Correlative atom probe tomography and scanning transmission electron microscopy reveal growth sequence of LPSO phase in Mg alloy containing Al and Gd

Atom probe tomography (APT) and transmission electron microscopy (TEM)/scanning transmission electron microscopy (STEM) have been used correlatively to explore atomic-scale local structure and chemistry of the exactly same area in the vicinity of growth front of a long-period stacking ordered (LPSO) phase in a ternary Mg–Al–Gd alloy. It is proved for the first time that enrichment of Gd atoms in four consecutive (0001) atomic layers precedes enrichment of Al atoms so that the formation of Al6Gd8 clusters occurs only after sufficient Al atoms to form Al6Gd8 clusters diffuse into the relevant portions. Lateral growth of the LPSO phase is found to occur by ‘ledge’ mechanism with the growth habit plane either {1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{1}$$\end{document}1¯00} or {11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{2}$$\end{document}2¯0} planes. The motion of ledges that give rise to lateral growth of the LPSO phase is considered to be controlled by diffusion of Al atoms.

www.nature.com/scientificreports/ The existence of the in-plane ordering of M and RE atoms in the four consecutive atomic layers together with pure Mg atomic layers indicates that the LPSO phase should be described with the concept of the order-disorder (OD) structure but not as a 'LPSO' phase in a strictly sense in crystallography [7][8][9][10][11] . Hereafter, the Mg-M-RE LPSO phases are designated as 'LPSO/OD' phases. LPSO/OD phases in Mg-M-RE alloys play a crucial role in providing high strength and good ductility to the low weight Mg-M-RE alloys. Therefore, the crystal structures and the deformation behaviors of these LPSO/OD phases have been the subjects of intensive studies in the last decade [4][5][6][7][8][9][10][11][12][13][14][15][16] . When compared with the extent of understanding for their crystal structures and the deformation behaviors, however, the formation process of these LPSO/OD phases have received less attention in spite of its technological importance, except for some works by scanning transmission electron microscopy (STEM) 9,17 and by synchrotron X-ray diffraction 18,19 . We believe that more in-depth study with better three-dimensional (3D) spatial resolution for structure and chemistry is needed for better understanding the formation process of these LPSO/OD phases, such as how chemical modulation synchronizes with structural modulation. STEM with angstrom spatial resolution, in particular Z(atomic number)-contrast imaging by high-angle annular dark-field (HAADF)-STEM has been provided various structural and chemical information of LPSO/ OD phases on an atomic scale such as stacking sequences, enrichment of M/RE atoms and their in-plane ordering to form M 6 RE 8 clusters [4][5][6][7][8][9][10][11] . However, this technique has its own limitation arising from the fact that the obtained atomic-resolution image is just a two-dimensional projection along a particular crystallographic direction so that 3D information lacks inevitably unless additional imaging along other directions is made. This means that even with Z-contrast imaging, chemical information obtained on atomic scale is only that averaged over each atomic column along the projection. On top of that, since the intensity of each atomic column is proportional to the square of Z averaged over atoms in the respective atomic column, differentiating atoms with close atomic numbers is usually very difficult to be made. Differentiating Mg (Z = 12) and Al (Z = 13) in Mg-Al-Gd ternary alloys is one of the typical cases. Atom probe tomography (APT), by which 3D elemental map can be reconstructed at (sub-) nanometer spatial resolution for a needle specimen [20][21][22] , is a unique method that possesses high analytical sensitivity independent of atomic number and high mass-resolving capability that can distinguish even isotopes. This means that APT can provide elemental information that is difficult to obtain simply by atomic-resolution Z-contrast STEM imaging. However, since the spatial resolution in APT analysis is material-dependent and is sometimes insufficient to capture crystallographic information on crystal and defect structures as TEM/STEM imaging can do. In view of the fact that the capabilities of TEM/STEM and APT analyses are complementary, their correlated application to the exactly same area of analysis with the use of an identical specimen can provide complete information on local structure and chemistry on an atomic scale 23,24 .
