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[Digvijay Singh](https://orcid.org/0000-0003-4357-957X), [Alok Singh](https://orcid.org/0000-0001-5515-8305), [Takahiro Sawaguchi](https://orcid.org/0000-0002-9405-002X)

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[Elucidating deformation pathways and interface characteristic of self-accommodated dual γ/ε phase microstructure in Fe–Mn–Si–Al alloy](https://mdr.nims.go.jp/datasets/457a9a9f-4add-4bbe-8601-deab786cca0c)

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Elucidating deformation pathways and interface characteristic of self-accommodated dual γ/ε phase microstructure in Fe–Mn–Si–Al alloy  Digvijay Singha, Alok Singha, Takahiro Sawaguchia*   aResearch Center for Structural Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan   Digvijay Singh singh.digvijay@nims.go.jp  Alok Singh alok.singh@nims.go.jp  Takahiro Sawaguchi sawaguchi.takahiro@nims.go.jp      * Corresponding author:  Takahiro Sawaguchi sawaguchi.takahiro@nims.go.jp National Institute for Materials Science,  1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Phone: +81-29-859-2416, Fax: +81-29-859-2401          Manuscript File Click here to view linked Referencesmailto:singh.digvijay@nims.go.jpmailto:alok.singh@nims.go.jpmailto:sawaguchi.takahiro@nims.go.jpmailto:sawaguchi.takahiro@nims.go.jphttps://www.editorialmanager.com/materialschar/viewRCResults.aspx?pdf=1&docID=38876&rev=0&fileID=671060&msid=dc0ae272-79bd-480d-918c-e45e0fe56d28https://www.editorialmanager.com/materialschar/viewRCResults.aspx?pdf=1&docID=38876&rev=0&fileID=671060&msid=dc0ae272-79bd-480d-918c-e45e0fe56d28Abstract  There has been an intense scientific interest in investigating the phenomenon of deformation-induced ε-ε martensite (hcp) interaction owing to the thermodynamically paradoxical reverse transformation and mechanical twinning. In this study, detailed transmission electron microscopy has been employed to examine the crystallographic orientation relationship, phase stability and boundaries between the intersection phases on the ε-ε intersections in a 10% tensile deformed Fe–30Mn–4Si–2Al alloy. The transformation/twinning scheme is systematically summarized initiating from the austenite matrix (γ) and two deformation-induced ε-martensite variants. It involves diverse intersection reactions: mechanical ε-twins, a 90º-rotating γ-phase from the γ matrix, and 90º-rotate ε-phase re-transformed from the intersection γ. All these phases share a common <101>γ || <21̅1̅0>ε axis that is equivalent to the intersection axis of the crossing {111}<12̅1>γ shears and interrelated with rotational angles with respect to the axis. The boundaries between the intersection γ and neighboring ε-phase are inclined from the corresponding {111}γ||{101̅1}ε planes. By means of the phenomenological theory of martensite crystallography (PTMC), the inclination of the boundary is rationalized by considering the lattice-invariant shear on the double {111}γ plane inside the intersection γ to satisfy the invariant plane condition of the boundary.   Keywords: Martensite transformation, Twinning, TRIP steels, Transmission electron microscopy (TEM), ε-martensite     1. Introduction  Fe-Mn-Si-based alloys are well known for their shape memory effect, owing to their unique reversible phase transformation characteristics which occur when exposed to a specific stimulus, such as temperature or stress [1]. The phase transformation involves a deformation induced transformation of γ-austenite (fcc) to hexagonal close packed (hcp) ε-martensite, which is recoverable upon heating [2]. The shape memory effect in Fe-Mn-Si-based alloys is of significant importance due to its potential applications in various fields, including aerospace, medical, and automotive industries [3–5]. Additionally, their high damping capacity and excellent corrosion resistance make them attractive for use in structural and damping applications, for example fish plate couplings of rails of industrial cranes [6] and seismic dampers [7].  