Characterization of the Fe-rich corner of Al-Fe-Si-Ti.

The quaternary system Al-Fe-Si-Ti was studied in the iron-rich corner for sections at 50, 60 and 70 at.% Fe at 900 °C. Isothermal phase equilibria were investigated by a combination of optical microscopy, X-ray powder diffraction (XRD) followed by Rietveld refinement and Electron Probe Microanalysis (EPMA). Phase boundaries of the phases, in particular of the Laves phase (Fe2Ti) and of the extended phase field of A2/B2/D03, were investigated. Selected samples containing the Laves phase and the B2 phase were characterized by microhardness measurements at different compositions throughout the quaternary homogeneity range of the phases.

Introduction

TiAl-based alloys [1] range among of the most advanced materials for high-temperature structural applications and are considered for applications in e.g. aero-engine and automotive industry because of their combination of high strength and light weight [2], [3]. Disadvantages of TiAl-alloys are poor ductility and fracture toughness at low temperature. Fe–Al-based alloys, on the other hand, are highly interesting for the development of new light-weight structural materials and show excellent corrosion resistance, but suffer from lack of strength at high temperatures [4]. Alloying with additional elements is always a good strategy to improve the properties of materials and a sound knowledge of phase equilibria of multicomponent systems is the basis of further alloys development.

The ternary phase diagram Al–Fe–Ti is already very well investigated due to its importance for alloy development [5]. In the current work, a detailed study of the Fe-rich part of the quaternary system Al–Fe–Si–Ti is given. This work is part of a research project with the aim to systematically characterize Al-TM-Si systems which are of potential interest for various applications. Previous studies included e.g. Al–Fe–Si [6], Al–Ni–Si [7], Al–Co–Si [8], Al–V–Si [9] and Al–Mo–Si [10]. For the quaternary system Al–Fe–Si–Ti, literature data are only available in the aluminium corner and have been reviewed by Zakharov et al. [11]. For the iron-rich corner, which is in focus of the current study, no experimental data are available up to now. A short review on the current knowledge of phase diagrams in the limiting binary and ternary systems is given below.

Binary subsystems Al–Fe, Fe–Si and Fe–Ti

As the current study is focused on the Fe-rich area of Al–Fe–Si–Ti, only sub-systems including Fe will be discussed. Phase equilibria in the binary systems Al–Fe, Fe–Si and Fe–Ti are generally well known and are given in Massalski's Handbook of Binary Alloy Phase Diagrams [12]. The binary Al–Fe phase diagram was recently re-investigated and discussed by Stein and Palm [13]. The iron-rich part is dominated by the extended solid solution of Al in α-Fe (A2), and adjacent AlFe (B2) and AlFe3 (D03) ordered phases [14], [15]. The D03 ordered phase is only stable at temperatures below 600 °C. The binary Fe–Si system in [12] is already accepted from [16]. As for Al–Fe, the iron-rich alloys exist in both ordered, B2 and D03, and in disordered A2 modification. At 900 °C the solubility of Si in the D03 phase is about 27 at.%. Additional compounds established in the Fe-rich part of the system are Fe2Si (β) [17], Fe5Si3 [18] and FeSi [19]. The Fe-rich region of the Fe–Ti system [20], [21] is much less complicated. At 900 °C, the solubility of Ti in (αFe) (A2) is about 4 at.%. The hexagonal Laves phase Fe2Ti (C14) [22], [23] shows a homogeneity range from around 66 to 72 at.% Fe and melts congruently at 1427 °C. Cubic FeTi (B2 structure) [24] shows a homogeneity range of about 2 at.% and melts in a peritectic reaction at 1317 °C. A summary of all relevant binary and ternary phases is given in Table 1.

Table 1

Binary and ternary phases relevant for the current study.

Phase	Structure type	Strukturbericht designation	Pearson symbol	Space group	Reference
AlFe	CsCl	B2	cP2	Pm3¯m	[12]
AlFe3	BiF3	D03	cF16	Fm3¯m	[12]
Fe3Si (α1)	BiF3	D03	cF16	Fm3¯m	[12]
Fe3Si (α2)	CsCl	B2	cP2	Pm3¯m	[12]
Fe5Si3	Mn5Si3	D88	hP16	P63/mcm	[18]
FeSi	FeSi	B20	cP8	P213	[19]
Fe2Ti	MgZn2	C14	hP12	P63/mmc	[22]
FeTi	CsCl	B2	cP2	Pm3¯m	[24]
FeSiTi (τ2)	FeSiTi		oI36	Ima2	[37]
Fe40Si31Ti13, Fe4Si3Ti (τ3)	Pd40Sn31Y13		hP168	P6/mmm	[25]

Ternary subsystems Al–Fe–Si, Al–Fe–Ti and Fe–Si–Ti

Fig. 1 shows isothermal sections for the three relevant ternary systems at 900 °C which were taken from Marker et al. [6] for Al–Fe–Si (a), from Palm and Lacaze [5] for Al–Fe–Ti (b), and from Schuster et al. [25] for Fe–Si–Ti (c).

Fig. 1

Ternary isothermal sections at 900 °C used as reference in the current study: (a) Al–Fe–Si [6]; (b) Al–Fe–Ti [5]; (c) Fe–Si–Ti [25].

The ternary system Al–Fe–Si was frequently investigated and is quite complicated due to the large number of ternary phases. A number of detailed investigations were performed especially in the aluminium-rich corner. A comprehensive compendium of evaluated constitutional data including recent updates is given in [26], [27], [28]. For the current study the experimental isothermal section at 900 °C given recently [6] was used. The iron-rich corner is dominated by an extended A2/B2/D03 phase field. At temperatures below 600 °C it was found that phase separation between B2/D03 and A2/D03 occurs in the ternary system [29], [30]. At 700 °C, however, no phase separation was observed [29]. At 900 °C the A2 modification ranges from approximately 26 at. % Al in Fe–Al to 13.5 at.% Si in Fe–Si. The line separating the B2 and D03 phase field was not included in the original drawing in [6], but has been assessed (estimated) later based on Rietveld refinement of several samples annealed at 900 °C [31]. FeSi dissolves about 12 at.% of Al while Fe5Si3 does not show any significant solubility for Al.

Detailed compilations of the ternary system Al–Fe–Ti are given by Raghavan [32] and Ghosh [33]. For our work the assessment of the ternary system given by Palm and Lacaze [5] was taken. Three ternary phases are reported in the system, but only two of them were confirmed by [5], [33]: Al2FeTi with primitive tetragonal crystal structure which shows a wide homogeneity range, and cubic Al8FeTi3 (L12 structure, cP4, Pmm, AuCu3-type). In the Fe-rich part a two-phase field between B2 and L21 exists. Phase fields of A2/B2 and B2/L21 are separated by second order transition lines. The Laves phase (Fe2Ti) and FeTi show extended solubilities for Al [34]. The solid solubility of Ti in α-Fe (A2) and AlFe (B2) increases with increasing temperature reaches up to approximately 10 at.% at 900 °C. The D03 ordered phase is only present in the ternary and shows a solubility of up to approx. 25 at.% Ti at 900 °C [5], [35]. This means a significant stabilization of D03 by the addition of Ti, as the D03/B2 transition temperature increases from 574 °C in the binary to 1212 °C in the ternary system [34]. Note that this phase field is denoted L21 (corresponding to the ternary ordered variant) in Fig. 1(b), but will be designated as D03 throughout the current work for the sake of consistency.

The ternary system Fe–Si–Ti is reviewed by Raghavan [36]. Similar to Al–Fe–Si it is a rather complex system with many ternary compounds. For the current investigation only two ternary phases are of interest: orthorhombic FeSiTi (τ2) [37] and Fe4Si3Ti (τ3) with hexagonal Pd40Sn31Y13-structure type. Schuster et al. [25] report a large solubility of more than 25 at.% Si in the Laves phase Fe2Ti. At 900 °C, the composition of FeSiTi (τ2) is varying between 31.7–37.0 at.% Fe, 30.5–33.5 at.% Si and 31.0–37.5 at.% Ti. A solubility of 9.5 at.% Ti was found for Fe5Si3 [25]. The solubility of Ti in FeSi is limited to 1 at.%. The maximum solubility of Ti in the A2/B2/D03 phase field was found to be around 9 at.% [25].

Experimental

More than 70 samples were prepared from pure elements using aluminium slug (99.999% Alfa Aesar, Karlsruhe, Germany), iron sheet (99.95%, melted and cast in vacuum), silicon lump (99.9999% Alfa Aesar, Karlsruhe, Germany) and titanium rod (99.99% Alfa Aesar, Karlsruhe, Germany). Calculated amounts of the elements were weighed to an accuracy of better than 0.06% and then arc melted on a water-cooled copper plate under an argon atmosphere of 0.5 bar, using zirconium as a getter material. After the first melting, each ingot was pulverized, pressed to a pellet and re-melted for homogenization. The samples were weighed back after this procedure in order to check for mass losses, which were found to be between 0.2 and 0.6%. For equilibration the ingots were wrapped in Mo-foil, sealed in evacuated quartz glass tubes and annealed at 900 °C for 360–1030 h in a muffle-furnace. The variation of annealing time for different sample series did not have significant effects on the observed phase compositions. Although it cannot be ruled out that some of the samples were not fully equilibrated after annealing, we conclude that the annealing time was generally sufficient to reach equilibrium at 900 °C. All steps involving vacuum and inert gas were done with due care in order to minimize or exclude oxygen incorporation. After quenching in water, the samples were separated into several pieces that were used for subsequent characterization.

For metallographic investigations, pieces of the quenched samples were incorporated into a mixture of resin and carbon powder. The embedded samples were ground and polished in order to perform optical microscopy as well as electron probe microanalysis (EPMA). For the investigation by optical microscopy a Zeiss Axiotech 100 microscope equipped for operation under darkfield, brightfield and polarized light was used.

Selected samples were analysed by EPMA in order to determine reliable compositions of the various phases. Measurements were performed on a Cameca SX 100 electron probe and a JEOL JXA8800 micro-analyser, using wavelength dispersive X-ray spectroscopy (WDS) for quantitative analysis. Pure element standards (aluminium, iron, titanium and silicon) were used for calibration before the measurement with a relative accuracy of about ±1%. The measurements were carried out at 15–20 kV and 20–30 nA. Conventional ZAF matrix correction was used to calculate the final compositions.

X-ray powder diffraction was performed with Cu Kα-radiation, using a Bruker D8 Advance diffractometer in Bragg–Brentano geometry. An energy-dispersive detector (Sol-X, Lithium drifted Silicon detector) was used in order avoid background/peak ratio problems related to the X-ray fluorescence of Fe caused by Cu Kα-radiation. The X-ray powder diffractograms were refined with the program TOPAS® 3 [38].

Microhardness measurements were performed using the microhardness tester FISCHERSCOPE® HM2000 Analyser on the embedded samples previously analysed with EPMA. All measurements were performed under the following condition: F = 50 mN for 20 s. From the recorded measurement plot, the Vickers hardness HV was used for characterization. Evaluation of data was done with the WIN-HCU® software [39], which is a computer-controlled measuring system for microhardness testing and determination of material parameters according to ISO 14577-1.

Results and discussion

Isothermal sections at 900 °C

A full isothermal section of a quaternary system can only be represented in three dimensions (in the form of a composition tetrahedron), which is, however, not very practical for use. In the current work three two-dimensional isothermal sections at 900 °C and at fixed Fe-content of 50, 60 and 70 at.% respectively are presented. It should be pointed out, that (similar to e.g. vertical sections in the ternary) these graphical sections do not contain the full phase diagram information, as they refer to phase compositions that usually do no lie within the section. Therefore a full list of experimental results for all investigated samples (including phase compositions measured by EPMA and cell parameters refined by powder XRD) is given in Table 2.

Table 2

Experimental phase compositions and cell parameters of selected samples at 900 °C in the sections of 50, 60 and 70 at.% Fe. –Not measured due to fine microstructure, *–additional sample.

Sample no.	Nominal sample composition (at.%)	Annealing temperature/Time (°C)/h	Phase (XRD)	Cell parameter (Å)			Phase composition determined by EPMA
							Al (at.%)	Fe (at.%)	Si (at%)	Ti (at%)
01	Al5Fe50Si5Ti40	Quartz 900; 400	Fe2Ti	a = 4.832(1)		c = 7.846(1)	5.4(1)	50.7(1)	8.3(1)	35.6(1)
			FeTi	a = 2.976(1)			4.8(2)	47.1(1)	0.6(1)	47.5(2)
02	Al5Fe50Si10Ti35	Quartz 900; 400	Fe2Ti	a = 4.804(1)		c = 7.774(1)	4.0(2)	49.4(1)	11.4(2)	35.2(1)
03	Al5Fe50Si15Ti30	Quartz 900; 400	Fe2Ti	a = 4.806(1)		c = 7.777(1)	2.3(1)	48.5(1)	17.2(1)	32.0(1)
			D03	a = 5.953(1)			26.0(1)	55.2(1)	1.6(1)	17.2(2)
04	Al5Fe50Si20Ti25	Quartz 900; 400	Fe2Ti	a = 4.795(1)		c = 7.711(1)	2.4(1)	46.6(3)	21.7(1)	29.3(2)
			D03	a = 5.770(1)			23.6(4)	66.9(7)	5.5(3)	4.0(8)
05	Al5Fe50Si25Ti20	Quartz 900; 400	Fe2Ti	a = 4.794(1)		c = 7.676(2)	2.2(3)	46.2(5)	25.0(2)	26.6(5)
			D03	a = 5.705(2)			11.0(1)	66.2(1)	17.3(1)	5.5(1)
			FeSiTi	a = 6.994(2)	b = 10.813(3)	c = 6.275(2)	0.0(1)	34.2(1)	33.2(1)	32.6(1)
06	Al5Fe50Si30Ti15	Quartz 900; 400	B2	a = 2.827(1)			8.9(1)	61.7(1)	26.4(1)	2.9(1)
			Fe4Si3Ti	a = 17.218(6)		c = 7.991(5)	0.7(1)	47.7(1)	35.8(1)	15.7(1)
			FeSiTi	a = 6.987(1)	b = 10.811(1)	c = 6.271(1)	0.2(1)	35.5(2)	32.8(1)	31.5(1)
07	Al5Fe50Si35Ti10	Quartz 900; 400	B2	a = 2.829(1)			9.9(4)	57.2(7)	27.8(6)	5.0(5)
			FeSi	a = 4.518(1)			6.8(1)	50.1(1)	42.7(3)	0.4(1)
			Fe4Si3Ti	a = 17.230(1)		c = 7.980(1)	0.8(1)	48.1(3)	35.8(3)	15.3(6)
			FeSiTi	a = 6.971(2)	b = 10.810(4)	c = 6.264(2)	1.4(4)	38.9(9)	33.1(9)	26.7(3)
08	Al5Fe50Si40Ti5	Quartz 900; 400	B2	a = 2.828(1)			10.3(2)	60.6(3)	26.6(1)	2.5(3)
			FeSi	a = 4.515(1)			6.1(1)	50.3(1)	43.4(1)	0.2(1)
			Fe4Si3Ti	a = 17.229(3)		c = 7.983(2)	0.8(1)	48.1(3)	36.0(1)	15.2(4)
			FeSiTi	a = 7.055(7)	b = 10.693(1)	c = 6.388(1)		Trace
09	Al20Fe50Si5Ti25	Quartz 900; 400	Fe2Ti	a = 4.823(1)		c = 7.815(1)	11.0(1)	48.6(1)	10.4(1)	30.0(1)
			D03	a = 5.865(1)			25.7(2)	51.0(1)	1.0(1)	22.3(1)
10	Al20Fe50Si10Ti20	Quartz 900; 400	Fe2Ti	a = 4.809(2)		c = 7.753(4)	8.2(3)	46.5(3)	16.9(1)	28.4(3)
			D03	a = 5.827(3)			32.7(4)	53.5(2)	1.8(2)	12.0(4)
11	Al20Fe50Si15Ti15	Quartz 900; 400	Fe2Ti	a = 4.808(1)		c = 7.697(3)	6.9(1)	44.7(1)	22.6(1)	25.7(2)
			B2	a = 2.890(1)			33.6(7)	56.0(1)	6.1(5)	4.4(4)
			FeSiTi	a = 7.011(5)	b = 10.802(8)	c = 6.285(5)	0.4(5)	34.1(5)	32.4(4)	33.0(5)
12	Al20Fe50Si20Ti10	Quartz 900; 400	B2	a = 2.860(2)			27.0(3)	55.8(2)	14.9(2)	2.4(1)
			FeSiTi	a = 6.992(5)	b = 10.810(8)	c = 6.279(5)	–	–	–	–
13	Al20Fe50Si25Ti5	Quartz 900; 400	FeSi	a = 4.535(2)			11.0(1)	50.0(1)	38.5(1)	0.5(1)
			B2	a = 2.843(2)			23.5(2)	52.8(4)	21.9(2)	1.9(1)
			FeSiTi	a = 6.995(4)	b = 10.829(1)	c = 6.271(5)	–	–	–	–
14	Al35Fe50Si5Ti10	Quartz 900; 600	Fe2Ti	a = 4.821(1)		c = 7.730(1)	10.6(1)	44.5(2)	19.1(1)	25.8(3)
			B2	a = 2.913(1)			38.9(1)	52.2(2)	2.0(1)	6.9(1)
15	Al35Fe50Si10Ti5	Quartz 900; 400	B2	a = 2.889(3)			38.5(2)	52.2(1)	7.3(2)	1.9(1)
			FeSiTi	a = 7.004(1)	b = 10.818(1)	c = 6.285(1)	5.8(1)	35.9(1)	29.5(1)	28.8(1)
16	Al27.5Fe50Si5Ti17.5	Quartz 900; 430	Fe2Ti	a = 4.834(1)		c = 7.785(9)	13.3(3)	44.4(1)	14.4(2)	27.9(1)
			B2	a = 2.926(4)			33.1(1)	51.4(2)	1.2(1)	14.4(1)
17	Al30Fe50Si5Ti15	Quartz 900; 430	Fe2Ti	a = 4.826(4)		c = 7.766(7)	12.7(5)	46.1(2)	15.1(2)	26.0(4)
			B2	a = 2.923(3)			35.5(4)	52.0(3)	1.3(2)	11.3(4)
18	Al32.5Fe50Si5Ti12.5	Quartz 900; 430	Fe2Ti	a = 4.825(1)		c = 7.748(1)	10.9(1)	46.6(1)	16.8(2)	25.6(1)
			B2	a = 2.920(4)			37.8(1)	51.8(1)	1.4(1)	9.0(1)
19	Al35Fe50Si5Ti10	Quartz 900; 430	Fe2Ti	a = 4.823(1)		c = 7.725(1)	12.8(9)	44.5(3)	18.4(5)	24.4(7)
			B2	a = 2.917(5)			39.7(1)	51.8(1)	1.8(1)	6.7(1)
20	Al37.5Fe50Si5Ti7.5	Quartz 900; 430	B2	a = 2.913(6)			40.3(2)	51.9(4)	2.0(3)	5.7(3)
			FeSiTi	a = 6.991(1)	b = 10.825(1)	c = 6.282(1)	5.6(1)	36.9(1)	29.0(1)	28.5(1)
			Fe2Ti	–		–	10.2(1)	43.8(1)	20.3(1	25.9(1)
21	Al40Fe50Si5Ti5	Quartz 900; 430	B2	a = 2.907(1)			42.4(2)	51.6(2)	2.9(1)	3.2(1)
			FeSiTi	a = 7.000(4)	b = 10.821(1)	c = 6.281(7)	4.1(1)	36.6(1)	30.2(1)	29.1(1)
22	Al30Fe50Si15Ti5	Quartz 900; 430	B2	a = 2.871(1)			33.4(2)	52.4(1)	12.5(1)	1.6(1)
			FeSiTi	a = 6.998(3)	b = 10.807(7)	c = 6.286(4)	8.1(1)	40.1(1)	28.2(1)	23.7(1)
23	Al30Fe50Si19Ti1	Quartz 900; 430	B2	a = 2.850(1)			30.3(1)	50.1(1)	18.9(1)	0.7(1)
24	Al17.5Fe50Si17.5Ti15	Quartz 900; 430	Fe2Ti	a = 4.798(2)		c = 7.684(4)	6.4(2)	46.1(3)	22.5(1)	25.0(3)
			B2	a = 2.883(1)			30.6(1)	58.9(5)	6.8(1)	3.7(4)
			FeSiTi	a = 6.998(4)	b = 10.799(6)	c = 6.276(3)	0.1(1)	33.9(1)	32.8(1)	33.3(1)
25	Al13.8Fe50Si20Ti16.2	Quartz 900; 430	Fe2Ti	a = 4.796(1)		c = 7.687(1)	5.7(3)	46.1(1)	23.3(1)	25.0(2)
			B2	a = 2.869(1)			24.7(2)	61.8(2)	10.2(2)	3.3(3)
			FeSiTi	a = 7.007(1)	b = 10.814(1)	c = 6.275(1)	0.1(1)	34.0(2)	32.7(1)	33.1(1)
26	Al10Fe50Si22.5Ti17.5	Quartz 900; 430	Fe2Ti	a = 4.799(3)			4.0(1)	46.3(6)	23.8(2)	25.9(5)
			B2	a = 2.860(2)			17.6(2)	65.0(1)	13.4(1)	3.9(1)
			FeSiTi	a = 7.001(5)	b = 10.815(7)	c = 6.280(4)	0.0(1)	34.6(3)	32.7(1)	32.7(2)
27	Al2Fe50Si43Ti5	Quartz 900; 600	FeSi	a = 4.500(1)			*–	*–	*–	*–
			Fe4Si3Ti	a = 17.212(2)		c = 7.982(1)	*–	*–	*–	*–
28	Al4Fe60Si4Ti32	Quartz 900; 480	Fe2Ti	a = 4.804(1)		c = 7.826(1)	4.9(4)	60.5(2)	2.1(3)	32.6(2)
29	Al4Fe60Si12Ti24	Quartz 900; 480	Fe2Ti	a = 4.784(2)		c = 7.764(2)	2.3(2)	55.8(4)	13.5(3)	28.4(4)
			A2	a = 2.893(1)			7.2(6)	71.5(3)	7.6(5)	13.7(3)
30	Al4Fe60Si20Ti16	Quartz 900; 480	Fe2Ti	a = 4.781(2)		c = 7.693(4)	1.2(1)	51.9(4)	22.0(2)	24.9(4)
			D03	a = 5.712(3)			6.8(2)	73.1(2)	15.9(2)	4.2(2)
31	Al4Fe60Si24Ti12	Quartz 900; 480	Fe2Ti	a = 4.785(4)		c = 7.665(6)	1.8(1)	49.1(3)	24.9(3)	24.1(1)
			D03	a = 5.687(4)			4.8(1)	67.4(3)	21.2(2)	6.6(2)
			FeSiTi	a = 6.992(5)	b = 10.804(8)	c = 6.270(5)	0.0(1)	34.7(4)	32.9(2)	32.3(2)
32	Al4Fe60Si28Ti8	Quartz 900; 480	D03	a = 5.657(4)			4.6(1)	65.0(2)	26.3(2)	4.2(1)
			Fe4Si3Ti	a = 17.212(1)		c = 7.984(6)	0.5(1)	48.0(1)	36.0(1)	15.6(1)
			FeSiTi	a = 6.977(6)	b = 10.785(8)	c = 6.266(5)	0.1(1)	35.8(4)	33.0(3)	31.1(2)
33	Al4Fe60Si32Ti4	Quartz 900; 480	B2	a = 2.819(1)			5.3(1)	64.2(2)	28.4(1)	2.2(1)
			FeSi	a = 4.502(2)			4.2(1)	50.3(2)	45.4(2)	0.1(1)
			Fe4Si3Ti	a = 17.208(8)		c = 7.978(4)	0.3(1)	53.6(3)	37.1(1)	9.0(2)
			Fe5Si3	a = 6.851(4)		c = 4.718(4)	–	–	–	–
34	Al8Fe60Si8Ti24	Quartz 900; 480	Fe2Ti	a = 4.797(1)		c = 7.792(2)	4.9(3)	56.1(3)	9.5(3)	29.5(4)
			A2	a = 2.904(1)			19.1(2)	75.2(2)	0.3(1)	5.4(2)
35	Al8Fe60Si12Ti20	Quartz 900; 480	Fe2Ti	a = 4.787(5)		c = 7.751(8)	3.4(3)	52.5(4)	16.0(2)	28.1(5)
			A2	a = 2.900(3)			18.0(2)	77.8(3)	1.4(2)	2.8(3)
36	Al8Fe60Si16Ti16	Quartz 900; 480	Fe2Ti	a = 4.785(5)		c = 7.706(8)	2.6(2)	50.6(4)	20.8(2)	26.0(4)
			D03	a = 5.761(6)			15.0(1)	73.3(3)	8.5(1)	3.2(2)
37	Al8Fe60Si20Ti12	Quartz 900; 480	Fe2Ti	a = 4.788(3)		c = 7.671(5)	3.1(1)	48.9(2)	24.0(2)	24.1(2)
			D03	a = 5.706(4)			10.5(2)	67.1(3)	17.1(2)	5.3(3)
38	Al8Fe60Si24Ti8	Quartz 900; 480	D03	a = 5.676(1)			9.1(1)	65.1(3)	21.8(2)	4.1(3)
			FeSiTi	a = 6.986(3)	b = 10.804(7)	c = 6.270(4)	0.1(1)	35.7(4)	32.5(3)	31.7(3)
39	Al8Fe60Si28Ti4	Quartz 900; 480	B2	a = 2.826(1)			8.8(1)	62.4(2)	26.4(2)	2.4(1)
			Fe4Si3Ti	a = 17.219(8)		c = 7.981(5)	0.7(1)	48.3(2)	35.9(2)	15.2(2)
40	Al12Fe60Si4Ti24	Quartz 900; 480	Fe2Ti	a = 4.794(1)		c = 7.803(1)	7.7(4)	59.3(2)	5.0(2)	28.0(4)
			B2	a = 2.914(1)			23.0(2)	61.4(3)	0.5(1)	15.1(3)
41	Al12Fe60Si12Ti16	Quartz 900; 480	Fe2TiD03	a = 4.789(4)		c = 7.725(6)	4.3(1)	51.4(2)	18.4(2)	25.9(2)
				a = 5.799(5)			21.0(2)	71.8(4)	3.9(2)	3.2(4)
42	Al12Fe60Si20Ti8	Quartz 900; 480	Fe2Ti	–		–	6.0(7)	48.3(8)	25.8(8)	20.0(9)
			D03	a = 5.698(3)			13.6(2)	65.7(3)	16.9(2)	3.7(2)
			FeSiTi	a = 6.987(5)	b = 10.812(8)	c = 6.273(4)	0.6(2)	36.3(3)	32.0(3)	31.1(4)
43	Al12Fe60Si24Ti4	Quartz 900; 480	B2	a = 2.843(2)			12.3(1)	62.5(2)	22.8(2)	2.4(1)
			FeSiTi	a = 6.974(7)	b = 10.853(3)	c = 6.251(2)	1.0(1)	38.4(1)	32.0(1)	28.5(1)
44	Al16Fe60Si12Ti12	Quartz 900; 480	Fe2Ti	a = 4.787(5)		c = 7.704(8)	5.4(2)	50.6(3)	19.6(2)	24.4(2)
			D03	a = 5.777(6)			23.2(3)	67.7(3)	5.7(2)	3.4(3)
45	Al20Fe60Si4Ti16	Quartz 900; 480	Fe2Ti	a = 4.789(4)		c = 7.778(6)	7.7(3)	55.7(3)	10.1(2)	26.5(4)
			D03	a = 5.823(5)			24.2(4)	61.8(3)	1.4(2)	12.7(3)
46	Al20Fe60Si12Ti8	Quartz 900; 480	Fe2Ti	a = 4.795(6)		c = 7.689(7)	7.4(5)	50.8(1)	20.3(6)	21.5(2)
			B2	a = 2.875(7)			23.7(5)	63.8(6)	8.7(3)	3.9(6)
47	Al28Fe60Si4Ti8	Quartz 900; 480	Fe2Ti	a = 4.798(5)		c = 7.742(7)	15.7(5)	54.7(39)	11.5(3)	18.1(3)
			B2	a = 2.902(3)			29.9(2)	61.9(2)	2.2(1)	6.0(1)
48	Al28Fe60Si8Ti4	Quartz 900; 480	Fe2Ti	a = 4.797(1)		c = 7.695(2)	*–	*–	*–	*–
			B2	a = 2.881(1)			28.5(2)	61.4(2)	7.0(1)	3.1(1)
49	Al2Fe60Si36Ti2	Quartz 900; 618	D03	a = 5.645(1)			3.5(3)	64.8(4)	30.1(5)	1.7(1)
			FeSi	a = 4.500(1)			1.5(1)	52.9(1)	43.9(1)	1.7(1)
			Fe5Si3	a = 6.786(1)		c = 4.727(1)	1.8(2)	61.2(6)	34.6(6)	2.4(1)
50	Al10.8Fe60Si27.2Ti2	Quartz 900; 618	FeSi	a = 4.515(1)			*–	*–	*–	*–
			B2	a = 2.825(1)			10.6(3)	58.9(7)	28.3(3)	2.1(4)
51	Al17Fe60Si21Ti2	Quartz 900; 618	B2	a = 2.840(1)			16.8(2)	59.2(1)	22.0(3)	2.0(0)
52	Al10.9Fe60Si25.9Ti3.2	Quartz 900; 618	B2	a = 2.828(1)			11.2(1)	59.5(2)	27.0(1)	2.3(1)
			FeSiTi	a = 6.997(4)	b = 10.775(1)	c = 6.270(4)	0.2(4)	36.0(5)	34.5(1)	29.3(8)
53	Al5Fe60Si33Ti2	Quartz 900; 1030	D03	a = 5.647(1)			3.7(1)	65.3(1)	28.5(1)	2.5(1)
			FeSi	a = 4.894(1)			*–	*–	*–	*–
			Fe4Si3Ti	a = 17.321(1)		c = 8.000(1)	*–	*–	*–	*–
			Fe5Si3	a = 6.846(1)		c = 4.723(1)	0.2(2)	56.1(2)	37.6(1)	6.1(1)
54	Al5Fe60Si34Ti1	Quartz 900; 1030	D03	a = 5.648(2)			2.3(1)	66.7(1)	28.1(1)	2.9(1)
			FeSi	a = 4.896(2)			*–	*–	*–	*–
			Fe4Si3Ti	a = 16.777(7)		c = 8.112(7)	0.0(1)	55.5(2)	37.6(2)	6.9(2)
			Fe5Si3	a = 6.826(3)		c = 4.724(2)	0.3(2)	56.4(2)	37.6(2)	5.7(1)
55	Al1.8Fe70Si1.8Ti26.4	Quartz 900; 360	Fe2Ti	a = 4.785(1)		c = 7.800(1)	1.4(1)	67.0(3)	1.9(2)	29.6(2)
			A2	a = 2.882(1)			4.2(1)	90.4(2)	0.1(1)	.0.5.3(2)
56	Al3Fe70Si6Ti21	Quartz 900; 360	Fe2Ti	a = 4.781(1)		c = 7.784(1)	1.5(1)	61.7(2)	7.9(1)	28.9(1)
			A2	a = 2.884(1)			6.1(1)	88.9(3)	0.6(1)	4.3(1)
57	Al3Fe70Si12Ti15	Quartz 900; 360	Fe2Ti	a = 4.776(5)		c = 7.733(8)	0.9(1)	56.1(2)	17.0(1)	26.0(2)
			A2	a = 2.875(3)			5.4(1)	87.4(3)	4.9(1)	2.3(2)
58	Al3Fe70Si18Ti9	Quartz 900; 360	Fe2Ti	a = 4.775(3)		c = 7.693(5)	0.5(1)	53.2(2)	21.5(1)	24.8(2)
			D03	a = 5.708(4)			3.9(1)	77.2(2)	15.7(1)	3.2(2)
59	Al3Fe70Si21Ti6	Quartz 900; 360	Fe2Ti	a = 4.785(3)		c = 7.673(6)	0.5(1)	51.8(2)	23.0(1)	24.6(2)
			D03	a = 5.690(1)			3.0(1)	71.5(2)	20.3(2)	5.3(1)
60	Al3Fe70Si24Ti3	Quartz 900; 360	D03	a = 5.668(4)			2.9(1)	70.8(2)	23.2(1)	3.1(2)
61	Al6Fe70Si3Ti21	Quartz 900; 360	Fe2Ti	a = 4.785(4)		c = 7.796(6)	3.7(1)	63.2(2)	4.2(1)	28.9(2)
			A2	a = 2.895(2)			11.0(1)	84.0(2)	0.2(1)	4.8(2)
62	Al9Fe70Si6Ti15	Quartz 900; 360	Fe2Ti	a = 4.782(1)		c = 7.778(1)	3.9(1)	58.3(3)	10.6(1)	27.2(2)
			A2	a = 2.897(1)			14.3(1)	81.8(2)	0.6(1)	3.3(2)
63	Al9Fe70Si12Ti9	Quartz 900; 360	Fe2Ti	a = 4.780(6)		c = 7.704(9)	2.1(1)	53.1(3)	20.1(2)	24.8(3)
			A2	a = 2.879(4)			12.2(2)	78.2(2)	7.6(1)	2.0(1)
64	Al9Fe70Si18Ti3	Quartz 900; 360	D03	a = 5.698(1)			8.9(1)	70.6(2)	17.4(1)	3.1(1)
65	Al15Fe70Si3Ti12	Quartz 900; 360	Fe2Ti	a = 4.788(1)		c = 7.791(2)	7.4(4)	59.4(6)	7.5(3)	25.7(7)
			A2	a = 2.903(1)			19.4(1)	76.1(2)	0.2(1)	5.3(1)
66	Al15Fe70Si6Ti9	Quartz 900; 360	Fe2Ti	a = 4.786(1)		c = 7.748(1)	4.4(2)	53.5(2)	16.0(1)	26.1(3)
			A2	a = 2.901(5)			19.6(2)	76.9(1)	1.5(1)	2.0(1)
67	Al15Fe70Si12Ti3	Quartz 900; 360	B2	a = 2.867(5)			14.9(1)	70.3(2)	11.7(1)	3.1(1)
68	Al21Fe70Si3Ti6	Quartz 900; 360	Fe2Ti	a = 4.785(2)		c = 7.768(6)	6.0(5)	54.0(3)	14.3(4)	25.7(5)
			B2	a = 2.910(1)			23.2(2)	72.5(2)	1.1(1)	3.2(1)
69	Al21Fe70Si6Ti3	Quartz 900; 360	Fe2Ti	a = 4.787(8)		c = 7.7090(x)	8.2(4)	56.2(3)	16.4(3)	19.2(3)
			B2	a = 2.893(5)			21.6(1)	70.9(2)	5.3(1)	2.2(1)
70	Al16.4Fe70Si1Ti12.6	Quartz 900; 618	Fe2Ti	a = 4.800(7)		c = 7.817(1)	8.5(3)	61.6(2)	3.0(1)	26.9(2)
			A2	a = 2.905(4)			18.6(1)	76.1(1)	0.0(1)	5.3(2)

For the depiction of experimental data points in the sections, the projection of the intersection between phase field and section plane is given in the respective figures. This procedure is shown schematically in Fig. 2. A four-phase field has the form of a general tetrahedron which may intersect with the section plane in the form of a triangle (if three of the phase compositions lie on one side of the plane, and one on the opposite side), or a quadrangle (if two of the phase compositions lie on each side of the plane). Likewise, the projection of a three-phase field in the plane is a line, and the projection of a two-phase field is a point within the plane (not shown in Fig. 2). Knowing the composition of the phases (Table 2), the piercing points within the section plane can be easily determined by vector calculation. All experimental data points shown in Fig. 3, Fig. 4, Fig. 5 (sections at 50, 60 and 70 at.% Fe) were determined by this procedure. The lines in Fig. 3 and 4 show the intersection line of the measured tie-triangle with the isothermal section (they are projections of the tie-triangles within the plane). The endpoints of these lines denote exactly the positions of the phase boundary (zero-fraction lines).

Fig. 2

(a) Schematic representation of the intersection of three- and four-phase equilibria with a two-dimensional section within a composition tetrahedron. Intersection lines and planes to be shown within the two-dimensional section are highlighted in (b).

Fig. 3

Isothermal section of Al–Fe–Si–Ti at 900 °C and 50 at% Fe. Single-phase field: blue, two-phase field: orange, three-phase field: violet, four-phase field: white. Experimental intersection points from samples situated within the section are shown as filled circles, points from samples situated in other sections are shown as open circles. The dotted line separates B2 and D03 phase fields. Note that the lines shown in the three-phase fields are projections of the measured tie-triangles within the plane. They should not be confused with tie-lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4

Isothermal section of Al–Fe–Si–Ti at 900 °C and 60 at% Fe. Single-phase field: blue, two-phase field: orange, three-phase field: violet, four-phase field: white. Experimental intersection points from samples situated within the section are shown as filled circles, points from samples situated in other sections are shown as open circles. The dotted lines separate A2, B2 and D03 phase fields. Note that the lines shown in the three-phase fields are projections of the measured tie-triangles within the plane. They should not be confused with tie-lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5

Isothermal section of Al–Fe–Si–Ti at 900 °C and 70 at% Fe. Single-phase field: blue, two-phase field: orange, three-phase field: violet. Experimental intersection points from samples situated within the section are shown as filled circles, points from samples situated in other sections are shown as open circles. The dotted lines separate A2, B2 and D03 phase fields. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Furthermore it should be pointed out, that the projection of a specific equilibrium may show up in more than one section. For example, sample number 05 in Table 2 contains phases with Fe-contents of 34 (FeSiTi), 46 (Fe2Ti) and 66 (D03) at.% Fe. Thus, the projection of this specific three-phase equilibrium can be draw in the sections at 50 as well as at 60 at.% Fe.

Besides the investigation of phase compositions by EPMA, the crystallographic structures of all coexisting phases were identified by X-ray powder diffraction. Cell parameters and other crystallographic parameters were refined by the Rietveld method. This data are of special importance for the identification of phases with extended composition range and furthermore allow the distinction between A2, B2 and D03 phase regions, which form a common phase field in the quaternary system. It should be emphasized, however, that the distinction of A2, B2 and D03/L21 is not always unambiguous. It is known that the ordering transitions cannot always be suppressed by quenching, and that A2 disorder can be attained by pulverizing B2 or D03 ordered samples for powder XRD investigations. Thus, the course of the lines separating these fields have to be taken with some caution, and additional experiments, e.g. with transmission electron microscopy would be helpful to check these results.

Fig. 3, Fig. 4, Fig. 5 show the sections at 50, 60 and 70 at.% Fe, respectively. Different colouring was used to distinguish single-, two-, three- and four-phase regions. Experimental data points (piercing points) are given as small circles, which are connected with lines in case of three- and four-phase fields. Black circles correspond to samples lying within the section; while withe circles correspond to samples lying in an adjacent section. The course of the second order transition lines between A2, B2 and D03 (L21) phase fields are shown in dotted lines. All limiting ternary phase equilibria were taken from the isothermal sections at 900 °C shown in Fig. 1.

The section at 50 at.% Fe

The section at 50 at.% Fe given in Fig. 3 shows two single-phase fields, the Laves phase Fe2Ti which extends continuously from the ternary Al–Fe–Ti to the ternary Fe–Si–Ti system, and a small V-shaped phase field of B2/D03 which is situated around the Al50Fe50 corner. In this section, the Laves phase shows a solubility of about 13–19 at.% Al and 13 - 23 at.% Si. In addition, the solid solution of Al in FeSi is situated at 50 at% Fe in the limiting ternary system Al–Fe–Si. This phase does not have a significant solubility for Ti. Six two-phase fields were observed in the section, including the extended fields [B2/D03 + Fe2Ti] and [B2/D03 + τ2]. Four of the six three-phase fields found in the section originate from the ternary Fe–Si–Ti system. In the Si-rich part, two four-phase equilibria, [B2 + FeSi + τ2 + τ3] and [D03 + Fe5Si3 + FeSi + τ3] are observed. These four-phase equilibria touch the limiting Al–Fe–Si system at the solid solution of Al in FeSi. Note that the four-phase equilibrium [B2 + FeSi + τ2 + τ3] was found in two samples (numbers 07 and 08) which differ significantly regarding the composition of B2. The compositions determined from sample 08 were found to be more reliable due to better homogeneity of the sample and also due to much better agreement with the results from the section at 60 at.% Fe, so these values were taken to draw the section in Fig. 3.

The section at 60 at.% Fe

The section at 60 at.% Fe given in Fig. 4 is dominated by the two-phase field [A2/B2/D03 + Fe2Ti] which covers a large part of the section. It is bordered by the single-phase field of B2/D03 and the Laves phase Fe2Ti in the Ti-rich corner. The latter again shows a continuous extension from the ternary Al–Fe–Ti to the ternary Fe–Si–Ti system. Three samples in the section at 60 at.% Fe show the equilibrium A2+ Fe2Ti. Supplemented by the tie-lines of samples from the section at 70 at.% Fe, the course of the line separating the A2 and D03 fields was assessed. Equilibria with A2 do not extend to the limiting ternaries but form an island in the quaternary. Fe5Si3 does not show a significant extension to the quaternary. The same two four-phase equilibria as in the previous section are found in the Si-rich corner. The phase field [B2 + FeSi + τ2 + τ3] is already very small in the section at 60 at.% Fe. The phase field [D03 + Fe5Si3 + FeSi + τ3] was confirmed in two samples (numbers 53 and 54) by XRD, but the exact composition of FeSi could not be determined due to the fine microstructure of the samples.

The section at 70 at.% Fe

Phase equilibria at 70 at.% Fe (Fig. 5) are comparably simple. The section is dominated by a large single-phase field B2/D03 originating from the phase field in the ternary Al–Fe–Si system, and by the two-phase field [A2/D03 + Fe2Ti]. The solubility of Ti in B2/D03 within the section varies between 5 and more than 10 at.%. In agreement with the ternary Al–Fe–Ti phase diagram shown in Fig. 1, the second order B2/D03 transition is drawn to open up into a two-phase field near the ternary system. However, the extension of this phase field is only tentative, as none of our samples was situated within the two-phase field. Several samples in the section at 70 at.% Fe show the equilibrium A2+ Fe2Ti. The respective tie-lines connect the Laves phase with A2 at Fe-contents higher than 75 at.%. The extensions of the single-phase field of Fe2Ti, the two-phase field [D03 + Fe5Si3] and the three-phase field of [B2 + Fe2Ti + D03] are only small; no samples were situated within them. In agreement with [25], the Fe-rich phase Fe7Si2Ti was not found in any of the samples annealed at 900 °C.

Crystallographic parameters and homogeneity ranges

The phase field A2/B2/D03

It is well known that the B2 structure (CsCl-type, Pmm) can be formed in a second order transition from a disordered A2 (W-type, Imm) solid solution, e.g in the binary Al–Fe system [14]. Ordering occurs between nearest neighbour atoms where the Fe-atoms occupy the corners of the cubic cell, while the body-centered sites are occupied statistically by Fe- and Al-atoms. Another ordering transition leads to the D03 structure (BiF3-type, Fmm. This transition is connected with a doubling of the cubic cell parameter (i.e. the cell volume is increased by a factor of 8). In ideal Fe3Al (D03), the Fe-atoms occupy the crystallographic 8c and 4a sites, while the Al-atoms occupy the 4b sites. The Fe-atom in the 4a site has eight Fe-atoms as nearest neighbours, while the Fe-atom in the 8c site has four Fe-atoms and 4 Al-atoms, as nearest neighbours [14]. Further ternary ordering may lead to the formation of the L21 structure (Heusler phase, AlCu2Mn-type, Fmm), where the 4a and 8c sites are occupied by different transition metals, or at least different mixtures of atoms. This structure type has been reported in the ternary Al–Fe–Ti system [5].

First order transition A2→D03 and second order transitions A2 → B2 and B2 → D03 have been reported in the binary Fe–Al and Fe–Si systems and the respective phase fields extend to the ternary systems Al–Fe–Si, Fe–Si–Ti and Al–Fe–Ti, so it is clear that they are also present in the quaternary Al–Fe–Si–Ti system. These transitions have significant impact on the mechanical and physical properties of the materials and are therefore important from the application point of view. In the current work, we carefully analysed the powder diffraction patterns of all samples containing A2/B2/D03-type phases in order to identify the structure type and to determine reliable cell parameters. The main diffraction lines of A2, B2 and D03 are identical, so identification is only possible based on a few, relatively weak superstructure reflections (compare Fig. 6). Thus, it is often difficult to detect the extra reflections, especially if the phase is only present as minority component in a multi-phase sample. No attempt was made to distinguish L21 and D03 ordering and all samples showing the corresponding superstructure lines are listed as D03 in Table 2. The superstructure identification performed on all samples was used to fix the second order transition lines shown dotted in Fig. 3, Fig. 4, Fig. 5. The possible limitations of this method have been discussed in the previous section.

Fig. 6

X-ray powder diffractograms at room temperature of sample No.68 (Al15Fe70Si12Ti2; single-phase B2) and sample No.61 (Al3Fe70Si24Ti3; single-phase D03). The calculated patterns for A2, B2 and D03 structures are shown below.

Most of the samples investigated in the current study contain more than one phase. So the refined cell parameters of A2/B2/D03 phases listed in Table 2 correspond to a rather arbitrary selection of quaternary phase compositions, mostly situated at the phase boundary of this phase. Therefore it is not possible to systematically discuss the change of cell parameters with the composition. Nevertheless, by sorting our data according to certain fixed element ratios it was still possible to reveal some trends of cell parameter variation. It can be stated that the change of the cell parameter with the composition is in excellent agreement with size considerations based on the covalent radii of Al (1.25 Å), Fe (1.16 Å), Si (1.17 Å) and Ti (1.32 Å); i.e. the cell parameter decreases with increasing content of Fe and Si. An example is given in Fig. 7, showing the experimentally observed cell parameters of B2 for several samples at fixed Fe- and Al- content.

Fig. 7

Change of the cell volume of the B2-type phase as a function of the Si-content. The content of Al and Fe is fixed to 40(2) at.% and 52(1) at.%, respectively.

Rietveld analysis of site occupations was tried for selected samples containing more than 80% of the B2 phase. Although it is principally not possible to make an unambiguous statement on site occupations in the case of multi-component substitution, it can be stated that our refinements largely support a simple substitution model extrapolated from the ternary and binary subsystems. Considering stoichiometric “FeAl” as ideally ordered B2 phase, Fe substitution on the Al sublattice is the principal mechanism for deviation of the composition to the Fe-rich side. A similar statement can be made for the B2 phase in the binary Fe–Si system. In the ternary system Al–Fe–Ti it was found that Ti-atoms preferentially occupy the Fe-sublattice [40] [41],. Thus we suggest the substitution model (Fe,Ti)1(Al,Si,Fe)1 for the quaternary system which is generally in good agreement with the results from Rietveld refinement.

The Laves phase

The Laves phase C14 (hP12, P63/mmc MgZn2-type) is found in the binary Fe–Ti system around the composition Fe2Ti and shows considerable ternary homogeneity ranges in the Al–Fe–Ti as well as in the Fe–Si–Ti system (Fig. 1). In the current work, a continuous connection of these ternary phase fields was observed. Two of the quaternary samples investigated in the current study were single-phase Fe2Ti (samples No.2 and No.28) and many more were situated in various two- and three- phase fields containing Fe2Ti in equilibrium with A2/B2/D03, FeTi and τ2. The hexagonal cell parameters were evaluated for all samples and are listed in Table 2 together with the respective phase compositions. General trends of cell parameter variation with the composition are consistent with the respective covalent radii and are discussed in more detail below. The c/a ratio is varying between approx. 1.65 and 1.60 and appears to decrease with increasing Si-content.

Fe2Ti has three crystallographically independent positions: 2a and 6h occupied by Fe-atoms and 4f occupied by Ti-atoms. Binary Fe2Ti shows a significant homogeneity range which is mainly found at the Fe-rich side of the stoichiometric composition and was found to be due to excess of Fe-atoms on the Ti-sites [42]. In the ternary system Al–Fe–Ti a solubility of 47.5 at.% Al in Fe2Ti is reported at 1000 °C [34] and a the investigation of site preferences by Yan et al. [43] showed that Al enters both Fe-sites at different mixing levels with site preference of Al for the 2a site. The corresponding mechanism in Fe–Si–Ti was not studied in detail, but given the extension of the phase in the ternary (at more or less constant Ti-content) it is likely that Si primarily enters the Fe-sites. The simplified site occupation model for the quaternary phase is thus (Fe,Al,Si)2(Fe,Al,Si)6(Ti,Fe)4. Rietveld refinements of selected samples constrained by the overall phase composition are generally in line with such model. However, it is impossible to distinguish between Al and Si, due to their similar scattering factors.

For a general evaluation of the cell parameter variation with the composition, the crystallographic data for the Laves phase listed in Table 2 were used for a non-linear regression fit using the fit equationwhere p denotes the cell parameters a, c in Å and the cell volume V in Å3, x(Al) and x(Si) are the contents Al and Si in at.% and Δx(Ti) denotes the deviation of the Ti content from the ideal composition Fe2Ti, i.e. 33-x(Ti) in at.%. This fit equation reflects the proposed basic mechanism of nonstoichiometry discussed above: Al- and Si- substitution on the Fe sublattice and Fe- substitution on the Ti-sublattice. The fit of data shows reasonable correlation between measured and predicted cell parameters as shown in Fig. 8. The regression parameters v1, v2, v3 listed in Table 3 may be interpreted as follows: the cell parameter a increases considerably with the Al-content and weakly with the Si-content, and it decreases considerably when Ti is exchanged by Fe. The cell parameter c increases with the Al-content and decreases with the Si-content, and it also decreases when Ti is exchanged by Fe. The cell volume increases with the Al-content, decreases when Ti is exchanged by Fe and is independent from the Si-content. This behaviour is in agreement with the proposed substitution mechanism considering the covalent radii of Al (1.25 Å), Fe (1.16 Å), Si (1.17 Å) and Ti (1.32 Å). However, it should be emphasized that the regression parameters give only general trends and are certainly not suitable to reliably predict cell parameters of the quaternary Laves phase. A systematic investigation of cell parameters of single-phase samples would be necessary for a deeper understanding of the substitution mechanism.

Fig. 8

Correlation of experimental cell parameters for the quaternary Laves phase with predicted values based on a non-linear fit according to Eq. (1). Fit parameters are listed in Table 3.

Table 3

Coefficients for non-linear regression fit on cell parameters of the quaternary Laves phase according to Eq. (1)

Cell parameter	Coefficient v1	Coefficient v2	Coefficient v3
a/Å	0.00398(26)	0.000680(95)	0.00256(26)
c/Å	0.00466(76)	−0.00405(28)	0.00378(76)
V/Å3	0.335(23)	−0.0495(90)	0.241(23)

The extension of the quaternary Laves phase field exhibits an unexpected feature highlighted in Fig. 9, which shows all measured phase compositions of the Laves phase in the two-phase field [Fe2Ti + A2/B2/D03]. It can be seen that the phase boundary of the Laves phase in the quaternary is significantly curved towards the Fe–Al–Si system. According to the phase boundary data listed in Table 2, the simultaneous substitution of Al and Si to Fe2Ti strongly shifts the Ti-poor phase boundary. Ti-contents of less than 20 at.% have been found in some of the quaternary samples (e.g. No.46 and No.69), which is much lower than any value reported for the binary and ternary systems. Up to now we do not have any explanation for this behaviour, but it might be interesting to study this effect in more detail in future studies.

Fig. 9

Fe-rich phase boundary of the Laves phase in the quaternary system Al–Fe–Si–Ti showing a pronounced curvature towards the Ti-poor side.

Microhardness measurements

Microhardness measurements were performed and evaluated for the Vickers hardness HV on selected metallographic samples containing either the Laves phase or the B2 phase. The results of these measurements are compiled in Table 4 (Laves phase) and Table 5 (B2 phase). Samples have been selected to cover a wide range of compositions within the respective homogeneity area. However, it should be pointed out that the phase compositions are spread out more or less randomly over the homogeneity area and thus do not correspond to certain well defined composition lines. Therefore it is only possible to evaluate rough trends of hardness with the composition.

Table 4

Vickers hardness of the Laves phase in selected quaternary samples and binary Fe2Ti.

Sample no.	Phase composition, Laves phase				HV (50 mN for 20 s)	Standard deviation
	Al at.%	Si at.%	Ti at.%	Fe at.%
01	5.4	8.3	35.6	50.7	1210	–
02	4.0	11.3	35.2	49.4	1390	170
03	2.3	17.2	32.0	48.5	1472	70
04	2.4	21.7	29.3	46.6	1295	86
10	8.2	16.9	28.4	46.4	1219	30
11	6.9	22.6	25.7	44.7	1349	130
28	4.9	2.1	32.6	60.5	1145	36
29	2.2	13.5	28.5	55.7	1296	38
30	1.2	22.0	24.9	51.9	1480	32
34	4.9	9.5	29.5	56.1	1302	35
35	3.4	16.0	28.1	52.6	1280	25
36	2.6	20.8	26.0	50.6	1385	–
40	7.8	5.0	28.0	59.3	1160	65
41	4.3	18.4	25.9	51.4	1253	130
55	1.4	1.9	29.6	67.0	1139	40
56	1.5	7.9	28.9	61.7	1210	–
57	0.9	17.0	26.0	56.1	1326	180
Fe2Ti	0.0	0.0	34.0	66.0	1242	59

Table 5

Vickers hardness of the B2 phase in selected quaternary samples.

Sample no.	Phase composition				HV (50 mN for 20 s)	Standard deviation
	Al at.%	Si at.%	Ti at.%	Fe at.%
11	33.6	6.1	4.4	56.0	875	28
12	27.0	14.9	2.4	55.8	776	8
13	23.5	21.9	1.9	52.8	916	43
14	38.9	2.0	6.9	52.2	512	33
15	38.5	7.3	1.9	52.2	659	45
16	33.1	1.2	14.4	51.4	701	63
17	35.5	1.3	11.3	52.0	733	70
19	39.7	1.8	6.7	51.8	734	68
20	40.3	2.1	5.7	51.9	722	53
22	33.4	12.5	1.6	52.4	816	30
23	32.9	16.4	0.9	49.9	922	25
23	30.3	18.9	0.7	50.1	870	43
24	30.6	6.9	3.7	58.9	755	64
26	17.6	13.4	3.9	65.0	923	–
50	10.5	28.2	2.2	59.1	905	7
51	16.8	22.0	2.0	59.2	876	29
52	11.2	27.0	2.3	59.5	955	23
69	21.6	5.3	2.2	70.9	586	21

For the Laves phase (Table 4), the measured values at room temperature vary between 1100 and 1500 HV (50 mN for 20 s), depending on the composition. Binary Fe2Ti was also prepared and tested with the same experimental procedure as a reference. For this compound a value of 1242 HV was measured. The composition dependence of the Vickers hardness was evaluated with a similar substitution-model based non-linear regression equation as used for the cell parameters:

The correlation between the measured and predicted values for HV is shown in Fig. 10. The coefficients w1 = −17.1 ± 5.4, w2 = 11.7 ± 2.3 and w3 = 11.0 ± 6.1 show that Al decreases the Vickers hardness while Si increases HV. This is in a good agreement with the results found by Löffler et al. [44]. The substitution of Ti with Fe on the Ti-sublattice decreases the Vickers hardness. In addition, with regard to the above described correlation between the cell parameters and the Al, Si and Ti amount it can be stated that HV increases with decreasing cell-volume and decreasing c/a ratio. Sauthoff et al. observed different correlations during hardness and compression tests of the ternary C14 Laves phases (Ni,Al)2Nb and (Fe,Al)2Ta, for which the hardness and yield strength, respectively, increased with increasing cell volume and increasing Al [45], [46]. However, the standard errors for the parameters w1 (Al) and w3 (Ti) are relatively large, so the trends observed in this study have to be taken with some caution.

Fig. 10

Correlation of experimental Vickers hardness for the quaternary Laves phase with predicted values based on a non-linear fit according to Eq. (2).

In the B2 phase, the Vickers hardness was found to vary between 500 and 1000 HV (50 mN/20 s). The graphical representation of all data shown in Fig. 11 again shows a considerable increase of the Vickers hardness with the Si-content. This general trend is in good agreement with the results of Shin et al., who observed a linear increase of HV with increasing Si amount in Fe-(9–12 at%)Si alloys with B2 structure [47].

Fig. 11

Vickers hardness for selected compositions of the B2 phase shown as a function of the Si-content.

Summary

Phase equilibra have been studied in the Fe-rich corner of the quaternary system Al–Fe–Si–Ti system at 900 °C using a combination of powder-XRD and EPMA measurements. All experimental data were evaluated and combined with available sections of the ternary limiting systems Al–Fe–Si, Al–Fe–Ti and Fe–Ti–Si, to yield a consistent description of isothermal phase equilibria presented in three sections at 50, 60, and 70 at.% Fe. Special efforts were taken to distinguish between the disordered A2 and ordered B2 and D03 structures by analysis of the XRD powder patterns. Trends of cell parameter variation and site occupations with the composition were discussed for the B2 and Laves phase. Microhardness measurements were performed on selected samples in order to determine HV of the B2 and Laves phase in the quaternary. An investigation of the quaternary phase reactions and melting behaviour in the Fe-rich corner based on DTA measurement is currently performed and will be published separately.