Solute segregation and precipitation in a creep-resistant Mg–Gd–Zn alloy

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Acta Materialia 56 (2008) 6061–6076 www.elsevier.com/locate/actamat

Solute segregation and precipitation in a creep-resistant Mg–Gd–Zn alloy J.F. Nie a,c,*, K. Oh-ishi b, X. Gao a, K. Hono b a

Department of Materials Engineering, Monash University, Vic. 3800, Australia National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan c International Centre for Young Scientists, National Institute for Materials Science, Japan b

Received 2 March 2008; received in revised form 5 August 2008; accepted 9 August 2008 Available online 23 September 2008

Abstract Solute segregation and the precipitate phases in a creep-resistant Mg–1Gd–0.4Zn–0.2Zr (at.%) alloy aged isothermally at 250 and 200 °C have been examined using a three-dimensional atom probe and high-angle annular dark-field scanning transmission electron microscopy. Co-segregation of Gd and Zn atoms is detected in the as-quenched condition, and this contributes to the large hardness increase in this condition. Precipitation during isothermal ageing involves the formation of metastable phases c00 and c0 , with c00 as the key strengthening phase. The equilibrium phase c is not detected for ageing up to 1000 h at 250 °C. The c00 phase has an ordered hexagonal structure (space group P 62m, a = 0.560 nm, c = 0.444 nm) and an atomic composition of approximately Mg70Gd15Zn15, and forms as (0 0 0 1)a plates with a thickness of a single unit cell height. The c0 phase has a disordered hexagonal structure (space group P 3m1, a = 0.321 nm, c = 0.781 nm) and an atomic composition of about MgGdZn. The c0 phase also forms as thin (0 0 0 1)a plates, but it has a much larger aspect ratio. The formation of the c0 phase involves a large shear strain, and it often forms in twin-related plates to self accommodate this shear strain. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Magnesium alloys; Ageing; Precipitation; STEM; 3DAP

1. Introduction Rare-earth-containing magnesium alloys have received considerable interest in recent years due to their potential for achieving higher strength and better creep resistance. The notable examples include experimental and commercial alloys based on the Mg–Gd, Mg–Gd–Y, Mg–Gd–Nd and Mg–Y–Nd systems [1–10]. Most of these alloys are precipitation hardenable, and the precipitation of transition phases provides the useful strength and creep resistance to these alloys. In the Mg–Gd-based alloys and the Mg–Y–Nd alloys, the key strengthening precipitate phases are b’ and b1 [3–5]. The b’ phase has a base-centred ortho* Corresponding author. Address: Department of Materials Engineering, Monash University, Vic. 3800, Australia. Tel.: +61 3 9905 9605; fax: +61 3 9905 4940. E-mail address: [email protected] (J.F. Nie).

rhombic structure (a = 0.64 nm, b = 2.22 nm, c = 0.52 nm) and the b1 phase has a face-centred cubic (fcc) Bravais lattice (Fm3m, a = 0.74 nm [5]). During prolonged ageing, the b1 phase transforms in situ into the equilibrium phase b, 43m, which has a structure isomorphous to Mg5Gd (F  a = 2.23 nm) [3,5]. The structure and morphology of these precipitate phases and the precipitation sequence in the alloys have been relatively well established. None of the precipitate phases in these alloys form as plates on the basal plane of the a-Mg matrix phase. Binary Mg–Gd alloys exhibit little age hardening response when the Gd content is less than 1.5 at.%. This poor age hardening response is due to the sparse distribution of coarse precipitates and the lack of an appreciable volume fraction of precipitates. However, a recent study [11] has demonstrated that additions of 0.4–0.8 at.% Zn can generate a strong precipitation hardening response in and significantly enhance the creep resistance of Mg–Gd

1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.08.025

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alloys containing a significantly smaller amount of Gd (1 at.%). Furthermore, the hardness of the Zn-containing alloy is much higher (17 VHN) than that of the Zn-free alloy even in the as-quenched condition. This increase in hardness in the as-quenched condition represents 65% of the maximum hardness increment in the alloy. This is remarkable given that only 0.4 at.% Zn is added. One obvious question is whether clusters of solute atoms form during or immediately after water quench and, if so, whether these solute clusters contribute to the hardness increase. The enhanced age hardening response in the Zn-containing alloy is due to a denser distribution of (0 0 0 1)a precipitate plates that is not achievable in the binary counterpart alloy. Examination of peak-aged microstructures does not reveal the existence of any precipitates commonly observed in the binary alloys, i.e. b”, b’, b1 and b phases. While it was speculated [11] that the basal plates in the Mg–1Gd–0.4Zn– 0.2Zr (at.%) alloy are not the long-period structures and stacking faults that have been reported to form in Mg– Y–Zn alloys [12–18], the structure and composition of these strengthening precipitate plates have not been firmly established. Very recently, Yamasaki et al. [19] reported the formation of stacking faults and 14H phase on (0 0 0 1)a in an Mg–2Gd–1Zn alloy, in addition to the b’, b1 and b phases, Table 1. The concentrations of Gd and Zn in their alloy are almost twice of those in the Mg–1Gd–0.4Zn–0.2Zr alloy. The 14H phase forms from not only the supersaturated solid solution phase of a-Mg, but also the decomposed pri3m, a = 0.72 nm) mary intermetallic particles Mg3Gd (Fm that have formed in the as-cast microstructures. This phase is thus inferred to be an equilibrium phase in this alloy and other alloys of similar compositions [19–22]. The 14H phase is reported to have a structure identical to that in Mg–Y–Zn alloys [12,16], i.e. a long-period hexagonal structure (a = 0.321 nm, c = 3.66 nm) with closely packed planes stacking in the sequence of ABABABACBCBCBCA. Another study suggests that the aaxis of the 14H structure might be 1.11 nm instead of 0.321 nm [23]. The stacking faults reported in the Mg– 2Gd–1Zn alloy are intrinsic in character, and segregation of Gd and Zn atoms into the two atomic planes around each single stacking fault is observed. During isothermal

Table 1 Precipitation reactions reported in literature in Mg–Gd–Zn and Mg–Gd– Y–Zn alloys Alloy (at.%)

Ageing Precipitation sequence temperature (°C)

Mg–2Gd–1Zn [19]

400 300 200

Mg–2Gd–1.2Y–1Zn–0.2Zr [22] 225 SF, stacking faults.

