Effects of normal strain on pyramidal I and II 〈c + a〉 screw dislocation mobility and structure in single-crystal magnesium

Sunday Temitope Oyinbo; Ryosuke Matsumoto

doi:10.1515/ntrev-2024-0082

Article Open Access

Effects of normal strain on pyramidal I and II 〈c + a〉 screw dislocation mobility and structure in single-crystal magnesium

Published/Copyright: August 19, 2024

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From the journal Nanotechnology Reviews Volume 13 Issue 1

Abstract

In this study, atomistic simulations were used to analyze the effects of nonglide stress and temperature on the mobility and structure of pyramidal-I (Pyr-I) and pyramidal-II (Pyr-II) 〈c + a〉 screw dislocations in single-crystal Mg. At a very low temperature (10 K), the pyramidal screw dislocations stably exist on Pyr-II planes and tend to glide on Pyr-I planes. The critical resolved shear stresses (CRSSes) of the pyramidal screw dislocations depend on the migration direction. Once a Pyr-II dislocation is transformed into a stuck core, a very high shear stress (243 and 391 MPa) is required to escape from the immobilized structure. Furthermore, their CRSSes increase with increasing compressive strain and decrease with increasing tensile strain normal to the slip planes. At the intermediate temperature range of 200 K ≤ T ≤ 400 K, the CRSSes of Pyr-I screw dislocations are weakly affected, whereas those of Pyr-II screw dislocations drastically decrease. Thus, both Pyr-I and Pyr-II screw dislocations have similar CRSS values at 400 K. At a higher temperature (500 K), Pyr-I screw dislocations frequently emit basal- 〈 a 〉 dislocation loops, and the remained dislocations are momentarily immobilized. The basal- 〈 a 〉 dislocation loops emitted from the 〈c + a〉 dislocations are quickly retracted, and the core structure is recovered as the shear deformation continues. This phenomenon can reduce the mobility of Pyr-I 〈c + a〉 screw dislocations at a higher temperature. The emission of basal- 〈 a 〉 dislocation loops is enhanced under compression.

Keywords: pyramidal screw dislocation; critical resolved shear stress; normal stress; molecular dynamics; magnesium

1 Introduction

To satisfy the von Mises requirement for the deformation of polycrystals, deformation along the 〈 c 〉 direction is necessary in hexagonal closed-packed (HCP) metals. On the other hand, deformation along the 〈 c 〉 direction is also necessary in single crystals, which is frequently used as micro- and nanoscale components in nanotechnology fields, when the resolved shear stress along 〈 a 〉 direction is small. Since slip through 〈 c 〉 dislocations are more difficult [1,2], plastic strain in the 〈 c 〉 axis is predominantly produced by dislocations with the 〈c + a〉 Burgers vector on pyramidal-I (Pyr-I) and pyramidal-II (Pyr-II) planes or deformation twinning. Nevertheless, 〈c + a〉 slip is often regarded as a challenging phenomenon as it requires the application of high stress [3,4,5]. Therefore, an understanding of the 〈c + a〉 slip behaviors of HCP metals on pyramidal planes is required to effectively manufacture their wrought products.

The use of HCP Mg is limited owing to its poor ductility and low fracture toughness at room temperature [6,7]. Recent studies have linked poor ductility to a thermally induced nonglide and glide stress-dependent transformation of glissile 〈c + a〉 edge dislocations on either Pyr-I or Pyr-II planes into a sessile basal-dissociated structure [3,8,9,10]. We recently found that a typical basal-dissociated 〈c + a〉 edge dislocation on Pyr-II plane is mobile. Thus, the limited ductility might be originated from other mechanisms [11]. In coarse grains in usual metals, the behavior of long dislocations with loop shape, which consist of edge, screw, and mixed components, controls the macroscopic deformation property. However, in fine grains in nanostructured metals and nanosized components, a slip deformation tends to occur with straight dislocations with a specific component (i.e., edge, screw, or mixed component) since the volume is too small to form a dislocation loop. Thus, understanding the detailed behavior of each dislocation component is more important in nanomaterials and nanotechnology fields. Here, we focus on 〈c + a〉 screw dislocations on the pyramidal planes.