In the present study, we investigate variations of atomic structures and elemental distributions on an atomic scale occurring at the interface region between the LPSO/OD and Mg phases in a Mg-Al-Gd alloy by correlative atom prove tomography and TEM/STEM made in the exactly same regions, in order to better understand how chemical modulation synchronizes with structural modulation in the growth sequence of the 'synchronized' LPSO phase in Mg with better 3D spatial resolution.

Results
Correlated TEM and APT observations. An interference-fringe TEM image formed with reflections of the [000l] systematic row and APT maps for Al and Gd in a 15-nm-thick slice selected from the whole maps obtained from an identical needle specimen of the LPSO/OD phase in the Mg-Al-Gd systems are shown in Fig. 1a-c, respectively. The vertical direction in Fig. 1 corresponds to the needle axis that is parallel to the [0001] direction of the LPSO/OD phase. The fringe spacing in the TEM image of Fig. 1a corresponds to a thickness of each of block layers consisting of Gd/Al-enriched atomic layers and Mg atomic layers. The fringe contrast occurs regularly at the interval of about 1.6 nm in most areas, conforming the occurrence of the polytype of the 18R-type that consists of Gd/Al-enriched four consecutive atomic layers and two Mg atomic layers. However, some irregularities are noted here and there, indicating the occurrence of other polytypes; those of the 14H-and 10H-types, in which three and one Mg atomic layers respectively constitute their block layers together with Gd/Al-enriched four consecutive atomic layers, are found at positions #1-4 and #6-9 and at a position #5, respectively, in Fig. 1a. Atomic layers enriched with Al and Gd are observed in the APT maps of Fig. 1b,c with some irregularities in their intervals. Surprisingly, the irregularities observed for the occurrence of atomic layers enriched with Al and Gd in the APT maps of Fig. 1b,c completely coincide with those observed for the fringe contrast in the TEM image of Fig. 1a. This clearly indicates that the irregularities for the occurrence of polytypes can be used as a marker to successfully make correlated TEM and APT analyses of the LPSO/OD phase in the Mg-Al-Gd system. www.nature.com/scientificreports/ spots with a so-called double-dagger pattern is observed in the region of the 18R-type LPSO/OD phase due to high degree of in-plane ordering of Al 6 Gd 8 clusters with L1 2 -type atomic arrangement on the lattice points of a 2 √ 3a Mg × 2 √ 3a Mg two-dimensional primitive hexagonal lattice in each structural block of the 18R-type LPSO/ OD phase, as reported by Yokobayashi et al. 7 , where a Mg refers to the magnitude of the a-axis of the hexagonal unit cell of Mg. The bright double-dagger markings of Al 6 Gd 8 clusters in the LPSO/OD phase in the bottom half of the figure are observed to align regularly in their basal planes due to the in-plane ordering, forming bright marking rows parallel to (0001) and these bright rows appear regularly at the interval of the c-axis dimension of the structural block of the 18R type polytype. To be noted in the HAADF-STEM image of Fig. 2b, the occurrence of a faintly bright line parallel to (0001) planes at a distance of the c-axis dimension of the structural block of the 18R type from the top bright marking row of the LPSO/OD phase, as indicated by an arrow. In the highresolution TEM image of Fig. 2a, the atomic layers in the region where a faintly bright line parallel to (0001) planes is observed in the HAADF-STEM image are observed to exhibit the hcp-type stacking. These indicate that in the thickening process of the LPSO/OD phase in Mg, enrichment of Gd atoms occurs on (0001) planes without disturbing the hcp stacking of Mg in the close vicinity of the interface between the LPSO/OD and Mg phases. This is consistent with previous observations by Kishida et al. 9 .

Correlated atomic-resolution HAADF-STEM and APT observations.
