# Towards Superior High Temperature Properties in Low Density AlCrFeNiTi
Compositionally Complex Alloys

Silas Wolff-Goodrich<EMAIL_ADDRESS>Sebastian Haas  Uwe Glatzel
Christian H. Liebscher  Max-Planck-Institut für Eisenforschung GmbH, Max-
Planck-Straße 1, 40237 Düsseldorf  Universität Bayreuth, Lehrstuhl Metallische
Werkstoffe, TAO-Gebäude, Prof.-Rüdiger-Bormann-Str. 1, 95447 Bayreuth

###### Abstract

Three novel precipitation strengthened bcc alloys which exhibit a smooth
microstructural gradient with composition have been fabricated in bulk form by
induction casting. All three alloys are comprised of a mixture of disordered
A2-(Fe, Cr) and L21-ordered (Ni, Fe)2AlTi type phases both as-cast and after
long-term annealing at 900 ∘C. The ratio of disordered to ordered phase,
primary dendrite fraction, and overall microstructural coarseness all decrease
as Cr is replaced by Al and Ti. Differences in phase composition are
quantified through domain averaged principal component analysis of energy
dispersive spectroscopy data obtained during scanning transmission electron
microscopy. Bulk tensile testing reveals retained strengths of nearly 250 MPa
up to 900 ∘C for the alloys which contain a nanoscale maze-like arrangement of
ordered and disordered phases. One alloy, containing a duplex microstructure
with ductile dendritic regions and highly creep resistant interdendritic
regions, shows a promising balance between high temperature ductility and
strength. For this alloy, tension creep testing was carried out at 700, 750,
and 800 ∘C for a broad range of loading conditions and revealed upper bound
creep rates which surpass similar ferritic superalloys and rival those of
several conventionally employed high temperature structural alloys, including
Inconel 617 and 718, at much lower density and raw material cost.

###### keywords:

Compositionally Complex Alloy, Alloy Design, Creep, Structural Alloy, Nickel
Aluminide

††journal: Acta Materialia

##  1 Introduction

The high entropy alloy (HEA) and compositionally complex alloy (CCA) design
approaches have in recent years yielded many promising new alloys for high
temperature structural applications. Numerous studies have been published on
fcc-structured CCAs strengthened by L12 precipitates, analogous to Ni-base
superalloys, which show impressive high temperature mechanical properties, in
both compression and tension [1, 2, 3, 4]. While fcc-structured CCAs typically
have superior ductility, several bcc-structured CCAs have shown promising high
temperature strengths with reasonable ductility. Lim et al. studied the high
temperature compression behaviour of the equiatomic AlCoCrFeNi alloy and found
a yield strength of 201 MPa with over 50% plastic strain at 900 ∘C. This alloy
was found to be composed of nearly equal parts of dendritic regions, with a B2
matrix and A2 structured cuboidal precipitates, and interdendritic regions,
with interpenetrating A2 and B2 domains [5]. Stepanov et al. explored a series
of alloy compositions in the system Fe36X21Cr18Ni15Al10 and
Fe35X20Cr17Ni12Al12Ti4 with X=(Co, Mn), and found a compressive yield stress
of 285 MPa and over 50% strain-to-failure at 800 ∘C for the
Fe35Co20Cr17Ni12Al12Ti4 composition, which contains a mixture of ordered and
disordered bcc phases, with small amounts of disordered fcc phases near grain
boundaries [6]. In a related work, Shaysultanov et al. measured a tensile
yield stress of 310 MPa and strain-to-failure of 55% for the
Fe36Mn21Cr18Ni15Al10 alloy at 600 ∘C [7]. A compressive yield stress of nearly
400 MPa at 800 ∘C was reported by Zhou et al. for the B2 strengthened bcc-
structured Fe34Cr34Ni14Al14Co4 alloy [8]. In general, however, there is
presently a lack of high temperature tensile test data for bcc-structured
CCAs—let alone creep data—presumably due to the low tensile ductility that is
often observed in such alloys.

The Al-Cr-Fe-Ni-Ti alloy system comprises several well studied binary and
ternary systems. Of particular relevance to the present work are the Al-Cr-Fe,
Al-Cr-Ni, Al-Fe-Ti, and Al-Ni-Ti systems. The phase and microstructure
formation for large portions of the composition space for each of these
systems is well understood, especially in regions of single and dual phase A2,
B2, and/or L21 (Heusler phase) stability. B2-structured FeAl and
D03-structured Fe3Al as structural materials have the benefits of relatively
low cost, low density, very good high temperature oxidation resistance, and
moderate high temperature strength [9, 10]. Similarly, B2-structured NiAl and
L12-structured Ni3Al show the same benefits as FeAl, but have higher high-
temperature strength and better creep resistance [11, 12]. The addition of
titanium to both the Al-Fe and Al-Ni systems allows formation of the
L21-structured Heusler phase, as well as Laves phases. Single phase
L21-Ni2TiAl as well as dual phase B2-NiAl+L21-Ni2TiAl ($\beta-\beta^{\prime}$)
have been shown to possess high temperature creep resistance that is directly
comparable with high-performing $\gamma-\gamma^{\prime}$ Ni-base superalloys
up to around 1000 ∘C [11, 13, 14]. For applications with rotating components,
where the maximum stress is proportional to the alloy density, these Heusler
phase alloys may surpass the creep resistance of Ni-base superalloys.

The main issue with the intermetallic alloys mentioned above is their very low
ductility and fracture toughness in polycrystalline form, even at elevated
temperatures. One prominent class of alloys that was originally developed as a
low cost alternative to Ni-base superalloys for structural applications up to
approximately 760 ∘C which do not suffer from this drawback are so called Fe-
base superalloys. This class of alloys makes use of coherently precipitated
B2-NiAl and/or L21-Ni2TiAl as the primary strengthening phase(s) for an A2 Fe-
rich matrix [15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. While certainly more
ductile than the pure B2/L21 alloys, these alloys are inherently limited in
their maximum application temperature by the rapid decrease in strength and
creep resistance of the A2 matrix at temperatures above about 700 ∘C. One way
to maintain the high temperature mechanical properties is to increase the
ordered phase content, however, above a certain amount of Ni and Al, there is
no longer a clear matrix precipitate relationship, as the ordered phase
domains become fully continuous [25]. Such maze-like or lamellar
microstructures are widely reported in the HEA/CCA literature ([26, 27, 28,
29, 30] to list just a few) and, while apparently very strong, have been shown
to be very brittle [28, 30].

In a previous investigation, we screened the phase and microstructure
formation across a large portion of the Al-Cr-Fe-Ni-Ti composition space [30].
Microstructures consisting of a primary A2 matrix with equiaxed B2/L21
precipitates and interdendritic B2/L21 domains were observed, as well as
microstructures consisting entirely of a fine maze-like arrangement of A2 and
B2/L21 domains. One alloy, with composition Al20Cr20Fe35Ni20Ti5 , was found to
consist of primary dendrites containing the A2 matrix-B2/L21 precipitate
morphology, and interdendritic regions containing the maze-like morphology,
with the interdendritic regions occupying a slightly larger total portion of
the structure. A similar microstructure has been observed in the work of Tian
et al. for equiatomic AlCoCrFeNi, where the authors observed a room
temperature compressive yield stress of about 1630 MPa with 16% strain to
failure [29].

In the present work, we explore a set of low density CCAs where maximised
contributions from precipitation hardening and solid solution strengthening
combine for exceptional high temperature mechanical properties up to 800 ∘C.
We will illustrate the effects of adjusting the ratio of matrix-precipitate to
maze-like morphology, as well as the phase compositions, on the high
temperature performance of these alloys. We have tailored a microstructural
gradient consisting of three compositions, centered at Al16Cr25Fe35Ni20Ti4 ,
where Al and Ti are substituted for Cr while holding Fe and Ni constant. The
compositions of the three alloys to be studied can be designated as
Al4xCr5∗(9-x)Fe35Ni20Tix for $x\in\\{4,5,6\\}$ (in at.%). The particular ratio
of Al:Ti=4:1 was chosen based on findings that an optimum tension creep
resistance is achieved when the ordered phase domains in such alloys form a
hierarchical mixture of B2 and L21 subdomains [18, 19, 20, 22, 23, 24].

##  2 Experimental Methods

Bulk alloys were produced by vacuum induction casting of 99.9% purity base
elements into water cooled cylindrical copper moulds. The cylindrical cast
rods had nominally 25 mm diameter. Sections of rod were removed for further
processing and analysis by wire electrical discharge machining (wire EDM).
Circular cross section samples with nominally 1.5 mm thickness were removed
from a region central to the rod length for preparation of samples to be
analysed by X-ray diffraction (XRD) and scanning electron microscopy (SEM). In
addition, thin disks were removed at several locations along the rod for wet
chemical composition analysis to ensure adherence to the nominal composition
and that the elements were homogeneously distributed along the length of the
rod. Sections of cast rod with 65 mm length were removed for annealing heat
treatment. Annealing was carried out at 900 ∘C for 100 h in an Ar atmosphere,
followed by furnace cooling.

Both as-cast and annealed samples with surface normal parallel to the cast rod
cylinder axis were prepared for XRD and SEM analysis by surface grinding using
SiC abrasive paper, followed by diamond polishing, and finally by vibratory
polishing using a colloidal silica oxide polishing suspension with a mean
particle diameter of 50 nm. XRD was carried out with a Bruker D8 Advance
instrument in Bragg-Brentano geometry and with Co as the X-ray source.
Rietveld refinement of the XRD patterns was performed using the MAUD software
package to determine lattice constants and estimate phase volume fractions.
Samples were imaged in a Zeiss Sigma field emission SEM using primarily
backscattered electron (BSE) imaging contrast. The BSE imaging was carried out
with a four quadrant solid-state detector. Energy Dispersive Spectroscopy
(EDS) was also performed in the SEM, using an EDAX Octane Elect silicon drift
detector. SEM-EDS quantification was carried out using standardless eZAF
correction with the EDAX APEX® software.

BSE images were analysed using in-house Python programs which made use of a
watershed image segmentation algorithm [31] for determination of average
equivalent planar particle radii, $\langle r_{s}\rangle$, and areal number
density, $N$, for regions of the samples with equiaxed precipitates in a
matrix phase. Precipitate volume fractions, $f$, and equivalent true radii,
$\langle r\rangle$ were calculated making use of stereological corrections
according to [32],

$\langle r\rangle=\frac{4}{\pi}\langle r_{s}\rangle,\\\ $ (1)
$f=\frac{32}{3\pi}\langle r_{s}\rangle^{2}N.\\\ $ (2)

Adaptive thresholding was used for determination of area fractions of ordered
and disordered phases in regions of material with an interpenetrating maze-
like morphology. Phase volume fraction in these regions was assumed equivalent
to the measured area fraction. Average domain width in maze-like regions was
determined by manual measurement.

