Orientation relationship of eutectoid FeAl and FeAl2

Scherf, A.; Kauffmann, A.; Kauffmann-Weiss, S.; Scherer, T.; Li, X.; Stein, F.; Heilmaier, M.

doi:10.1107/S1600576716000911

research papers

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 49| Part 2| April 2016| Pages 442-449

https://doi.org/10.1107/S1600576716000911

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Orientation relationship of eutectoid FeAl and FeAl₂

A. Scherf,^a ^* A. Kauffmann,^a S. Kauffmann-Weiss,^b T. Scherer,^c,^d X. Li,^e F. Stein ^e and M. Heilmaier ^a

^aInstitute of Applied Materials (IAM-WK), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany, ^bInstitute for Technical Physics (ITEP), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany, ^cInstitute of Nanotechnology (INT), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany, ^dKarlsruhe Nano Micro Facility (KNMF), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen, 76344, Germany, and ^eStructure and Nano-/Micromechanics of Materials, Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany
^*Correspondence e-mail: anke.scherf@kit.edu

Edited by K. Chapman, Argonne National Laboratory, USA (Received 30 September 2015; accepted 15 January 2016; online 24 February 2016)

Fe–Al alloys in the aluminium range of 55–65 at.% exhibit a lamellar microstructure of B2-ordered FeAl and triclinic FeAl₂, which is caused by a eutectoid decomposition of the high-temperature Fe₅Al₈ phase, the so-called ∊ phase. The orientation relationship of FeAl and FeAl₂ has previously been studied by Bastin et al. [J. Cryst. Growth (1978 ), 43, 745] and Hirata et al. [Philos. Mag. Lett. (2008 ), 88, 491]. Since both results are based on different crystallographic data regarding FeAl₂, the data are re-evaluated with respect to a recent re-determination of the FeAl₂ phase provided by Chumak et al. [Acta Cryst. (2010 ), C66, i87]. It is found that both orientation relationships match subsequent to a rotation operation of 180° about a 〈112〉 crystallographic axis of FeAl or by applying the inversion symmetry of the FeAl₂ crystal structure as suggested by the Chumak data set. Experimental evidence for the validity of the previously determined orientation relationships was found in as-cast fully lamellar material (random texture) as well as directionally solidified material (∼〈110〉_FeAl || solidification direction) by means of orientation imaging microscopy and global texture measurements. In addition, a preferential interface between FeAl and FeAl₂ was identified by means of trace analyses using cross sectioning with a focused ion beam. On the basis of these habit planes the orientation relationship between the two phases can be described by ( $[{\overline 1}]$ 01)_FeAl || (114) $[_{{\rm FeAl}_2}^{\rm Chumak}]$ and [111]_FeAl || [1 $[\overline{1}]$ 0] $[_{{\rm Fe Al}_2}^{\rm Chumak}]$ . There is no evidence for twinning within FeAl lamellae or alternating orientations of FeAl lamellae. Based on the determined orientation and interface data, an atomistic model of the structure relationship of Fe₅Al₈, FeAl and FeAl₂ in the vicinity of the eutectoid decomposition is derived. This model is analysed with respect to the strain which has to be accommodated at the interface of FeAl and FeAl₂.

Keywords: iron aluminides; eutectoid decomposition; electron backscatter diffraction; interfaces.

1. Introduction

Iron aluminides are potential candidates for structural applications at high temperatures due to their outstanding oxidation resistance, low density and low material cost. However, mechanical properties such as moderate room-temperature ductility and a sharp drop in strength at 873 K limit their usability. Moreover, above 40 at.% Al the brittle-to-ductile transition temperature increases to about 1023 K (Risanti et al., 2005 ). However, in the aluminium range of 55–65 at.% the high-temperature ∊ phase Fe₅Al₈ (space group $[I{\overline 4}3m]$ , No. 217, Pearson symbol cI52) (Stein et al., 2010 ) decomposes by a solid-state eutectoid reaction into B2-ordered FeAl ( $[Pm{\overline 3}m]$ , No. 221, cP2) (Stein et al., 2010) and triclinic FeAl₂ ( $[P{\overline 1}]$ , No. 2, aP19) (Chumak et al., 2010). This reaction results in a lamellar microstructure, which may yield an improvement of the mechanical properties similar to what is commonly known from TiAl-based alloys (Huang, 1992 ). In the case of TiAl-based alloys, it has been shown that the mechanical properties strongly depend on colony size, lamellar spacing and lamellar orientation with respect to the loading axis (Yamaguchi et al., 2000 ; Fujiwara et al., 1990 ). The influence of the latter was evaluated using single crystals consisting of single colonies (Fujiwara et al., 1990; Inui et al., 1992 ). By applying the knowledge about this anisotropic behaviour it is possible to optimize the microstructural development and, therefore, mechanical properties – for example by a suitable directional solidification process. However, the control of the eutectoid microstructure by directional solidification in the case of Fe–Al needs a detailed characterization of the relationship between the decomposing ∊ phase and the resulting phases FeAl and FeAl₂.

