect dislocations in TiC was revealed using weak-beam TEM, and the results yielded rather high SFE's, ranging from 130 to 300 mJ/m², depending on the C concentration [9]. It was not possible to determine whether or not the two Shockley partials further dissociated because of the narrow width between them. However, the SFE was found to dramatically decrease in TaC with increasing concentration of C vacancies [10], which in turn, caused an increase in the separation of dissociated dislocations. Thus, it was anticipated that investigation of dislocation reactions in ZrN with a high concentration of N vacancies, might provide further insight into possible dislocation reactions in transition-metal carbides and nitrides. The present paper describes defect structures observed in ZrN by TEM.

2. Experimental Procedures

2.1. Sample Preparation

A 50 mm thick foil of high-purity a-Zr was sealed in a quartz tube under an atmosphere of high-purity N and annealed for 2 hr at 1200°C. The N content of the foil was determined to be 31.9 at.% from the increase in weight of the nitrided specimen compared with the initial high-purity Zr foil. To produce a homogeneous distribution of N throughout the foil and to obtain a two-phase mixture of a-Zr + ZrN, the nitrided foil was further annealed for 10 hr at 1200°C in a sealed quartz tube filled with high-purity Ar and then quenched into cold water.

Disks 3 mm in diameter were cut from the foil using an ultrasonic cutter and several thinning methods were employed to prevent destroying the brittle nitrided samples.

(1) A double-jet technique was used to electrolytically thin the disks. An electrolyte of perchloric acid and methanol with a ratio of 3:97 by volume was used, and the disk specimens were thinned at 18V and at -50°C. Additional final thinning was obtained by ion-beam milling the foils in a liquid-nitrogen holder for 1hr.

(2) The 3mm diameter disk was glued onto an oval Cu grid using epoxy and dimpled to ~20 mm thickness. Final thinning was performed by ion-beam milling in a liquid-nitrogen holder at 5kV for 6 hrs.

(3) A tripod polisher was used to thin the 3 mm disks on both sides to achieve a thickness of ~15 mm. Final thinning was performed by ion-beam milling in a liquid-nitrogen holder at 5kV for about 4 hrs.

2.2. TEM Procedures

The thinned specimens were examined in a JEOL 2000FXII TEM operating at 200 kV. The Burgers vectors of dislocations were determined by recording bright-field (BF) TEM images under different two-beam diffracting conditions. Centered dark-field (CDF) images were used to determine the intrinsic/extrinsic nature of the SF's. Typical contrast analysis criteria [11,12] were used to judge the visibility or invisibility of the dislocations and SF's. For example, a single dislocation with a Burgers vector b was considered as invisible when g·b = 0, where g was the diffracting vector, because only faint residual contrast generally occurs in practice when g·b = 0, but g·b_e and g·b´u ¹ 0, where u is the dislocation line direction. When g·b = 2, a dislocation was expected to give rise to a double image. In the case of the SF's, when g·R_f is equal to 0 or ±1, where R_f is the displacment vector of the fault, the SF should not display fringe contrast, as compared to when g·R_f = ±1/3 or ±2/3, where the SF displays strong fringe contrast. The partials bounding the SF are more difficult to determine. Normally, when a SF has no fringe contrast, partial dislocations with g·b = 0 are invisible. When the SF has strong fringe contrast, partial dislocations with g·b = ±1/3 are practically invisible, while those with g·b = ±2/3 or ±4/3 are visible [13]. To clearly analyze the Burgers vectors of dislocations bounding SF's, g = 113 and 220 two-beam conditions were used to eliminate SF fringe contrast. The dislocation line direction was determined by trace analysis [11] using three BF images with different beam directions and Desktop Microscopist^TM software.

3. Results and Discussion

3.1. Defects in ZrN

Figure 1 shows some of the defects observed in the ZrN phase of the alloy. These included dislocations, SF's and SF tetrahedra. The defects were formed during quenching of the nitrided Zr foil from the homogenization temperature of 1200^oC. The presence of relatively wide SF's indicates that dislocation dissociation occurred in the ZrN phase. A detailed contrast analysis of the SF's was performed in order to determine the fault plane of the SF's, the Burgers vectors and dislocation line directions of perfect dislocations and partial dislocations bounding the SF's, the displacement vector of the faults, the intrinsic/extrinsic nature of the faults, and the SFE (g_I).