Samples for scanning transmission electron microscopy (STEM) analysis were
primarily prepared using a Thermo Fisher Scientific SCIOS® DualBeam® SEM and
focused ion beam (FIB) system equipped with Ga+ ions. Cross section specimens
were removed from the previously prepared SEM samples by milling trenches
using an ion beam accelerating voltage of 30 kV and currents between 50 nA and
300 pA. Final thinning of the TEM lamellas to $\approx$50 nm thickness was
carried out using 2 kV and 35 pA ion beam accelerating voltage and current.
One crept specimen was prepared by electropolishing using a Struers Tenupol-5
with 22 V potential and 16 ∘C in a 10% perchloric acid-90% acetic acid
electrolyte.

High resolution STEM was performed using both probe and image aberration
corrected FEI Titan Themis 60-300 instruments (Thermo Fisher Scientific)
operated at an acceleration voltage of 300 kV. STEM-EDS was conducted using
four synchronised EDS detectors (ChemiSTEM system, Thermo Fisher Scientific).
For STEM imaging and EDS, a semi-convergence angle of 23.8 mrad was used.
Several high angle annular dark-field (HAADF) detector camera lengths were
used in this study; the majority of HAADF images were collected with
collection angles of 73 to 200 mrad, while the images in Fig. 9(e) and (f)
result from collection angles of 25 to 154 mrad and are thereby referred to as
low-angle annular dark-field (LAADF). All other LAADF images were acquired
with collection angles of the annular dark field detector of 18 to 73 mrad.
The beam current was set to approximately 500 pA for STEM-EDS and lowered to
80 pA for image acquisition. Dark-field imaging shown in inset images of Fig.
4(d) were acquired using a JEOL 2100Plus operated at 200 kV acceleration. Non-
negative matrix factorization principle component analysis (NMF-PCA) was
carried out using the open-source electron microscopy analysis python package,
HyperSpy [33].

Tensile testing was carried out using a Zwick/Roell Z100 universal testing
machine. All tests were conducted under displacement control with a constant
strain rate of $10^{-4}$ s-1, using the laserXtens 2-120 HP/TZ laser
extensometer. Rectangular cross-section specimens were machined using wire EDM
followed by surface grinding to remove surface oxide. Specimens had dog-bone
geometry with 2 mm thickness, 5 mm width in the gauge-length, 30 mm gauge-
length, 5 mm radius to grips. Specimens were positioned in form-fit grips. A
three zone high temperature furnace was used for specimen heating, with dual
thermocouples placed directly on the specimen surface and digital temperature
control. Samples were tested in air with a maximum heating rate of 20 K/min.

Static creep testing was performed using live image tracking with a video
extensometer on a purpose-built testing apparatus, as described in [34, 35].
Specimens were tested in air using a radiation furnace, with temperature
measured using an S-type thermocouple directly in contact with the specimen
surface. Rectangular cross-section specimens with 1 mm thickness, 2 mm gauge
width and 8 mm gauge length were tested in form-fit grips. Samples were loaded
only after the target temperature had been reached and was observed to be
stable within $\pm 5$ ∘C. Both single loading and step loading tests were
conducted. For single loading tests, a constant load was hung from the sample
and the sample was either crept until failure or interrupted once a constant
steady-state creep rate was observed by turning off the furnace and letting
the sample cool under load. Step loading tests were conducted by allowing the
sample to reach a steady-state creep rate at the initial load and then adding
successive load only after the creep rate was observed to reach a new steady-
state. Data points from step loading tests were only considered to be valid if
the strain rate at the previous load step was not observed to have increased
prior to the load addition.

##  3 Results

The nominal and measured (wet chemical) compositions of the three cast alloys
studied here are listed in Table 1, along with an estimate of their densities
based on a weighted sum of the nominal pure elemental components. The measured
compositions for all elements deviate by no more than 0.4 at.% from the
nominal values, which is acceptably near to refer to the nominal values
throughout the rest of the article.

Table 1: Nominal and measured compositions (in at.%) and calculated densities of alloys produced by vacuum induction casting. Uncertainties in the measured compositions indicate the experimental measurement error. Sample ID | Density | Nominal Composition | Measured Composition
---|---|---|---
[g/cm3] | Al | Cr | Fe | Ni | Ti | Al | Cr | Fe | Ni | Ti
D1 | 6.6 | 16 | 25 | 35 | 20 | 4 | 15.9$\pm$0.1 | 24.9$\pm$0.1 | 35.1$\pm$0.2 | 19.9$\pm$0.2 | 4.22$\pm$0.05
D2 | 6.4 | 20 | 20 | 35 | 20 | 5 | 19.8$\pm$0.1 | 20.2$\pm$0.1 | 35.0$\pm$0.2 | 20.0$\pm$0.2 | 5.03$\pm$0.05
D3 | 6.1 | 24 | 15 | 35 | 20 | 6 | 23.7$\pm$0.1 | 15.1$\pm$0.1 | 35.4$\pm$0.2 | 19.8$\pm$0.2 | 5.94$\pm$0.05

###  3.1 Phase and Bulk Lattice Parameter Determination

We conducted XRD to identify the phases that formed in both the as-cast and
annealed conditions. The obtained patterns are shown in Fig. 1 over the scan
range $2\theta\in 25^{\circ}-105^{\circ}$. We have conducted a Rietveld
refinement of the patterns, and found that they are fitted well by A2
($\alpha$-Fe) and L21 ($\beta^{\prime}$-Ni2TiAl) phases. We note that the B2
($\beta$-NiAl) phase could also be used in fitting the patterns, however, due
to the similarity between B2 and L21 phases, as well as the difficulty in
distinguishing their contributions from XRD analysis alone, we have chosen to
fit just the L21-ordered phase. During the fitting process we refined mainly
the lattice parameter to achieve the best fit for all peaks in the scan range
$2\theta\in 25^{\circ}-130^{\circ}$. From the patterns we note that the
splitting between individual A2 and L21 primary peaks (due to different
lattice parameters), which is most prominently seen for the
A2-$\left\\{211\right\\}$/L21-$\left\\{422\right\\}$ peaks, increases from
alloy D1 to alloy D3, especially in the as-cast patterns. For the D1 alloy in
the annealed condition we observe a noticeable splitting of the ordered phase
peaks, especially for the $\left\\{422\right\\}$ reflection. This could
indicate the presence of multiple ordered phase variants in this alloy, which
might arise due to compositional heterogeneities in the sample.

Figure 1: XRD patterns for all three compositions in both the as-cast and 100
h annealed conditions.

Lattice parameters extracted from the refined patterns are listed in Table 2.
The domain averaged A2 lattice parameter is found to slightly increase from
alloy D1 to D3—that is, with increasing Al and Ti content and decreasing Cr
content—for both as-cast and annealed conditions. For all three alloys the A2
lattice parameter does not appear to change significantly upon annealing.
Directly comparing the L21 phase lattice parameter for the three alloys in
both the as-cast and annealed state, one observes effectively the same lattice
constant for all three alloys, with a slightly lower value for alloy D3. One
also observes a slight increase in L21 lattice parameter after annealing heat
treatment

Of great importance to the phase morphology in these alloys, and thereby to
the high temperature mechanical properties, is the misfit between the ordered
and disordered phase lattice parameters. This misfit is calculated as,

$\delta_{L2_{1}-A2}=\frac{\frac{a_{L2_{1}}}{2}-a_{A2}}{0.5(\frac{a_{L2_{1}}}{2}+a_{A2})}.\\\
$ (3)

and values for the three alloys have also been included in Table 2. In both
as-cast and annealed conditions, the misfit is seen to decrease from
approximately 1% in alloy D1 to approximately 0.62% in alloy D3. In other
words, the lattice mismatch decreases with increasing Al and Ti and decreasing
Cr content. Finally, we observe that the lattice parameter misfit increases
upon annealing for all three alloys.

Table 2:  Domain averaged lattice parameters from refined XRD patterns in both
as-cast and annealed conditions, as well as calculated lattice misfit values.
Values within parentheses are non-significant.

ID - Composition $a_{A2}$ [Å] $a_{L2_{1}}/2$ [Å] $\delta_{L2_{1}-A2}$ [%] as-
cast annealed as-cast annealed as-cast annealed D1 - Al16Cr25Fe35Ni20Ti4
2.87(9) 2.87(9) 2.90(8) 2.91(2) 1.00 1.13 D2 - Al20Cr20Fe35Ni20Ti5 2.88(4)
2.88(3) 2.90(9) 2.91(1) 0.86 0.97 D3 - Al24Cr15Fe35Ni20Ti6 2.88(8) 2.88(7)
2.90(6) 2.90(9) 0.62 0.77

###  3.2 Microstructural Characterisation

To characterise the segregation behavior of alloys D1-D3 in the as-cast and
annealed conditions we employed SEM-EDS. Fig. 3 shows EDS elemental mappings
of the five constituent elements for all three alloys in both conditions. One
observes clearly defined dendritic segregation structures in all five
elemental maps for alloys D1 and D2, with much less noticeable segregation
also present in alloy D3. The primary dendrites in both D1 and D2 are enriched
in Fe and Cr and depleted in Al, Ni, and Ti, indicating that the primary phase
to form was of A2 structure. Inverse segregation behavior is seen in
interdendritic regions. The primary dendrites occupy a much larger portion of
the sample in alloy D1 than in alloy D2, where the primary dendrites occupy
less area than the interdendritic region. Noteworthy are the maps of Ti
content, where for alloy D1 the dendritic structures are less defined than for
the other elements, and for alloy D2, there is a nearly continuous gradient of
Ti content from the dendrite cores to the grain boundaries. Alloy D3 shows the
opposite segregation behavior as alloys D1 and D2, with slight dendritic
enrichment of Al and Ni, and depletion of Fe and Cr. The exception is Ti,
which appears to be depleted in the dendrite cores but which, again, shows a
nearly continuous positive gradient towards the grain boundaries.

Figure 2: Low magnification SEM-EDS mappings of alloys D1-D3 in both annealed
and as-cast conditions. Elemental concentrations (in at.%) are included in
each map for both dendritic (d-) and interdendritic (i-) regions. Elemental
depletion is indicated by colored text on a black background, and enrichment
by black text on a colored background.