Deformation induced martensitic transformation and mechanical twinning is of immense interest in various austenitic alloys, including austenitic stainless steel, medium Mn-, and high-Mn steel, owing to the transformation induced plasticity (TRIP) and twinning induced plasticity (TWIP) phenomenon which results in outstanding synergy between strength and ductility observed in these materials [8–10]. The stacking fault energy (SFE), deformation level (strain/strain rate), and crystal orientations of the parent phase are the key factors that governs the deformation mechanisms in various austenitic alloys [11–15]. Depending upon the SFE and thermodynamic phase stability, several modes of martensitic transformation have been established, namely direct transformation (γ →  ε/ά) or two-step transformation (γ →  ε → ά) [16–19]. Sawaguchi et al. developed a low SFE based Fe-15Mn-10Cr-8Ni-4Si damping alloy [20], which shows excellent low-cycle fatigue properties with the aid of bi-directional transformation induced plasticity (B-TRIP) or reversible γ ⇌ ε martensitic transformation [21]. Besides SFE criteria, crystallographic orientation relationship plays an important role in martensitic transformation. The fcc to hcp transformation (γ → ε) is achieved through the orderly {111}<12̅1>γ Shockley partial shear movement within alternative {111} close pack planes of γ-lattice. Based upon Schmidt criteria, several ε-variants with different habit planes may operate simultaneously under critical stress invariant in the parent γ-matrix. Due to the orderly-tetrahedral geometry of {111}γ cubic planes, multiple variants of ε-martensite with different habit planes intersect each other, which results in the change of atomic arrangements within the intersection volume [22–24]. Hence, at a particular temperature and with a specific chemical composition in an alloy, multiple intersection products can coexist, and their presence is determined by the crystallographic orientation. Zhang et al. observed that the ε-intersection reaction is significantly driven by the orientation of the intersecting shears, which can be classified into two types: Type I with crossing shears perpendicular to the intersection axis and Type II with crossing shears inclined at an angle of 30 degrees [22]. Moreover, the ε-ε intersection volume has been identified as a potential nucleation site for α-martensite (bcc) phase in metastable austenitic steels [25]. Alongside α-martensite, several other intersection products, including 90º reverted austenite and ε-martensite phases (γ90, ε90), γ-twins, and ε-twins (101̅2, 101̅1) have been observed at ε-ε intersection volume in Fe-Mn-Si-based damping alloys [2,22–26].  The ε-ε intersection structures in γ matrix are highly significant concerning the material performance, including shape memory effects, strain hardening, and fatigue properties [2,7,20,21,27–31]. The ε-ε intersection structures act as a source, barrier, or sink of dislocations during deformation by generating new interfaces with the adjacent phases. An initial study utilizing transmission electron microscopy (TEM) was conducted by Yang and Wayman [23,24]. They engaged in comprehensive discussions and speculations concerning potential structures. Interestingly, some of the structures initially identified as 'secondary variants' were later revealed to be twins of the ε-phase, as demonstrated by Matsumoto et al. [26]. Zhang et al. conducted an electron backscatter diffraction study to investigate the orientation dependence of ε-martensite in polycrystalline high-Mn steels, with a specific focus on the intersection of ε plates [22]. After a 10% tensile deformation, microstructural observation strongly showed orientation dependent structures, primarily attributed to the Schmid factor. Grain orientations near <414> exhibited only a single variant of ε martensite, whereas a very few ε plates were observed in grains oriented along <001>, which is an orientation for easy slip. In addition, a new γ-phase with 90º orientation from the parent γ phase was discovered at Type-I intersection along <001> ― <101> [23–25] . Furthermore, {101̅2} ε-twin were identified at Type II intersections along <001> ― <111>. Furthermore, the twinning mechanism of the ε-martensite in the Fe–30Mn–6Si shape memory alloy was thoroughly explored by Zhang and Sawaguchi [32]. Their findings revealed the existence of {101̅2} and {101̅1} type twinning in specimens deformed at room temperature, corresponding to Type I and Type II intersection, respectively. Although there have been detailed studies by EBSD and some by dark field TEM, the crystallographic and interface orientations were not clearly brought out. The crystallographic orientation relationships and interface configuration of these ε-ε intersection structures are crucial for understanding the microstructure evolution, underlying accommodation mechanism, and the mechanical properties exhibited by these materials. The martensitic transformation and twinning processes are strongly influenced by the crystallographic orientation of the parent