3.2. Burgers Vector Analysis of Dissociated Dislocations

Dislocation dissociation occurs in ZrN, as shown in Figures 1, 2, 4 and 5. Perfect 1/2<110> dislocations were observed to separate into 1/6<112> partial dislocations bounding a SF. Figure 2 shows a series of BF and CDF TEM images of a dissociated dislocation obtained under different two-beam diffracting conditions. The complete contrast analysis of the Burgers vectors of the dislocations and the displacement vector of the SF's formed by this dislocation reaction are given in Table 1. Table 1 shows that dislocation dissociation in ZrN is consistent with the following reaction:

.

The analytical results in Table 1 accurately coincide with the experimental results shown in Figure 2. For example, the single dislocations with a Burgers vector b = display a double image in Figure 2(a) when g·b = 2 and disappear in Figures 2(b) and 2(e) when g·b = 0. When the SF's display fringe contrast, the Shockley partials on the left side with a Burgers vector b = disappear in Figures 2(b), (e) and (f) with g·b = ±1/3, and show contrast in Figure 2(c) when g·b = 2/3. When the SF's display no fringe contrast, the Shockley partials on the left disappear in Figure 2(i) when g·b = 0. The displacement vector of the SF's between the two Shockley partials R_f = and the SF's show no fringe contrast in Figures 2(a), (g), (h), (i) and (j) when g·R_f = 0 or ±1.

3.3. Nature of Stacking Faults in ZrN

Figure 2(d) is a CDF image formed by tilting the weak g = vector, which is opposite to the g = 002 vector used in the BF image in Figure 2(c), onto the optic axis inside the objective aperture. If one places the vector g = in the center of the SF's, it points toward the bright outer fringe. Since g is of the type {200}, rules for identifying the nature of SF's [11,12] show that the SF's in the ZrN phase are intrinsic SF's. Venables [14] has observed extrinsic SF's in TiC_x. Formation of these planar defects was thought to be due primarily to segregation of impurities such as B. Such defects were subsequently identified as TiB₂ precipitates. Zhao et al. [15] has reported that extrinsic SF's formed within TiC_x subgrains, where large stress concentrations exist. In contrast to these results in TiC, no evidence of extrinsic SF's was found in the ZrN phase in this study.

It is reasonable to compare the SF results in ZrN with those in FCC metals because the NaCl-prototype structure of ZrN can be viewed as two interpenetrating FCC lattices. In general, the fault energies of intrinsic and extrinsic SF's are nearly equal in FCC metals [16]. However, the simulation results of Hirth and Hoagland [17] indicate that extrinsically faulted single-dislocation dissociations are not usually observed because of a kinematic barrier which prevents their formation. As Hirth and Hogland [17] suggested, a perfect dislocation CA(d) can form an extrinsically faulted configuration that is bounded by two partials, dA and Cd on the (111) plane, and two other partials, dB and Bd, on the plane immediately above it. Due to the attractive interaction between dB and Bd, this configuration is unstable and collapses, and is finally converted into a simple set of partials, dA and Cd, which bound an intrinsic SF. This same mechanism can be used to explain the intrinsic SF's observed in ZrN.

Hirth and Hoagland [17] also pointed out that extrinsic SF's can be stable in FCC alloys. The glide interaction of the coplanar dislocations, BA(d) and CB(d) separated by one (111) interplanar spacing, can form an extrinsically faulted configuration. This configuration is bounded by two partials, dB and Cd on the (111) plane, and two other partials, dA and Bd, on the plane immediately above it. This kind of configuration remains stable as an extrinsically dissociated array by some rearrangements in the core. Furthermore, recent atomic simulations in FCC Ni [18] have shown that an extended barrier consisting of two symmetrically located Shockley partials and an a/3[110] stair-rod dislocation, can transform into an asymmetric configuration containing extrinsic SF's under 2.3% strain. These results suggest that a stress concentration may aid in the formation of stable extrinsic SF's. Such stresses might be encountered at the pile up of extrinsic fault-like defects with bounding partial dislocations, which probably occurs in the cases reported by Zhao et al. [15] in TiC subgrains, and Derep and Beauprez [19] in 5mm thick TiN_x coatings on a Mo substrate.

3.4. Line Direction and Character of Perfect Dislocations

Trace analysis was used to analyze the line direction of the single dislocations shown in Figure 2 and thereby determine whether or not the perfect dislocations and Shockley partials bounding the SF's were coplanar. Figures 2(c), 2(f) and 2(j) were used for the trace analysis by measuring the angle q between the chosen plane (the g vector of the two-beam condition in reciprocal space) and the normal to the projected line direction of the dislocation for the three cases. The angles measured from Figures 2(c), 2(f) and 2(j) were 63°, 0° and 20°, respectively. From these measured angles, it is possible to obtain the pole by rotating 63° counterclockwise from the (002) pole in a [100] zone axis. The pole is found directly in a [110] zone axis and the pole can be obtained by rotating 20° counterclockwise from the pole in a [111] zone axis. Drawing a great circle through these three poles, , and , gives the pole of the great circle, which is the line direction of the perfect dislocation, as u = . These results are shown on the stereographic projection in Figure 3.