SSSS ? SF ? 14H SSSS ? SF SSSS ? b1 ? b SSSS ? b’ ? b1 ? b SSSS ? b” ? b’ ? b1 SSSS ? 14H

ageing of the Mg–2Gd–1Zn alloy, the stacking faults and the 14H phase form reportedly at intermediate and high temperatures (300–500 °C), while the b’, b1 and b phases form at low temperatures (200 °C). It has further been suggested [19] that the 1 at.% Zn addition to the Mg– 2Gd alloy reduces the stacking fault energy and therefore promotes the formation of stacking faults and the 14H phase. If these reported results are representative, then it is difficult to understand why the stacking faults form preferentially only at intermediate and high temperatures rather than at both high and low temperatures, i.e. in the temperature range 25–500 °C. It is also not clear why the stacking faults reported in the Mg–2Gd–1Zn alloy are different from those in the Mg–Y–Zn alloys. The major aim of the present study is to clarify the structure and compositions of precipitate phases formed in an important group of alloys based on the Mg–Gd–Zn system and to establish whether the large hardness increase in the as-quenched condition is associated with solute clusters. Specifically, the objective is to report results of an examination of solute distribution and the structure and chemistry of nanoscale precipitate plates in an Mg–1Gd–0.4Zn–0.2Zr alloy subjected to different ageing times at 250 and 200 °C. A three-dimensional atom probe (3DAP) was used to examine the solute distribution and the composition of precipitate plates. The structure of precipitate plates is examined using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). 2. Experimental procedures The nominal composition of the alloy was Mg–1Gd– 0.4Zn–0.2Zr (at.%) or Mg–6Gd–1Zn–0.6Zr (wt.%) (note that atomic percentage is used for all the alloy compositions in this paper). This alloy was prepared from high purity (P99.9%) Mg, Gd and Zn and an Mg–33 wt.% Zr master alloy (Zirmax) by induction melting in a mild steel crucible at approximate 760 °C under an argon atmosphere and casting into a steel mould pre-heated to 200 °C. To facilitate preparation of specimens suitable for atom probe experiments, an Mg–1Gd–0.4Zn alloy was also made. Alloy ingots were solution treated for 16 h at 500 °C. The solution treated samples were quenched into hot water of 70 °C, then subsequently aged at 200 and 250 °C. Discs of 3 mm diameter were punched from the heat-treated strips, ground to a thickness of 0.15 mm and twin-jet electropolished in a solution of 5.3 g of lithium chloride, 11.2 g of magnesium perchlorate, 500 ml of methanol and 100 ml of 2-butoxy-ethanol, at –55 °C and 0.1 A. Characterization of precipitates was performed in a Philips CM20 transmission electron microscopy (TEM), a Tecnai G2 F30 TEM and a locally built 3DAP. HAADF-STEM images were obtained from the Tecnai G2 F30 TEM operating at 300 kV and with a nominal HAADF-STEM resolution of 0.19 nm. Atom probe specimens with dimensions of 0.5  0.5  15 mm3 were cut from bulk samples. They were

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then ground to a cross-section of approximately 0.1  0.1 mm2 and subsequently electropolished into shape needles in a solution of 5 vol.% perchloric acid and 95 vol.% butoxy-ethanol at 14–20 V of direct current. The tips were then examined in locally built energy-compensated 3DAPs equipped with a CAMECA optical tomographic atom probe detector and an Oxford nanoscience delay line detector, and a locally built laser-assisted tomographic atom probe. A mixture of neon (4  104 Pa) and hydrogen (2  104 Pa) was used as the imaging gas to observe field ion microscope (FIM) images of precipitates, and the temperature of the imaged specimen was 60 K. A pulse fraction of 0.2 and a pulse frequency of 1 kHz were used for the energy-compensated position-sensitive 3DAP, at a temperature of 30 K under an ultrahigh vacuum of 1  108 Pa. To obtain near-atomic resolution maps of basal precipitate plates, most specimens were probed along directions nearly parallel to [0 0 0 1]a.

formly distributed in this volume. Careful tilting and inspection of this volume, and those obtained from other samples, did not reveal any visually detectable clusters of Gd and/or Zn atoms. To examine whether there existed any interactions between Gd and Zn atoms in the solid solution phase of magnesium, a statistical approach, namely contingency table analysis [24–26], was used in the present study. This approach compares experimentally observed frequencies of atoms of the two elements in individual compositional blocks with those expected for a perfectly random distribution of atoms of the two elements. The contingency table provided in Table 2(a) shows the detected frequencies of Gd and Zn atoms based on a block size of 200 atoms in the as-quenched sample. These observed frequencies were compared with those expected for a random distribution of Gd and Zn atoms (Table 2(b)) and the difference is measured by the v2 statistic [24–28]:

3. Results

v2 ¼

3.1. Co-segregation of Gd and Zn atoms The as-quenched microstructure using transmission electron microscopy and selected area electron diffraction (SAED) revealed no evidence of precipitation, within the experimental limit of the techniques. It was also difficult to detect any excessive dislocations inside individual magnesium grains. Therefore, 3DAP was employed to reveal whether or not there were any solute clusters in the asquenched condition. Fig. 1 shows a three-dimensional (3D) reconstruction of an analysed volume of the asquenched specimen that shows the distribution of Gd and Zn atoms. The dots inside the volume represent individual atoms, with blue spots representing Gd atoms and the red spot Zn atoms. Both Gd and Zn atoms appeared to be uni-

2 r X c X ðnij  n0ij Þ n0ij i¼1 j¼1

ð1Þ

where r and c are the number of rows and columns in each table, respectively, and (r  1)(c  1) represents the degree of freedom. The notion of a perfectly random distribution of Gd and Zn atoms is tested by comparing the probability of the v2 statistic with the values of the v2 distribution for the appropriate number of degrees of freedom [24–26]. For the observed and expected frequency values provided in Table 2, the calculated value of v2 was 50.40 with 14 degrees of freedom. This value was significantly larger than that (34.528) corresponding to 0.001 probability of a deviation greater than v2 (Appendix E of Ref. [26]), indicating that the probability of a random distribution of Gd and Zn atoms was extremely low. Therefore, there was a significant departure from a random distribution of Gd and Zn atoms, i.e. co-segregation of Gd and Zn atoms had occurred in the as-quenched condition. The average concentrations of Gd, Zn and Zr atoms in magnesium grains in the as-quenched condition were measured to be 1.03, 0.34 and 0.04 at.%, respectively, within experimental error. These measured values were in good Table 2 Contingency tables for Gd and Zn in the as-quenched sample

Fig. 1. 3DAP maps showing distribution of Gd, Zn and Zr atoms in the as-quenched condition.