In the APT maps of Fig. 2c,d, the occurrence of enrichment of Al and Gd atoms on (0001) planes in a periodic manner is evident in the LPSO/OD phase in the bottom half of the figures. The occurrence of enrichment of Gd atoms on (0001) planes in the region where a faintly bright line parallel to (0001) planes is observed in the HAADF-STEM image is also evident from the correlative APT and STEM/TEM analysis. Of interest to notice is that in the region that exhibits a faintly bright line parallel to (0001), while Gd enrichment is clearly observed (Fig. 2c), Al enrichment is not as significant as Gd enrichment (Fig. 2d). Such information about Al distributions cannot be obtained by HAADF-STEM imaging because of the too close atomic numbers for Mg and Al atoms. This is further evidenced by the number density profiles of Al and Gd of Fig. 2e formed from the atom maps of Fig. 2c,d. In the LPSO/OD phase, the number density ratio of Al and Gd atoms in the (0001) row of Al 6 Gd 8 clusters that exhibit bright double-dagger markings in the HAADF-STEM image is 1.39 ± 0.04 when averaged over 20 (0001) rows, which is a bit larger than that (1.33) expected from the formation of Al 6 Gd 8 clusters. But, in the region that exhibits a faintly bright line parallel to (0001), not only the number density of Gd atoms but  Gd-enriched atomic layers in the transition region at the interface are observed to change in the HAADF-STEM contrast from a row of double-dagger patterns (right-hand side) to a slightly bright line (left-hand side) (Fig. 3a). In these (0001) Gd-enriched atomic layers in the transition region, while Gd enrichment is observed to extend across the areas where the HAADF-STEM contrast changes, Al enrichment is observed to be limited only in the layers where a row of double-dagger patterns is observed. This again confirms that the formation of Al 6 Gd 8 clusters occurs only after Al atoms sufficient to form Al 6 Gd 8 clusters reach to the relevant portions.
Cross-sectional views of the APT maps are formed from the maps of Fig. 3b,c at three different sections shown in the HAADF-STEM image in Fig. 4 (the identical to Fig. 3a). Figure 4a,b are Mg, Al and Gd maps at the sections containing the transition regions with Gd-enriched layers, while Fig. 4c corresponds to Mg, Al and Gd maps at the Mg phase. Crystallographic directions on (0001) are determined from the pole pattern of the six-fold symmetry consisting of central < 0001 > pole and < 1120 > zone lines, as indicated in Fig. 4c 25 . In Fig. 4a,b, the LPSO/OD phase regions are observed in the right-hand side as is evident from the higher and lower number densities of Al and Mg atoms, respectively. In the two sections of the transition region of Fig. 4a,b, the LPSO/ OD phase region seems to have habit planes parallel to either {1100} or {112 0} planes. This is consistent with the result from electron tomography experiment that lateral growth of the LPSO/OD phase in the Mg-Zn-Gd system occurs with habit planes parallel to either {1100} or {112 0} planes with some preference of {1120} 26 . More work is definitely needed to unambiguously determine the growth habit plane (either {1100} or {112 0} planes) for the LPSO/OD phase in the Mg-Al-Gd system.

Discussion
We now discuss the growth sequence of the LPSO/OD phase in the Mg-Al-Gd alloy. The growth sequence seems to be consistent basically with that Kishida et al. 9 proposed previously. They pointed out that (1) enrichment of Gd and Al atoms in four consecutive (0001) atomic layers keeping the hcp stacking, followed by (2) the formation of Al 6 Gd 8 clusters with the L1 2 -type atomic arrangement in the four consecutive atomic layers introducing a stacking fault (fcc-type stacking) in the middle of the four consecutive atomic layers. In the present study, however, enrichment of Gd atoms in four consecutive (0001) atomic layers is observed to precede enrichment of Al atoms so that the formation of Al 6 Gd 8 clusters occurs only after Al atoms sufficient to form Al 6 Gd 8 clusters reach to  (1) is not wrong but that more strictly speaking, there is a sequential order for enrichment of Gd and Al atoms in the four consecutive (0001) atomic layers. This could be experimentally proved because of the capability of APT analysis to easily differentiate Al and Mg atoms. Although there is a sequential time lag for enrichment of Gd and Al atoms in the consecutive (0001) atomic