Effects of Cerium Addition on Non-basal Slip in Magnesium Single Crystals

Abstract

Cerium, a rare earth element, was alloyed at various ratios with magnesium to create Mg–Ce single crystals which were then subjected to $[\bar{1}100]$ and $[11\bar{2}0]$ tensile tests to clarify effects of cerium on activation of non-basal slips at room temperature. Mg–0.016 mol%Ce alloys yielded due to $\{ 10\bar{1}1\} $ twins in $[\bar{1}100]$ tension tests. Mg–0.052 mol%Ce single crystals yielded due to $\{ 11\bar{2}2\} \langle \bar{1}\bar{1}23\rangle $ second order pyramidal ⟨c+a⟩ slip (SPCS), similar to pure magnesium single crystals, in $[11\bar{2}0]$ tensile tests. Cerium addition decreased critical resolved shear stresses (CRSS) for $\{ 10\bar{1}1\} $ twinning and SPCS. The decrease in CRSS for SPCS likely results from the frequency of sessile (c+a) dislocations decreasing with decreasing stacking fault energy of second order pyramidal planes.

 

This Paper was Originally Published in J. Japan Inst. Light Metals 69 (2019) 125–127.

1. Introduction

Magnesium has gained attention for use in transport industries as it is the lightest structural metal and has high specific strength. However, deformation mechanisms of magnesium remain unclarified. As a hexagonal close-packed (hcp) metal, magnesium has multiple slip and twin systems due to low symmetry of the hcp structure compared to body-centered cubic or face-centered cubic structures. Also, metals with identical hcp structures may display disparate slip and twin activity, complicating hcp metal deformation mechanism clarification.

The main slip system in magnesium is basal. However, with independent slip systems numbering only two, this is insufficient for the von Mises criterion.¹⁾ As a result, magnesium shows low ductility at room temperature. Therefore, non-basal slip activities are required to improve ductility.

It has been reported that the addition of cerium increases room temperature ductility of magnesium²⁾ and that 0.035 mol% cerium added to magnesium results in alloy strength identical to pure magnesium but with higher ductility due to non-basal slip in compression tests at room temperature.³⁾ However, effects of cerium addition on non-basal slip systems in magnesium-cerium (Mg–Ce) alloys have yet to be elucidated. This study investigates effects of cerium addition on non-basal slip systems in magnesium by subjecting Mg–Ce alloy single crystals to tensile tests with loading direction parallel to basal planes at room temperature.

2. Experimental Procedures

Mg–Ce alloy ingots were produced using magnesium of 99.97% purity and cerium of 99.9% purity with a high frequency induction furnace. From these ingots, two types of alloy single crystals were grown by the Bridgman method: Mg–0.016 mol%Ce and Mg–0.052 mol%Ce. The specimen size was approximately 0.3 × 3 × 20 mm³ with surfaces parallel to basal planes and longitude direction parallel to $[11\bar{2}0]$ or $[\bar{1}100]$. Each specimen was crystallographically analyzed by the X-ray back reflection Laue method. Tensile tests were carried out at room temperature under an initial strain rate, $\dot{\varepsilon }$, of 3.7–4.6 × 10⁻⁵/s. In the tensile tests, specimens were unloaded just after yielding in order to investigate deformation behavior. Slip lines and twins were observed using Nomarski optical microscopy.

3. Results and Discussion

Figure 1 shows stress-strain curves obtained from $[\bar{1}100]$ tensile tests of Mg–0.016 mol%Ce alloy single crystals; arrows indicate yield and fracture points. Data of a pure magnesium single crystal under identical tensile conditions⁴⁾ is also shown in Fig. 1 for comparison. In this study, extensometers and strain gauges were unable to be attached to single crystalline specimens due to their small size and the low strength. For tensile tests, holders were attached to each single crystal specimen using an adhesive. The specimens with holders were attached to a tensile testing machine using jigs. Displacement obtained from the tensile testing machine was corrected in consideration of strains of jigs and folders, and the corrected value was used as a strain of single crystalline specimens. In pure magnesium single crystals, slip deformation occurred in $[11\bar{2}0]$ tensile tests as described below, but not in $[\bar{1}100]$ tensile tests. The cause of this remains unclear. In contrast, Mg–Ce alloy single crystals yielded and showed a slight ductility of 0.06% in $[\bar{1}100]$ tensile tests. Thus, it is found that cerium addition improves the ductility of magnesium.