Screw dislocations are distinguished from edge and mixed dislocations by their ability to cause cross-slip to another plane containing the dislocation line. Therefore, the cross-slip phenomenon of screw dislocations with a 〈c + a〉 Burgers vector is considered crucial in improving the ductility of Mg and its alloys [12]. Several atomistic simulations have been conducted to investigate 〈c + a〉 screw dislocations on both Pyr-I and Pyr-II planes. The results showed instances of cross-slip occurring from Pyr-I to Pyr-II planes [13], or vice versa [14,15,16]. Moreover, certain solutes could speed up the cross-slip and double cross-slip of 〈c + a〉 dislocations on Pyr-I planes, rapidly forming new 〈c + a〉 dislocation loops [17].

Since one 〈c + a〉 axis is shared by two Pyr-I planes and one Pyr-II plane, screw dislocations with a 〈c + a〉 Burgers vector can cause cross-slip between these planes. We use Pyr-I and Pyr-I’ to distinguish two Pyr-I planes that share the 〈c + a〉 Burgers vector. The energy barrier for cross-slip highly depends on the energy difference per unit length between screw dislocations on Pyr-I and II planes [12]. Several molecular dynamics (MD) simulations conducted at very low temperatures (T < 100 K) have shown that 〈c + a〉 screw dislocations mostly undergo gliding on Pyr-I planes after their nucleation from cavities or free surfaces [13,18,19]. Various intricate pathways were suggested to lead to the cross-slip behavior of a Pyr-I 〈c + a〉 screw dislocation [2,20]: the first pathway involves cross-slip onto the Pyr-II plane, followed by gliding on the Pyr-II plane for a certain distance, and then cross-slip to a Pyr-I plane that is parallel to the original plane (Pyr-I → Pyr-II → Pyr-I). Another possible cross-slip pathway may be observed, which resembles the first pathway. However, in this case, the dislocation undergoes cross-slip onto an alternative Pyr-I plane (Pyr-I′) after a certain amount of glide on the Pyr-II plane (Pyr-I → Pyr-II → Pyr-I′). The third possible pathway involves the dislocation that might cross-slip right into the next adjacent parallel Pyr-I plane, with a Pyr-I interplanar distance separating the two planes ((Pyr-I → adjacent Pyr-I)). The cross-slip process involves forming a pair of atomic-scale jogs on the Pyr-II plane, which links the two Pyr-I planes. The fourth scenario is the occurrence of a dislocation cross-slip from the initial Pyr-I plane to an alternative Pyr-I plane ((Pyr-I → Pyr-I′)). In the case of Pyr-II 〈c + a〉 slip, the Peierls stresses obtained from experiments span a relatively wide range [21] and strongly depend on temperature and strain rate [22]. Furthermore, the material unexpectedly undergoes thermal hardening [20,22].

Atomistic simulations can be an alternative approach for analyzing the slip behavior of dislocations compared to experimental studies. Especially, the MD approach is important to examine the basic nanoscale phenomena, which occur in nanoseconds. Here, we perform MD simulations to systematically examine the behavior of 〈c + a〉 screw dislocations on Pyr-I and Pyr-II planes. We provide data showing how temperature and nonglide stress affect the core structure and mobility of 〈c + a〉 screw dislocations introduced on Pyr-I and Pyr-II planes.

2 Computational modeling

2.1 Interatomic potential for Mg

The behavior of 〈c + a〉 screw dislocations on pyramidal planes was thoroughly investigated using MD simulations, which were conducted via the large-scale atomic/molecular massively parallel simulator code [23]. 〈c + a〉 screw dislocations initially located on a Pyr-I or Pyr-II plane were studied [2,24]. The interatomic interactions of Mg were described using a modified embedded-atom method (MEAM)-type interatomic potential developed by Ahmad and Wu [2]. The potential was verified by comparing it with not only the available reference data in the literature but also other important potentials available online, such as the embedded-atom method (EAM) potential developed by Wilson and Mendelev [25] (the updated EAM potential from Sun et al. [26]), and MEAM potential developed by Wu et al. [27]. The potential used in this work is an updated version of the MEAM interatomic potential developed by Wu et al. [27] and is specially parameterized to model dislocation plasticity and fracture behaviors. This MEAM potential provides a more accurate description of Mg lattice parameters, cohesive energy, and defect energies compared to those reported by Kim et al. [28] and Wu et al. [27], enabling the prediction of the core structures of 〈c + a〉 screw dislocations when the dislocation is placed on both Pyr-I and Pyr-II planes, which is consistent with density functional theory calculations [29,30]. In addition, this potential has been used in various atomistic simulations to investigate Mg deformation and dislocation behaviors [2,31,32,33].