In the present study, the orientation relationship, as determined previously by Bastin et al. (1978) and Hirata et al. (2008), will be confirmed and the supposed differences will be examined. In addition, the interface of the FeAl and FeAl₂ lamellae is investigated by means of local orientation determination and cross sectioning. In contrast to the investigation of Bastin et al. (1978), a distinct preferential interface can be identified. By applying the experimental data, the atomistic details of the relationship of the involved crystal structures are discussed. A possible orientation and interface relationship of FeAl and FeAl₂ to the high-temperature ∊ phase during the eutectoid reaction is proposed.

2. Experimental

Two rods of an alloy with a nominal composition of 60.5 at.% Al were produced by arc melting and subsequent casting into a copper mould with dimensions of Ø 13.5 × 170 mm. One of the rods was directionally solidified using additional zone melting. The velocity was 18 mm h⁻¹ at a temperature gradient of roughly 30 K mm⁻¹.

In order to investigate the orientation relationship of FeAl and FeAl₂, orientation imaging microscopy by electron backscatter diffraction (EBSD) and texture analysis by X-ray diffraction (XRD) were carried out. EBSD was performed utilizing a Zeiss Auriga cross-beam scanning electron microscope (SEM) operated at 20 kV (with 120 µm aperture) and equipped with an EDAX DigiView EBSD detector. The orientation maps of 100 × 100 µm were obtained by indexing patterns of 686 × 686 pixels (maximum resolution) with eight to ten bands at a point rate of about 25 s⁻¹ and a step size of 0.1 µm. The fraction of indexed points is above 99.8%. For the maps on as-cast material and on directionally solidified material 70 and 73%, respectively, of the points were recorded with confidence indices (CIs) above 0.1. The contribution of low CIs is mainly attributed to regions with overlapping patterns of both phases near the phase boundaries. Thus, small lamella spacing and low inclination with respect to the surface locally result in a higher fraction of low CIs. Nevertheless, for all investigated regions reliable information for the lamella orientations was observed. The maps in Figs. 4 and 5 below are shown without any cleaning operation. Cross sectioning was performed using the focused Ga ion beam (FIB) of the Auriga microscope at 30 kV and 16 nA. XRD texture measurements were carried out on a Bruker D8 diffractometer equipped with an Eulerian cradle. The Cu X-ray tube was operated at 40 kV and 40 mA. In order to determine the exact Bragg positions on the directionally solidified material, measurements with ω offset were initially performed. Using ω offset, peak positions of inclined (with respect to the sample surface) sets of crystallographic planes can be analysed. For this kind of measurement a motorized slit of 0.7 mm and a 2.5° axial Soller slit were used at the source as well as two motorized slits of 9 mm, a 2.5° axial Soller slit and an Ni filter at the Lynxeye-XE detector. For texture measurements a Göbel mirror, circular slit of 1 mm in diameter and collimator of 1 mm were used at the source as well as two motorized slits of 9 mm at the Lynxeye-XE in 0D mode with three channels. The pole figures were determined between 0 and 360° in φ as well as 0–80° in Ψ with steps of 4°. The defocusing-induced intensity decrease with increasing tilting angle was estimated by accompanying measurements on powder samples of different materials. For both kinds of experiments, cross sections were prepared by a standard metallographic procedure including grinding up to a grid of P4000 and subsequent polishing with 1 µm diamond suspension as well as oxide polishing suspension OP-S provided by Buehler.

3. Results and discussion

3.1. Crystallographic data from literature – revisited

The orientation relationship of FeAl and FeAl₂ was previously investigated by Bastin et al. (1978) and Hirata et al. (2008) using the Weissenberg technique and transmission electron microscopy, respectively. Thereby, Bastin et al. revealed $[[{\overline 1}11]_{\rm FeAl}\, ||\, [100]_{{\rm FeAl}_{2}}^{\rm Bastin}]$ and $[(0{\overline 1}1)_{\rm FeAl}\, ||\, (002)_{{\rm FeAl}_2}^{\rm Bastin}]$ based on a pseudo-monoclinic description of the FeAl₂ crystal structure in directionally solidified, fully lamellar material (Livingston, 1973 ).¹ Despite the fact that Bastin et al. investigated fully lamellar material, they were not able to identify preferential interface planes between the two structures. Hirata et al. (2008) determined $[[{\overline 1}11]_{\rm FeAl}\, ||\, {\rm N}(241)_{{\rm FeAl}_2}^{\rm Corby}]$ and $[(110)_{\rm FeAl}\, ||\, (2{\overline 2}1)_{{\rm FeAl}_2}^{\rm Corby}]$ using crystallographic data (triclinic description) for FeAl₂ provided by Corby & Black (1973 ). Note that the angle between N(241)_FeAl₂^Corby and $[{\rm N}(2{\overline 2}1)_{{\rm FeAl}_2}^{\rm Corby}]$ is 91.26° whereas $[[{\overline 1}11]_{\rm FeAl}]$ and N(110)_FeAl are perpendicular. This issue is addressed in §3.2. In their approach, an Al-lean alloy with 55 at.% Al, exhibiting a B2 matrix with FeAl₂ particles, was used. Because particles were analysed, preferential interfaces were not obtained. Since it cannot easily be rationalized whether the two relationships are similar or not, a comparison of the two data sets was carried out first. For this purpose, suitable transformations of the crystallographic data were examined with respect to a recent re-determination described as follows.

Crystallographic data by Chumak et al. (2010) are used as the reference data for FeAl₂. The lattice parameters are summarized in Table 1. For comparison, the original crystallographic data, as used by Bastin et al. (1978) and Hirata et al. (2008), are included in Table 1 as well. In the case of Corby & Black (1973), a suitable transformation is given by the Inorganic Crystal Structure Database (ICSD, collection code 150477) as a′ = a, b′ = −b and c′ = a − c. The transformation of the data, determined by Bastin et al. (1978), was derived to be a′ = c, b′ = a + c and c′ = $[\textstyle{1 \over 2}]$ (b + c). For the description of the crystal structure in a pseudo-monoclinic framework, Bastin et al. (1978) used a non-primitive unit cell exhibiting twice the volume of the primitive unit cell evaluated by Chumak et al. (2010). In order to visualize the derived transformations, the basis vectors transformed accordingly are presented in stereographic projection in Fig. 1 with respect to the unit cell of Chumak et al. (2010).

Table 1
Comparison of lattice parameters of FeAl₂ according to the relevant references and appropriate transformations

Reference/transformation	a (Å)	b (Å)	c (Å)	α (°)	β (°)	γ (°)	Volume (Å³)
Chumak et al. (2010)	4.8745	6.4545	8.7361	87.93	74.396	83.062	262.79
Corby & Black (1973)	4.878	6.461	8.800	91.75	73.27	96.89	263.69
Transformation by a′ = a, b′ = −b, c′ = a − c	4.878	6.461	8.748	87.93	74.45	83.11	263.69
Bastin et al. (1978)	7.594	16.886	4.862	89.55	122.62	90.43	525.10
Transformation by a′ = c, b′ = a + c, c′ = ½ (b + c)	4.862	6.442	8.806	88.24	73.48	83.15	262.55

Figure 1
Stereographic projection of the transformed basis vectors according to the different descriptions of the FeAl₂ phase with respect to the unit cell reported by Chumak et al. (2010

The congruence of [100]_FeAl₂^Chumak ≡ [100]_FeAl₂^Corby ≡ [001]_FeAl₂^Bastin, [010]_FeAl₂^Chumak ≡ $[[0{\overline 1}0]_{{\rm FeAl}_2}^{\rm Corby}]$ ≡ [101]_FeAl₂^Bastin as well as of [001]_FeAl₂^Chumak ≡ $[[10{\overline 1}]_{{\rm FeAl}_2}^{\rm Corby}]$ ≡ $[[0{{1}\over{2}} {{1}\over{2}}]_{{\rm FeAl}_2}^{\rm Bastin}]$ in the stereographic projection in Fig. 1 illustrates that the descriptions of FeAl₂ are similar and can be transformed appropriately. In order to compare the previously determined orientation relationships, transformed and reoriented data for the triclinic FeAl₂ phase will be used in the following.