layers, the introduction of stacking faults occurs only when Al 6 Gd 8 clusters are formed after enrichment of Gd and Al atoms of full amounts completes in the relevant atomic layers. This means that chemical modulation (enrichment of Gd atoms) seems proceed by enrichment of Gd atoms without the disturbance of the stacking sequence, chemical modulation synchronizes with structural modulation by the stacking fault introduction due to Al enrichment to form Al 6 Gd 8 clusters. Because the atomic radius of Gd (0.180 nm) is larger than that (0.150 nm) of Mg, the lattice misfit between the hcp Mg matrix and the four consecutive Gd enriched atomic layers is expected to arise, which should make the isolated occurrence of the layered enrichment of Gd unfavorable from the viewpoint of elastic strain energy. Therefore, the preceding layered enrichment of Gd preferentially at the growth front of the Mg-Al-Gd LPSO/OD phase as observed in the present alloy 9 is considered to be assisted mainly by the chemical interactions between Gd atoms and the pre-existing plates of the Mg-Al-Gd LPSO/OD phase. Kishida et al. 9 proposed that the above processes (1) and (2) are followed by (3) the thickening by enrichment of Gd and Al atoms at a distance of two or three close-packed Mg atomic layers high from the pre-existing four consecutive layers so as to form another structural block. In the present study, this is confirmed to occur by 'ledge' mechanism with the growth habit plane either {1100} or {112 0} planes. It has been revealed that a local concentration gradient of solute atoms, which is sufficient for the lateral growth of the precipitation phase by the 'ledge' mechanism, is developed in the vicinity of the ledge by diffusion 27 . In the case of the growth of the Mg-Al-Gd LPSO/OD phase, both Gd and Al atoms should diffuse into the growth front region. In view of the fact that Al 6 Gd 8 clusters are not formed until a sufficient amount of Al atoms diffuses into the relevant position, the motion of ledges that give rise to the lateral growth of the LPSO/OD phase in Mg is considered to be controlled by diffusion of Al atoms. This should be reasonable because the concentration of Al in hcp Mg adjacent to the Mg-Al-Gd LPSO/OD phase is considerably lower than that of Gd as shown in Fig. 2e, even though the diffusion coefficient of Gd in Mg is about one order of magnitude lower than that of Al 28 .
They also proposed that (4) the in-plane ordering of Al 6 Gd 8 clusters occurs so that they occupy regularly the lattice points of the two-dimensional 2 √ 3a Mg × 2 √ 3a Mg primitive hexagonal lattice and the stacking of structural blocks (OD layers) changes to that energetically more favorable 9 . In the present study, the change in the HAADF-STEM contrast from a row of double-dagger patterns to a slightly bright line is proved to correlate well with the sudden change in enrichment of Al atoms (Fig. 3). This clearly indicates that once Al 6 Gd 8 clusters are formed in the transition region, they tend to form in an ordered manner so that the in-plane ordering completes from the beginning. In the beginning of precipitation, however, while growth occurs keeping the in-plane ordering of Al 6 Gd 8 clusters in each of structural blocks, the stacking of structural blocks is not yet that www.nature.com/scientificreports/ energetically favourable (as is evident from irregularities in the position of double dagger markings of Al 6 Gd 8 clusters in structural blocks in the HAADF-STEM image of Fig. 3a). Precisely speaking, the change in the stacking of structural blocks occurs towards that energetically more favorable after the in-plane ordering of Al 6 Gd 8 clusters in each of structural blocks in the statement of (4).

Conclusions
The growth sequence of the LPSO/OD phase in a Mg-Al-Gd alloy have been investigated by correlative atom probe tomography and scanning transmission electron microscopy. The results obtained are summarized as follows.
1. Enrichment of Gd atoms in four consecutive (0001) atomic layers precedes enrichment of Al atoms so that the formation of Al 6 Gd 8 clusters occurs only after sufficient Al atoms to form Al 6 Gd 8 clusters diffuse into the relevant positions. 2. Lateral growth of the LPSO/OD phase occurs by 'ledge' mechanism with the growth habit plane parallel to either {1100} or {112 0} planes. Since Al 6 Gd 8 clusters are confirmed not to form until a sufficient amount of