2.2 Simulation details

The MD study involves the introduction of a screw dislocation core onto either a Pyr-I or Pyr-II plane inside a perfect HCP Mg lattice using a homemade program. The dimensions of the lattice are ∼27.5 nm along the x-axis, 21.8 nm along the y-axis, and 6.0 nm along the z-axis. The y-axis is perpendicular to the pyramidal plane (initial slip plane), whereas the z-axis is aligned with the dislocation line (parallel to the 〈c + a〉 Burgers vector). The details of the simulation model are shown in Figure 1a with the 〈c + a〉 screw dislocation core at the center of the Pyr-II plane. The Pyr-I and Pyr-II systems contain a total of 145,420 and 147,000 atoms, respectively. In both systems, the z-axis is subjected to periodic boundary condition (PBC), whereas the other two directions are subjected to traction-free conditions. As mentioned in the introduction, one 〈c + a〉 Burgers vector is shared by two Pyr-I planes and one Pyr-II plane, as shown in Figure 1b. The motion of atoms inside the uppermost (positive y-axis) and lowermost (negative y-axis) five layers (i.e., boundary atoms) is fixed.

Figure 1

Initial simulation model of single-crystal HCP Mg (a) with a 〈c + a〉 screw dislocation core at the center of the Pyr-II planes and (b) schematic illustration of the relation among two Pyr-I and one Pyr-II planes containing a common 〈c + a〉 direction. The red atoms in (a) represent the fixed boundary atoms, whereas the mobile atoms are represented in other colors based on the crystal structures categorized by CNA (a color version of the figure is available online).

Once screw dislocations are introduced into the system, the conjugate gradient method is used to minimize the energy. The energy is minimized with an energy tolerance of 10⁻⁸, while keeping boundary atoms immobile in all directions. To conduct simulations at finite temperatures, the locations of atoms are first scaled from their positions at absolute zero (0 K) to positions that are appropriate for the lattice constants at the desired finite temperature. Subsequently, the velocities of atoms are assigned randomly according to the Gaussian distribution, which gives the target temperature. Simulations are performed at various temperatures (T = 10, 50, 100, 200, 300, 400, and 500 K). To maintain a constant temperature throughout the computation, a Berendsen thermostat [34] is used. The simulation model is relaxed at the intended temperature for 20 ps. A nonglide strain normal to the slip plane (a normal strain, ε y y = −5.0, −3.0, −1.0, 1.0, 3.0, or 5.0%) is imposed with a strain rate of 10⁸ s⁻¹ by moving boundary atoms along the y-axis. The relaxation of simulation cell sizes is not implemented in these simulations. The simulation setup for the calculations is shown in Table 1.

Table 1

Summary of simulation models and calculation conditions

Number of atoms	145,420
Model size
L _x × L _y × L _z [nm³]	∼ 27.5 × 21.8 × 6.0
PBC	Along z
Timestep [fs]	1.0
Boundary velocity [m/s]	1 (strain rate: γ y z ˙ = 1.01 × 10 8 s ‒ 1 )
Interatomic potential	MEAM [2]
Ensemble	NVT
Temperature [K]	Constant at 10, 100, 200, 300, 400, and 500
Normal strain ( ε y y )	−5.0 to 5.0%
	Normal strain	−5 to −1%	0%	5–1%
Duration of simulation [ps]	Pyr-I	∼100 to 120	∼100 to 200	∼60 to 100
	Pyr-II	∼120 to 180		∼40 to 110

To ensure that the MD simulations closely resemble experimental conditions, the dislocation motion is induced by applying boundary-velocity-controlled loading on the top and bottom boundary atoms in opposing directions along the z-axis at a velocity of 1 m/s. The velocity in the x- and y-directions of boundary atoms is set to zero. If the dislocations exhibit smooth motion along the original pyramidal planes, the average speed of dislocation is approximately 180 m/s. MD simulations are conducted using a time step of 1 fs throughout a duration of 200,000 timesteps. Data are recorded at intervals of 1 ps. The dislocations are examined using the dislocation extraction algorithm [35] and common neighbor analysis (CNA) [36], both of which are included in the OVITO software [37]. Figures 1, 2, 5, and 6 depict the arrangement of atoms in different crystal structures (i.e., HCP, body-centered cubic , and face-centered cubic). These crystal structures are represented in cyan, blue, green, and yellow, respectively. The atoms in the dislocation core are predominantly shown in yellow.