Gd 0

1

2

3

Zn (a) 0 1 2–200

145 70 22

237 148 48

212 128 89

154 113 65

Zn (b) 0 1 2–200

118 79 40

216 144 73

214 142 72

166 110 56

4

5

6

7–200

88 73 47

30 34 16

10 13 8

7 8 3

104 69 35

40 27 13

15 10 5

9 6 3

(a) Experimentally observed frequencies of Gd and Zn atoms; (b) calculated frequencies for a random distribution of Gd and Zn atoms. A block size of 200 atoms is used.

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agreement with the nominal concentrations of Gd and Zn in the alloy. The measured content of Zr was significantly lower than the nominal value (0.2 at.%). This discrepancy was probably due to the presence of Zr particles in the microstructure. Fig. 2 shows a 3D reconstruction of five analysed volumes of specimens aged for different times at 200 and 250 °C, respectively. Inspection of the distributions of Gd and Zn atoms inside these volumes did not detect any Gd and Zn clusters. These distributions of Gd and Zn atoms were quite similar to that observed in the as-quenched condition (Fig. 1). However, the v2 values obtained from these samples indicated that the co-segregation of Gd and Zn atoms gradually became difficult to detect during isother-

mal ageing at 200 °C (Table 3). At 250 °C, the co-segregation of Gd and Zn atoms became less obvious even after 2 h ageing, and appeared to be replaced by a random distribution after 8 h (Table 3).

Table 3 Values of v2, degrees of freedom (D) and probability for deviations larger than v2 (P) obtained from samples in the as-quenched and aged conditions 250 °C

As-quenched 2

v D P

200 °C

#1

#2

#3

0.5 h

2h

8h

20 h

200 h

50.40 14 <0.001

80.34 14 <0.001

72.90 14 <0.001

42.85 16 <0.001

12.16 15 <0.7

1.37 5 <0.95

24.26 8 <0.01

10.91 6 <0.1

Fig. 2. 3DAP maps showing distribution of Gd, Zn and Zr atoms in samples aged for (a) 0.5 h at 250 °C, (b) 2 h at 250 °C, (c) 8 h at 250 °C, (d) 20 h at 200 °C and (e) 200 h at 200 °C.

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3.2. Precipitate phases During isothermal ageing at 250 °C, precipitation involved the formation of plate-shaped particles formed exclusively on the basal plane of the a-Mg matrix. Fig. 3 shows the distribution of precipitate plates in samples aged for 1, 5, 500 and 1000 h at 250 °C, respectively. In the sample aged for 1 h at 250 °C, i.e. the under-aged condition, only some sparsely dispersed plate-like precipitates were observed in the microstructure (Fig. 3(a)). These plates were typically 60 nm long and less than 1 nm thick in h11 20ia projected images, i.e. their aspect ratio was in the order of 60:1. For the purpose of clarity, these plate-like precipitates were designated c00 phase. With a progress in ageing time, the number density of the c00 plates increased. The microstructure typical of the sample aged for 5 h (peak-aged) is shown in Fig. 3(b). It now contained a uniform and relatively dense distribution of c00 precipitates. While the microstructure contained predominantly the small plates of c00 , it was possible to detect some large pre-

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cipitate plates. Most of these large plates had an aspect ratio (length over thickness) of over 500:1 in the h11 20ia images. These large plates were designated c0 phase. With continued ageing at 250 °C, the small plates of c00 were gradually replaced by the large plates of c0 (Fig. 3(c)). The microstructure contained predominantly c0 plates after 1000 h at 250 °C (Fig. 3(d)). The c0 plates often formed in pairs and clusters. They had excellent thermal stability. The thickening rate of these plates was extraordinarily low; their thickness was still less than 1 nm even after 1000 h of ageing at 250 °C. Precipitation during isothermal ageing at 200 °C appeared to be similar to that observed at 250 °C, except the kinetics of the precipitation was now much slower (Fig. 3(e) and (f)). The structure and composition of c00 plates in the peakaged samples were analyzed using SAED, HAADF-STEM and 3DAP. In the [0 0 0 1]a zone axis pattern obtained from a matrix region containing c00 precipitates, precipitate reflections were clearly visible at the 1/3{1120}a and 2/ 3{1120}a positions (Fig. 4(b)). In the h1010ia zone axis

Fig. 3. Transmission electron micrographs showing distribution of precipitate plates in samples aged for (a) 1 h, (b) 5 h, (c) 500 h and (d) 1000 h at 250 °C. (e,f) Precipitate plates formed in samples aged for 20 and 200 h, respectively, at 200 °C.

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Fig. 4. (a) Transmission electron microscopy images of precipitate plates viewed in [0 0 0 1]a direction and (b) corresponding SAED pattern. (c) 20ia SAED patterns. The sample was aged for 5 h at h10 10ia and (d) h11 250 °C.

