Lattice Correspondence and Growth Structures of Monoclinic Mg 4 Zn 7 Phase Growing on an Icosahedral Quasicrystal

: Mg 4 Zn 7 phase, with a monoclinic unit cell, a layered structure and a unique axis showing pseudo-tenfold symmetry, grows over icosahedral quasicrystalline phase in a manner similar to a decagonal quasicrystal. In this study, the relationship of this phase to icosahedral quasicrystal is brought out by a transmission electron microscopy study of Mg 4 Zn 7 phase growing on icosahedral phase in a cast Mg-Zn-Y alloy. Lattice correspondences between the two phases have been determined by electron diffraction. Planes related to icosahedral ﬁvefold and pseudo-twofold symmetry are identiﬁed. Possible orthogonal cells bounded by twofold symmetry-related planes have been determined. Mg 4 Zn 7 phase growing on an icosahedral phase exhibits a number of planar faults parallel to the monoclinic axis, presumably to accommodate the quasiperiodicity at the interface. Two faults were identiﬁed, which were on {200} and {201} planes. Their structures have been determined by high resolution imaging in TEM. They produce two different unit cells at the interface.


Introduction
The first report of an icosahedral quasicrystal phase exhibiting the fivefold symmetry forbidden in classical crystallography and a quasiperiodic translational order took the scientific community by surprise [1]. The reciprocal space of this crystal are densely filled with spots of various intensities, and are characterized by an icosahedral symmetry which has six fivefold symmetry axes, 10 threefold symmetry axes (through the twenty triangular faces) and 15 twofold symmetry axes. Soon after, a tenfold symmetry two-dimensional quasicrystal was also reported, called the decagonal phase [2,3]. The unique tenfold symmetry axis in such a lattice can be generated by reflection of a fivefold axis. The lattice is periodic along the tenfold symmetry axis. Growth of the decagonal phase over an icosahedral phase has often been reported, in which the tenfold axis of the decagonal quasicrystal grows along a fivefold axis of the icosahedral phase [4][5][6]. The structure of quasicrystals are described as tilings; Penrose tilings (in two-dimensions and generalized to three-dimensions) show fivefold and tenfold symmetry [7,8]. These tilings consist of two kinds of tiles, a thin rhombus (acute angle of 36 • ) and a thick rhombus (acute angle of 72 • ). There are crystalline phases with large unit cells and a complex structure close to quasicrystalline phases. Called rational approximant structure (RAS) or phases, they are crystalline, but show icosahedral motifs in the unit cells [9,10]. Although the reciprocal spots in their diffraction patterns are periodically arranged, their intensities bring out motifs characteristic of atom clusters of icosaehdral or related symmetry. There are a number of well . There are three pairs of differently oriented rhombic prisms required to make the structures (each type indicated by a different color in the figure, labelled 1-6). The members of each pair are distinguished by different shading intensities and differ in the z-coordinates of the Mg atoms and side-centered Zn atoms. Similarly, there is a pair of irregular hexagonal Zn-deficient sites (7)(8), members of each pair again distinguished by the atom z-coordinates.
Similar to the observations in aluminum alloys, a decagonal phase forming on icosahedral phase has also been reported in Mg-Zn-Y alloys [15]. Besides this, formation of Mg 4 Zn 7 on decagonal phase has also been reported in the same alloys, with orientation relationship [D10] [010] [15]. The same study also determined the composition of the decagonal phase to be about Mg 35 Zn 60 Y 4.4 , while the Mg 4 Zn 7 phase did not show any yttrium. In dilute Mg-Zn-Y/RE alloys, however, no decagonal phase is reported. The Mg 4 Zn 7 phase is often observed to grow directly over the icosahedral phase. Figure 2 shows an example of Mg 4 Zn 7 growing on an icosahedral phase in an extruded Mg-Zn-Ho alloy [29]. The Fast Fourier Transform (FFT) (inset in Figure 2a) shows the icosahedral phase to be in a twofold symmetry zone axis orientation. Fivefold (5f) and twofold (2f) reciprocal directions are marked. The FFT of Figure 2b shows that the Mg 4 Zn 7 phase grows with its c-axis along a fivefold axis. There appears to be a high density of planar faults along the c-axis, producing a continuous diffuse intensity on the a − c plane. Thus, there are similarities to the growth of decagonal phase growing over an icosahedral phase [4][5][6]. The interplanar spacing of the {020} Mg 4 Zn 7 (2.62 Å) is nearly coincident with the strongest spot {422222} along a fivefold axis (spacing 2.43 Å; Elser's indexing is followed here [30]).  [29]. The icosahedral phase is in twofold zone axis orientation, as shown by the Fast Fourier Transform (FFT) inset in (a). The FFT in (b) shows that the monoclinic phase is oriented with its c-axis along a fivefold direction of the icosahedral phase. Fivefold and twofold symmetry reciprocal directions are marked.
In this study, we have investigated the structural relationship of the Mg 4 Zn 7 to the icosahedral quasicrystalline phases by electron diffraction and determined the nature of lattice defects by high resolution transmission electron microscopy.