Figure 2

Time evolution of shear stress for (a) Pyr-I and (b) Pyr-II planes. P and N represent the positive and negative shear directions at different times, respectively. The atomistic pictures of dislocation core structures encountered during the cross-slip process are shown by drawing only non-HCP atoms near the core atoms identified using CNA.

3 Results and discussion

3.1 Cross-slip transition of Pyr-I and Pyr-II 〈c + a〉 screw dislocations at low temperature

Figure 2(a) and (b) illustrates the time-dependent progression of shear stress and the associated transition pathways of the dislocation glide on the Pyr-I and Pyr-II planes, respectively, at a temperature of 10 K. The insets in Figure 2(a) and (b) depict the atomistic images of dislocation core structures found during the cross-slip process by showing only non-HCP atoms near the dislocation core as detected by CNA. The symbols P and N denote the positive and negative shear directions at various points in time, respectively (i.e., for P, the upper boundary moves in the positive z-direction and dislocation moves the negative x-direction, whereas for N, the upper boundary moves in the negative z-direction and dislocation moves in the positive x-direction).

When the dislocation on the Pyr-I plane is subjected to a positive shear direction, the core transforms into the Pyr-II plane at ∼52 MPa and remains on the Pyr-II plane until the shear stress reaches ∼139 MPa. Subsequently, it exhibits frequent cross-slip between the Pyr-I and Pyr-II planes during the stress drop (i.e., during migration) but glides primarily on the Pyr-I plane, as depicted in Figure 2(a). A prior study found a slightly higher stress of ∼166 MPa [15] and 155 MPa [27] under homogenous strain loading conditions. Moreover, Zhang et al. [16] reported a stress of ∼283 MPa while observing the gliding of the Pyr-I core in the positive shear direction under a shear stress rate (stress rate loading) of 1.0 MPa/ps (close to our calculation). A shear stress of ∼218 MPa was obtained under homogenous strain loading conditions.

The Pyr-I core glides smoothly on the Pyr-I plane at ∼54 MPa in the negative shear direction. Interestingly, in the simulations with a negative shear direction, the Pyr-I core behaves very differently after the initial migration on the Pyr-I plane. The core causes cross-slip to a Pyr-II plane at 53 ps, remains immobile (stuck core), and becomes shrunk on the Pyr-II plane until the shear stress increases to ∼243 MPa, as shown in Figure 2(a), after which it glides on the Pyr-II plane without going through the Pyr-I plane again. No cross-slip was observed during migration. A slightly higher stress of ∼311 MPa [16] during a stress-rate loading of 1.0 MPa/ps was previously reported under homogenous strain loading conditions. The reason for the uneven behavior in different shear directions is considered to be due to the asymmetry of the leading and trailing partials [13].

The glide and cross-slip behaviors of the Pyr-II plane under shear in the positive direction can be explained as follows: the Pyr-II 〈c + a〉 screw dislocation cross-slips to another accessible Pyr-II plane parallel to the original Pyr-II plane without dwelling on the Pyr-I plane. The cross-slip depends on the direction of shear, with a shear stress of approximately 180 MPa, corresponding to the shear stress in the positive shear direction. Consequently, a discernible shear stress reduction occurs as the dislocation starts to glide with frequent cross-slips between other accessible Pyr-II planes parallel to the original Pyr-II plane.

In the negative shear direction, the Pyr-II core experiences a continuous increase in shear stress (up to ∼391 MPa) because the dislocation remains immobile (stuck core) and shrinks on the Pyr-II plane, as shown in Figure 2(b), after which it causes cross-slip onto the Pyr-I plane and starts to glide smoothly without any noticeable cross-slip during migration on the Pyr-I plane.