pattern, streaking parallel to the [0 0 0 1]a direction and at the 1/3{11 20}a and 2/3{11 20}a positions was observed (Fig. 4(c)). In the h11 20ia pattern, pronounced streaking was visible along the [0 0 0 1]a direction and at the (0 0 0 )a and {10 10}a positions. No precipitate reflections were observed. These diffraction patterns were similar to those observed in Mg–Nd–Zn [29] and Mg–Ca–Zn–Nd alloys [30], and they could be indexed according to either an ordered GP zone [31] or a hexagonal structure, with a = 0.556 nm and c = 0.521 nm [29]. HAADF-STEM images of c00 precipitates are shown in Figs. 5 and 6. These images allow the thickness and the structure of the c00 precipitates to be determined unambiguously. They also offered a unique opportunity [32] to show qualitatively the distribution of Gd and Zn atoms in the c00 plates, since the brightness of a HAADF-STEM image is proportional to the square of atomic number. In the lowmagnification images (Fig. 5), small plates of c00 and large plates of c0 both appeared as bright lines, implying a high concentration of Gd and/or Zn atoms in these precipitates. Fig. 6 shows two Fourier-filtered HAADF-STEM images of a c00 plate at the atomic column resolution. It is immediately clear from the figure that the plate had three atomic layers; the top and bottom layers were the brightest, while the middle layer had a brightness between the brightest layers and that of Mg atoms in the matrix. Since Gd has the highest atomic number of the three elements in the alloy (64 for Gd, 30 for Zn and 12 for Mg), it is conceivable that the brightest spots corresponded to atomic columns of a higher Gd concentration and that the brighter spots in the middle layer were columns of atoms containing a higher Zn content. Viewed in a h11 20ia direction, coherent

Fig. 5. HAADF-STEM images showing c00 (short) and c0 (long) precipitate plates in samples aged for 2 h at 250 °C. Electron beam was parallel to (a) h1120ia and (b) h1010ia.

matching between c00 plates and a-Mg was noticed in the habit plane. However, the interplanar spacing of c00 plates along the [0 0 0 1]a direction was noticeably smaller than that of (0 0 0 1)a. The measured thickness of c00 plates was about 0.444 nm based on the assumption that ca = 0.521 nm. Therefore, the misfit between the c00 and a-Mg phases was 0.16. On the basis of HAADF-STEM images, it was unambiguous that the c00 plates were not the ordered GP zones reported by Ping et al. [31]. The combined observations from the HAADF-STEM images and SAED patterns suggested that the c00 plates had an ordered hexagonal structure, with a P 62m space group and lattice parameters a = 0.556 nm and c = 0.444 nm (Fig. 7). This structure is subtly different from that reported recently for the basal plates formed in an Mg–2Gd–1Zn alloy [33] in terms of the distribution of Zn atoms and the c value of the unit cell. The orientation relationship between c00 and a-Mg phases was such that (0 0 0 1)c0 0 // (0 0 0 1)a and [1010]c0 0 // [2110]a. The simulated SAED patterns for this structure are also shown in Fig. 7. These simulated patterns were in good agreement with those observed experimentally (Fig. 4). Note that,

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Fig. 6. Fourier-filtered HAADF-STEM images showing c00 precipitate plates viewed in (a) h1120ia and (b) h1010ia directions. The sample was aged for 2 h at 250 °C.

for the h10 10ia pattern, it was difficult to clarify whether the simulated pattern was fully consistent with the observed patterns, as the precipitate reflections at 1/2{0 0 0 2}a positions might be masked by the streaks running through (0 0 0)a and {0 0 0 2}a reflections. The composition of the c00 precipitates was analyzed by 3DAP. To obtain 3DAP maps with higher spatial resolution, and therefore to obtain more accurate data, most specimens were probed along the [0 0 0 1]a direction, i.e. in the direction normal to the broad surface of the c00 plates. The FIM images of c00 plates in peak- and over-aged samples are shown in Fig. 8. These images were taken with a mixture of neon and hydrogen as imaging gases. The precipitates appeared as bright concentric arcs or rings when they were viewed along the [0 0 0 1]a direction. It was common to observe some closely spaced, paired precipitates, marked in Fig. 8(d), in the over-aged samples. Since Gd atoms had a higher evaporation field than Mg atoms, any precipitates enriched in Gd atoms would appear bright in the FIM images. These FIM images indicated clearly that precipitate plates in both under- and peak-aged samples contained an appreciable concentration of Gd. In the present study, it was difficult to distinguish the small plates of c00 from the large plates of c0 in FIM images

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and 3DAP maps obtained from under- and peak-aged samples. All 3DAP maps of precipitate plates were similar (Fig. 9). Since c00 precipitates were the dominant phase in the under- and peak-aged microstructures, the precipitates in those 3DAP maps obtained from under- and peak-aged samples were assumed to be the c00 phase. Fig. 10 shows 3DAP maps of Gd and Zn in three c00 precipitates. Zr was not shown in these maps because the data obtained from a range of samples indicated that Zr atoms did not segregate preferentially to precipitates. The composition profile in the direction normal to the habit planes of the c00 plates is also shown in Fig. 10. The concentrations of Gd and Zn in each precipitate were approximately the same, even though they varied from precipitate to precipitate. For the three precipitates shown in the figure, the averaged concentration of Gd in the plates was 15 at.% and the Zn content was also 15 at.%. The c0 plates could be readily distinguished from the c00 plates by their aspect ratio and their contrast in HAADFSTEM images. Fig. 11(a) shows Fourier-filtered HAADFSTEM images of three c0 plates in samples aged 2 h at 250 °C. In contrast to c00 plates, the c0 plates did not exhibit any periodic bright spots that were characteristic of c00 . In both h1120ia and h1010ia images (Fig. 11(b) and (c)), two layers of bright spots were observed in the middle of each c0 plate, and these two layers corresponded to two neighbouring closely packed planes. The segregation of Gd, or Y, and Zn atoms into two successive closely packed planes has also been observed in the 14H structure in Mg–Gd–Zn [19] and the 6H structure in Mg–Y–Zn alloys [14,15]. The contrast between the bright spots and the surrounding grey spots was not as strong as that in the c00 plates. Furthermore, the separation distance between individual bright spots was beyond the resolution of the microscope when the c0 plates were viewed in a h1010ia direction, i.e. it was difficult to see any individual bright spots inside each c0 plate (Fig. 11(c)). The absence of the periodic bright spots suggested that the structure of c0 precipitates was probably disordered. In fact, the [0 0 0 1]a SAED patterns obtained from a-Mg matrix regions containing c0 plates in over-aged samples did not show any precipitate reflections (Fig. 12). The precipitate reflections at the 1/3{11 20}a and 2/3{1120}a positions – a feature characteristic of the ordered structure of the c00 phase – were absent. The h1120ia and h1010ia images of the plate-like precipitates indicated that the structure of the c0 precipitates was distinguishably different from that of c00 . In the direction normal to the habit plane, the atomic planes of c0 precipitates appeared to have an ABCABC stacking sequence without any internal structural order, and their interplanar spacing was very similar to that of the basal plane of a-Mg (Fig. 11(a)). If this ABCABC stacking sequence, the occupancy of Gd and Zn atoms in the B and C layers, and the disordered structure and perfect matching with aMg in the habit plane, were all taken into account, then a possible structure of c0 precipitates was hexagonal (or trigonal), with a = 0.321 nm, c = 0.781 nm. The unit cell of