Quantification of the average elemental concentrations within the dendritic
versus interdendritic portions of the alloys is also indicated in Fig. 2. From
the values in the figure it is clear that the magnitude of segregation
decreases for all elements from alloy D1 to alloy D3. As this behavior can
have many different causes, it is important to consider the relative degree to
which each element segregates. For as-cast alloys D1 and D2, Ti shows the
strongest segregation, with 4 at.% lower Ti content in the D1 dendrites (where
the nominal alloy contains 4 at.% Ti), and 2 at.% lower D2 dendrites (where
the nominal alloy contains 5 at.% Ti). Ni and Cr show the second strongest
segregation (their behavior being nearly perfectly inverse), with D1 dendrites
having 11% greater Cr (nominal 25%) and 9% lower Ni (nominal 20%) than the
interdendritic regions, and D2 dendrites having 6% greater Cr (nominal 20%)
and 5% lower Ni (nominal 20%) than the interdendritic regions. Al shows
marginally less segregation, with D1 primary dendrites having 4% lower Al
content than interdendritic regions (nominal 16%), and D2 primary dendrites
having 3% lower Al content than interdendritic regions (nominal 20%). Finally,
Fe shows the lowest degree of dendritic segregation, with D1 dendrites having
7% greater Fe content and D2 dendrites having 4% greater Fe content (both with
nominally 35%). For both alloys, this behavior remains the same after
annealing, but the degree of segregation decreases slightly for alloy D1. For
alloy D3, Ni segregates the most (2% greater in dendrites, with 20% nominal),
followed by Al (2% greater in dendrites, 24% nominal), Cr (1% lower in
dendrites, 15% nominal), Fe (1% lower in dendrites, 35% nominal), and finally
Ti (same content in dendritic and interdendritic regions). While annealing
appears to also have little effect on the overall segregation trends in alloy
D3, we do observe a slight increase in segregation magnitude. Although the
quantified elemental concentrations give us a good indication of the trends
across the three alloys, we note the prevalence of several systematic errors.
Namely, the quantified Al content in all six mappings is between 1 and 2 at.%
higher than expected from the wet chemical composition results, the Ni content
is between 1 and 2 at.% lower than expected, and the Cr and Fe contents are
about 1 at.% higher and lower then expected, respectively.

With the systematic errors taken into account, the findings indicate that Cr
content is the main driver for segregation in these alloys, with Cr showing
poor solubility in Ni rich regions and vice versa. Furthermore, Ti appears to
show low solubility in Cr rich regions, but also shows a tendency across all
alloys to become increasingly enriched towards the grain boundaries. In alloy
D3, this behavior is the least pronounced, reflecting the expected behavior
that Ti has a greater solubility in Ni-Al rich (and thereby more ordered
phase) regions. The strong dendritic segregation in alloys D1 and D2 is
expected to result in very different phase fractions and morphologies in the
dendritic and interdendritic regions of these alloys, with high Fe and Cr
content in the primary dendrites suggesting that a high volume fraction of A2
phase should be present in these regions. The opposite is true in the
interdendritic regions of D1 and D2, where high Al, Ni, and Ti content should
lead to a high ordered phase volume fraction. For alloy D3, a high ordered
phase volume fraction is expected throughout the structure. Higher resolution
characterisation is necessary to investigate the respective phase fractions
further.

BSE imaging contrast was chosen to characterise the microstructural
morphologies of the alloys at higher magnification in the SEM, as this imaging
mode allows efficient and clear identification of the A2 and B2/L21 phase
domains due to the different average atomic number of the ordered and
disordered phases [30]. In all BSE images, disordered domains appear with
bright contrast, having higher average atomic number than ordered domains,
which appear dark. BSE SEM images of samples before and after annealing heat
treatment are shown in Fig. 3. For alloys D1 and D2, the elemental segregation
that was observed in Fig. 2 is resolved and reveals distinct phase morphology
in the dendritic and interdendritic areas.

Figure 3: BSE SEM images of alloys D1-D3 in both annealed and as-cast
conditions with same scale across all images. Inset in as-cast images shows
higher magnification of representative region, with same scale across all
insets. In all images, bright domains have been identified as the A2 phase,
and dark domains as B2/L21. Dendritic (d) and interdendritic (i) regions have
been identified for alloys D1 and D2. A region with more maze-like appearance
and one with more lamellar appearance are indicated in the inset for as-cast
alloy D3.

For alloy D1, the primary dendrites are made up of an A2 matrix with equiaxed
precipitates ranging from 120 to 700 nm in diameter in the as-cast state and
from 0.3 to 2 $\mu$m in the annealed state. As-cast, most precipitates show a
cuboidal shape with strong faceting in certain orientations. The ordered
precipitates make up $\approx$ 33% (volume fraction, determined as described
in Section 2, Experimental Methods) of the dendritic regions as-cast and
$\approx$ 30% in the annealed condition. The interdendritic regions contain
alternating domains of A2 and B2/L21 structure which have a lamellar
arrangement which is perpendicular to the dendrite-interdendrite interface,
and grows coarser towards the grain boundaries. The A2 domain width varies
between about 100 and 800 nm in the as-cast state and between about 0.2 and 2
$\mu$m after annealing, with ordered phase domains being larger than
disordered domains in both conditions. In some especially coarse ordered phase
domains in the as-cast state, very fine particles and needles of the
disordered phase can be observed, and likely formed by a secondary
decomposition reaction upon cooling. In the interdendritic regions, the L21
precipitates make up $\approx$ 59% of structure in the as-cast state and
$\approx$ 57% in the annealed state.

For alloy D2, the primary dendrites are also made up of an A2 matrix with
equiaxed cuboidal precipitates, however, these are somewhat finer than in the
D1 alloy, ranging from 100 to 500 nm in diameter in the as-cast state and from
0.2 to 2 $\mu$m in the annealed state. Similar to D1, the precipitates in the
dendritic region show faceted interfaces with the disordered matrix. After
annealing, the precipitates are no longer mostly equiaxed, showing irregular
shapes in some grains, possibly due to particle coalescence. The ordered
precipitates make up $\approx$ 34% of the dendritic regions in the as-cast
condition and $\approx$ 30% in the annealed condition. The interdendritic
regions, which make up the majority of the alloy volume, contain a fine maze-
like arrangement of A2 and B2/L21 phases. The A2 domain width in these regions
ranges from about 60 and 380 nm in the as-cast state and between about 0.12
and 1.2 $\mu$m in the annealed state, with the A2 domains being slightly
narrower than the ordered phase domains. Within the interdendritic regions,
the ordered phase comprises $\approx$ 55% of the structure in both the as-cast
and annealed states.

For alloy D3, it is very difficult to distinguish between dendritic and
interdendritic regions from SEM images alone. There is a tendency for regions
identified as dendritic to have a more maze-like appearance, and for regions
identified as interdendritic to have a more lamellar appearance, however, this
is difficult to distinguish, especially at low magnifications. Furthermore,
there is no strict boundary between regions of maze-like and lamellar
appearance, as for alloys D1 and D2, but rather a gradient between the
regions, as can be seen in the inset in Fig. 3(c). The A2 domain width in this
alloy ranges between 50 and 250 nm in the as-cast state, and between 0.1 to
0.9 $\mu$m in the annealed state. The ordered phase makes up $\approx$ 58% of
the structure both as-cast and after annealing.

From our observations of the phase morphologies we see that all three alloys
coarsen at similar rates. Furthermore, coarsening in the primary dendrites of
alloys D1 and D2 appears to occur slower than the coarsening in the maze-
like/lamellar regions of alloys D2 and D3. While the interdendritic regions of
alloy D1 appear related to those in alloy D2 and the structure throughout
alloy D3, they have a slightly coarser appearance which is reminiscent of
eutectic phase formation, while the structures in D2 and D3 are more likely to
have formed by a solid-state decomposition mechanism.

###  3.3 As-cast Phase Chemistry and Interface Structure

Higher resolution observations of the phase chemistry and interface structure
between A2 and B2/L21 phases have been captured using STEM-EDS mapping and low
angle annular dark field (LAADF) diffraction contrast imaging, as shown in
Fig. 4. Principle component analysis (PCA) based on non-negative matrix
factorization (NMF) has been used to decompose the spectral images into two
unique components, which coincide with the ordered and disordered phases
(labeled as A2 and L21). The chemical composition of these components is
displayed in Fig. 4 for dendritic and interdendritic regions in alloys D1 and
D2, and for the entire structure in alloy D3. We have highlighted the boundary
between dendritic and interdendritic regions in (a) and (b), as well as the
location of a grain boundary (GB) in (c). Note that due to the approximating
nature of taking a finite number of components from the decomposition of the
spectra, low elemental contributions, which appear as noise in the elemental
maps, do not appear in the final compositions. The quantified compositions are
therefore mainly useful in comparing trends between the three alloys and in
understanding the morphologies which form in different regions of the samples.

Figure 4: First row images show loadings from NMF-PCA decomposition of STEM-
EDS maps of D1-D3 in the as-cast condition. Quantified phase compositions (in
at.%) are indicated directly in the images for ordered (B2/L21) and disordered
(A2) phases. Scale for all three maps is the same. Second row images show
phase structure and interfacial dislocation networks, imaged using a low angle
annular dark-field (LAADF) detector which shows both atomic number and
diffraction contrast. Scale for all three images is the same. Inset dark field
images in (d) were taken from the same area with $g_{1\overline{1}1_{L2_{1}}}$
and $g_{2\overline{2}2_{L2_{1}}}$ diffraction vectors. Locations of
superlattice APBs are indicated with white arrows for
$g_{1\overline{1}1_{L2_{1}}}$. Inset HAADF images in (e) and (f) have been
Fourier filtered to remove high frequency noise, and each show a single
interface between ordered and disordered phase domains in alloys D2 and D3.