In summary, the dislocation tends to stay on the Pyr-II plane and mainly glides on the Pyr-I plane after it causes cross-slip. However, although the Pyr-I plane facilitates the gliding of screw dislocations, it does not always occur. Once the Pyr-II dislocation is transformed into a stuck core (only observed for negative shear), the shear stress reaches a very high value (243 and 391 MPa) to escape from the immobilized structure.

3.2 Effects of normal strain on Pyr-I and II 〈c + a〉 screw dislocations at low temperature

Defining critical resolved shear stresses (CRSSes) in the negative shear direction was difficult because of the presence of several peaks related to cross-slips and core structure changes and the dislocation motion on the inclined plane, as shown in Section 3.1 and Figure 2. Here, we discuss the influences of normal strain perpendicular to the original slip plane on CRSSes in the positive shear direction. Figure 3(a) shows the CRSSes ( τ y z ), defined by the maximum shear stress attained, for Pyr-I and Pyr-II 〈c + a〉 screw dislocations in the positive shear direction under different normal strains ( ε y y = −5.0, −3.0, −1.0, 0, 1, 3.0, and 5.0%) at 10 K. The dislocations glide after possible cross-slips to the plane parallel to the original plane. The CRSS for Pyr-I corresponds to the stress for cross-slip back to Pyr-I from Pyr-II before migration, whereas the CRSS for Pyr-II corresponds directly to the stress required for migration on Pyr-II. For comparison, the time evolutions of the shear stress for Pyr-I and Pyr-II 〈c + a〉 screw dislocations are shown in Figure 3(b)–(e).

Figure 3

(a) CRSS (the first peak value of the shear stress) as a function of normal strain for Pyr-I and Pyr-II 〈c + a〉 screw dislocations at 10 K. Time evolution of the shear stress for the Pyr-I 〈c + a〉 screw dislocation under (b) compression and (c) tension. Time evolution of the shear stress for the Pyr-II 〈c + a〉 screw dislocation under (d) compression and (e) tension. (f) GSFE curves for the Pyr-I dislocation.

The CRSS for the 〈c + a〉 screw dislocation during shear deformation gliding on Pyr-II planes is ∼180 MPa, which is higher than that on Pyr-I planes (∼139 MPa) at 0% strain, verifying that the CRSS for Pyr-I is lower than that of Pyr-II under all normal-strain conditions. Previous MD simulations have also shown that Pyr-I screw dislocations exhibit higher mobilities than Pyr-II screw dislocations at relatively low temperatures [14]. The CRSSes for the Pyr-I and Pyr-II 〈c + a〉 screw dislocations increase with the compressive strain and decrease with the tensile strain. This result could be because the generalized stacking fault energies (GSFEs) on Pyr-I and Pyr-II planes increase under compression normal to the slip plane and decrease under tension, as shown by the GSFE curves along the 〈c + a〉 direction (z-axis) for Pyr-I (Figure 3(f)). In addition, the stacking fault energy of prismatic slip increases under compression and decreases under tension, remarkably changing the mobility of prismatic screw dislocations [38].

3.3 Effect of temperature on Pyr-I and II 〈c + a〉 screw dislocations

Figure 4(a) and (b) shows the CRSSes in the positive shear direction for the Pyr-I and Pyr-II screw dislocations at higher temperatures along with the CRSSes, as shown in Figure 3(a). The CRSSes are plotted as a function of the applied normal strain at 10, 200, 300, 400, and 500 K for Pyr-I and II slip. The cases for which the dislocation glides with or without the cross-slip behavior are shown by the filled symbols, whereas those with basal dislocation emission and recovery (discussed in Section 3.4) are shown by the half-open symbols.

Figure 4

CRSS (the maximum peak value of the shear stress) as a function of normal strain for (a) Pyr-I and (b) Pyr-II 〈c + a〉 screw dislocations at different temperatures. The half-filled symbols in (a) represent the stress at which Pyr-I dislocations undergo basal dislocation emission and recovery.