phase, and the resulting microstructure is highly dependent on the crystallographic orientation relationship and interface configuration of the ε-martensite and parent γ-regions. Therefore, a detailed understanding of these phenomena is essential for tailoring the mechanical properties of Fe-Mn-Si-based alloys and optimizing their performance in various applications. Although we have primarily demonstrated ε-ε intersections using EBSD, it's important to note that EBSD has resolution limitations, which hinder a clear resolution of the intricate microstructures at the interface. To address these challenges, here we present a detailed TEM study that provides a clear view of interfaces and traces of plane within the ε-martensite plates. The observations are explained by modifying the phenomenological theory of martensite crystallography (PTMC) and possible sequence of transformations.  Figure 1: Epsilon martensite plates viewed in a grain oriented along a <110> zone axis. Two variants of martensitic plates ε1 and ε2 are observed along traces of two {111} planes indexed as (11̅1) and (1̅1̅1). 2. Experimental  A polycrystalline Fe-30Mn-4Si-2Al (mass %) alloy was prepared by induction melting. The resulting alloy was hot forged and hot rolled at 1000 ºC, and then subjected to water quenching. Subsequently, it was subjected to a solution treatment at 1000 ºC. The specimen was plastically deformed to 10% strain in tension, with the deformation direction being along the rolling direction. The deformed samples were thinned by mechanical grinding and then using jet polishing for observation and analysis using transmission electron microscopy (TEM) on a JEOL 2000FX microscope.  3. Results  A bright field micrograph along <110> zone axis of matrix γ phase in Fig. 1 shows plates along two directions, labeled ε1 and ε2. The inset diffraction pattern shows that these two sets of plates occur on two variants of {111} parent γ phase. A diffraction spot at 1/2 {111} corresponds to (0001) reciprocal vector of the ε phase. Thus, taking lattice parameter of the γ phase to be 3.61 Å, cε ~ 4.17 Å. Two intersections of two sets of plates ε1 and ε2 are shown in Fig. 2. The structure of these two intersections will be examined in detail in the following. One of the two intersection of two variants of ε plates in Fig. 2 is shown in Fig. 3. The crystallographic relationship of the matrix γ with each variant of ε plates is shown in the diffraction patterns. The γ-ε phases follow Shoji-Nishiyama (S-N) orientation relationship. From these diffraction patterns, the aε parameter of ε is determined to be 2.55 Å. In the bright field image, the ε plates are along {111} plane traces of parent γ phase, designated γ1. Inside the ε plates parallel lines are observed, which are presumed to be stacking faults formed during transformation. Inside the intersection region of the plates, γ phase was found, designated γ2, as will be described here. In this γ2 region, two sets of parallel lines are observed, which are traces of faults on {111} planes of this phase. Traces of these planes show that the orientation of γ2 is 90º rotated about <110> axis of γ1.  Figure 2: A bright field micrograph showing details of two intersection sites of ε plates ε1 and ε2 in a grain oriented along a <110> zone axis. ε-γ interfaces are outlined.  Twinning is an important deformation mode in hexagonal phases, commonly of {101̅2} type. Twinning was observed inside the ε plates. Fig. 4 shows twins in a plate of ε1 variant. Twin boundaries are pointed out by open arrows. The inset diffraction pattern shows that these twins are of the type {101̅2}. A coincident {101̅2}spot is marked in the figure. The twin boundaries in the bright field micrograph are observed to be roughly on {101̅2} planes.     Figure 3: (a) A bright field micrograph showing one of the intersections shown in Fig. 2. Two variants of martensite plates ε1 and ε2 are along planes (11̅1) and (1̅1̅1), respectively, of matrix γ1. The orientation and the crystallographic relationship of the martensite plates with respect to the matrix are shown in the composite diffraction patterns in (b) and (c), for the two variants ε1 and ε2. c-axes of ε phase are marked by arrows. At the intersection of the plates in (a) occurs another variant of the FCC matrix, γ2.  