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Fig. 7. (a) Schematic diagram showing the unit cell of c00 phase (defined by red lines) and its relationship with a-Mg lattice. Simulated SAED patterns for 10]a and (d) [0 0 0 1]a zone axes. Black spots represent a-Mg reflections; red spots are c00 reflections. (For interpretation of color (b) [2 1 10]a, (c) [10 mentioned in this figure the reader is referred to the web version of the article.)

Fig. 8. FIM images of precipitate plates in samples aged for (a,b) 8 h and (c,d) 120 h at 250 °C. The viewing direction is [0 0 0 1]a in (a–c) and approximately perpendicular to [0 0 0 1]a in (d).

Fig. 9. 3DAP maps of c00 precipitate plates formed in samples aged for (a) 200 h at 200 °C and (b) 2 h at 250 °C.

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spatial resolution of the 3D reconstruction maps was not sufficiently high to allow these two atomic layers to be defined, the compositional data of the c’ phase inevitably contained a significant amount of Mg atoms from the surrounding a-Mg matrix phase, and therefore would underestimate the Gd and Zn contents in the c0 phase. Examination of well over-aged samples (1000 h at 250 °C) revealed that the microstructure contained predominantly c0 precipitates (Fig. 15). The thickness of most c0 precipitate plates was still less than 1 nm, but their length was remarkably long – often in the order of the diameter of a-Mg grains. It was common to detect c0 plates formed in pairs or in clusters, marked by arrows in Fig. 15(a). At this stage of ageing, a minor fraction of precipitates of the equilibrium b-Mg5Gd phase was also detected in the microstructures. However, precipitates of the 14H structure (designated c) that has been reported to form during isothermal ageing of supersaturated solid solutions of Mg– Gd–Zn and Mg–Gd–Y–Zn alloys [19–22] were not detected in the present study. 4. Discussion 4.1. Effects of co-segregation of Gd and Zn atoms on hardness

Fig. 10. (a) 3DAP maps showing distribution of Gd and Zn atoms in three c00 precipitate plates formed in samples aged for 8 h at 250 °C; (b) composition profile of the three c00 precipitates in (a).

this disordered hexagonal structure is shown in Fig. 13. It contained three atoms, with an atomic composition of MgGdZn. The positions of these three atoms in the unit cell are (0, 0, 0) for Mg, (2/3, 1/3, 1/3) for Gd and Zn (50% occupancy each) and (1/3, 2/3, 2/3) for Gd and Zn (50% occupancy each). The space group for this structure was P  3m1. The orientation relationship was such that 1 10]c0 // [2 1 10]a, and the habit (0 0 0 1)c0 // (0 0 0 1)a and [2 plane was parallel to (0 0 0 1)c0 // (0 0 0 1)a. Fig. 14 shows a 3D reconstruction of a volume obtained from an over-aged sample (120 h at 250 °C). There were two precipitates in this volume and they were taken as the c0 plates on the basis of the ageing time. These two c0 plates contained both Gd and Zn elements, and the Gd:Zn atomic ratio was again approximately 1:1. The measured concentrations of Gd and Zn in these two particles were each approximately 12 at.%. It was noted that these measured concentrations of Gd and Zn were lower than the stoichiometry indicated by the unit cell, i.e. approximately 33 at.% each for Gd and Zn. Since Gd and Zn atoms were distributed in two neighbouring atomic planes and the

The addition of 0.4 at.% Zn to the Mg–1at.% Gd alloy leads to a remarkable increase in hardness even in the asquenched condition [11]. Since the solid solution strengthening effect from the 0.4 at.% Zn alone is expected to be negligible [34,35], it is natural to speculate whether the hardness increase is associated with solute clusters that might have formed in the as-quenched samples. Careful examination of the as-quenched specimens using 3DAP indicates, however, that they do not contain any clusters of Gd and/or Zn atoms. Clusters of solute atoms are not detected even in samples aged isothermally at 250 and 200 °C. Therefore, the large increase in hardness in the as-quenched condition is not associated with any hardening effects arising from solute clusters. The statistic analysis of the 3DAP data suggests, however, that co-segregation of Gd and Zn atoms has occurred in the supersaturated solid solution of magnesium in the asquenched condition. With a progress in ageing time at 200 and 250 °C and concomitant precipitation of c00 and c0 , the co-segregation phenomenon becomes less easy to detect. The co-segregation phenomenon of Gd and Zn atoms is, at least phenomenologically, attributable to the atomic size difference between the solute and the solvent. The atomic radius is 0.180 nm for Gd, 0.133 for Zn and 0.160 for Mg. According to the hard-sphere model, substituting an Mg atom by a Gd atom leads to a large positive misfit (0.125) and a compression strain, while replacing an Mg atom by a Zn atom causes a slightly larger but negative misfit (0.169) and therefore an extension strain. It is therefore conceivable that Gd and Zn atoms in the solid solution tend to segregate to each other in order to

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 a and (b) an enlarged image of precipitate 1 in (a) after Fig. 11. Fourier-filtered HAADF-STEM images showing (a) three c0 precipitates viewed in h1120i 90° anti-clockwise rotation. (c) Two c0 precipitates viewed in a h1010ia direction. The precipitate–matrix interface is indicated by white lines in (b) and (c). Note that the precipitates marked 1 and 3 in (a) are two different variants of c0 . The sample was aged for 2 h at 250 °C.

Fig. 13. Schematic diagrams showing (a) a unit cell of c0 phase and (b) a perspective view of the structure along the [0 0 0 1] direction.