Fig. 1

Stress-strain curves of Mg–0.016 mol%Ce alloy and pure magnesium single crystals; tensile directions are parallel to $[\bar{1}100]$.

Stress-strain curves obtained from $[11\bar{2}0]$ tensile tests of Mg–0.052 mol%Ce alloy single crystals and pure magnesium single crystals⁵⁾ are shown in Fig. 2. When 0.052 mol% cerium was added, Mg–Ce alloy single crystals yielded at lower stress than pure magnesium single crystals. Mg–0.052 mol%Ce alloy single crystals showed work hardening after yielding in a manner identical to that of pure magnesium single crystals. Also, Mg–0.052 mol%Ce alloy single crystals fractured at a strain of approximately 1.19%. Conversely, pure magnesium single crystal fractured at a strain of approximately 3.2%, as shown in Fig. 2, meaning that the ductility of magnesium decreases by the addition of cerium.

Fig. 2

Stress-strain curves of Mg–0.052 mol%Ce alloy and pure magnesium single crystals; tensile directions are parallel to $[11\bar{2}0]$.

Figure 3 shows optical micrographs of (a) Mg–0.016 mol%Ce alloy single crystals at a strain of 0.06% in $[\bar{1}100]$ tensile tests, and Mg–0.052 mol%Ce alloy single crystals at a strain of (b) 0.68% and (c) 1.19% in $[11\bar{2}0]$ tensile tests. Twins parallel to $[11\bar{2}0]$ were observed on (0001) in Mg–0.016 mol%Ce alloy single crystals. The twins were analyzed by the X-ray back reflection Laue method. Results showed that the twins rotated by 56° around $[11\bar{2}0]$ from initial orientation and were characterized to be $\{ 10\bar{1}1\} $ twins, while no slip lines or twins were observed in pure magnesium single crystals.⁴⁾ These results indicate that cerium addition facilitates activation of the $\{ 10\bar{1}1\} $ twin, resulting in Mg–Ce alloy single crystals displaying slight ductility of 0.06% in the $[\bar{1}100]$ tensile test. In contrast, fine slip lines perpendicular to $[11\bar{2}0]$ were observed on (0001) in Mg–0.052 mol%Ce alloy single crystal, as shown in Fig. 3(b). Of note is that slip lines were not observed on $(\bar{1}100)$, the side surface of the specimen — that is, the slip direction was parallel to $(\bar{1}100)$ — meaning that the slip lines were caused by $\{ 11\bar{2}2\} \langle \bar{1}\bar{1}23\rangle $ second order pyramidal ⟨c+a⟩ slip (SPCS). Pure magnesium single crystals have been reported to yield due to SPCS in $[11\bar{2}0]$ tensile tests.^4–6) Thus, we found that cerium addition no more than 0.052 mol% does not change the slip system. When strain increased up to 1.19%, slip lines became clear and the width of each slip band expanded, as shown in Fig. 3(c). However, the area of slip band did not expand through the whole specimen but was limited to local areas.

Fig. 3

Optical micrographs of Mg–0.016 mol%Ce after 0.06% elongation in $[\bar{1}100]$ tensile tests (a) and Mg–0.052 mol%Ce after 0.68% (b) and 1.19% (c) elongation in $[11\bar{2}0]$ tensile tests.

Critical resolved shear stresses (CRSSs) for $\{ 10\bar{1}1\} $ twin and SPCS were respectively calculated from the results shown in Fig. 1–3. Figure 4 shows CRSSs for $\{ 10\bar{1}1\} $ twin and SPCS as a function of cerium contents. For comparison, the same data for pure magnesium^6,7) are also shown in Fig. 4. Each CRSS decreased due to cerium addition. Effects of cerium addition on activation of SPCS are discussed below.

Fig. 4

Relationship between cerium content and CRSS for $\{ 10\bar{1}1\} $ twin and second order pyramidal slip.