The stereographic projections presenting the orientation relationship between FeAl and FeAl₂ according to Bastin et al. (1978) and Hirata et al. (2008) are shown in Fig. 2. This clearly reveals that the two orientation relationships are not necessarily identical. It is possible to achieve congruence of both data sets by a rotation operation of 180° about a $[\langle 112\rangle_{\rm FeAl}]$ direction in the centres of Figs. 2(a) and 2(b) or by applying the inversion symmetry of the FeAl₂ phase, which is assumed by the crystallographic data in Chumak et al. (2010). In the latter case, both orientation relationships describe the same situation. In contrast, a 180° rotation about a $[\langle 112\rangle_{\rm FeAl}]$ axis corresponds to the common twin system $[\{112\}\langle 11{\overline 1}\rangle]$ of body-centred cubic metals (Christian & Mahajan, 1995 ) as well as of the ordered structures derived from that (Cahn & Collect, 1961 ). In principle, the two twin-related orientations of FeAl can be caused by either twin boundaries within a single FeAl lamella which form during the transformation of the ∊ phase to FeAl or growth of two different variants of FeAl separated by the FeAl₂ phase. These two possibilities can be examined with automated orientation imaging microscopy using EBSD as has been done in this study. The occurrence of inversion symmetry of FeAl₂ or inversion twinning within FeAl₂ cannot be investigated by the applied methods.

Figure 2
Stereographic projection of the orientation relationship between FeAl and FeAl₂ according to (a) Bastin et al. with $[[{\overline 1}11]_{\rm FeAl} \,||\, [100]_{{\rm FeAl}_2}^{\rm Bastin}]$ and $[(0{\overline 1}1)_{\rm FeAl} \,||\, (002)_{{\rm FeAl}_2}^{\rm Bastin}]$ [in terms of the Chumak data (Chumak et al., 2010

): $[[1{\overline 11}] _{\rm FeAl} \,||\, {\rm N}(2 {\overline 4}1)_{{\rm FeAl}_2}^{\rm Chumak}]$ and $[(0{\overline 1}1)_{\rm FeAl}\, ||\, (221)_{{\rm FeAl}_2}^{\rm Chumak}]$ ], (b) Hirata et al. with $[[{\overline 1}11]_{\rm FeAl} \,||\, {\rm N}(241)_{{\rm FeAl}_2}^{\rm Corby}]$ and $[(110)_{\rm FeAl} \,||\, (2{\overline 2}1)_{{\rm FeAl}_2}^{\rm Corby}]$ [in terms of the Chumak data (Chumak et al., 2010

): $[[{\overline 1}11]_{\rm FeAl} \,||\, {\rm N}(2{\overline 4}1)_{{\rm FeAl}_2}^{\rm Chumak}]$ and $[(110)_{\rm FeAl} \,||]$ (221)_FeAl₂^Chumak]. For the pole projection of lattice planes, the normal vector of the planes is used.

3.2. As-cast material

Figs. 3(a) and 3(b) show examples of the obtained electron backscatter patterns for the later orientation determination of FeAl₂ and FeAl, respectively. Despite a low number of zone axes in the case of FeAl₂, a robust assignment of zone axes was possible in order to determine phase and orientation within the probed sample volume.

Figure 3
Electron backscatter patterns of (a) FeAl₂ and (b) FeAl.