The intersection of ε plates could be complex, consisting of twins of ε and variant γ2 of the matrix phase γ1. Fig. 5 shows a complete sequence of transformations. At the top of the scheme is a matrix γ unit cell oriented along a <110> axis. A shear along either of the {111} planes results in hexagonal unit cell in orientation ε1 or ε2. A twinning on one of the two {101̅2}planes (parallel to this orientation) in each of ε1 and ε2 produces a twin, in orientations described as positive or negative. This type of twins is reported to form at the ε variant intersections [26]. Note that the ε have near S-N orientation relationship, but not precisely; their basal planes are nearly parallel to either of {111} planes of the γ2, but deviate by approximately 4º. Formation of twins in the negative sense are unfavorable under shear I+II reaction. Twins of ε1 and ε2 are oriented differently from each other. In a third possibility, a shear on the prismatic plane of ε can transform it again to γ phase. This γ phase (γ2) is oriented 90º with respect to the parent γ phase. Whether transforming from ε1 or ε2, the orientation of the γ2 remains the same. Thus, it can form at the intersections of ε1 and ε2. The γ2 was theoretically predicted by Sleeswyk [33], and experimentally determined by EBSD [22,25]. Yang and Wayman proposed that the γ2 immediately re-transformed into ε, designated as ε90(1) and ε90(2) [23,24]. The ε90 has the exact S-N orientation relationship with γ2.   Figure 4: A bright field micrograph showing twins in a martensite plate ε1. The twin boundaries are marked with arrows. The inset diffraction pattern from one of the twins shows that the twin boundaries are on a {101̅2} plane common to the ε1 matrix and its twin. Another example is taken from Fig. 2 and shown in detail along with diffraction patterns in Fig. 6. A thick plate of ε2 runs nearly vertically through the center of the micrograph in Fig. 6(a). The thickness and number of ε1 plates running on either side of intersection with ε2 plate are not uniform. In the diffraction patterns of Fig. 6(b) and (c), (0001)ε spots corresponding to ε1 and ε2 are observed. In addition, one more (0001) spot occurs, which corresponds to the twin of ε2 (marked ε2T), as predicted by schematic in Fig. 5. The crystallographic orientation of γ1 is marked by a hexagon in the diffraction pattern of Fig. 6(b). Plates of ε1 and ε2 follow the S-N orientation relationship with γ1. In Fig. 6(c) the orientation of γ2 is marked by a similar hexagon (diffraction spots of γ2 are very prominent in this diffraction pattern). It is clearly observed that the twin of ε2, ε2T, forms S-N orientation relationship with γ2.    Figure 5: A scheme of transformations from the parent phase γm (or γ1, shown at the top). MT shear along orientations I or II lead to transformation to ε phases ε1 or ε2. Twinning shears lead to twins ε1T or ε2T, while an RT shear transforms an ε phase to another variant γ2 of the parent γ phase. A further MT shear on the γ2 phase leads to 90º variants of ε phase. The orientations of crystals are represented by rotation angles (clockwise: positive) of {111}γ or {0001}ε planes with respect to {111}γm.  γ2 phase occurs in the upper part of the intersection of ε1 and ε2 plates in Fig. 6(a). Below this, a segment of ε2 plate appears again, but which is twinned in to ε2T on the right side. Immediately below occurs γ2 phase. Thus there occurs a sandwich of ε2T between γ2 phase, which maintain the S-N orientation relationship between them. It can be roughly seen that the interface between these phases is on {111}γ2 and (0001)ε2T. In the lower part of the micrograph, ε2T occurs at the intersection of ε1 and ε2. This ε2 twin is sandwiched between two slabs of ε2, but the interface is clearly not on {101̅2} planes.  Occurrence of γ2 at the intersection of plates can be clearly made out in Fig. 3(a) by the visible faults on its {111} planes. Below the intersection, the plate orientation is ε2T, instead of ε2. It makes a matching interface with γ2 on {111}γ2 || (0001)ε2T planes.  Plate configuration in a wider area are shown in Fig. 7. A ε2 plate runs vertically through the middle of the micrograph, and is twinned in to a band of ε2T in the lower part. The diffraction patterns in Fig. 7(b) shows the orientation of γ1, (c) shows diffraction pattern of ε2T twin, (d) shows the orientation relationship of γ1 with ε1 and ε2, and (e) shows the orientation of the γ2 phase and its orientation relationship with ε2T. In Fig. 7(a), γ1 located at the bottom right establishes interfaces with ε1 and ε2, as seen in the diffraction pattern of Fig. 7(d). The γ2 phase at the intersection of ε1 and ε2 plates does not make any major orientation relationship with either ε1 or ε2, as observed in the diffraction pattern of Fig. 7(f). However, to the left of this γ2 phase occurs ε1T, Fig. 7(g), but with no apparent interface with ε1. To the left of it occur alternate layers of γ2 and ε1T. A diffraction between these two is shown in Fig. 7(h) and (i). Both (h) and (i) show the same diffraction pattern, but (h) highlights the crystallographic relationship of γ1 to ε2 while (i) highlights the relationship of γ2 to ε1T by drawing hexagons to show the orientations of γ1 or γ2.    