Further confirmation of a perfect dislocation with a line direction u = in the plane can be obtained from Figure 2(f), where the g = vector is perpendicular to the edge-on single dislocation. This perfect dislocation cannot glide in the plane because its Burgers vector does not lie in that plane, i.e., it has a super-jog character [16]. Configuration of the 1/2<110> super-jog dislocation dissociating into two Shockley partials is also evident in Figure 4, where the configuration of the perfect and dissociated dislocations is clearly not coplanar.

3.5. Possible Slip Systems in ZrN

Stacking faults with a displacement vector should have a (111) fault plane, and this is supported from the images taken in different zone axes in Figure 2. For example, when the electron beam direction changes from [100] or [110] to [111], the lengths of the two Shockley partials bounding the SF's increases. Since the lengths of the dislocations depend on their projection along the electron-beam direction, they are longest when the fault plane is normal to the electron-beam direction, as in Figure 2(j). They display their actual length in this [111] orientation and this decreases as the plane is tilted away from this direction.

The fault plane of the SF's can be further confirmed using the additional BF TEM images in Figure 5. Figure 5(a) shows several inclined SF's in a [100] zone-axis orientation. The nearly edge-on orientation of the same SF's is shown in Figure 5(b) and they are perpendicular to the g = 111 vector indicated on the figure. This demonstrates that the SF's lie on (111). Another interesting feature in Figure 5, is that the perfect dislocations tend to appear straight and lie perpendicular to the g = vector. This also indicates that the line direction of the dislocations is contained in the plane, as previously discussed in Section 3.4. When considered with the previous result that the perfect dislocations have a Burgers vector b = , it is possible to conclude that slip on the system can occur in ZrN.

3.6. Stacking-Fault Energy in ZrN

When dissociated dislocations achieve their equilibrium configuration, the attractive force that results from increasing the area and hence, the energy of the SF, is equal and opposite to the repulsive elastic force between the partial dislocations. A balance between these forces yields the following equation, which can be used to determine the SFE [16]:

,

where r_e is the equilibrium separation between the two partial dislocations (171.4 nm), m is the elastic shear modulus (194 GPa [25]), n is Poisson's ratio (0.19 [26]), b is the magnitude of the Burgers vector of the partial dislocation (0.46nm/), and b is the angle between the dislocation line direction and the Burgers vector of the perfect dislocation (70°). Using this equation, one finds that the SFE of ZrN is 4.1mJ/m². This value is very low compared to the relatively high SFE's observed for TiC and TaC, which have values of 130-300mJ/m² [9,23]. The SFE in ZrN is low even compared to values for FCC metals with low SFE's such as Ag and Cu alloys, with typical values of 20-40 mJ/m² [20]. The presence of SF tetrahedra in Figure 1 also indicates that ZrN has a low SFE, since these structures only form in relatively low SFE alloys. A likely reason for the low SFE in ZrN is that many vacancies are present in the phase and these vacancies exhibit some short-range ordering (SRO). The fact that vacancies are present is evidenced by the presence of diffuse intensity maxima at {1,1/2,0} positions in electron diffraction patterns of ZrN, as shown for the [100] orientation in Figure 6. The details of SRO in ZrN are discussed elsewhere [24], but vacancies are clearly present in the structure. A dramatic decrease in SFE with increasing vacancy concentration has been reported to occur for TaC [10]. In addition, the SFE of substoichiometric TiN_x with a large vacancy concentration is as low as about 3.5mJ/m² [19].

3.7. Dislocation Dissociation Modes in ZrN

Possible modes of dislocation dissociation in TiC, which has the same crystal structure as ZrN, have been analyzed theoretically by Kelly and Rowcliffe [2]. They expect dislocation dissociation to occur differently than in usual FCC alloys. The stacking sequence of the {111} planes in TiC is:

···AgBaCbAgBaCb···

where C atoms occupy planes designated by Greek letters and Ti (or metal) atoms occupy those specified by Roman letters. The dislocations have three different possible dissociation modes and three stacking sequences of the planes are possible [2]:

(1) If dislocation dissociation occurs on close-packed planes of Ti atoms, the stacking sequence produced within the SF is:

···AgBaCbAgCbAgBaCb···

(2) If dislocation dissociation occurs on close-packed planes of C atoms, the stacking sequence produced within the SF is:

···AgBaCbAbAgBaCb···

(3) If each of the two partial dislocations dissociates into two further partial dislocations, one on a plane of C atoms and the other on an adjacent plane of Ti atoms, the stacking sequence produced within the SF is:

···AgBaCbAbCbAgBa···

In order to avoid tetrahedral coordination of C as shown by the sequence AgC in dissociation mode (1) and A upon A stacking in dissociation mode (2), dissociation mode (3) is the most favorable in such interstitial alloys, which means that each of the two initial Shockley partials will further dissociate into two Shockley partials. Simulation results based on a tight binding model by Harris and Bristowe [21] confirmed this mechanism and showed that the SFE of dissociation mode (3) was 1.7J/m², which is lower than the SFE of dissociation mode (1), which was 3.2J/m² for TiC_1.0. In contrast to these results, the experimental data in Figure 2 show no evidence of further dissociation of the two bounding Shockley partial dislocations. A reason for this difference can again be attributed to the large vacancy concentration in ZrN. If one assumes that many vacancies are present on the g (N) plane and that dissociation occurs on an adjacent plane of Zr atoms (which is possible because SRO of N occurs), then the vacancies on the g planes in the AgC configuration can dramatically decrease the configurational energy associated with the N atoms. As a result, dislocation dissociation in ZrN with a large vacancy concentration occurs by dissociation mode (1) shown above. The same mechanism also has been used to explain the stacking sequence of an intrinsic stacking fault in a non-stoichiometric VC [22].

4. Conclusions

(1) Perfect 1/2<110> dislocations dissociate into two 1/6<112> Shockley partial dislocations bounding an intrinsic SF in ZrN. The perfect 1/2<110> dislocations have a super-jog character and are not coplanar with the dissociated Shockley partials. All dislocations and SF's in ZrN were found to lie on {111} planes and a possible slip system is .

(2) The large width of the SF's and the existence of SF tetrahedra in ZrN indicate that the SFE is low. A value of approximately 4.1mJ/m² was experimentally determined from the width of the SF's in BF TEM images. This low SFE can be explained by a high vacancy concentration in ZrN and this was confirmed by the appearance of diffuse intensity maxima, which comes from SRO of N vacancies, in electron diffraction patterns.

(3) The dislocation dissociation mode in ZrN is the same as that observed in usual FCC alloys. Further dissociation of Shockley partials does not occur and this does not agree with the theoretical analysis of Kelly and Rowcliffe [2]. A possible reason for this difference may be that the configurational energy due to AgC stacking of the {111} planes in ZrN is dramatically decreased by vacancies occupying positions on the g planes.

5. Acknowledgements

This research was supported by the National Science Foundation under grant DMR-9908855. The authors also thank Prof. G. C. Weatherly for his help with the ZrN system.

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Figure 1. BF TEM image of defects in ZrN phase.

(a) BF image with g=, B=[100] (b) BF image with g=, B=[100]

(c) BF image with g=, B=[100] (d) CDF image with g=, B=[100]

(e) BF image with g=, B=[110] (f) BF image with g=, B=[110]

(g) BF image with g=, B=[110] (h) BF image with g=, B=[111]

(i) BF image with g=, B=[111] (j) BF image with g=, B=[111]

Figure 2. TEM images of perfect and dissociated dislocations under different two-beam diffracting conditions.

Figure 3. [100] stereographic projection showing the results from a trace analysis of the perfect dislocation line direction in Figure 2.

(a) BF image with g=, B=[100] (b) BF image with g=, B=[100]

Figure 4. Two-beam BF TEM images showing non-coplanar nature of perfect super-jog dislocations (arrows) and dissociated partial dislocations.

(a) BF image with g=, B=[100] (b) BF image with g=, B=

Figure 5. BF TEM images of (a) inclined, and (b) nearly edge-on, stacking faults and dislocations.

Figure 6. Electron diffraction pattern from ZrN taken in a [100] zone axis, showing diffuse intensity at the {1,1/2,0} position (arrow) due to SRO of vacancies.

Figure #	Zone axis	g vector	bsingle	bleft	bright	Rf
2(a)	[100]		2	1	1	-1
2(b)	[100]		0	1/3	-1/3	-1/3
2(c)	[100]		1	2/3	1/3	-2/3
2(e)	[110]		0	1/3	-1/3	-1/3
2(f)	[110]		-1	-1/3	-2/3	1/3
2(g)	[110]		1	1	0	-1
2(h)	[111]		1	1	0	-1
2(i)	[111]		1	0	1	0
2(j)	[111]		-2	-1	-1	1

Table 1. Values of g·b for different two-beam diffracting conditions.