Experimental Procedure
A Mg-3at%Zn-0.5at%Y alloy was made from high purity elements in an electric furnace and studied by transmission electron microscopy (TEM). Samples for TEM were prepared by cutting thin slices of the cast ingot and then mechanical polishing followed by ion milling. TEM observations were made on a JEOL 2000FX-II microscope (Jeol, Tokyo, Japan) operating at 200 kV, a high resolution JEOL 4000EX microscope operating at 400 kV, and also an FEI Tecnai G2 F30 microscope (FEI, Hillsboro, OR, USA) operated at 300 kV.

Figure 3a
shows coexisting icosahedral and Mg 4 Zn 7 phases. Due to a strong contrast, the interface between them is not visible clearly. Figure 3b shows a diffraction pattern from [010] zone axis of the Mg 4 Zn 7 phase, which is parallel to a fivefold axis of the icosahedral phase. The composite diffraction patter is shown in Figure 3c  (d) in one region [010], zone axis diffraction patterns in two orientations were observed, shown in this composite diffraction pattern. Indices for one variant are written with brackets, while, for the other orientation, without brackets.
During the observation of this grain, a complex diffraction pattern shown in Figure 3d was recorded. This diffraction pattern is indexed as a superimposition of two Mg 4 Zn 7 diffraction patterns, both in [010] zone axis orientation. The a and c axes of these two orientations are marked 1 and 2. Indices of diffraction spots for one orientation are shown with brackets while for the other without brackets. It is observed that the coincident [010] axes of the two variants are in opposite directions (180 • rotation). The lattices are reflected across (403) 1 -(403) 2 plane. (206) diffraction spot of one is coincident with (12 0 1) of another. The OR of the second variant is shown on a stereogram as OR2 in Figure 4b. Both variants are nearly equivalent. It is also observed in this diffraction pattern that there are streaks along the a* reciprocal direction in both the variants and along [201]* direction in one, indicating planar faults perpendicular to these directions. These will be further elaborated later. The approximant phases have a periodic lattice, but with an icosahedral motif. Therefore, the diffraction patterns are periodic, but resemble those from a quasicrystal phase due to intensity modulation because of the motif. Intense diffraction spots of an approximant phase will correspond to the intense spots of a quasicrystal phase, which are along fivefold and twofold reciprocal vectors in an icosahedral phase. Table 1 lists the most intense diffraction peaks of the Mg 4 Zn 7 ; the intensity values are taken from powder diffraction data (JCPDF file 29-0878; [19]). Intensity values calculated from the crystal structure using program VESTA [31] are also given. The corresponding icosahedral vector is given in the last column. The planes with planar spacings of about 2.2 to 2.5Å correspond to the {422222} spot along fivefold and {442002} spot along twofold axes, being the most intense spots in the icosahedral reciprocal space.  [19], as well as calculated intensities using program VESTA [31], and their correspondence to icosahedral reciprocal vectors (5f, 3f and 2f denote fivefold, threefold and twofold icosahedral reciprocal vectors, respectively. 5f is highlighted in bold).

Peak Indices Planar Spacing (Å)
Intensity ( The correspondence of the major reciprocal vectors, as well as resemblance of the diffraction patterns was confirmed by tilting the sample in the goniometer to obtain prominent diffraction patterns. Figure 5 shows diffraction patterns from zone axes marked M to R on the stereogram of Figure 4a. Besides the pseudo-fivefold axis along [010], another fivefold related axis is at M. A composite diffraction pattern is shown in Figure 5a and the corresponding Mg 4 Zn 7 diffraction pattern in (b). In this pseudo-fivefold pattern, the icosahedral twofold vectors are mimicked by (206) Figure 5k shows a composite diffraction pattern from a 'diamond' zone axis (in which a fivefold reciprocal vector occurs perpendicular to a twofold) at R, in which pseudo-twofold vector (12 0 1) is perpendicular to pseudo-fivefold vector (115).