A clear trend of increasing Al content in the disordered phase is observed,
with the alloy D1 A2 phase having about 1 at.% Al in dendritic and
interdendritic regions, and the alloy D3 A2 phase having about 7 at.% Al. The
Cr content in the A2 phase also follows a fairly linear trend, decreasing by
about 10 at.% from alloy D1 to alloy D3, with alloy D2 having an intermediate
amount. The Fe content in the A2 phase shows a more complicated relationship,
with the alloy D1 and D2 A2 phases showing approximately equal concentrations
in the respective dendritic and interdendritic regions, while the alloy D3 A2
phase has more than 3 at.% greater Fe content than that in alloys D1 and D2.
The Al content in ordered phase domains is seen to increase from alloy D1 to
alloy D2, however, the Al content in the alloy D3 ordered phase domains is
slightly lower than for alloy D2. For all three alloys, the ordered phase
domains have non-stoichiometric Al + Ti content, which suggests that there is
some degree of Fe and Ni anti-site defects on the Al and Ti sublattice(s) [36,
37, 38, 39]. In conjunction with this observation we must note, however, that
for all elemental maps, a low total Al + Ti content was observed for all
B2/L21 phases, possibly due to a combination of residual matrix phase above or
below the precipitates and channeling effects in regions which were aligned
near zone-axis orientation [40]. Another important trend worth pointing out is
the fraction of Fe on the (Fe, Ni) sublattice of the ordered phase. Alloy D1
is seen to have the lowest Fe occupation at about 21% and 24% of the (Fe, Ni)
sublattice occupation in dendritic and interdendritic regions, respectively.
Alloy D2 has a greater fraction, at around 26% in both dendritic and
interdendritic regions. Alloy D3 has the highest with around 38% Fe on the
(Fe, Ni) sublattice. This variation in Fe:Ni occupation occurs despite the
fact that the Fe and Ni contents in all three alloys is the same. This can be
viewed as arising from the mutual solubility of Fe in the B2 and L21 phases
over a wide temperature and composition range [41]. As a simple explanation,
the Fe/Ni ratio in the ordered phase increases from alloy D1 to D3 because the
Ni content alone is not high enough to accommodate the increasing total volume
fraction of ordered phase that is encouraged to form in the alloys as the
combined Al and Ti content is increased, thereby necessitating increased Fe
occupation in the ordered phase domains.

The LAADF image in Fig. 4(d) shows dense networks of interfacial dislocations
between ordered and disordered phase domains in the D1 sample, reflecting the
relatively high lattice parameter mismatch between the ordered and disordered
phases, as indicated in Table 2. The LAADF image of alloy D1 also shows
contrast variations within the disordered and ordered phases, as well as
several dislocations in the bulk of the disordered phase. Higher resolution
observations of the spot-like contrast within both phases indicates that
secondary phase decomposition has occurred to some extent, with nanometer-
scale spherical ordered precipitates forming in the disordered phase, and
disordered clusters forming in the ordered phase. The boundaries of the fine
disordered clusters in the ordered phase have a bright contrast, indicating
either coherency strains or the presence of dislocation loops. In the center-
left of the image, one can observe a long dislocation bowing through the
disordered phase, with additional bowing points occurring at fine ordered
phase precipitates along the dislocation line. The superlattice DF images
shown in the inset of Fig. 4(d) show contrast arising exclusively from the L21
ordered phase in the dendritic portion of the D1 alloy. In the top inset
image, acquired with the L21 ($1\overline{1}1$) superlattice reflection, one
observes the presence of networks of curved antiphase boundaries (APBs) in the
ordered phase domains. These may have been formed as a result of coalescence
of individual precipitates, by thermal stresses, or due to rapid continuous
ordering from B2 to L21, as has been suggested in several works where similar
domain structures were observed [42, 43, 44, 18]. In the bottom inset image,
taken with a superlattice reflection corresponding to both B2
($1\overline{1}1$) / L21 ($2\overline{2}2$), a more or less homogeneous
contrast is observed and one can no longer locate the APBs, indicating that
the primary precipitates are almost entirely L21 ordered. One does however
observe nanometer scale regions with dark contrast in the DF images,
suggesting that secondary A2 precipitates have formed in the L21 particles.

The LAADF image of alloy D2 in the as-cast state, Fig. 4(e), also shows both
dendritic and interdendritic regions. The interdendritic region at the bottom
half of the image does not show any dislocation networks, however, the
interfacial dislocations still occur at the phase boundaries, as indicated by
the bright lines separating the ordered and disordered phases. The interfacial
dislocation networks are not observed to the same extent in Fig. 4(e) as in
(d) due to the different zone axis orientation under which the images were
acquired; in (e), the cube-on-cube oriented phase boundaries are primarily
viewed edge-on, whereas in (d) they are mostly inclined. One does observe,
however, that the dendritic region in the top half of (e) contains several
dislocation networks where interfaces between ordered and disordered phases
occur within the foil thickness. From these networks, we can comment that the
density of interfacial dislocations between ordered and disordered phases in
alloy D2 is similar to that observed in alloy D1, reflecting the similar
degree of lattice misfit in the two alloys. The atomic resolution HAADF image
shown as an inset in Fig. 4(e) shows a mostly coherent interface between
ordered and disordered domains in the interdendritic region of the sample,
however, we do observe the presence of a single interface dislocation. One
also observes several dislocations in the disordered phase, which bow between
ordered phase domains. Interestingly, there is little to no nanometer-scale
secondary precipitation observable in as-cast alloy D2.

Alloy D3 once again shows the finest arrangement of phases, with some domains
being separated by only tens of nanometers. The strain contrast of the D3
LAADF image shows a much lower density of interfacial dislocations than for
either alloy D1 or D2, again corresponding well with the XRD analysis. This is
reflected by the atomically resolved HAADF inset image in Fig. 4(e), where the
interface between an ordered and disordered domain is seen to be fully
straight and coherent. One observes that the phase arrangement favors two
preferred habit planes. One of these is the expected $\left\\{001\right\\}$
habit plane, designated HP1, which results in interfaces such as that seen in
the inset HAADF image. The habit plane which deviates from
$\left\\{001\right\\}$, designated HP2, is inclined relative to the $\langle
001\rangle$ zone axis and results in bands decorated with interfacial
dislocations. The orientation of these two habit planes has been highlighted
in the phase map shown in (c) as well as the LAADF image shown in (f). Similar
to alloy D2, alloy D3 shows little to no secondary precipitation.

###  3.4 Annealed D2 Phase Chemistry and Interface Structure

We have investigated the nanoscale structure and chemistry of annealed alloy
D2 only, as this alloy consists of regions which are representative of both
alloy D1 and alloy D3. An overview LAADF-STEM image is shown in Fig. 5 (a), as
well as an inset HAADF-STEM image showing a higher magnification of the
structure within individual A2 and B2/L21 domains. NMF-PCA from EDS mapping of
a small portion of the overview image is indicated in (b). We see that the
composition in the portion of the annealed sample that we measured is
effectively the same as in the as-cast sample. We note that secondary B2
precipitates are discernible in the A2 domain in the EDS mapping, but given
their small size, these are largely obscured by the A2 phase above and below.
In the HAADF inset we see these secondary precipitates clearly and have
determined their diameters to range between about 10 and 25 nm. It is likely
that these secondary precipitates formed during cooling from the annealing
heat treatment. In the interdendritic region seen in the bottom right of the
LAADF overview image, we note a higher number of dislocations in both ordered
and disordered phases, with one region (indicated in the image) showing a
particularly high density of dislocations in the disordered phase. Closer
inspection of this region reveals clear bowing of dislocations around
secondary precipitates in the disordered phase. It is not clear why this
region has a higher density of dislocations than we otherwise see in the
untested as-cast or annealed structures, but may be related to stresses
induced during the sample preparation.

Figure 5: (a) LAADF image of annealed alloy D2 showing both dendritic and
interdendritic regions. White arrows indicate region of high dislocation
density. HAADF inset in bottom left shows magnified image of phase structure
within center of dendritic region. (b) NMF-PCA phase mapping from single
interface near the boundary between dendritic and interdendritic regions,
indicated in (a).

###  3.5 Elevated Temperature Tensile Testing

Engineering stress-strain curves for all three alloys in both the as-cast and
the annealed conditions can be seen in Fig. 6 for tests conducted at 700 ∘C
and 900 ∘C. The 0.2% offset yield strength, ultimate tensile strength, and
total plastic strain at onset of fracture have been extracted from the stress-
strain curves and are indicated in Table 3. For tests conducted at 700 ∘C,
both as-cast alloys D1 and D3 were observed to fracture before yielding over
several test attempts, with alloy D3 being particularly prone to brittle
fracture at a stress well below the expected yield point of the material.
Alloy D2, by contrast, showed yielding behavior in the as-cast state, but
fractured before measurable plastic deformation could take place. In the
annealed condition, alloy D1 was able to reach yielding and showed a small
degree of plastic deformation before failure. Alloy D2 showed nearly the same
behavior, but had a significantly higher yield point and slightly greater
strain-to-failure. Finally, for alloy D3, it is unclear whether the material
was able to reach yielding before failure in the annealed condition, but
likely would have had the highest yield point of all the alloys if it had
reached yielding.

Figure 6:  Representative tensile engineering stress-strain curves of alloys
in both annealed and as-cast conditions tested at 700 ∘C (a) and 900 ∘C (b).
Note that a different stress-axis scaling is necessary for the two test
temperatures.

For tests conducted at 900 ∘C, the curves appear very similar to those for the
700 ∘C tests, but generally reached lower stresses and slightly higher strain-
to-failure. Once again, the as-cast alloy D3 failed well before yielding,
indicating that even at 900 ∘C, this alloy is still extremely brittle. For as-
cast alloy D1, it is also unclear whether the material was able to reach
yielding before unstable crack growth began, despite conducting multiple tests
on the material. In the annealed condition, alloys D1 and D3 both likely
reached yielding, but proceeded to fail catastrophically shortly after. The
annealed alloy D3 showed the highest yield strength of all three alloys also
at this temperature. Alloy D2 showed the highest strain to failure in both as-
cast and annealed conditions, and had a yield stress near that of annealed
alloy D3.

Table 3: Results of bulk high temperature tensile tests. Results from samples
which failed prior to yielding have been marked with an asterix (*).