Fig. 12. (a) h11 20ia, (b) h1010ia and (c) h0 0 0 1ia SAED patterns recorded from a-Mg matrix regions containing c0 precipitates in samples aged for 1000 h at 250 °C.

minimize the elastic strain associated with individual atoms of Gd or Zn. Since clusters (typically containing more than a dozen solute atoms) of Gd and Zn atoms are not detected, it is reasonable to assume that the Gd and Zn atoms have formed into dimers in the solid solution phase of magnesium in the as-quenched condition.

If the notion of Gd–Zn dimers is accepted as being plausible, then the Gd–Zn dimers may act as a more effective barrier than those from individual atoms of Gd or Zn to the motion of gliding dislocations, and therefore could contribute to the large hardness increase in the as-quenched condition compared to that of the as-quenched Mg–Gd binary alloy. Deformation of magnesium alloys at room temperature occurs predominantly by basal slip propagation of lattice dislocations (b = 1/3h2110ia) on (0 0 0 1)a [36,37]. Fig. 16 shows an edge dislocation gliding on (0 0 0 1)a. This schematic diagram also applies to the edge component of a dislocation if it has both edge and screw characters. The line direction of this dislocation is parallel

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Fig. 15. Transmission electron micrographs showing precipitates in samples aged for 1000 h at 250 °C. The electron beam was parallel to h1120ia in (a) and (b).

Fig. 14. (a) 3DAP maps showing the distribution of Gd and Zn atoms in c0 precipitate plates in samples aged for 120 h at 250 °C. (b) Composition profile of the two c0 precipitates in (a).

to the viewing direction, [0 110]a. As shown in this diagram, if there is a segregation of solute atoms larger in radius (Gd) than Mg to the extension region of the dislocation core and a concomitant partition of smaller solute atoms (Zn) to the compression region of the dislocation core, then the extension and compression strains associated with the dislocation core, and the compression strain associated with the Gd atoms and the extension strain associated with Zn atoms, may all be reduced. This event might occur when a dislocation run into a single, or pair of, Gd–Zn dimer(s). The minimization of elastic strains of both gliding dislocations and solute atoms provides a stronger pinning effect on the gliding dislocation than that expected for a single addition (either Gd or Zn) of solute atoms.

Fig. 16. Schematic diagram showing segregation of Gd and Zn atoms to the extension and compression regions, respectively, near the core of an edge dislocation in a-Mg. For clarity, only one layer of atoms is shown and the atoms above and below this layer are omitted.

The mechanism of dislocation pinning by dimers comprising a larger and a smaller solute atom can also explain

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the enhanced creep resistance of Mg–Gd and Mg–Y alloys containing controlled additions of Zn [11,17,18]. The dislocation creep is often the dominant creep deformation mechanism in these alloys [18], in which dislocation climb and/or viscous dislocation glide is responsible for the plastic deformation. It has been reported that the steady-state creep strain rate of Mg–Y solid solution alloys is increased by an order of magnitude when they are microalloyed with Zn [18]. Note that Y has an atomic size (radius 0.181 nm) similar to that of Gd, and the addition of Zn to an Mg– Y alloy may lead to the formation of Y–Zn dimers that may contribute to the enhanced creep resistance of the alloy. It would be interesting to examine whether dislocations in crept samples of these alloys are associated with such dimers, or Cottrell atmosphere [38]. 4.2. c00 precipitates It has been demonstrated in the present study that most precipitate plates in the peak-aged microstructures are a metastable phase designated c00 . The c00 phase has an ordered hexagonal structure, with a = 0.556 nm and c = 0.444 nm. The unit cell shown in Fig. 7(a) indicates that the space group is P  62m. This structure is similar to that reported recently in a rapidly solidified Mg97Ce2Zn alloy [39]. The experimental evidence obtained in the present study is insufficient to conclude whether the arrangement of Zn atoms in the middle layer of the unit cell is also ordered. Nevertheless, if the atomic ratio of Mg and Zn in this layer is identical to that of Gd and Mg in the layers above and below, then the Mg:Gd:Zn atomic ratio in the unit cell is 4:1:1, i.e. Mg4GdZn. This atomic ratio means that the stoichiometric concentration of Gd and Zn in the c00 phase is approximately 16.6 at.% each. The measured concentrations of Gd and Zn in c00 plates (15 at.% each) are in excellent agreement with the model outlined in Fig. 7(a). The c00 phase forms as (0 0 0 1)a plates, and its thickness is often of a single unit cell height. While this phase is coherent with the matrix in its habit plane, a relatively large misfit (0.16) is observed in the direction normal to the habit plane. A large volumetric strain is therefore associated with the formation of c00 phase. While the number density of the c00 phase in the peak-aged microstructure is not low, one would expect an even higher nucleation rate of the c00 phase if the volumetric strain could be minimized by expanding the unit cell dimension along the [0 0 0 1]c0 direction. An increased number density of precipitates is technologically important as it can lead to an enhanced hardening response and therefore a higher strength [40]. It has been reported in a recent study [41] that additions of Ag to the Mg–1Gd–0.4Zn alloy lead to a further increase in the age hardening response and that this enhanced hardening response is associated with an increased number density of (0 0 0 1)a precipitate plates. Since the precipitates formed in the Ag-containing alloy are structurally similar to the c00 plates in the Ag-free alloy

[41], and since Ag has larger atomic size than Zn (the atomic radius is 0.145 nm for Ag), it would be interesting to investigate whether the misfit between the precipitates and the matrix is reduced by segregation of Ag atoms into the precipitates. A partial replacement of Zn atoms by Ag might increase the c-axis of the c00 phase and therefore reduce the misfit along this direction. 4.3. c0 Precipitates The c00 phase is gradually replaced by c0 during prolonged ageing at 250 °C. The structure of the c0 phase is distinguishably different from that of c00 . In contrast to the ABAB stacking sequence of the c00 phase, the closely packed planes of the c0 phase has an ABCABC stacking order. While it is difficult in the present study to establish the precise structure of the c0 phase, the accumulated experimental observations indicate that it may have a disordered hexagonal structure (a = 0.321 nm, c = 0.781 nm). Similar to the c00 phase, the c0 precipitates also form as plates of a single unit cell height on (0 0 0 1)a. However, their aspect ratio is considerably larger than that of c00 . The c0 plates are perfectly coherent with the matrix phase, not only in their habit plane but also in the direction normal to their habit plane. If the proposed structure of the c0 phase is correct, then it is structurally similar to an fcc lattice. The formation of a c0 precipitate inside an a-Mg grain is therefore similar to that associated with hcp/fcc transformations [42–45]. As shown in Fig. 17(a), a single unit cell of c0 can be generated by the nucleation and gliding of a Shockley partial dislocation (b = 1/3h1010ia) on the second (0 0 0 1)a plane above the designated A plane. If such Shockley partial dislocations form and glide on every second (0 0 0 1)a, then the stacking sequence of the closely packed planes is changed from ABABAB (hcp) to ABCABC (fcc). The existence of a mirror plane in the a-Mg lattice normal to the [0 0 0 1]a direction allows two variants of c0 phase to be generated via such a mechanism (Fig. 17(a–c)). These two variants are twin related and have opposite shear. The formation of a c0 precipitate of a single unit cell height, therefore, generates a shape change and this shape change imposes a shear strain of about 0.35 to the surrounding matrix phase. If this precipitate plate is fully constrained by the a-Mg matrix, then the elastic strain energy per unit volume of the precipitate, Ee, can be estimated by the equation developed for an invariant plane strain transformation [46,47]: Ee ¼ E s þ Ev ¼

pGð2  mÞ 2 pG es þ e2 8Að1  mÞ 4Að1  mÞ v

ð2Þ

where Es is the shear strain energy, Ev is the volumetric strain energy, G is the shear modulus of the matrix and the precipitate plate, v is Poisson’s ratio, ev is the volumetric strain, es is the shear strain, and A is the aspect ratio of the precipitate plate (defined as the ratio of plate diameter and plate thickness). Since the misfit between c0 and a-Mg

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Fig. 17. Schematic diagrams showing the structural change from a-Mg to c0 . The structure of c0 can be generated by the passage of a Shockley partial dislocation (\) on the second plane (a) above or (b) below an (0 0 0 1)a plane that is designated A. The thickness of c0 is indicated by a pair of horizontal lines in each diagram. The shape change is illustrated by the shape of blocks. The shape change in (a) and (b) are in opposite directions and are twin related (c). The dashed line in (c) illustrates local and overall shape change. Inside a single magnesium grain, the structural change from a-Mg to c0 can also occur by the passage of a Shockley partial on the second plane above (d) or below (e) an (0 0 0 1)a plane that is designated B. Note that the shape changes in (d) and (e), (a) and (d) or (b) and (e) are in opposite directions and are again twin related. (f) Two twin related c0 variants separated by three atomic layers.

is close to zero within the habit plane and in the direction normal to the habit plane, the volumetric strain associated with the formation of a single c0 plate is approximately zero. Therefore, the total strain energy is dictated almost exclusively by the shear strain energy. As indicated by Eq. (2), the shear strain energy is inversely dependent on the plate aspect ratio: the larger the plate aspect ratio,

the smaller the shear strain energy. Therefore, the large shear strain energy associated with the formation of a plate can be elastically accommodated to the maximum level if the precipitate plate adopts a substantially large aspect ratio – with the thickness corresponding to a single unit cell height and the length reaching the size of a-Mg grains. This is perhaps why the c0 plates remain very thin and long even

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after long-term ageing at 250 °C. Also note that the large shear strain involved in the formation of c0 precipitates can also impose a large barrier to the nucleation of a growth ledge or a transformation disconnection [48,49] on the otherwise planar c00 /a-Mg interface. If the growth ledges or transformation disconnections are energetically difficult to nucleate on the broad surface of a c0 plate, then the thickening rate of the plate is expected to be considerably low. It is noteworthy that the ABCA stacking of the closely packed planes of c0 is structurally equivalent to an hcp lattice containing an appropriate stacking fault. Stacking faults in magnesium and its alloys include intrinsic faults ISF1 and ISF2 and extrinsic fault ESF [50]. An ISF2 fault can be generated directly by the passage of a Shockley partial dislocation on (0 0 0 1)a or by directly shearing the hexagonal lattice by a displacement of 1/3h10 10ia. The passage of the Shockley partial, or the shearing, changes the stacking sequence of closely packed planes from: ABABABAB to ABABCACA (ISF2), or from BABABABA to BABACBCB (ISF2). The ISF1 fault is produced by removing the B (or A) plane (usually via the condensation of aggregates of vacancies) above an A (or B) plane and then shearing the remaining planes above the A (or B) plane by a displacement of 1/ 3h10 10ia. In this case, the stacking order of the closely packed planes is changed from: ABABABAB to ABABACAC (ISF1), or from ABABABAB to ABABCBCB (ISF1). In contrast to an ISF2 fault that is bound by a pair of Shockley partial dislocations, a single ISF1 fault is bound by a pair of Frank partials (b = 1/6h20 23ia). The extrinsic fault ESF can be generated by inserting a C plane into the ABAB stacking sequence. The stacking of the closely packed planes is then changed from: ABABABAB to ABABCABAB (ESF), or from ABABABAB to ABABACBAB (ESF). Note that it is the ISF2 fault, rather than ISF1, that yields the ABCA stacking that is characteristic of the c0 structure. While the ESF fault can also generate the ABCA stacking, the packing order of closely packed planes outside the ABCA segment is distinguishably different from that associated with the ISF2 fault. If the ABCA segment is taken as a precipitate plate, then the closely packed planes of the magnesium lattice at both sides of the plate are symmetrically arranged for the ESF fault, and asymmetrically stacked for the ISF2 fault. Yamasaki et al. [19] reported that precipitation in an Mg–2Gd–1Zn alloy involves the formation of two types of intrinsic stacking faults, in addition to the 14H, b’, b1 and b phases, when this alloy is aged isothermally in the temperature range 200–500 °C (Table 1). These faults have respectively the form of:

ABABCACA, and ABABACBCB. Note that these two types of faults are both ISF2 (the ABABACBCB fault is not an ISF1 fault because it contains an extra A plane). In fact, these two types of faults correspond to those illustrated in Fig. 17(a) and (e), respectively, and are the same variant of the c0 phase. Fig. 5 in the paper published by Yamasaki et al. [19] also shows an intrinsic fault CACACBABA that is identical to the one shown in Fig. 17(d) and precipitate 3 in Fig. 11(a). This fault generates a shear that is opposite to that from the fault ABABCACA, and the combination of this fault with the ABABCACA fault leads to whole self-accommodation of the shear strain. This may explain why the c0 plates often form in pairs or clusters (Figs. 3(d), 8(d) and 15(a)). Given that these faults form long after the formation of the metastable c00 phase, instead of in the as-quenched condition or during the early stages of ageing, it is more appropriate to name them a precipitate phase (c0 ), particularly in the context of precipitate reaction. It is equally noteworthy that the faults observed in the Mg–Gd–Zn alloys appear to be different from those formed in Mg–Y–Zn alloys. The planar features formed on basal planes in the Mg–Y–Zn alloys are commonly accepted as stacking faults and are bound by Frank partials, i.e. 1/ 6h2023ia. The association of Frank partials with such planar features implies that they are ISF1 rather than ISF2 faults, if they are indeed stacking faults. While it is unquestionable that such planar features have a 1/3h1010ia displacement vector, i.e. the Burgers vector of Shockley partials, it remains to be unambiguously established whether they also have a 1/ 2[0 0 0 1]a displacement vector, and whether the stacking sequence of closely packed planes is consistent with the ISF1 faults. Note that the experimental evidence in literature indicates that the equilibrium solid solubility of Y is considerably reduced when Zn is added to the Mg–Y alloys and, therefore, precipitates may form even in dilute Mg–Y–Zn alloys heat treated at elevated temperatures. It is currently unclear whether the planar features in Mg–Y–Zn alloys are stacking faults or precipitate plates whose formation generates a shear with a displacement of 1/3h1010ia. If they were the latter, then the faults would be ISF2 and identical to those observed in the Mg–Gd–Zn alloys. While the precise structure of the c0 phase and that of the 14H phase remain to be established, it is perhaps interesting to note that the reported stacking sequence of closely packed planes of the 14H phase [12,16,19], ABABABACBCBCBCA, can be obtained if two twin related variants of c0 are separated by three closely packed planes. For example, if we combine the two twin related variants in

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Fig. 17(d) and (e) and allow them to be separated by three atomic planes, then the following stacking sequence is obtained, Fig. 17(f): BCBCABABABACBCB. This stacking order is identical to: ABABABACBCBCBCA, except the latter does not reflect the mirror plane in the stacking. This unique arrangement of the c0 variants not only leads to complete self-accommodation of the shear strain on a macroscopic scale, but also provides a structural environment for the in situ transformation to the 14H phase. Even though the c0 phase is metastable, it is remarkably thermally stable during isothermal ageing at 250 °C. This phase is still less than 1 nm thick and is the dominant precipitate phase in the microstructure after isothermal ageing for 1000 h at 250 °C. While some particles of the equilibrium intermetallic phase b, Mg5(Gd,Zn), start to form after this prolonged ageing (Fig. 15), the c phase (14H) that is commonly reported to exist in alloys of similar systems, i.e. Mg–Gd–Zn [19,20], Mg–Gd–Y–Zn [21,22] and Mg– Y–Zn [12,16], is not detected. Furthermore, the metastable phases, such as b”, b’ and b1, are not observed either. While the alloy used in the present study has lower contents of Gd and Zn than Mg–2Gd–1Zn and Mg–2.5Gd–1Zn alloys [19,20], the Gd:Zn atomic ratio is similar to those in the latter two alloys. It is currently difficult to rationalize the observations in different alloys due to a lack of isotherm sections of the ternary Mg–Gd–Zn phase diagram. Nevertheless, one plausible explanation is that the 200– 250 °C ageing temperature range is above the solvus lines of b”, b’ and b1 for the Mg–1Gd–0.4Zn composition but below the solvus lines of these metastable phases for the Mg–2Gd–1Zn alloy. 5. Conclusions 1. The statistic analysis of the 3DAP data obtained from the as-quenched samples of an Mg–1Gd–0.4Zn–0.2Zr (at.%) alloy indicates that co-segregation of Gd and Zn atoms has occurred in the as-quenched condition. This co-segregation in the form of Gd–Zn dimers can provide more effective pinning of gliding dislocations, and therefore contributes to the large hardness increase in the as-quenched samples compared to that of the Mg– 1Gd binary alloy. 2. Precipitation during isothermal ageing at 250 °C involves formation of metastable phases c00 and c0 . The key strengthening precipitate phase in samples peakaged at 250 °C is c00 . The c00 phase is gradually replaced by c0 precipitates during prolong ageing at 250 °C. For ageing treatments up to 1000 h at 250 °C, precipitates of the c phase (14H – commonly inferred to be an equilibrium precipitate phase) are not detected.

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3. The c00 phase has an ordered hexagonal structure (space group P 62m, a = 0.560 nm, c = 0.444 nm) and a composition of approximately 70 at.% Mg, 15 at.% Gd and 15 at.% Zn. The c00 phase forms as (0 0 0 1)a plates, with a thickness of a single unit cell height and an aspect ratio typically of 60:1. The orientation relationship between c00 and a-Mg phases is such that (0 0 0 1)c00 // (0 0 0 1)a and [1010]c00 // [2110]a. 4. The c0 phase has a disordered hexagonal structure (space group P 3m1, a = 0.321 nm, c = 0.781 nm). The closely packed planes in this structure have an ABCABC stacking sequence, with Gd and Zn atoms distributed in the B and C planes. The orientation relationship is 1 10]a. such that (0 0 0 1)c0 // (0 0 0 1)a and [2110]c0 // [2 0 The c phase forms as (0 0 0 1)a plates, with a thickness of a single unit cell height and an extraordinarily large aspect ratio. It remains less than 1 nm thick even after 1000 h at 250 °C. 5. A single unit cell of c0 can be generated by the propagation of a Shockley partial dislocation (b = 1/3h10 10ia) on the second (0 0 0 1)a plane. This formation mechanism of the c0 phase leads to a large shear strain, together with a negligible volumetric strain, in the a-Mg matrix surrounding individual c0 plates. The formation of two twin related variant (with opposite shear) c0 plates in the microstructure is a signature of shear strain selfaccommodation.

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