Figure 5.
Composite icosahedral phase-Mg 4 Zn 7 diffraction patterns and corresponding Mg 4 Zn 7 diffraction patterns from axes in the stereogram of Figure 4a marked (a,b) M, (c,d) N, (e,f) O, (g,h) P, (i,j) Q and (k) R. Fivefold (5f) and twofold (2f) symmetry reciprocal directions are marked in the icosahedral symmetry diffraction patterns.
As mentioned earlier, the structure of Mg 4 Zn 7 can be described as layers along the unique axis [010] [19]. There are two primary layers with pentagons (and triangular arrangements), shown in Figure 1b, identical to each other but rotated with respect to each other by 180 • . Intermediate layers contain zinc atoms at the centers of pentagons of primary layers on each side. Two inverted pentagons with zinc atoms on either side make an icosahedral unit. Zinc atoms on intermediate layers are connected to form "thick" rhombuses, with acute angle 72 • . In between two unit cells, hexagons can also be defined (purple color in Figure 1). These hexagons can be decomposed into a thick and two thin rhombic tiles (acute angle 36 • ). Figure 6a shows a lattice resolution interface between the icosahedral phase and the monoclinic phase, where 5 f [010] Mg 4 Zn 7 . FFT from the icosahedral phase (Figure 6d) shows that the arrangement of a ring of ten spots of large lattice spacings (marked with circles) is not very symmetrical. Planar defects mainly in two directions, marked by two lines, originate at the interface. The FFT pattern in Figure 6e shows streaking in direction [200] * and [201] * , indicating planar defects on the corresponding planes. A high density of such faults are imaged in Figure 6b, with a corresponding FFT in Figure 6f. Figure 6c shows another type of fault, one of them marked by an arrow, which appear to be low angle grain boundaries. Short streaks are produced by them in the FFT pattern (Figure 6g), which are roughly in the [202] * direction. Another example of icosahedral-monoclinic phases interface is shown in Figure 7. The icosahedral phase region does not show a very clear lattice structure; however, an FFT pattern from this area (inset) shows a definite fivefold pattern. A composite diffraction pattern is also shown. Both the FFT and the diffraction pattern show that, while the prominent spots (marked by circles in the diffration pattern) with lower planar spacings are arranged in perfect circles, the spots closest to the center are not (as also mentioned above with reference to Figure 6). The monoclinic phase lattice adjacent to the icosahedral phase is not aligned along the zone axis [010] perfectly. In one region, planes in one orientation are observed prominently, in another region a plane in another orientation. With correspondence to the diffraction pattern (and FFT patterns not shown here), these planes are marked (803) and (12 0 1) in the figure. However, lattice fringes in each of these two orientations are a result of several periodicities, such as (201), (401) and (602), which are roughly along (803). Thus, the quasicrystallinity enforces planar defects and small misorientations in the crystalline monoclinic lattice.

Discussion
It is well known that approximant phases to decagonal quasi-crystals can be orthorhombic or monoclinic and that their structure can generally be described as layered. In case of monoclinic approximants, the spacing along its unique axis corresponds to the periodicity of the decagonal phase along its decagonal axis, and the monoclinic angle is close to 72 • (∼ 2π 5 ). Al 3 Fe (Al 13 Fe 4 ) and Al 13 Co 4 are well known as examples of decagonal phase approximants in aluminium alloys [32][33][34]. In case of the Zn-Mg-RE decagonal phase, the periodicity along its decagonal axis is 0.255 nm [13][14][15], which is comparable to the lattice spacing along (020) of Mg 4 Zn 7 and (0002) of magnesium. MgZn 2 and Mg 4 Zn 7 have been reported to be two crystalline phases related to the decagonal phase, the latter of which can coexist with the decagonal phase [15].
In case of the dilute Mg-Zn-RE alloys containing icosahedral phase, the Mg 4 Zn 7 phase often forms over the icosahedral phase, instead of a decagonal phase. This could possibly be due to the chemistry, whereby no yttrium or RE elements is left in the solid solution of the magnesium matrix after the solidification of the icosahedral phase. This can cause nucleation of the Mg 4 Zn 7 phase instead of the decagonal phase. However, this can cause lattice incompatibility. A decagonal phase grows over an icosahedral phase with its tenfold quasiperiodic planes (each atomic layer possessing a fivefold symmetry) over a fivefold plane, and thus there is a complete compatibility or epitaxy. However, the Mg 4 Zn 7 phase (010) plane is periodic, even though it contains units compatible with fivefold symmetry. Thus, planar faults are introduced during its growth over the icosahedral phase. This will be analyzed in a later subsection. Since the Mg 4 Zn 7 phase grows directly over the icosahedral phase, we first analyze the structural relationship between these two phases.