Figure 6: (a) A complex intersection of ε1 and ε2 plates showing twins ε2T of ε2 and reoriented matrix γ2, as marked on the micrograph. (b) and (c) show the same diffraction pattern from the whole region. Diffraction from matrix γ1 is marked in (b) while that from γ2 is marked in (c), showing their crystallographic relationships with martensite plates and their twins. In the bright field micrograph of (a), c-axes of ε phase are marked by arrows and traces of {111} planes of γ2 are marked by lines.   Figure 7: (a) Epsilon martensite plates and their twins viewed in a grain oriented along a <111> zone axis. (b) A diffraction pattern from the matrix γ1. (c) Diffraction from plate ε2 and its twin ε2T observed at bottom center of the micrograph in (a) (matrix γ1 spots are also present). (d, e) A composite diffraction pattern from the matrix γ1, plates ε1 and ε2, and twin ε2T, as well as γ2. γ2 is observed at the intersection of plates ε1 and ε2 in (a). Diffraction spots of γ1 and its relationship to ε1 and ε2 are marked in (d), while γ2 and its relationship to epsilon phase twin ε2T is marked in (e). (f) A diffraction pattern from γ2 (diffraction spots from ε1 and ε2 are also observed). (g) Diffraction pattern from a region related to ε1 by twinning, ε1T, observed in the upper left of the micrograph in (a). (h, i) A composite diffraction pattern from matrix γ1, ε2, ε1T and γ2 observed in the upper center region of the micrograph in (a). γ1 and its relationship to ε2 is marked in (h), while γ2 and its relationship to ε1T is marked in (i).    Figure 8: (a) A bright field micrograph showing interaction of martensite plates and their twins. A band of twin occurs in ε1 plate. A segment of ε2 plate is its own twin ε2T, next to which grows a ε2 plate. A diffraction pattern in (b) confirms the ε1 twin and (c) shows the ε2 twin. The latter diffraction pattern shows ε1, ε2 and ε2T with respect to (d) γ1 and (e) γ2.  Fig. 8 shows interaction of ε1 and ε2 plates and their twins. At left center in Fig. 8(a) is γ2 phase at an intersection of ε1 and ε2 plates. The upper neighbor of the γ2 is in not ε2, but its twin ε2T. The ε1 block dominating this micrograph shows a diagonal twin band across it, the twin boundaries being on the {101̅2} planes. The diffraction pattern of this twin is shown in Fig. 8(b). From the geometry of the plates, the upper edge of the twinned domain ε1T should make an interface with a γ1. However, the upper part of the twin in fact makes an interface with a domain of ε2. This ε2 domain makes an interface with ε2T on left, with which it is crystallographically twin related (Fig. 8(c)). The interface is, however, not on a twinning plane {101̅2}, but on the original interface of ε2T with γ1. It can be argued that this region of ε2 forms to minimize the interfacial energies between ε1T, γ1 and ε2T phases. γ1 does not form matching crystallographic orientations with ε1T or ε2T. ε2 forms as a buffer, with Shoji-Nishiyama orientation relationship with γ1 and twin relationship with ε2T. The exact matching length of the interface of ε1T with ε2 indicates that the formation of ε2 is triggered by ε1T. The interface between ε1T and ε2 is nearly perpendicular (~85º) to the basal planes of ε2 (the basal planes of ε2 and ε1T are about 18º apart). Observation at the lower end of the ε1T band also indicates triggering of formation of ε2 plates in γ1.  4. Discussion  In martensitic transformation, orientation relationship between austenite and product martensite phases, shape strain from displacive character, and the nature of interfaces are among the important crystallographic features [34–39]. Understanding the microstructure evolution, accommodation mechanism, and mechanical properties exhibited by high-Mn steels relies heavily on the crystallographic orientation relationships and interface configuration of the ε-ε intersection structures. The crystallographic orientation of the parent phase significantly impacts both the martensitic transformation and twinning processes. As a result, the resulting microstructure is highly contingent upon the crystallographic orientation relationship and interface configuration between the ε-martensite and parent γ-regions [32,38]. Olsen and Cohen proved that the coherent interface could incorporate specific type of partial dislocation that play a crucial role in facilitating lattice deformation during the transformation between the two phases and ensuring the continuity of the lattice structure [40]. Thermodynamically there are two phases in the deformed Fe-Mn-Si-Al alloy, but two different orientations of γ phase and four orientations of ε phase, each making interfaces with neighboring phases. Thus, it appears that interfacial energies are important for the stability of the microstructure. All observations here show that all the interfaces are very sharp. Inside the phases transformed from γ1 (ε and γ2), planar defects parallel to the basal hexagonal plane or {111} planes are observed, marking the orientation of these planes clearly.  Orientation relationships are plotted on stereographic projections in Fig. 9. In the S-N orientation relationship between γ and ε plates, at the interface of planes {111}γ with {0001}ε, three equivalent prominent match of directions occur: <110>γ || <112̅0>ε. There are three planar matches of the kind {110}γ ||{12̅10}ε. Fig. 9(b) shows the orientation relationship of γ2 and ε plates. There is a planar match of {111}γ2 ||{0110}ε, in which occur a match of <110>γ || <112̅0>ε directions and two near matches of <110>γ2 || <21̅1̅3>ε.  The orientation relationship between γ2 and εT twin is similar to that between γ and ε. Similarly, the orientation relationship between γ and twin εT is the same as that between γ2 and ε. The similarity also holds for the interfaces between the phases. In Fig. 7(a), an interface is observed between ε1T and γ1 phases in the left part of the micrograph. Inside the γ1 phase, fine plates of ε2 are observed, seemingly originating from the interface with ε1T. Thus, there is an interface between ε2 and ε1T, whose orientation is the same as the orientation of the interface between γ2 and ε2 to the right of it. This interface orientation is different from the orientation of the interface between γ1 and ε1 phases (e.g., on the right in this micrograph). The orientation of this interface halfway between a set of {111} planes each in γ1 (on which plates of γ2 occur) and in γ2 (on which plates of ε1T occur). In other words, the interface intersects the angle between the basal planes in ε1T and ε2 plates.   Figure 9: Stereographic projections showing the orientation relationships between (a) γ and ε phases and (b) γ2 and ε. The austenite phases (γ and γ2) are depicted using colored lines, while ε phase is indicated by black lines.  The interfaces between γ1 and ε1 or ε2 are on {111} planes of γ and {0001} plane of ε phase, as would be expected from the crystallographic and transformation mechanism. Similar relationship holds between γ2 phase and twin ε2T. However, interfaces of γ2 and ε phases at intersections are not on any major planes of either phase. This will be analyzed and discussed below. Analysis based on trace of the planes and the corresponding diffraction patterns show that these interfaces are on planes at mid orientations between {111}γ1 and {111}γ2 corresponding to the interfaces γ1–ε and γ2–ε, respectively. The angle between these {111} planes of γ1 and γ2 are about 19.5º, the mid plane roughly corresponding to {755} of either phase. A {033̅1} plane of ε makes interface with the {755} plane of γ2. The position of the interface plane is shown by a dashed line in the stereogram of Fig. 9(b), bisecting {1̅11}γ2 and (0001)ε planes.   Figure 10: Possible mechanism of formation of interfaces at intersections. (a) Orientation of two sets of {111} planes in γ matrix, observed along a <110> axis. (b) An intersection of ε plates with the γ matrix in the same orientation. The intersection region γ2 is rotated with respect to the matrix γ by 90º. (c) Similar configuration as in (b), but in which intersection region γ2 is rotated with respect to the matrix by 19.5º (after [23]). (d, e) Derived from (b), two different configurations of interfaces between γ2 region and ε plates are shown. In both cases the interfaces are intersections of the matrix γ {111} plane and the γ2 {111} plane.  