The orientation mapping [colour code according to the inverse pole figure (IPF) of the sample surface normal, see insets and description of Fig. 4(a)] of the as-cast state in Fig. 4(a) shows four different colonies of varying orientation. The volume fractions of the phases are approximately 40 and 60 vol.% for FeAl and FeAl₂, respectively. This is higher than the theoretical evaluation which leads to 28 and 72 vol.% based on the phase diagram and the crystallographic data. The shift of the relative proportions might be attributed to the high cooling rate in the water-cooled copper mould. The rotation of the lamellar traces on the surface for the colony in the centre of Fig. 4(a) is marked by blue dashed lines indicating maximum deviation from the mean rotation. The stereographic projection in Fig. 4(c) illustrates the determined orientation relationship of the two phases within the colony in the centre of the image [the complete set of stereographic projections for all colonies in Fig. 4(a) is provided as supporting information]. In accordance with the previous investigations, [111]_FeAl is almost parallel to $[{\rm N}(2{\overline 4}1)_{{\rm FeAl}_2}^{\rm Chumak}]$ and $[({\overline 1}10)_{\rm FeAl}]$ is parallel to (221)_FeAl₂^Chumak in all cases. Nevertheless, as mentioned before the angle between $[{\rm N}(2{\overline 4}1)_{{\rm FeAl}_2}^{\rm Chumak}]$ and N(221)_FeAl₂^Chumak remains 91.26°, indicating that $[({\overline 1}10)_{\rm FeAl}]$ and N(221)_FeAl₂^Chumak are not the habit planes of these structures. In order to determine the interface plane of the lamellae, the inclination of the colonies was determined on cross sections prepared by FIB. A cross section in Fig. 4(a) is shown in Fig. 4(b). The rotation and inclination with respect to the horizontal image edge and the sample surface, respectively, were determined from Figs. 4(a) and 4(b). These are included in the stereographic projections in Fig. 4(c) as blue lines in the radial and peripheral directions. The intersections of these lines correspond to the interface plane normal. In all investigated cases, (114)_FeAl₂^Chumak with minor deviations was found as the common plane between FeAl and FeAl₂. Owing to the distinct orientation relationship, this coincides well with $[(1{\overline 1}0)_{\rm FeAl}]$ . An according low-indexed direction in FeAl₂ within (114)_FeAl₂^Chumak could be identified as $[[1 {\overline 1}0]_{{\rm FeAl}_2}^{\rm Chumak}]$ . Moreover, $[[1 {\overline 1}0]_{{\rm FeAl}_2}^{\rm Chumak}]$ is found to be parallel to [111]_FeAl. Thus, the orientation relationship between FeAl and FeAl₂ can now be expressed in terms of the habit planes in the following way: $[[111]_{\rm FeAl}\, ||\, [1 {\overline 1}0]_{{\rm FeAl}_2}^{\rm Chumak}]$ and $[({\overline 1}01)_{\rm FeAl}\, ||\, (114)_{{\rm FeAl}_2}^{\rm Chumak}]$ . This is discussed on the basis of a crystallographic model in §3.4 in more detail. In addition, there is no evidence for an alternating orientation change or twinning of the FeAl lamellae.

Figure 4
(a) Orientation mapping according to the inverse pole figure of the surface normal on a cross section of the arc-melted button (see insets; centre of the IPF of FeAl₂ corresponds to [001]_FeAl₂^Chumak, standard triangle of FeAl encloses $[[100]_{\rm FeAl}}]$ , [110]_FeAl and [111]_FeAl). Blue lines indicate minima and maxima of the lamella trace rotation with respect to the horizontal edge of the colony in the centre of the image. (b) An example of a SEM micrograph on a cross section prepared by FIB (secondary electron contrast, tilt-corrected). The blue dashed line indicates the mean of the lamella trace inclination with respect to the sample surface obtained from several cross sections. The standard deviation is highlighted by dotted lines. (c) Stereographic projection of the determined orientations of the colony in the centre of (a). Blue lines indicate rotation and inclination of the lamella traces according to (a) and (b). The complete set of stereographic projections for all colonies in (a) is provided as supporting information. For the pole projection of lattice planes, the normal vector of the planes is used.

3.3. Directionally solidified material

An orientation mapping of the directionally solidified material analogous to Fig. 4 is presented in Fig. 5(a). The volume fractions of FeAl and FeAl₂ are in agreement with the theoretical calculations with approximately 30 and 70 vol.%, respectively. The solidification direction is perpendicular to the plane of the image. The map is characterized by a rotation angle of about (53 ± 2)° with respect to the horizontal edge (blue dashed lines) of the lamellae on the prepared surface as well as homogeneous crystallographic orientations of FeAl and FeAl₂ with respect to the solidification direction. Hence, the boundaries between the colonies visible in Fig. 5(a) are small-angle colony boundaries. The inclination of the lamellae into the depth of the investigated material is uniform, too. The inclination angle is about (75 ± 3)° with respect to the sample surface as highlighted by blue dashed lines in Fig. 5(b). The stereographic projection in Fig. 5(c) (centre represents the solidification direction) illustrates the determined orientation relationship of the directionally solidified material which is the same as found for the as-cast state (see Fig. 4c) and the relationships presented in Fig. 2. The orientation relationship seems to be robust with respect to different conditions of formation: it is observed not only during precipitation of FeAl (Hirata et al., 2008) but also during fast and slow cooling of fully lamellar material. Again, no alternating FeAl orientations or twinning of FeAl occurred. The determination of the interface plane normal by the measurement of rotation and inclination of the lamellae also reveals the congruence (114)_FeAl₂^Chumak ≡ $[(1{\overline 1}0)_{\rm FeAl}]$ within the interface.

Figure 5
(a) Orientation mapping according to the inverse pole figure of the solidification direction on the cross section of the rod (same insets as in Fig. 4

). Missing points in the centre of the image are caused by beam damage. (b) An example of a SEM micrograph on a cross section prepared by FIB (secondary electron contrast, tilt-corrected). The rotation and inclination with respect to the horizontal image edge and the sample surface, respectively, are highlighted by blue lines. The mean value obtained by analysing several colonies is indicated by a dashed line – the standard deviation by dotted lines. (c) Stereographic projection of the determined orientations of the colony in the centre of (a). Blue lines indicate rotation and inclination of the lamella traces according to (a) and (b). For the pole projection of lattice planes, the normal vector of the planes is used.

In order to verify the local results on a large scale, texture measurements using an X-ray goniometer were carried out. The experimental pole figures are shown in Figs. 6(a)–6(d). Distinct spots within the pole figures indicate strong texturing of the investigated material. In the case of FeAl₂, the low crystal symmetry causes single spots within the range of the measurement. The slightly increased intensity at high tilt angle visible in Figs. 6(a)–6(d) is caused by insufficient correction of defocusing. Additional signals in the measured pole figures might be caused by overlapping Bragg positions at the chosen 2Θ value. By applying the obtained orientation information, a stereographic projection is calculated and presented in Fig. 6(e) (the simulations of the pole figures are included in the supporting information). FeAl exhibits an alignment of ∼ $[\langle 110\rangle _{{\rm FeAl}}]$ parallel to the solidification direction. As previously shown in the local analysis by EBSD, the global texture measurement provides evidence for the same orientation relationship between FeAl and FeAl₂.

Figure 6
Texture analysis of directionally solidified material: (a) to (d) experimental XRD pole figures of FeAl₂ and FeAl (defocusing corrected). (e) Stereographic projection of FeAl and FeAl₂ revealing an alignment of the solidification direction near to the $[\langle 110\rangle_{\rm FeAl}]$ axis of the FeAl phase as well as an orientation relationship according to $[(01{\overline 1})_{\rm FeAl} \,||\, ({\overline 114})_{{\rm FeAl}_2}^{\rm Chumak}]$ and $[[11{\overline 1} ]_{\rm FeAl} \,||\, [{\overline 1}10]_{{\rm FeAl}_2}^{\rm Chumak}]$ . For the pole projection of lattice planes, the normal vector of the planes is used.

3.4. Crystallographic model

Based on the experimental determination of the orientation relationship and interface plane between FeAl and FeAl₂, a model of the crystallographic relationships of the phases participating in the eutectoid decomposition can be derived. As previously pointed out by Stein et al. (2010), the unit-cell parameter of the high-temperature Fe₅Al₈ phase is approximately three times larger than that of FeAl. The unit cell of Fe₅Al₈ is indeed a 3³ superstructure with 52 atoms and two vacancies in comparison to the W prototype. Thus, a cube-on-cube relation is to be expected.

Fig. 7 shows the atomic sites based on crystallographic data determined close to the decomposition temperature (Stein et al., 2010). In Fig. 7(a), the crystal structures of Fe₅Al₈ and FeAl are displayed with a [111] viewing direction. The assumption of a cube-on-cube relation seems to be reasonable owing to the common hexagonal arrangement of atomic columns in both phases. According to the determined orientation and interface relationship, FeAl₂ is viewed from $[[1 {\overline 1}0]_{{\rm FeAl}_2}^{\rm Chumak}]$ with a (114)_FeAl₂^Chumak plane towards a $[({\overline 1}01)_{\rm FeAl}]$ of FeAl. The hexagonal arrangement of atomic columns is observed, too. The hexagonal arrangement is formed by (114)_FeAl₂^Chumak, $[({\overline {11}}3)_{{\rm FeAl}_2}^{\rm Chumak}]$ and (221)_FeAl₂^Chumak planes (note that $[[1 {\overline 1}0]_{{\rm FeAl}_2}^{\rm Chumak}]$ describes the intersection line of all three planes accurately). These planes show the highest structure factors of FeAl₂ indicating the closest-packed planes within this structure. The highest structure factor and, thus, highest atomic packing is found for (114)_FeAl₂^Chumak. This might result in the exclusive selection of the observed habit planes since $[({\overline 1}01)_{\rm FeAl}]$ is the closest-packed plane for FeAl. Fig. 7(b) provides a scheme of the atomic sites within the interface between FeAl and FeAl₂. Thus, $[({\overline 1}01)_{\rm FeAl}]$ and (114)_FeAl₂^Chumak are arranged in-plane whereas the viewing directions of the aforementioned Fig. 7(a) are pointing upwards.

Figure 7
Schematic drawings of the crystallographic model based on the determined orientation relationship and interface of FeAl and FeAl₂. A possible orientation relationship of Fe₅Al₈ is also proposed. (a) [111]_Fe₅Al₈ of the high-temperature ∊ phase, $[[1 {\overline 1}0]_{{\rm FeAl}_2}^{\rm Chumak}]$ of FeAl₂ and [111 ]_FeAl are pointing out-of-plane. The interface planes of FeAl₂ and FeAl are $[(114)_{{\rm FeAl}_2}^{\rm Chumak}\,||\, ({\overline 1}01)_{\rm FeAl}]$ . (b) Atomic sites within the interface planes $[({\overline 1}01)_{\rm FeAl}]$ and $[(114)}_{{\rm FeAl}_2}^{\rm Chumak}]$ . Semi-transparent sites are off the interface plane of the particular phases. The drawings are based on VESTA (Momma & Izumi, 2011

) graphics using crystallographic data at 1373 K (Fe₅Al₈) and 1353 K (FeAl₂ and FeAl). The translations between the phases are anticipated or arbitrary. For characterization of the viewing directions, the normal vectors of the lattice planes are used and symbolized by N $[(\ldots)]$ .

The strains between FeAl and FeAl₂ which have to be accommodated at the interface can be analysed by the lattice plane distances provided in Fig. 7(b). At the maximum a deviation of 0.14% is observed within the interface, indicating a very good compatibility.

Future local high-resolution investigations with respect to lattice structure and chemistry of the interface should be performed in order to reveal the interface structure as well as the possibility of slip transfer between the investigated phases. {110}_FeAl surfaces are known to reorganize to FeAl₂ commensurate structures for energetic reasons (Baddorf & Chandavarkar, 1996 ). Hence, similar effects are also expected for the interface between FeAl and FeAl₂. This might be facilitated by the changing Al content in both phases during cooling which will lead to locally changing lattice parameters in the vicinity of the interface. In addition, the interface structure of branched lamellae, as shown in Fig. 4(b) and frequently found in this system, remains unclear.

4. Conclusions

This study provides the following main results regarding the orientation and interface relationship of FeAl and FeAl₂ resulting from a eutectoid decomposition of Fe₅Al₈:

(i) The orientation relationship determined by Bastin et al. and Hirata et al. was confirmed in fully lamellar as-cast and directionally solidified material.

(ii) In addition, the interface of FeAl and FeAl₂ lamellae is found to be $[({\overline 1}01)_{\rm FeAl}\, ||\, (114)_{{\rm FeAl}_2}^{\rm Chumak}]$ . Based on this habit plane the orientation relationship can be set up by $[[111]_{\rm FeAl} \,||]$ $[[1 {\overline 1}0]_{{\rm FeAl}_2}^{\rm Chumak}]$ .

(iii) There is no evidence for an alternating orientation change of FeAl lamellae suggesting that FeAl₂ has inversion symmetry.

(iv) The directional solidification leads to a near $[\langle 110\rangle_{\rm FeAl}]$ || solidification direction texture.

(v) The observed orientation and interface relationship can be described well by a crystallographic model. In addition, a possible orientation relationship to the high-temperature Fe₅Al₈ phase is proposed.

Supporting information

Orientation mapping according to the inverse pole figure of the surface normal on a cross section of the arc-melted button (see insets; center of the IPF of FeAl2 corresponds to [001]_FeAl2^Chumak). Blue lines indicate minima and maxima of the lamella trace rotation with respect to the horizontal edge in the different parts of the image. Stereographic projections of the determined orientations of the colonies A to D. Blue lines indicate rotation and inclination of the lamella traces. DOI: https://doi.org/10.1107/S1600576716000911/kc5028sup1.pdf

Texture analysis of directionally solidified material: experimental XRD pole figures of FeAl2 and FeAl (defocusing corrected). Simulation of the according poles observed in the experimental pole figures. The center of the pole figure corresponds to the solidification direction. Filled symbols represent poles which are actually used in order to match the orientation of the unit cells. DOI: https://doi.org/10.1107/S1600576716000911/kc5028sup2.pdf

Footnotes

¹Throughout the article, superscripts in crystallographic notations highlight the crystallographic data set and subscripts denote the phase. Moreover, […] and 〈…〉 are used for directions and crystallographically equivalent directions, respectively, whereas (…) and {…} are used for planes and crystallographically equivalent planes, respectively. The mathematical expression describing two parallel planes in the two structures (…)_FeAl || (…)_FeAl₂ holds true also for the plane normals of the mentioned planes. If directions are parallel to plane normals, the description by Hirata et al. in the form of […]_FeAl || N(…)_FeAl₂ is used.

Acknowledgements

The authors gratefully acknowledge funding by the German Research Foundation (DFG) within the project `Fein-lamellare Fe–Al in situ Kompositwerkstoffe' (HE 1872/26-1). AK thanks the Carl-Zeiss-Foundation for financial support in the form of a postdoctoral grant. This work was partly carried out with the support of the Karlsruhe Nano Micro Facility (KNMF, https://www.knmf.kit.edu/), a Helmholtz Research Infrastructure at Karlsruhe Institute of Technology (KIT, https://www.kit.edu/index.php). We gratefully acknowledge funding of the Bruker D8 through the Helmholtz Energy Materials Characterization Platform (HEMCP) initiated by the Helmholtz Association and coordinated by Forschungszentrum Jülich. Thanks are due to Professor John Perepezko, University of Madison, Wisconsin, and Professor Sharvan Kumar, Brown University, Providence, for fruitful discussions.

References

Baddorf, A. P. & Chandavarkar, S. S. (1996). Phys. B Condens. Matter, 221, 141–144. CrossRef CAS Web of Science Google Scholar
Bastin, G. F., van Loo, F. J. J., Vrolijk, J. W. G. A. & Wolff, L. R. (1978). J. Cryst. Growth, 43, 745–751. CrossRef CAS Web of Science Google Scholar
Cahn, R. W. & Collect, J. A. (1961). Acta Metall. 9, 138–148. CrossRef CAS Web of Science Google Scholar
Christian, J. W. & Mahajan, S. (1995). Prog. Mater. Sci. 39, 1–157. CrossRef Web of Science Google Scholar
Chumak, I., Richter, K. W. & Ehrenberg, H. (2010). Acta Cryst. C66, i87–i88. Web of Science CrossRef IUCr Journals Google Scholar
Corby, R. N. & Black, P. J. (1973). Acta Cryst. B29, 2669–2677. CrossRef CAS IUCr Journals Web of Science Google Scholar
Fujiwara, T., Nakamura, A., Hosomi, M., Nishitani, S. R., Shirai, Y. & Yamaguchi, M. (1990). Philos. Mag. A, 61, 591–606. CrossRef CAS Google Scholar
Hirata, A., Mori, Y., Ishimaru, M. & Koyama, Y. (2008). Philos. Mag. Lett. 88, 491–500. Web of Science CrossRef CAS Google Scholar
Huang, S.-C. (1992). Metall. Trans. A, 23, 375–377. CrossRef Web of Science Google Scholar
Inui, H., Oh, M., Nakamura, A. & Yamaguchi, M. (1992). Acta Metall. Mater. 40, 3095–3104. CrossRef CAS Web of Science Google Scholar
Livingston, J. D. (1973). Proc. Conf. In Situ Composites, Publication NMAB-308, Vol. I, p. 87. Washington, DC: National Academy of Sciences. Google Scholar
Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272–1276. Web of Science CrossRef CAS IUCr Journals Google Scholar
Risanti, D., Deges, J., Falat, L., Kobayashi, S., Konrad, J., Palm, M., Pöter, B., Schneider, A., Stallybrass, C. & Stein, F. (2005). Intermetallics, 13, 1337–1342. Web of Science CrossRef CAS Google Scholar
Stein, F., Vogel, S. C., Eumann, M. & Palm, M. (2010). Intermetallics, 18, 150–156. Web of Science CrossRef CAS Google Scholar
Yamaguchi, M., Johnson, D. R., Lee, H. N. & Inui, H. (2000). Intermetallics, 8, 511–517. Web of Science CrossRef CAS Google Scholar