Structural Relationship
To describe the structural relationship, orthogonal cells will be defined in the monoclinic structure. Approximant phases to the icosahedral quasicrystal have such unit cells, which are related to three mutually perpendicular twofold axes of icosahedral phase. Figure 9 shows a plot of plane normals to the icosahedral twofold symmetry-related planes parallel to the [010] axis (a pseudo-fivefold axis), superimposed on the monoclinic unit cell. Dashed lines indicate the rhomboidal units. A near-orthorhombic unit with major planes can be defined with each of these planes, with the help of stereogram in Figure 4a. Five sets of such planes are listed in Table 2. The actual angles between the near orthogonal planes are listed in Table 3. They range from 82.748 to 96.247 • .  It is observed in Figure 9 that the normal to the (12 0 1) plane is near-parallel to the a-axis and is directed from the center of one rhomboid to near the center of an adjacent rhomboid at ±0.5a Mg 4 Zn 7 . The remaining pseudo-twofold plane normals in the (010) plane do not connect centers of rhomboidal units. Since these rhomboidal units constitute the quasicrystalline motif present in the monoclinic structure, the variant containing this vector was selected as the most appropriate to define an orthogonal cell. Moreover, it is also observed from Table 3 that in the set of mutually near-orthogonal planes (115)-(12 0 1)-(023), all the angles of near-orthogonality are in the range 90.0066 to 92.585 • . Taking this set of near-orthogonal planes, shown schematically in Figure 10, determination of 'unit cell' size is attempted as follows: • (12 0 1): Since this vector connects adjacent rhomboidal units, ( Figure 10) the pseudo lattice parameter was taken as the ±0.5a Mg 4 Zn 7 . This has a magnitude of 12.48 Å, which is approximately 6 × d (

Structure at Planar Faults
The building blocks of the Mg 4 Zn 7 structure is a rhombus that connects the centers of icosahedral coordination units, Figure 1. Table 1 reports the various structures observed as variations of Mg 4 Zn 7 . The structures Tr(A) and Tr(B) reported by Rosalie et al. [23] are called transitional structures, referring to a transition to the MgZn 2 phase. Defects on plane (201) can be understood from Rosalie et al. [26], where it is shown that an icosahedron can be defined at hexagonal sites of the Mg 4 Zn 7 unit cell, whose one of the twofold axis is along this plane. The structural units defined at these two kinds of planar faults are shown in Figure 11, and the lattice parameters determined are listed in Table 4. It can be observed in Figure 11b that there is one more orientation of hexagonal unit. The lattice parameter of fault B shows a monoclinic angle of 108 • , whose acute complimentary angle is 72 • (i.e., 2π 5 ). An interesting question is about the stability of these structures. Similar modifications of the Mg 4 Zn 7 structure shown by us previously were tied to chemistry (local composition) [23]. In the present study, however, they seem to arise out of the lattice constraint of a periodic crystal growing on a quasiperiodic lattice. In this case, it is possible that these defects' structures are necessary for the stability of the interface.  Figure 11. Atomic structures at planar defects of Mg 4 Zn 7 (a) defect A and (b) defect B. Solid red lines outline the unit cell; dashed red lines represent the asymmetric unit. Mg atoms are represented by circles and Zn atoms by hexagons. There is one more pair (than the regular structure shown in Figure 1) of irregular hexagonal Zn-deficient sites (9 and 10), members of each pair again distinguished by the atom z-coordinates. Here, we also note of a report of an icosahedral phase growing on a Mg 4 Zn 7 phase precipitate [35]. In this case, the icosahedral phase also shows streaked diffraction spots (in the direction of the growth, perpendicular to a fivefold plane). The icosahedral phase is reported to have grown in layers, possibly relating to the local chemistry.

Conclusions
Structure of a monoclinic Mg 4 Zn 7 phase growing on an icosahedral phase has been studied by transmission electron microscopy in a cast Mg-Zn-Y alloy. The lattice correspondence has been studied by electron diffraction. The structure of planar faults have been studied by high resolution microscopy. The following conclusions are drawn: