Phase equilibria among η-Fe₂Al₅ and its higher-ordered phases

Figures & data

Table 1. Crystal structures of Al-rich intermetallic phases and identified phases in this study

Phase	Formula	Composition (approx., at.% Al)	Pearson symbol	Space group
ε	Fe5Al8	57–64	cI52	I$\bar{4}$3 m [28]
ζ	FeAl2	64–67	aP19	P$\bar{1}$ [29]
η	Fe2Al5	69–73	oC24	Cmcm [12]
η”	Fe3Al7+x	69–71	oP284^a	Pmcn^b [19]/Xmcm and Immm^c [17]
η^m	?	71–72	?	C2/m11 [30]
η’	Fe3Al8	72–73	mC44	C2/c [18,23]
η”’	–^c	72–73	–^c	P21/c(0b0)00 and P21/c(0b0)s0^c [17]
θ	Fe4Al13	74–77	mC102	C2/m [31]

^aFor M = 19 (19 unit cells of the η phase stacked along the c-axis direction).

^bFifth setting of Pnma.

^cIncommensurately modulated composite crystal structure.

Figure 1. Crystal structure of η phase (space group Cmcm) reported by Burkhardt [12], which consists of a full occupied framework structure with four Fe and eight Al atoms and partially occupied chains with two Al2 and four Al3 sites along the c-axis of the orthorhombic unit cell

Table 2. Transformation temperatures and reactions from DSC heating curves in Figure 3

Nominal composition (at.% Al)	Temperature (°C)	Reaction
69.0	1150–1167	ζ → η + ε → Lη + L → L
70.0	1152–1167	η → η + L → L
70.4	387	η” → η
	1150–1169	η → η + L → L
70.8	250–343	η^m → η^m + η” → η”
	361	η” → η
	1147–1168	η → η + L → L
71.0	250–343	η^m → η^m + η” → η”
	352	η” → η
	1146–1165	η → η + L → L
71.2	343	η^m → η + η”
	1150–1165	η → η + L → L
71.4	343	η^m → η + η”
	1135	η → η + θ
	1146–1165	η → η + L → L
71.5	312	η’ → η^m + η”’
	331	η^m + η”’→ η
	343	η^m → η + η”
	1110	η → η + θ
	1145–1162	θ → η + L → L
71.6	312	η’ → η^m + η”’
	331	η^m + η”’ → η
	1087	η → η + θ
	1146–1163	θ → η + L → L
71.8	312	η’ → η^m + η”’
	331	η^m + η”’ → η
	1053	η → η + θ
	1144–1162	θ → η + L → L
72.0	312	η’ → η^m + η”’
	312–331	η^m + η”’ → η”’
	~350	η”’ → η
	1027	η → η + θ
	1146–1166	θ → η + L → L
72.2	312	η’ → η^m + η”’
	312–331	η^m + η”’ → η”’
	~360	η”’ → η
	992	η → η + θ
	1146–1161	θ → η + L → L
72.4	312	η’ → η^m + η”’
	312–331	η^m + η”’ → η”’
	~380	η”’ → η
	941	η → η + θ
	1146–1161	θ → η + L → L
72.6	312	η’ → η^m + η”’
	312–331	η^m + η”’ → η”’
	~390	η”’ → η
	900	η → η + θ
	1146–1161	θ → η + L → L
73.0	~405	η”’ → η
	1146–1161	θ → η + L → L

Figure 2. Experimentally determined phase diagram: (a) enlarged low-temperature section and (b) overall view

Figure 3. (a) L-DSC and (b and c) H-DSC heating curves for samples equilibrated at 250°C. The vertical scale is shown next to the figure. The temperatures and reactions indicated by various symbols are listed in Table 2

Table 3. Lattice parameters and volumes calculated using Burkhardt’s unit cell [12]

	Lattice parameter (nm)			Volume (nm^3)
Specimen	a	b	c
Fe-70.4Al 250°C-WQ	0.7655 ± 0.0002	0.6417 ± 0.0002	0.4216 ± 0.0001	0.2071 ± 0.0002
Fe-71.4Al 250°C-WQ	0.7656 ± 0.0002	0.6414 ± 0.0001	0.4218 ± 0.0001	0.2071 ± 0.0002
Fe-71.4Al 800°C-WQ	0.7659 ± 0.0002	0.6412 ± 0.0002	0.4221 ± 0.0001	0.2073 ± 0.0002
Fe-72.6Al 250°C-WQ	0.7658 ± 0.0004	0.6412 ± 0.0003	0.4222 ± 0.0002	0.2073 ± 0.0003
Fe-72.6Al 800°C-WQ	0.7659 ± 0.0003	0.6412 ± 0.0002	0.4223 ± 0.0002	0.2074 ± 0.0002