The mobility of Pyr-I screw dislocation cores is weakly affected by temperature in the range studied, except 10 K where the CRSS becomes considerably high, as shown in Figure 4(a). These observations are consistent with previous findings [24]. In contrast, the CRSS for the Pyr-II screw dislocation mobility decreases with increasing temperatures (Figure 4(b)). Pyr-I screw dislocations have a lower CRSS and higher mobility than Pyr-II screw dislocations at 10 K, strongly indicating that, as anticipated from MD simulations [14], a slip mostly occurs on Pyr-I planes at low temperatures. The CRSSes of Pyr-II screw dislocations are substantially close to or even lower than the CRSSes of Pyr-I screw dislocations at 400 K. Therefore, the increased plasticity observed at the intermediate temperature range may be ascribed to the presence of both Pyr-II and Pyr-I slips. Furthermore, earlier studies have shown that the CRSSes of pyramidal dislocations in Mg and its alloys decrease with increasing temperature [39], and the increase in ductility observed above 300 K is attributed to the increased mobility of pyramidal dislocations with temperature [40]. The CRSSes of Pyr-I screw dislocations are marginally impacted by temperature based on the MD simulations, but the CRSSes of Pyr-II screw dislocations decrease with increasing temperature. Namakian et al. evaluated the temperature dependence of generalized stacking fault free energy of various slip systems in Mg [41]. They showed that the stacking fault energy of Pyr-II decreases rapidly than Pyr-I with increasing temperature, and Pyr-II slip is more favorable over 385 K. The temperature dependence of CRSS of screw dislocations obtained by our MD agrees well with Namakian’s report.

Finally, Pyr-I screw dislocations at ≥500 K tend to cause basal dislocation emission and recovery under compression and 0% normal strain. The stress for the Pyr-I screw dislocation at an extremely high compressive strain (ε _yy = −5%) for all temperatures except 10 K is not shown because the dislocation transforms into a sessile dislocation (basal dislocation emission without recovery) and lose the capacity to accommodate c-axis deformation, resulting in catastrophic deformation at a high shear stress. As a result, the contribution of Pyr-I screw dislocations to plasticity is reduced at increased compressive strains and higher temperatures, as experimentally shown at 673 K [42]. Pyr-II screw dislocations at 500 K and high compressive strain (ε _yy = −5%) also show a high tendency to basal dislocation emission but without recovery (the values are not shown in Figure 5b).

Figure 5

(a)–(c) Core structures of Pyr-I 〈c + a〉 screw dislocations at 500 K under normal strains of (a) zero, (b) −3%, and (c) −5%. Columns (i)–(iv) show the structure after relaxation, a typical structure during the transition, the structure showing easy glide dislocation core after transition recovery, and the structure during the second transition, respectively. Columns (iii) and (iv) in (c) show the nonrecovery behavior after the emission of basal dislocation. (d) Easy glide of a Pyr-I 〈c + a〉 screw dislocation at 500 K under a tensile strain of 1%.

3.4 Thermally activated process for Pyr-I and Pyr-II screw dislocations at high temperature

As mentioned in the introduction, Wu et al. [17] proposed a mechanism for enhancing ductility in Mg alloys. According to their theory, high ductility can be attained by sustained plastic strain in the 〈c〉 direction, achieved via the rapid generation of new dislocation loops, which counteract the immobilization of 〈c + a〉 dislocations caused by the basal dislocation emission. Here, we analyze the thermally activated strain-dependent process for 〈c + a〉 screw dislocations at an elevated temperature and normal strains of −5, −3, 0, and 1%.

The basal dislocation emission behavior of the Pyr-I 〈c + a〉 screw dislocation at a temperature of 500 K, where thermally activated processes are accelerated, is shown in Figure 5. The intense atomic vibration at 500 K can cause misjudgment in the structural analysis performed using CNA; thus, many yellow atoms (defects) appear around the dislocation core. Columns ((i)–(iv)) in Figure 5 show the structures of dislocation cores at specific instants. Figure 5(a–c)(i) shows the Pyr-I screw dislocation cores on Pyr-I planes at different normal strain levels ranging from 0 to −3%. At around 5 ps (column (ii) in Figure 5(a–c)), the dislocation causes cross-slip onto the Pyr-II plane and then emits the 〈a〉 dislocation loop onto the basal plane, and the dislocation becomes momentarily immobile. The basal- 〈 a 〉 dislocation loop emitted from the 〈c + a〉 dislocation is quickly overcome (i.e., recovered) as the shear deformation continues and the dislocation causes cross-slip back onto the Pyr-I plane. Here, we call this behavior “emission recovery.” The 〈 a 〉 dislocation emission and recovery occur in many stages during the shear deformation and involve several intermediate Pyr-I screw dislocation structures. Notably, the 〈 a 〉 dislocation loop length and recovery time increase with increasing compressive strain since the resolved shear stress on the basal- 〈 a 〉 slip increases. At very high compressive strain (ε _yy = −5%), as shown in Figure 5c(ii), the Pyr-I screw first causes cross-slip onto the Pyr-II plane, and then, a large 〈a〉 dislocation loop nucleates without recovery during the shear deformation, leaving the dislocation immobile, and the shear stress increases continuously. The immobile dislocations do not contribute to plastic straining and instead, serve as strong obstacles to the motion of other dislocations. Under tensile strain (ε _yy = 1% (Figure 5(d)), 3.0, and 5.0%), this basal dislocation emission was not confirmed in MD simulations.

Figure 6(a) and (b) shows the Pyr-II screw dislocation cores at zero and −5% normal strains during shear deformation in the positive shear direction at 500 K. In the strain range 0% ≤ ε _yy ≤ −3%, the dislocations move roughly with frequent cross-slips and no observable transition into the Pyr-I plane, as shown in Figure 6(a). Under a very high compressive strain (ε _yy = −5%) (Figure 6(b)), a large 〈a〉 dislocation loop nucleates without emission recovery during the shear deformation, leaving the dislocation immobile, and it does not contribute to plastic straining.

Figure 6

(a) Easy glide of a Pyr-II 〈c + a〉 screw dislocation at 500 K under zero strain And (b) the basal dislocation emission from a Pyr-II 〈c + a〉 screw dislocation at 500 K under a normal strain of −5%.

4 Conclusion

A detailed analysis of the effects of normal strain perpendicular to the slip plane and temperature on the mobility and structure of Pyr-I and Pyr-II 〈c + a〉 screw dislocations in single-crystal Mg was investigated by MD simulations. The main conclusions obtained are as follows:

The pyramidal screw dislocations were discovered to be stable on Pyr-II planes and tend to glide on Pyr-I planes at a significantly low temperature of 10 K. The dislocation glide direction determines the CRSSes of pyramidal screw dislocations on both Pyr-I and Pyr-II planes. A very high shear stress (∼243 and 391 MPa) is required to mobilize the core structure of Pyr-II dislocation after it has been transformed into a stuck core under deformation in a negative shear direction. Furthermore, the CRSS increases with increasing compressive strain and decreases with increasing tensile strain.
The CRSSes for Pyr-I screw dislocations are marginally influenced by temperature in the range of 200 K ≤ T ≤ 400 K. On the other hand, the CRSSes for Pyr-II screw dislocations experience a significant decrease. Consequently, the CRSS values for Pyr-I and Pyr-II screw dislocations are comparable at a temperature range of 300–400 K.
Pyr-I screw dislocations often emit a basal-〈a〉 dislocation loop at higher temperatures (500 K) and under compressive strains, while the remaining dislocation remains momentarily immobilized. As shear deformation continues, the core structure is restored, and the basal-〈a〉 dislocation loop emitted by the 〈c + a〉 dislocation is swiftly drawn back. Under an extremely high compressive stress, this recovery was not confirmed.

In this article, the detailed behavior of screw dislocations in Mg was analyzed. We believe some aspects obtained in this article are common in HCP metals, such as HCP-Ni nanoparticle [43], which are important in nanotechnology fields.

Acknowledgments

The authors would like to acknowledge financial support from the Japan Science and Technology Agency (JST) CREST (Grant Number JPMJCR2094). The authors also acknowledge Mr. Suraj Singhaneka for his contribution.

Funding information: This study was financially supported by the Japan Science and Technology Agency (JST) CREST (Grant Number JPMJCR2094).
Author contributions: Sunday Temitope Oyinbo: validation, formal analysis, investigation, data curation, writing – original draft, visualization, methodology. Ryosuke Matsumoto: conceptualization, methodology, software, validation, formal analysis, investigation, resources, writing – review and editing, visualization, supervision, project administration, funding acquisition. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: The authors state no conflict of interest.
Data availability statement: The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2024-01-23

Revised: 2024-07-13

Accepted: 2024-07-23

Published Online: 2024-08-19

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/ntrev-2024-0082

Keywords for this article

pyramidal screw dislocation; critical resolved shear stress; normal stress; molecular dynamics; magnesium

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