Possible ε intersection configurations are considered by Yang and Wayman [23]. Following this, Fig. 10(a) shows two sets of {111} planes of matrix γ phase viewed along a <110> axis. Yang and Wayman considered two possibilities of rotation of intersection region γ2 with respect to the matrix. In one, γ2 is rotated with respect to the matrix by 90º, and in another by 19.5º (90º - 70.5º, in positive or negative directions), as shown in Fig. 10(b) and (c), respectively. In the former case (Fig. 10(b)), all interfaces are perpendicular to γ111 planes, i.e., on the basal (0001) planes of ε plates. As has been seen in this study, this orientation relationship holds, but the actual interface orientations are not as drawn. From point marked A in this figure, two lines are drawn along intersections of the angle between the γ2 rhombus and traces of matrix {111} planes (dashed lines), shown as red lines. These two lines are close to the actual position of the interfaces. While in this diagram the intersection rhombus becomes a square or a rectangle, the experimentally observed rhombuses are defined by angles of 96º and 84º, as outlined in Fig. 2. Using this construction, two possible constructions of interfaces can be made. As shown in Fig. 10(d), this construction is made symmetrically to the opposite edge marked D. As a result, the area of γ2 is increased, and both plates ε1 and ε2 are thickened. In construction shown in Fig. 10(e), the other two edges are drawn inside of the γ2 rhombus. In this way, the area of γ2 and the thicknesses of plates ε1 and ε2 are nearly preserved. However, it requires that one segment of each of ε1 and ε2 shift sideways (as plates ε1 on the left and ε2 on top in Fig. 10(e).  The intersection shown in Fig. 6(a) has a very complex structure. This must be because the thickness and position of ε1 plates are not matched on either side of the intersection with ε2. However, the whole complex intersection is within a rhombus with a geometry as constructed in Fig. 10. This raises a possibility that ε1 plates formed after the formation of ε2 plates. γ2 forms in the upper parts of the intersection of ε1 and ε2. At the bottom part of the intersection, ε2T occurs. It forms wide interfaces with ε2 on two sides (with which it has twin relationship, but does not form interfaces on twin plane), with only a small segment with ε1.   Figure 11: The process of the ε to γ reverse transformation at ε − ε intersection.  4.1. Scheme of transformations  Thus, the orientation relationships between the intersection γ phase, ε1 and ε2 agree well with the Yang and Wayman (Y−M) model [23,24], but the observed boundaries between them are significantly inclined from the corresponding crystallographic planes of {1010}ε ||{111}γ. In this section, the reason for the inclination of the boundaries is discussed by means of the phenomenological theory of martensite crystallography (PTMC), which was developed for studying the crystallography for the γ to α’ martensitic transformation [41–44].  The first requirement in PTMC is that an austenite/martensite boundary should be an invariant plane in which all lines are neither distorted nor rotated [44]. In the γ to α’ martensitic transformation the lattice distortion proposed by Bain (Bain distortion) is widely accepted, which is consisting of a contraction along one <001>γ axis and uniform expansions along the other two <001>γ axes [45]. In the Bain distortion there is no invariant plane, and therefore a complementary shear and rotation are needed to obtain it. The second requirement of PTMC is that the complementary shear must be a lattice-invariant shear with which no change in crystal structure occurs. With using matrix calculation, the shape deformation Pγ→α can be expressed as the product of the Bain distortion Bγ→α, lattice-invariant shear Sγ→α, and rotation Rγ→α as follows [46–48].                      Pγ→α = Rγ→α Sγ→α Bγ→α                      (1) On the other hand, in the case of the γ to ε martensitic transformation, the lattice distortion is a simple shear displacement on the {111}γ ||{0001}ε plane. If we neglect the small shrinkage of lattice volume during the transformation, the {111}γ ||{0001}ε plane is invariant, and neither complementary shear nor rotation is needed to complete the shape deformation. The shape deformation Pγ→ε is equivalent with the homogeneous shear Bγ→ε, Pγ→ε = Bγ→ε. As a consequence, the γ /ε boundary is parallel to the {111}γ ||{0001}ε plane, and the crystallographic orientation relationship (S–N relationship: {111}γ ||{0001}ε, <101>γ || <112̅0>ε) is directly obtained with respect to the simple shear process.   Figure 12: The lattice correspondence between the phases. (a) S-N orientation relationship between γ1 and γ2, (b) approaching ε1, (c) lattice mismatch between the intersection γ1 with ε1 and ε2.  