Figure 4. Typical powder XRD patterns obtained from specimens that form a single phase except for the 72.6 at.%Al specimen equilibrated at 250°C. The reference peak positions of the η phase with the reported lattice dimension [12] and site occupancy [17] are appended with black bars. Miller indices indexed with the ordered η’ and η” phases [18,19] are also given in the enlarged graph

Figure 5. Composition-dependent changes in lattice parameters and volumes

Figure 6. SAED patterns obtained from the η phase and its higher-ordered η’, η”, η”’, and η^m phases with several beam incidences. Superlattice reflections are highlighted with colored rectangles

Table 4. Nominal and equilibrium compositions of alloys decomposed into dual phases

				Equilibrium composition (at.% Al)
Nominalcomposition (at.% Al)	Annealing temperature (°C)	Annealing time (day)	Phase 1/Phase 2	Phase 1	Phase 2
69.0^a	300	30	ζ/η”	67.11	70.36
69.0^a	800	3	ζ/η	66.59	70.27
69.0^a	1000	1	ζ/η	66.00	68.86
70.8^b	330	12	η”/η^m	70.74	70.85
71.5^b	250	60	η^m/η’	71.26	72.15
72.6^b	250	60	η’/η”’	72.39	72.98
73.0^a	250	60	η”’/θ (/η’)	72.69	75.40
73.0^a	330	12	η”’/θ	72.55	75.25
73.0^a	500	10	η/θ	73.15	76.10
73.0^a	800	0.5	η/θ	72.20	75.21
73.0^a	1000	0.5	η/θ	72.32	74.49

^aDetermined by SEM-EDS.

^bDetermined by STEM-EDS.

Figure 7. Typical dark-field TEM images of two-phase microstructures and corresponding chemical profiles obtained by STEM-EDS for (a) 70.8 at.%Al homogenized at 330°C (b) 71.5 at.%Al homogenized at 250°C, and (c) 72.6 at.%Al homogenized at 250°C. TEM image in (a) was taken using the 3$\bar{1}$1 superlattice reflection with the incidence [11$\bar{2}$]_Cmcm. TEM image in (b) was taken using the $\bar{3}$30 superlattice reflection with the incidence [112]_Cmcm. TEM image in (c) was taken using the 11$\bar{2}$ superlattice reflection with the incidence [111]_Cmcm.

Figure 8. Detailed in situ and ex situ powder XRD patterns. Scan speed was 0.2°/h

Figure 9. Quenching temperature dependence of L-DSC curve and SAED pattern for a 70.4 at.%Al specimen. To avoid possible error in composition among samples, these data were assembled through one specimen by repeatedly equilibrating at displayed temperatures (followed by water quenching) in order from the lowest to the highest temperatures

Figure 10. (a) [100]-projected HAADF-STEM images of η” phase obtained from 70.4 at.%Al specimens homogenized at 250°C (upper panels) and 800°C (lower panels). Respective FFT images are also appended. (b) Filtered images of (a) through iFFT process using FFT spots highlighted by yellow circles. (c and d) Corresponding geometrical phase (φ₁ and φ₂) images presented in the form of cosine, where φ₁ and φ₂ are assigned as FFT spots highlighted by yellow circles. (e) Density (|▽φ₁|and|▽φ₂|) maps, where|▽φ₁|and|▽φ₂|are scaled with blue and red, respectively. (f) Geometrical phase profiles of φ₁ and φ₂ along green lines given in (c–e)

Figure 11. Bivariate histograms with variables of |▽φ₁| and |▽φ₂| obtained from (a) upper and (b) lower panels of Figure 10(e) where N_p is the number of pixels

Table 5. Nominal composition of η” phase calculated based on APB models with different width δ for various M values

	M	2	4	6	8	10	12	14	16
Composition (at.% Al)	δ = 1 c	71.43	70.71	70.48	70.36	70.29	70.24	70.20	70.18
	δ = 3 c			71.43	71.07	70.86	70.71	70.61	70.54
	δ = 5 c					71.43	71.19	71.02	70.89

Figure 12. (a) Nominal composition of η” phase as a function of number of stacking oδrthorhombic η units M calculated based on APB model with different widths of δ = 1 c, 3 c, and 5 c. SAED patterns taken from η” phase in (b) a 70.4 at.%Al specimen homogenized at 250°C and (c) a 70.8 at.%Al specimen homogenized at 330°C

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