Ando et al.⁶⁾ have reported that, in pure magnesium single crystals, yield stress due to SPCS shows anomalous temperature dependence and proposed the deformation mechanism as described below. Extended edge dislocations of (c+a) dislocation loops generated from dislocation sources on second order pyramidal planes move some distance. However, thermally activated processes cause each extended dislocation to dissociate into ⟨c⟩ dislocations and ⟨a⟩ dislocations and thus immobilize. Therefore, to maintain constant strain rates, (c+a) screw dislocations need to double cross-slip to another second-order pyramidal planes and multiply dislocation loops. This results in slip bands expanding due to immobilization of dislocations and double cross-slip. The same deformation mechanism by SPCS has been also reported in cadmium; also, thermally activated process have been discussed as described below.⁸⁾ Strain rate, $\dot{\gamma }$ of specimen was calculated from the following equation.⁸⁾   

\begin{equation} \dot{\gamma} = A\times\cfrac{\exp\biggl(-\cfrac{Q_{c} - V^{*}\tau_{m}}{kT}\biggr)}{\exp\biggl(-\cfrac{Q_{s}}{kT}\biggr)\exp\biggl(-\cfrac{Q_{s}}{kT}\biggr)} \end{equation} (1)

Where T is temperature, k is Boltzmann constant, Q_c is constriction energy of extended screw dislocations on second order pyramidal planes, Q_s is activation energy of immobilization, $V^{*}$ is activation volume of cross-slip, τ_m is stress for cross-slip and A is a constant. The equation includes three thermally activated processes. The numerator indicates cross-slip frequency. The denominator is comprised of two processes: a decrease in mean free path due to immobilization of edge dislocations and a decrease in the length of screw dislocations. When immobilization of edge dislocation frequency decreases, expressed in the equation by denominator decrease, the frequency of cross-slip in the numerator decreases to maintain a constant strain rate. That is, τ_m decreases and as a result, yield stress by SPCS decreases. Here, the decrease in the frequency of cross-slip occurs due to decrease in the expansion rate of the slip band. In Mg–0.052 mol%Ce alloy single crystals, slip bands are limited to local areas even at a strain of 1.19%, as shown in Fig. 3(c). In contrast, Ando et al.⁶⁾ have reported that fine slip lines caused by SPCS were observed along the entire surface of pure magnesium single crystal specimens even immediately after yielding. Thus, cerium addition has shown to decrease the expansion rate of the slip band, and based on the mechanism described above, immobilization of (c+a) dislocation frequency would decrease due to cerium addition. The immobilization of (c+a) edge dislocations is discussed as described below.⁹⁾ (c+a) edge dislocations, as they are extended dislocations (partial dislocations), move on second order pyramidal planes. The partial dislocations then combine to form perfect (c+a) dislocations; finally each perfect dislocation dissociates to form ⟨c⟩ and ⟨a⟩ dislocations via thermally activated process. Theoretically, if cerium addition decreases stacking fault energy (SFE) of second order pyramidal planes, width (c+a) edge dislocations would extend and would thus result in a decrease in the frequency to combine partial dislocations into (c+a) perfect dislocations. In other words, the frequency to dissociate (c+a) dislocations into ⟨c⟩ dislocations and ⟨a⟩ dislocations decreases, i.e., the frequency of immobilization decreases. Therefore, the cause of decreasing yield stress is that cerium addition decreases SFE of second order pyramidal planes, decreasing the frequency of the immobilization of (c+a) dislocations. Since the c/a ratio of Mg–0.035 at%Ce is 1.624,³⁾ similar to that of pure magnesium, the effects of c/a ratio would be almost none. Sandlöbes et al.¹⁰⁾ have reported that the addition of rare earth elements decreases I₁ SFE in magnesium. Also, Sabat et al.¹¹⁾ have reported based on results of tension tests and crystal plasticity finite element modeling of Mg–0.2 mass%Ce alloys that relative ratios of CRSS for basal slips, second order pyramidal slips, and prismatic slips are reduced by cerium addition. From our results and references, cerium addition likely decrease SFE of second order pyramidal planes. Decreasing CRSS for twins by cerium addition will be discussed in the near future.

4. Conclusions

Mg–0.016 mol%Ce and Mg–0.052 mol%Ce alloy single crystals were subjected to tensile tests so as to investigate effects of cerium addition on non-basal slips in pure magnesium. Mg–0.016 mol%Ce alloy single crystals yielded due to $\{ 10\bar{1}1\} $ twinning in $[\bar{1}100]$ tensile tests. On the other hand, Mg–0.052 mol%Ce alloy single crystals yielded due to second order pyramidal slips in $[11\bar{2}0]$ tensile tests similar to pure magnesium. We found that cerium addition decreases critical resolved shear stresses for $\{ 10\bar{1}1\} $ twinning and second order pyramidal slips.

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