However, in the ε to γ reverse martensitic transformation at the ε – ε intersection, a significantly large lattice distortion must also be taken into the account. As schematically drawn in Fig. 11, the transformation from ε to the intersection γ is made by two steps: (1) the + 6.96 % expansion along [0001] (cε to √3/2aγ) and - 5.68 % contraction along [101̅0] (√3aε to 2/√3 aγ) accompanying atomic shuffling ((a) to (b)), and (2) reverse transformation shear ((b) to (c)). The distortion causes a lattice mismatch between the intersection γ with ε1 and ε2, as shown in Fig. 12. The ε2 has S–N orientation relationship with the parent γ phase (a) and encounters the aγ/6 {111}<12̅1>γ transformation shear (b) from the ε1 growing upward to the left. The intersection γ2 produced by the crossing transformation shear (c) has expanded surface which are incoherent with the neighboring ε phases. The {111}γ ||{0001}ε planes therefore do not satisfy the invariant plane condition, and the complementary lattice-invariant shear should be considered to find an invariant boundary plane.  Figure 13: A plausible mechanism for reverse transformation at ε - ε intersection.  The invariant boundary plane can be determined by finding two nonparallel invariant lines. One of such invariant lines is evidently the [101̅]γ || [21̅1̅0]ε axis (here we neglect the slight extension of the line of + 0.0419 %), while another invariant line can be determined by considering the geometry on the plane normal to the axis, as shown in Fig. 13. In this figure, we assume that the most plausible lattice-invariant shear is dislocation glide on two {111}γ planes inside γ2. To maintain the continuity of the matter, basal slip inside the ε phases should also be activated. The area ABDC in ε2 should be distorted into AB’D’C’ by the lattice distortion and then into AB” D” C” by the subsequent lattice-invariant shear. The point C” must stay at the intersection of C’D’ and XC, since C” is associated with C’ by the lattice invariant shear on (111)γ plane and with C by the lattice-invariant shear on (0001)ε plane. From this geometry, the angle θ in the figure is calculated as 5.04º. The same argument is applicable to the interface between the incident ε2 and γ2. The shape deformation at the ε–ε intersection Pε→γint can be expressed as the product of the lattice distortion described in Fig. 11 Bε→γint, and the lattice-invariant shear on double {111}γ plane Sε→γint, as follows.                            Pε→γint = Sε→γint Bε→γint                        (2) Without additional rotation, the lattice obtained through this calculation satisfy the experimentally observed orientation of the γ2 phase with the parent γ1, ε1, and ε2.  5. Conclusions   The detailed TEM investigation on the ε-ε martensite interaction in 10 % tensile deformed Fe-30Mn-4Si-2Al (mass %) austenitic alloy led to the following conclusions:   1. At the intersections of the ε plates, a variant γ2 of γ phase is formed, which is oriented with respect to the original matrix γ1 by a rotation of 90º about a <110> axis nearly perpendicular to the plane of deformation. At these intersections, the interface between ε plates and γ2 are not on major planes of ε prismatic and {111}γ2, but on a plane intersecting these two planes. 2. During deformation, the hexagonal ε plates twin by {101̅2} type of twinning (which rotates the c-axis by about 86º). These twins make the same orientation relationship, Shoji-Nishiyama orientation relationship, with γ2 phase as between ε and γ phases, with the interface being on {111}γ2 and {101̅1}εT prismatic planes. The overall interfacial energy is thus lowered on formation of ε twins. Various interfaces formed at plate-plate, plate-twin and twin-twin interactions are established clearly.  3. The phases γ1, ε1 and its twin ε1T, along with their orientational variants γ2, ε2 and ε2T make several configurations of interfaces. The ε2 (or ε1) plate adjacent to the intersection γ2 may twin (forming a ε2-ε2T (or ε1-ε1T) twin interface), such that a γ2-ε2 (or γ2-ε1) interface is replaced with a γ2-ε2T (or γ2 -ε1T) interface. 4. A scheme of shear deformations has been applied to show that on application of simultaneous shear on two adjacent {111} planes of the parent γ1 phase, two different variants ε1 and ε2 of ε can be formed. Application of shear on prismatic planes of these two variants can result in a γ phase of same variant, γ2.  5. A detailed model of such a transformation has been constructed to show the geometrical transformation of the interfaces.   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