ID - Composition Test Temp $\sigma_{0.2}$ [MPa] $\sigma_{uts}$ [MPa]
$\epsilon_{plastic}$ [%] [∘C] as-cast annealed as-cast annealed as-cast
annealed D1 - Al16Cr25Fe35Ni20Ti4 700 255* 256 255* 312 0.7* 2.2 D2 -
Al20Cr20Fe35Ni20Ti5 700 405 355 531 457 1.5 4.0 D3 - Al24Cr15Fe35Ni20Ti6 700
12* 422* 12* 422* 0.0* 0.0* D1 - Al16Cr25Fe35Ni20Ti4 900 74* 113 78* 115* 0.8*
0.5 D2 - Al20Cr20Fe35Ni20Ti5 900 223 183 265 211 2.7 6.1 D3 -
Al24Cr15Fe35Ni20Ti6 900 70* 248 70* 259 0.0* 0.8

###  3.6 Fracture Surface Characterisation

We conducted post-test fracture surface observations on the samples tested at
900 ∘C whose stress-strain curves are shown in Fig. 6 in order to better
understand the failure mode in these alloys. Secondary electron SEM images of
the entire fracture surfaces are shown in Fig. 7, with regions of identified
fracture mode indicated. Significantly, all three alloys showed some degree of
intergranular fracture in both as-cast and annealed conditions. Alloy D1
showed the most complex fracture surfaces, being comprised of regions of pure
intergranular type fracture, regions of ductile type fracture, and regions of
mixed intergranular-transgranular cleavage type fracture. The as-cast D1
sample tested at 900∘C contains one steep shear wall where the sample
contained either very weak grain boundaries or a pre-existing crack prior to
testing. This could possibly be the reason that the as-cast sample D1 showed a
lower yield strength than the annealed case. The annealed D1 fracture surface
shows three regions of ductile failure, but the majority of the fracture
surface shows mixed-mode intergranular-transgranular type fracture. Alloy D2,
in the as-cast state shows one small region where the sample failed in a
purely intergranular manner, but the majority of the fracture surface shows
mixed-mode ductile-intergranular fracture. The annealed D2 fracture surface
also shows almost entirely ductile-intergranular fracture, and the smaller
cross-sectional area of this sample relative to the other samples gives an
indication that this sample deformed to the greatest extent before failure.
Alloy D3 in both as-cast and annealed conditions shows regions of pure
intergranular fracture and regions of purely transgranular cleavage-type
fracture. These fracture surfaces are the flattest, reflecting the negligible
plastic deformation accommodated by this alloy.

Figure 7: Fracture surfaces of tensile specimens tested at 900 ∘C. Colors
indicate fracture mode.

###  3.7 Creep Tests

Due to the superior combination of moderate strain-to-failure and high tensile
yield strength, we chose to conduct creep testing on just alloy D2. Using data
from both stepwise-increasing loading tests and normal static loading tests,
we extracted the steady-state creep rate of as-cast and annealed alloy D2
under static stresses between 70 and 260 MPa at 700, 750, and 800 ∘C. This
data is shown on a double logarithmic scale in Fig. 8. For a given
temperature, data points which were taken from a stepwise-loading test all
have the same identifying number. As an example, the data points for the as-
cast condition, tested at 800 ∘C, come from one sample tested under 100, 110,
and 120 MPa loading, a second sample tested at 100 and 150 MPa, a third sample
tested at 200 MPa, a fourth sample, tested at 250 MPa, and a fifth sample,
tested at 70 MPa. Data points from stepwise-loading tests were only included
if the strain rate at the previous load step was not observed to increase
before the load was increased, and if the strain rate was observed to reach a
constant value before the next load increase or sample failure. Assuming
power-law creep behavior of the form,

$\dot{\epsilon}=C\sigma^{n},$ (4)

we extracted creep exponents for the six sets of data and show these directly
in the figure. Note that the logarithm of the minimum creep rate does not vary
linearly with the logarithm of stress for all loading conditions. For the 700
∘C annealed sample and the 750 ∘C as-cast and annealed samples, we observe
that the trend of minimum strain rate follows a concave path with increasing
applied stress. Upon re-examining the creep curves, we note that the strain
rate at the lowest stresses during these tests was likely lower than what was
measured, as we were near the measurement accuracy limit of the testing setup.
For this reason, we have not included these lowest stress data points in our
linear regression to extract creep exponents. Similarly, the 800 ∘C as-cast
material which was tested at 70 MPa shows a strong deviation from the behavior
at higher stresses, having a strain rate which falls well below the
extrapolated power law fit. This behavior suggests that there may be a
threshold stress for this material, below which no measurable deformation
occurs. The annealed material tested at 70 MPa and 800 ∘C shows deviation from
the extrapolated fit in the opposite direction. Aside from the deviations just
mentioned, we observe that the creep exponent generally decreases with
temperature for both as-cast and annealed conditions. Interestingly, we also
observe that the creep exponent strongly differs between the as-cast and
annealed condition, being lower in the as-cast condition at all temperatures.
The very low creep exponent of 1.7 in as-cast D2 at 800 ∘C above 100 MPa is
suggestive of a diffusion based creep mechanism at this temperature and stress
level, however, observations of the as-crept microstructure are needed to
confirm this.

Figure 8: Steady-state creep rate plot for alloy D2 tested at 700, 750, and
800 ∘C. Power-law exponents for each temperature and condition are indicated.

From the tests conducted at 700, 750, and 800 ∘C at 200 MPa loading, we have
extracted values of the creep activation energy, $Q$, by taking the slope of
the best fit line through an Arrhenius plot of $\ln{\dot{\epsilon}}$ versus
$1/T$ for as-cast and annealed strain rate data. For 200 MPa loading, the
creep activation energy was found to be 307 kJ/mol for the as-cast material
and 410 kJ/mol for the annealed material. The value of 307 kJ/mol coincides
exactly with the value of activation energy for 63Ni diffusion in
stoichiometric NiAl [45, 13]. We cannot comment on whether the activation
energy is also in agreement with that for diffusion in L21-Ni2TiAl, due to the
lack of diffusion data for this phase in the literature, but we assume here
that the activation energy for Ni diffusion is similar for B2 and L21 phases.
The activation energy for self-diffusion in $\alpha$-Fe is known to exhibit a
discontinuity at the Curie temperature (770 ∘C in pure $\alpha$-Fe), i.e. the
value in the ferromagnetic state (291 kJ/mol) is different than in the
paramagnetic state (239 kJ/mol) [46]. However, if data from above and below
the Curie temperature are evaluated as a “linear Arrhenius set”, a self-
diffusion activation energy of 307 kJ/mol has been found for polycrystalline
$\alpha$-Fe in the temperature range 700 to 900 ∘C [46]. As this temperature
range includes the temperatures of the creep experiments used to extract the
creep activation energies, we can consider this Fe self-diffusion activation
energy to be representative for the A2 phase in our alloys. The close
agreement between the activation energy for self-diffusion in $\alpha-Fe$ and
Ni diffusion in NiAl corresponds well with our observation that the steady-
state creep rate in as-cast D2 is controlled by bulk diffusion. The
significantly higher value of creep activation energy in annealed D2 suggests
that the controlling creep mechanism is not diffusion-based. We note, however,
that the real activation energy values under this stress level may be lower
than determined here, given our previous acknowledgement that the strain rates
in the as-cast and annealed condition at 700 ∘C, 200 MPa loading are likely to
be lower than reported.

###  3.8 Crept Microstructure Analysis

For as-cast and annealed alloy D2, we interrupted a creep test conducted at
800 ∘C under 200 MPa loading after the samples had reached the steady state
creep regime. For the as-cast sample, we interrupted the test at about 1.3%
strain, and for the annealed sample, at about 2.0% strain, at which point the
sample had just begun to show an increase in strain rate indicative of the
onset of tertiary stage creep. We conducted SEM observations on the surfaces
parallel to the stress axis after polishing. Regions of these surfaces are
shown in Fig. 9(a) and (d), where the stress axis has been indicated for both.

Figure 9:  Microstructures of as-cast and annealed alloy D2 after creep to
1.3% and 2.0% strain, respectively, at 800 ∘C and 200 MPa. (a) and (c) show
BSE SEM images of the grain structure, with creep cavities highlighted in
purple and indicated with white arrows. (b) shows an overview LAADF image of
the crept as-cast material, while (c) shows a higher magnification HAADF
image. Both (e) and (f) show HAADF images of the crept annealed material, with
the detector set to a longer camera length than in (c) to show specifically
strain contrast.

For the as-cast crept sample, a large number of thin cavities are observed
throughout the gauge length, almost all located at grain boundaries which lie
perpendicular to the stress axis. Other than the grain boundary cavities,
there are no noticeable changes to the alloy microstructure after creep to
1.3% strain in the SEM. Observations at higher magnification were conducted on
a thin foil of the crept material using scanning TEM. Fig. 9(b) shows a
diffraction contrast image of a representative region of the sample. We
observe very slight coarsening of the microstructure compared to the untested
as-cast material, but only a marginally greater density of mobile
dislocations, where the majority of these mobile dislocations are seen to be
located in the maze-like interdendritic regions of the material, with very few
seen in the matrix of the dendritic regions. This observation suggests that
dislocations are able to move much easier through the dendritic regions of the
sample and tend to collect in the interdendritic regions. We can also see from
the overview image that some of the mobile dislocations appear to be moving
through the ordered phase domains as well as through the disordered phase.
When compared to the LAADF image of the untested as-cast D2 specimen, shown in
Fig. 4(e), we see that the number of mobile dislocations in the disordered
phase of the crept specimen is only slightly greater than in the virgin
material, while in the ordered phase, dislocations appear only after creep
testing. This is somewhat surprising given that dislocation motion in the B2
and L21 phases should have a significantly higher energy barrier than in the
A2 phase. This behavior could be a result to the very high stress level that
the specimen was crept at, whereby dislocations in the disordered phase are
able to shear through the ordered phase and/or nucleation sources in the
ordered phase become activated. We take a closer look at the structure in Fig.
9(c) and observe clear indications of at least one dislocation in the ordered
phase.

For annealed alloy D2, we also observe several grain boundary cavities in the
crept state, however, these cavities are observed to occupy roughly half of
the area that they occupy in the as-cast sample, despite the annealed alloy
having been crept to a larger total strain level, in the tertiary regime. The
HAADF image of Fig. 9(e) shows a higher number of mobile dislocations in the
disordered phase domains than seen in the as-cast crept sample. Although not
shown here, we observe significant number of dislocations in the ordered phase
domains. We also observe the presence of large numbers of dislocation loops in
the ordered phase, which may have formed by Orowan looping around disordered
particles in the ordered phase. The interfacial dislocation networks in the
annealed specimen appear to have a finer spacing than in the as-cast specimen,
which could be related to the observation of a greater lattice parameter
mismatch in the annealed alloy than the as-cast alloy in the untested
condition, but could also arise from mobile dislocations being getting trapped
at the interfaces and being incorporated into the networks.

We observe a large degree of secondary precipitation in both phases in the
crept annealed specimen. Although not clearly seen in the HAADF image shown in
Fig. 9(f), the secondary precipitates in the ordered phase were found to be
finer, more numerous, and closer spaced than in the as-cast specimen, shown in
(c). Importantly, we note that the disordered phase in the annealed condition
contains a large number of very fine (5-10 nm diameter) secondary B2-ordered
precipitates, while in the as-cast condition, no secondary precipitation is
observed in the disordered phase. This suggests that these fine secondary
domains may have formed during the annealing heat treatment, or upon cooling
from same. The dislocations in the A2 phase seen in (f) are very wavy,
suggesting multiple pinning points were present and prevented free dislocation
motion during creep deformation. These pinning points are likely to correspond
to the secondary precipitates, although this has not been determined
definitively.

For both the as-cast and annealed specimens, we observe strong indications
that the specimens deformed to some degree by enhanced diffusion, especially
for the as-cast specimen. For the annealed specimen we also observe
deformation to occur by dislocation climb and glide in both ordered and
disordered phases. These observations align well with the observed creep
exponents obtained from the steady state creep curves, with the as-cast
condition showing a creep exponent which indicates mostly diffusion-based
deformation, and the annealed condition, having a creep exponent which is
better explained by dislocation glide and climb processes.

##  4 Discussion

Several microstructural features, at differing length scales, affect the
overall high temperature mechanical response of these three alloys. At the
lowest length scale is the composition of individual ordered and disordered
domains, and the effect that the composition has on phase stability, diffusion
rate, lattice parameter mismatch, and elastic response. The next
microstructural feature that varies across the three alloys is the
morphological relationship between ordered and disordered domains, with
regions of equiaxed ordered precipitates in a disordered matrix (matrix-
precipitate morphology) and regions of interpenetrating maze-like ordered and
disordered domains (maze-like morphology). The relative phase fraction,
precipitate size, domain width, and interfacial coherency are all expected to
strongly effect the properties of both morphology types observed. Within
individual grains, the ratio of matrix-precipitate to maze-like morphology
will influence the mechanical response, as will the phase character and
composition at grain boundaries. In the following sections, we present a
discussion of the various strengthening contributions across these three
alloys, a comparison of mechanical properties with other recently developed
HEA/CCAs intended for similar applications, and finally, a more detailed
analysis of the creep behavior in the D2 alloy.

###  4.1 Strengthening Contributions

We will discuss the different possible strengthening contributions in these
three alloys in the following order: $(i)$ lattice friction resistance in
terms of the Peierls barrier, $(ii)$ Orowan particle strengthening, $(iii)$
solid solution strengthening, $(iv)$ dislocation shearing of ordered phase
domains. As all three alloys have similar grain sizes in both as-cast and
annealed conditions, the average grain size is not expected to contribute to
differences in observed strength and ductility.

####  4.1.1 Lattice Friction Resistance

The first contribution to yield stress to consider is the Peierls flow stress.
We will carry out our analysis with the assumption that the first phase to
yield will be the disordered A2 phase. With that said, however, Schroll et al.
have compiled results from several studies of B2-NiAl which make use of
embedded atom method (EAM) potentials to calculate values of the Peierls
stress for different slip systems and have found values as low as 60 MPa
(edge-type) and 70 MPa (screw-type) for the “soft” $\langle
100\rangle\\{01\overline{1}\\}$ slip system in NiAl [47, 48]. These low values
for Peierls stress only occur for certain orientations, but may play a role
during deformation of the studied alloys. Very little data is available on the
Peierls barrier in L21-Ni2TiAl and -Fe2TiAl, but given the extra degree of
superlattice ordering in this phase, the operative slip system ($\langle
011\rangle\\{01\overline{1}\\}$) [14] has a greater Burgers vector length than
that in either A2 or B2 phases, and the resulting Peierls barrier will be
significantly higher.

Although there is great discrepancy in the literature as to the exact
formulation of the Peierls stress, one common feature between the analytical
expressions that have been developed is a linear dependence on the isotropic
shear modulus (we will not treat anisotropy in our analysis). The true flow
stress contribution from lattice friction will be lower than the Peierls
stress, especially at high temperatures, due to thermal activation of
dislocation motion, in particular due to the kink-pair mechanism of
dislocation glide [49, 50]. For a given temperature, however, the lattice
friction stress in individual disordered phase domains will vary across these
three alloys due only to differences in the shear modulus induced by
disordered phase composition. Based on data collected from several sources,
Ghosh and Olson have compiled values for the change in $\alpha$-Fe shear
modulus, $G$, with composition, $c_{x}$, for a large number of atomic species,
$x$ [51]. From the $dG/dc_{x}$ values listed in that work, we can relate the
change in shear modulus of the disordered phase due to composition according
to,

$\Delta G(c)=-100.85c_{Al}+34.06c_{Cr}-90.65c_{Ni}-74.59c_{Ti}.$ (5)

We assume here that there are no non-linear effects due to interaction of
solute species and that the chemical dependence of the shear modulus does not
change with temperature. For the compositions shown in Fig. 4, the calculated
increase in shear modulus of the A2 phase is about 14.2 GPa in alloy D1, 8.6
GPa in alloy D2, and 4.5 GPa in alloy D3. In order to see how the shear
modulus values of the three alloys compare at high temperature, we also have
to consider the shear modulus temperature dependence. For pure polycrystalline
$\alpha$-Fe, this has been fit empirically by [51],

$G(T)=8.407\left[1-0.48797\left(\frac{T}{T_{C}}\right)^{2}+0.12651\left(\frac{T}{T_{C}}\right)^{3}\right]\times
10^{10}~{}\mathrm{Pa},$ (6)

where $T_{C}$ is the Curie temperature (1043 K for pure $\alpha$-Fe). The
value of the shear modulus determined using the above equation ranges from 57
GPa at 700 ∘C to 47 GPa at 900 ∘C. Combining these values with the composition
dependence, the respective D1, D2, and D3 shear moduli are 71.3, 65.6, and
61.5 GPa at 700 ∘C, and 61.6, 55.9, and 51.8 GPa at 900 ∘C. Although the Al,
Ni, and Ti contents in the A2 phase are likely to be higher—and the shear
modulus increase correspondingly lower—than the values determined, the
calculated values indicate that the lattice friction resistance to dislocation
motion is greatest in alloy D1 and least in alloy D3. However, given the
observed variation in yield strength across the three alloys, with alloy D1
having the lowest yield strength, and alloy D3 having the highest yield
strength, other effects are expected to play a much larger role than the
magnitude of the Peierls stress.

####  4.1.2 Orowan Strengthening

We will consider the general Orowan bypass mechanism with the form [52],

$\sigma_{orowan}=0.81M\frac{Gb}{\lambda},$ (7)

where $M=2.9$ is the Taylor factor for randomly oriented bcc polycrystals
[53], $G$ is the temperature and composition adjusted shear modulus of the A2
phase, $b$ is the Burgers vector length, and $\lambda$ is the average ordered
phase domain separation within which dislocations will glide in the disordered
phase, which we will refer to as the interparticle distance. For the maze-like
domains, we take the average interparticle distance to be simply the average
A2 domain width, values of which have been determined from the BSE SEM images
of the alloy microstructures. This is similar to the method that is used to
estimate the Orowan stress in Ni-base superalloys with high
$\gamma^{\prime}$-Ni3Al phase content, where the interparticle distance is
taken as the average disordered phase channel width [54]. For the dendritic
domains in alloys D1 and D2, the interparticle distance can be calculated from
the average particle radius, $\langle r\rangle$, and volume fraction of
precipitates, $f$, according to [23],

$\lambda=\langle
r\rangle*\left[\sqrt{\frac{2}{3}}\left(\sqrt{\frac{\pi}{f}}-2\right)\right].$
(8)

With values for $\lambda$ determined for both morphology types in all three
alloys, we can compare the Orowan bypass stress expected for each of the
individual regions in both as-cast and annealed conditions. We show this
graphically in Fig. 10, where the Orowan stress curves have been calculated
using values of the shear modulus of the A2 phase at 900 ∘C, taking into
account contributions from solute species determined earlier. We observe that
although alloy D1 has a greater Orowan stress than the other two alloys for a
given interparticle distance, the greater values of interparticle distance
determined for the alloy lead to the lowest total Orowan stresses, in both as-
cast and annealed conditions. For alloys D1 and D2 in the as-cast state, the
average interparticle distance in the interdendritic regions is lower than in
the dendritic regions, indicating that the maze-like structure in the
interdendritic regions will have a higher yield strength than the matrix-
precipitate structure. However, the difference in strengthening is not very
large considering the difference in ordered phase volume fraction in the
respective regions. In the annealed condition, we see a larger spread in
average interparticle distances, especially between the dendritic and
interdendritic regions of alloys D1 and D2, but the overall Orowan
strengthening contributions show little spread, all lying between about 80 and
120 MPa.

Figure 10: Orowan bypass stress in the A2 phase versus average interparticle
distance in all morphology types present in alloys D1-D3. Shear modulus values
for the A2 phase are calculated at 900 ∘C. Scale bar in images is 2 $\mu$m.

We have included the 900 ∘C 0.2% offset yield stress values listed in Table 3
on the stress axis in Fig. 10. Comparing the values for Orowan bypass stress
with the determined yield stress we note several interesting trends. In the
as-cast condition, the Orowan stress for alloys D1 and D3 significantly
overestimates the yield stress, presumably due to premature failure of the
material. The pre-yield failure of the as-cast D3 material in all tested
samples indicates that the cohesion of the grain boundaries was too low to
allow even microplasticity, and/or that the maze-like structure does not allow
for continuous glide in the disordered phase channels. As alloy D2 was also
composed of predominantly the maze-like microstructure, yet was consistently
able to reach yielding, we conclude that the presence of the dendritic
regions, with their characteristic disordered matrix, allowed a smooth
increase in stress in these regions up to the point of yielding. This has been
observed in complementary FEM simulations and neutron diffraction experiments
for bulk materials with the same morphology as in the dendritic regions [21].
In as-cast alloy D1 we would have expected the samples to reach yielding as
well, as these samples had an even higher portion of the matrix-precipitate
morphology than the D2 alloy, but we were unable to obtain a sample which
showed true yielding behavior. This is likely due to the large fraction and
size of ordered phase domains near the grain boundaries, as well as high Ti
segregation to the grain boundaries, as seen in Fig. 2. It is also possible
that the presence of fine secondary B2 precipitates in the disordered phase,
as observed in Fig. 4(d), decreased the effective interparticle distance in
the dendritic regions, pushing the required Orowan bypass stress in these
regions higher. For as-cast alloy D2, where we observed almost 3% plastic
strain before failure, we see that the measured yield stress (223 MPa) is
slightly larger than the determined Orowan stress in the dendritic regions
(203 MPa) and is nearly the same as that in the interdendritic regions (219
MPa). However, given the observation that the maze-like microstructure was
unable to reach yielding for alloys D1 and D3, we assume that the Orowan
stress in the dendritic regions is closer to the real contribution to yield
stress due to the Orowan mechanism. We note that the yield stress determined
for as-cast alloy D2 is likely a lower bound for the material, given the high
degree of intergranular fracture observed throughout the fracture surface; the
appearance of yielding behavior may have corresponded with stable micro-crack
growth, rather than true plasticity. It remains to be determined how the
stress and strain evolve in maze-like regions in all three alloys, and indeed,
how the macroscopic yield stress and subsequent hardening behavior of alloys
D1 and D2 result from the interaction of these maze-like domains with the
dendritic matrix-precipitate type regions.

The calculated values of Orowan stress for the annealed samples in all cases
underestimate the observed yield stress values. For alloy D3 the calculated
Orowan stress (122 MPa) severely underestimates the 0.2% offset yield stress
(248 MPa), which indicates that the Orowan formulation may not accurately
describe the strengthening effect of the maze-like microstructure. The
observed yield stress in annealed alloy D2 (183 MPa) is also significantly
higher than the calculated Orowan strengthening contribution from either
interdendritic regions (117 MPa) or dendritic regions (93 MPa). Here, also, we
note that the strengthening contribution from interdendritic regions may be
much higher than the calculated value. A superposition of strengthening
contributions from dendritic and interdendritic regions may thereby result in
an overall bypass stress which is much closer to the observed value. The high
yield stress values in the annealed alloys may also be partially explained by
the presence of secondary precipitates in the disordered phase domains,
clearly seen for annealed alloy D2 in Fig. 5, which decrease the effective
interparticle distance. Whether these secondary precipitates remain stable and
are thereby able to contribute to a higher required bypass stress at high
temperatures is unclear, but depends on the solubility of the constituent
elements (mostly Ni and Al) at the testing temperature. For annealed alloy D1
the observed yield stress (113 MPa) is much closer to the Orowan strengthening
contributions (92 MPa interdendritic and 84 MPa dendritic), however, we note
from the low plastic strain to failure for this alloy (0.5%) that the
determined yield stress value may be a lower bound due to stable growth of
grain boundary cracks, rather than true yielding behavior.

####  4.1.3 Solid Solution Strengthening

The A2 phase in the three alloys studied contains large concentrations of
substitutional solute species, particularly Al and Cr, as seen in Fig. 4. The
resulting supersatured solid solution is strengthened by distortions in the
lattice caused by differential volumetric and shear modulus effects of the
solute species, which act as additional barriers to dislocation motion [55,
56, 57]. Takeuchi studied the solid solution strengthening effect of several
solute species in $\alpha$-Fe and found that the influence of increasing
solute concentration on modulus normalized critical resolved shear stress
(CRSS) follows a linear trend. For solutions containing up to 5.85 at.% Al,
the change in modulus normalized critical resolved shear stress with Al
concentration has been found to be $d(\tau_{ss}/G)/dc_{Al}=0.014$ [58]. In a
similar fashion the effect of Cr has been found to be
$d(\tau_{ss}/G)/dc_{Cr}=0.0074$ [59]. For the calculation of solid solution
strengthening contribution in these three alloys we then have,

$\Delta\sigma_{ss}=0.81MG_{c}\left[0.014c_{Al}+0.0074c_{Cr}\right],$ (9)

where $M=2.9$ is the Taylor factor for randomly oriented bcc polycrystals
[53], and $G_{c}$ is the shear modulus of the composition in question. The
respective D1, D2, and D3 solid solution strengthening contributions are then
581, 563, and 505 MPa at 700 ∘C, and 502, 480, and 425 MPa at 900 ∘C. These
values are in all cases much larger than the experimentally observed yield
stress values, but are closer in magnitude for the 700 ∘C results. This is
easily explained by thermal effects which reduce the effective free energy
barrier that prevents movement of dislocations past the substitutional
obstacles as temperature is increased. This strengthening contribution, along
with the Peierls barrier, are expected to play a larger role at lower
temperatures, where less thermal energy is available to overcome these
barriers. These lattice friction contributions may be the reason that the
yield stresses observed at 700 ∘C are significantly higher than the Orowan
bypass stresses present at this temperature, which are only slightly larger
than those calculated at 900 ∘C due to the increase in shear modulus with
decreasing temperature.

The relatively weak energetic barrier presented by homogeneously distributed
substitutional solute species may be substantially increased due to migration
of the solutes to defect cores, a phenomenon that results in so-called
Cottrell atmospheres [60, 50]. This leads to what is known as dislocation
locking, whereby the stress required for dislocation motion is increased as a
result of the increased interaction energy of the dislocation with the solute
atmosphere. This effect, if indeed active in these alloys, would be expected
to impact the performance of the annealed material greater than the as-cast
material since the long holding time at 900 ∘C allows relief of the thermal
stresses present from casting, and subsequent diffusion of the solute species
to the dislocations formed during the stress relief. Therefore solute
atmosphere locking is another possible mechanism that could explain the
discrepancy between the Orowan bypass strengthening contribution and the
observed yield strength for the annealed alloys. We point out, however, that
we do not observe indications of a yield drop which is characteristic for
strong dislocation locking in the stress strain curves shown in Fig. 6.

####  4.1.4 Dislocation Shearing of Ordered Phase Domains

A past work on Fe-base superalloys strengthened by B2 and L21 precipitates
calculated that the precipitate shearing mechanism requires stresses on the
order of 1 GPa, when the volume fraction of B2 precipitates was only 16% [61].
This calculation took into account stress arising only from the creation of
new APB surfaces, neglecting contributions from coherency strains and shear
modulus mismatch. As all alloys studied here have much higher ordered phase
volume fractions, the precipitate shearing stress arising from just the
creation of APB surfaces will be even larger than the value found be Vo et al.
We can thereby conclude that shearing is not likely to dictate the yielding
behavior in any of the morphologies and material conditions observed, without
needing to account for the other contributions to the ordered phase shearing
strengthening mechanism. The only case where this may not hold true is for
nanoscale secondary precipitates which may be present in some material
conditions, where the small average radii may allow dislocation shearing to
occur at stresses lower than those required for Orowan bowing.

###  4.2 High Temperature Specific Yield Stress Comparison

For high temperature applications involving rotating parts, where primary
stresses arise due to the weight of the part itself, the specific tensile
yield stress of the material is one of the main performance determining
properties. In this sense it is valuable to see how the specific yield stress
(SYS) of the D2 alloy compares to other high temperature oriented HEA/CCAs and
conventional alloys in the temperature range of interest. We have included
such a comparison in Fig. 11 between 600 and 1000 ∘C. We see that alloy D2 has
similar SYS to equiatomic AlCoCrFeNi [5] and Al14Co4Cr34Fe34Ni14 [8] CCAs,
which were both tested in compression. It is likely, however, that both of
these alloys will show lower SYS in tension. The AlCoCrCuFeNi alloy, which
contains both bcc and fcc phases, shows a lower SYS than alloy D2 between 700
and 900 ∘C [62]. An interstitially strengthened HEA (iHEA) based on the Cantor
alloy shows high SYS at 600 ∘C, but has lost much of this strength at 700 ∘C,
showing a SYS roughly half that of as-cast alloy D2 [63]. The ferritic
superalloy, FBB8, containing a bcc matrix with hierarchical L21+B2
precipitates by incorporation of 2.2 at.% Ti [21], shows a lower SYS at 700 ∘C
than both as-cast and annealed alloy D2. Perhaps most notably, the SYS of
alloy D2 competes directly with polycrystalline $\gamma-\gamma^{\prime}$
structured Al10Co25Cr8Fe15Ni36Ti6, even showing a higher SYS at 900 ∘C in the
as-cast state, while outperforming commercial Inconel 617.

Figure 11: Specific yield stress versus temperature for alloy D2
(Al20Cr20Fe35Ni20Ti5 ) as well as several other HEA/CCAs designed for high
temperature application, an optimized Fe-base superalloy, and Inconel 617.
After Refs [5, 62, 8, 2, 21, 63, 64].

###  4.3 Creep Behavior of Al20Cr20Fe35Ni20Ti5

We show the 800 ∘C steady-state creep rate values for alloy D2 in comparison
with two high temperature stainless steels [65, 66], two common Ni-base
superalloys [67, 68], and a high performing mechanically alloyed (MA) NiAl
alloy [69] in Fig. 12. We see that alloy D2 performs very well in comparison
to these other alloys at this temperature. In the as-cast condition, alloy D2
has only slightly higher strain rates than Inconel 718, and more
interestingly, has nearly the same power law exponent for stresses above 100
MPa. At this temperature, Inconel 718 has been observed to fail primarily by
the nucleation and linkage of voids in the structure [68], similar to what was
observed in the as-cast D2 material. This suggests that this process, which is
mainly controlled by diffusion and grain boundary cohesive strength, is
responsible for the low value of the creep exponent in as-cast alloy D2 at 800
∘C and above 100 MPa. Furthermore, it indicates that the as-cast structure has
sufficient resistance to dislocation glide and climb up to 200 MPa to cause
the weakest part of the structure, namely the grain boundaries, to fail. If
the grain boundaries can be strengthened, or eliminated altogether by
producing a single crystal of the material, the creep strain rates at this
temperature may be significantly lower. The creep rates in the as-cast
structure are therefore a hard upper bound to the true creep behavior of this
material. When the alloy was tested under 70 MPa loading, we observe a marked
decrease in strain rate, which suggests the presence of a threshold creep
stress, as has been observed to be in a similar range in other precipitation
strengthened alloys, notably several Fe-base superalloys tested at 700 ∘C [61,
21, 70]. For those studies, it was found that the threshold stress corresponds
to the stress necessary for general climb inhibited by elastic stresses
arising from lattice parameter mismatch between the matrix and precipitate
phases. In the case of as-cast alloy D2, however, stresses above about 70 MPa
at 800 ∘C lead to increasing rates of cavitation type creep, which is
controlled by a combination of bulk diffusion and dislocation movement.
Therefore, the underlying reason for the presence of threshold type behavior
must be more critically evaluated for this complex alloy.

Figure 12: Minimum steady-state creep rate plot for alloy D2 tested at 800 ∘C.
Minimum rates for several other high temperature alloys tested at 800∘C are
included for comparison. After Refs [65, 66, 67, 27, 69].

In analysing the creep behavior of as-cast alloy D2, one cannot neglect the
influence of the distinct dendritic and interdendritic morphologies. We saw
from our analysis of the Orowan stresses which arise from the different sample
regions that the dendritic regions should reach the yield point before the
interdendritic regions. In analogy, deformation processes which occur at lower
stress than dislocation glide, in particular dislocation climb, are also
expected to occur first in the dendritic regions of the sample. In our
observations of the as-cast D2 sample crept to 1.3% strain at 800 ∘C, 200 MPa,
we found a far lower density of mobile dislocations in the dendritic portion
of the sample than in the interdendritic portion. If this observation is
assumed to be representative of the general behavior within the material, this
suggests that dislocations are able to move relatively easily through the
dendritic pockets within the material but are comparatively trapped within the
interdendritic maze-like regions. The presence of such inhomogeneous yielding
behavior could lead to stress concentrations within the interdendritic
regions, with the ultimate outcome being grain boundary decohesion, as the
grain boundaries are nearly invariably located at the intersection of adjacent
interdendritic regions. Below a certain stress, dislocation motion, even by
general climb, may not be possible within the dendritic regions of the
material, with the result that stress concentrations at grain boundaries, and
resulting grain boundary decohesion, would no longer be present.

When we compare the power law fit for MA NiAl with that of annealed alloy D2,
we note a very similar creep exponent and slightly lower strain rates in alloy
D2. This suggests that the creep deformation in annealed alloy D2 may also
occur in large part in the ordered phase domains, rather than just in the
disordered phase. We must qualify this observation by noting that the creep
tests in MA NiAl were performed in compression rather than in tension. Still,
this finding is in accordance with our observations of mobile dislocations in
the ordered phase after creep in annealed alloy D2. The observed power law
exponent of approximately 4.8 is suggestive of a combined glide and climb
creep mechanism, however, these processes may be occurring simultaneously in
both the ordered and disordered phases.

####  4.3.1 Diffusion Rates

At the high temperatures and low strain rates encountered during creep, the
diffusion rate in the B2 and L21 phases plays a significant role in
determining the steady-state creep rate as well as the rate of coarsening.
Rudy and Sauthoff studied the creep behavior in B2 structured (Fe, Ni)Al
alloys and found that the maximum creep resistance in these alloys
corresponded to the alloy with the minimum interdiffusion coefficient [12].
The minimum interdiffusion coefficient was found to occur for stoichiometric
Al occupation and an Fe:Ni ratio of about 1:4, corresponding, respectively to
a maximum in long-range order parameter, and maximum (Fe, Ni) sublattice
disorder. The significance of these findings for the ordered phase domains in
the alloys studied here is that alloy D1 is observed to contain nearly an
ideal Fe:Ni ratio, especially in the dendritic regions, but is also expected
to have the greatest number of antisite defects, as indicated by the low Al
and Ti occupation. Alloy D2, which has a slightly greater Fe:Ni ratio, but a
significantly higher Al and Ti occupation, is expected to have an overall
lower set of ordered phase interdiffusion coefficients than alloy D1. Alloy D3
has nearly the same Al and Ti occupation as alloy D2, but has a higher than
optimal Fe:Ni ratio, indicating that the interdiffusion coefficients in this
alloy are also higher than in alloy D2. These findings suggest that alloy D2
may have the lowest overall diffusion based creep rate of the three alloys
studied, but could be further optimized by slightly reducing the Fe:Ni ratio,
and increasing the Al and Ti sublattice occupation.

The diffusion rate in the disordered phase domains of these three alloys may
play an even larger role on the creep response than the diffusion rate in the
ordered phase, due to climb of mobile dislocations in the disordered phase
past ordered phase obstacles, at stresses far below the yield stress. Although
a quantitative determination of the interdiffusion coefficients in the A2
phase is beyond the scope of this work, we can make some general remarks about
the trends that can be expected. From Darken’s second equation [71] one can
infer that increasing concentration of an element which has a greater solute
diffusion coefficient in a given phase than the self-diffusion coefficient of
the host species will increase the interdiffusion coefficient of the mixture
relative to the pure species. For $\alpha$-Fe (in the paramagnetic state) the
ratio of the solute diffusion coefficients of Al, Cr, Ni, and Ti to the self-
diffusion coefficient of Fe have been estimated as $D_{Al}/D_{Fe}=1.4$,
$D_{Cr}/D_{Fe}=1.4$, $D_{Ni}/D_{Fe}=1.0$, and $D_{Ti}/D_{Fe}=3.9$ [72]. From
these values, we see that Ti should have by far the largest effect on the A2
interdiffusion coefficient in these alloys, Al and Cr should have a much lower
effect, while Ni has little to no effect. It is tempting to draw firm
conclusions from these values, however, it is unclear over which composition
ranges these relationships hold. It is possible, for example, that when the
disordered phase approaches equal parts Fe and Cr, as is the case for alloys
D1 and D2, the interdiffusion coefficient may show anomalous behavior.
Furthermore, magnetic interactions in $\alpha$-Fe have been shown to play a
very large role in diffusional processes [15]. With these reservations in
mind, we reason that in all three alloys, the disordered phase interdiffusion
coefficient is governed by the presence of a trace Ti content, and will be
approximately the same for all three alloys within the accuracy of our
composition measurements.

##  5 Conclusions

Our characterisation of alloys D1 (Al16Cr25Fe35Ni20Ti4), D2
(Al20Cr20Fe35Ni20Ti5), and D3 (Al24Cr15\-
Fe35Ni20Ti6) reveals a clear gradient in several microstructural features that
closely follows the compositional gradient across the alloys. The first length
scale at which differences become noticeable is at the scale of individual
grains, where the composition difference between dendritic and interdendritic
areas is greatest for alloy D1 and least for alloy D3, as demonstrated in Fig.
2. For alloys D1 and D2, the large degree of dendritic segregation results in
noticeable phase fraction and morphology differences between dendritic and
interdendritic regions. Due to the high volume fraction of both ordered and
disordered phases, it is not reasonable to associate these alloys most closely
with either ferritic superalloys or aluminide/heusler phase materials. For the
composition range studied here, the resulting alloys would best be described
as ferrite-aluminide ($\alpha-\beta$) duplex alloys. For these duplex alloys
we have thoroughly characterized the as-cast and annealed structures, as well
as the high temperature tensile and creep behavior. We make the following
conclusions:

  * •

By varying the ratio of (Al+Ti):Cr, we are able to tune the degree of
dendritic segregation in these alloys.

    * –

On the high Cr end of the gradient, the majority of the structure is composed
of primary dendrites with an A2 matrix and equiaxed B2/L21 precipitates.

    * –

As Cr is replaced by Al and Ti, the volume of the primary dendrites is
replaced by increasing amounts of interdendritic structure, which is composed
of a fine maze-like arrangement of B2/L21 and A2 phases.

  * •

The average precipitate size within dendritic regions, as well as the average
domain width in maze-like regions were both found to decrease with increasing
Al and Ti content, likely due to a decrease in the respective ordering and
decomposition temperatures.

  * •

The coarsening rate in all three alloys was observed to be approximately
equivalent after 100 h annealing at 900 ∘C.

  * •

Disordered phase lattice parameters in both as-cast and annealed conditions
were found to slightly increase with increasing Al and Ti content and
decreasing Cr content, while ordered phase lattice parameters showed the
opposite behavior. Corresponding bulk averaged lattice parameter misfit was
found to decrease as Al and Ti were substituted for Cr.

  * •

Insights gained from calculations of the theoretical Orowan bypass stress in
different regions of the three alloys were used to explain the results of high
temperature tensile experiments:

    * –

Embrittlement in the interdendritic regions of D1 (Al16Cr25Fe35Ni20Ti4 ) led
this alloy to fracture prior to yielding in the as-cast state at both 700 and
900 ∘C. In the annealed condition, yield strengths were higher than predicted
by the Orowan strengthening mechanism, possibly due to either the presence of
nanoscale secondary precipitation, or solute atmosphere locking.

    * –

Fully lamellar alloy D3 (Al24Cr15Fe35Ni20Ti6 ) failed prior to yielding in the
as-cast state at both testing temperatures and furthermore showed near-zero
ductility in the annealed state indicating the absence of continuous pathways
for dislocation glide in the maze-like microstructure.

    * –

Duplex alloy D2 (Al20Cr20Fe35Ni20Ti5 ) showed a balance between moderate
ductility and high yield strength at high temperature, showing greater
ductility than alloy D1, with its large volume fraction of ductile disordered
matrix, and only slightly lower yield strength than the fully maze-like alloy
D3. The Orowan strengthening contribution for the dendritic regions was
predicted to be lower than that in the interdendritic maze-like regions,
indicating that yielding should occur first in the primary dendrites. Indeed,
at 900 ∘C, the observed as-cast yield strength was only slightly greater than
the calculated Orowan strengthening contribution from the dendritic regions.

  * •

Creep tests carried out on alloy D2 under a range of loading conditions at
700, 750, and 800 ∘C revealed promising creep resistance in both the as-cast
and annealed conditions. For tests carried out at 800 ∘C, investigation of the
crept microstructure revealed that deformation in the as-cast structure
occurred mainly by grain boundary cavitation, resulting in diffusion
controlled creep behavior. This indicates that observed creep rates are an
upper bound limited by grain boundary cohesion. Power law exponents in the
annealed state suggest dislocation glide and climb controlled creep behavior.
Observation of the annealed structure after creep testing reveals mobile
dislocations in both ordered and disordered domains, indicating that both
phases must be taken into account in predicting strain rates in the annealed
condition.

## Acknowledgements

This work was sponsored by the Deutsche Forschungsgemeinschaft (DFG) within
the priority programme SPP 2006 CCA-HEA, grant no. CL 2133/4-1. Dennis
Klapproth, Frank Rütters and Jürgen Wichert all deserve thanks for material
synthesis and heat treatment. Tristan Wickfeld and Bernd Deuerling are thanked
for tension and creep specimen preparation. The authors would like to thank
Benjamin Breitbach for XRD measurements and Andreas Janssen for tension
testing. The authors gratefully thank Dr. Frank Stein and Dr. Martin Palm for
fruitful discussions, as well as Professor Gerhard Dehm for careful and
insightful editing of the manuscript and for general support over the course
of this study.

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