Creep of Heusler-Type Alloy Fe-25Al-25Co

Creep of an alloy based on the intermetallic compound Fe2AlCo was studied by compressive creep tests in the temperature range from 873 to 1073 K. The stress exponent n and the activation energy of creep Q were determined using the multivariable regression of the creep-rate data and their description by means of sinh equation (Garofalo equation). The evaluated stress exponents indicate that the dislocation climb controls creep deformation. The estimated apparent activation energies for creep are higher than the activation enthalpy for the diffusion of Fe in Fe3Al. This can be ascribed to the changes in crystal lattice and changing microstructure of the alloy.


Introduction
Fe-Al-based alloys are potential candidates for new structural materials due to their outstanding corrosion resistance in various hostile environments, relatively low density and the low cost of both the basic constituting elements [1][2][3]. Insufficient creep resistance has been identified as an obstacle for their extensive application at high temperatures [4,5]. A number of methods have been proposed to overcome this problem. These include solid-solution hardening, strengthening by second-phase particles or ordering [6,7]. A promising method of strengthening is the addition of an element that leads to the formation of the Heusler compound [8,9]. These compounds are currently attracting research attention due the many interesting properties they possess. In the Fe-Al system, the compound can be formed by the addition of 3d-transition elements: Sc, Ti, V, Cr, Mn, Co, Ni, Cu, and Zn were considered theoretically by Gilleßen and Dronskowski [10]. Among these elements, Co leads to the largest increase of Young's modulus, and Voigt shear modulus [11]. A very high Curie temperature of 857 • C was also found in the Fe 2 CoAl compound [12]. In the previous study, quantum-mechanical calculations were used to investigate properties of four different polymorphs of Fe 2 AlCo and the occurrence of structural multiplicity at elevated temperatures was predicted [13]. Very few studies have experimentally investigated mechanical properties of Heusler compounds [14]. As far as we know, only Fe 2 AlTi-containing alloys were subjected to mechanical testing at elevated temperatures within the Fe-Al system [15][16][17]. The present study examines the creep behavior of a Fe 2 AlCo-based alloy and describes it in terms of the Garofalo equation [18]. The results are interpreted in terms of the available ternary phase diagrams and compared with the results of testing Fe-Al-Ti alloys.
The Fe 2 AlCo has, under 1000 K, a two-phase superalloy nanostructure with cuboids of a partly ordered phase coherently co-existing in a differently (or less) ordered matrix. The ordered phase has not the full-Heusler lattice (the L2 1 structure as a ternary analogue of D0 3 ) because quantum-mechanical calculations showed that it is mechanically unstable [13] and the inverse-Heusler structure, cf., Figure 1a, is both mechanically and thermodynamically more stable [10,13]. The inverse-Heusler is also in a better Although the composition of the studied alloy is close to the stoichiometric composition of Heusler alloys, we refer to our alloy as the Heusler-type alloy. In accordance with the more recent phase diagrams (see below), we assume that the A2 and B2 lattices coherently coexist at the nanoscale level (cuboids with the size of dozens of nm embedded in a matrix) at high temperatures.

Materials and Methods
The alloy was prepared using vacuum induction melting and casting under argon into a cylindrical cast of diameter 20 mm and exploitable length of 200 mm. The nominal composition of the alloy, 25 at. % Al and 25 at. % Co, is marked in parts of isothermal sections of the ternary Fe-Al-Co diagram in Figure 2 [20]. The grains are large and have an elongated shape with a mean aspect ratio of 4:1; the mean width is approximately 250 μm, see Figure 3.  Although the composition of the studied alloy is close to the stoichiometric composition of Heusler alloys, we refer to our alloy as the Heusler-type alloy. In accordance with the more recent phase diagrams (see below), we assume that the A2 and B2 lattices coherently coexist at the nanoscale level (cuboids with the size of dozens of nm embedded in a matrix) at high temperatures.

Materials and Methods
The alloy was prepared using vacuum induction melting and casting under argon into a cylindrical cast of diameter 20 mm and exploitable length of 200 mm. The nominal composition of the alloy, 25 at. % Al and 25 at. % Co, is marked in parts of isothermal sections of the ternary Fe-Al-Co diagram in Figure 2 [20]. The grains are large and have an elongated shape with a mean aspect ratio of 4:1; the mean width is approximately 250 µm, see Figure 3. high-temperature range, the arrangement of atoms may become even less ordered, exhibiting B2 and A2 lattices (Figure 1b,c). Although the composition of the studied alloy is close to the stoichiometric composition of Heusler alloys, we refer to our alloy as the Heusler-type alloy. In accordance with the more recent phase diagrams (see below), we assume that the A2 and B2 lattices coherently coexist at the nanoscale level (cuboids with the size of dozens of nm embedded in a matrix) at high temperatures.

Materials and Methods
The alloy was prepared using vacuum induction melting and casting under argon into a cylindrical cast of diameter 20 mm and exploitable length of 200 mm. The nominal composition of the alloy, 25 at. % Al and 25 at. % Co, is marked in parts of isothermal sections of the ternary Fe-Al-Co diagram in Figure 2 [20]. The grains are large and have an elongated shape with a mean aspect ratio of 4:1; the mean width is approximately 250 μm, see Figure 3.  Creep tests were performed in uniaxial compression on samples with a gauge length of 10 mm and a cross-section of 5 × 5 mm 2 . The compressive testing allows creep deformation not affected by the onset of fracture processes to be studied. On the other hand, because of the need for a specific compressive cage (reversible grips), the test arrangement does not allow rapid cooling of the test specimen, and not even cooling under the effect of load. Effective observation of the microstructure after creep is, therefore, limited. The samples were prepared by travelling wire electro-discharge machining and fine grinding of the surfaces. The tests were performed under a constant load on a dead-weight creep machine that was constructed in-house in a protective atmosphere of dry purified. The test temperature was held constant within ±1 K for each individual test. Changes in the gauge length were measured using a linear variable displacement transducer. The samples were subjected to stepwise loading, where the load was changed after the steady-state creep rate was established for a given load. The terminal values of the true stress and the creep rate, i.e., the true compressive strain rate, were evaluated for each step. Figure 4 shows the variation of creep rate ε with the applied stress σ at different temperatures T in a double-logarithmic plot. From the figure, it is obvious that a simple power law is not able to describe the measured data even in the area of the highest temperatures. The mean value of the power n′ is equal to 3.8 at 1073 K and 4.6 at 1023 K, but even at these temperatures, an increase in the power at higher stresses, which is commonly referred to in the literature as a power law breakdown, is observable. A single relation that satisfies conditions for both low and high stresses is the relationship proposed by Garofalo [18,21]. Creep tests were performed in uniaxial compression on samples with a gauge length of 10 mm and a cross-section of 5 × 5 mm 2 . The compressive testing allows creep deformation not affected by the onset of fracture processes to be studied. On the other hand, because of the need for a specific compressive cage (reversible grips), the test arrangement does not allow rapid cooling of the test specimen, and not even cooling under the effect of load. Effective observation of the microstructure after creep is, therefore, limited. The samples were prepared by travelling wire electro-discharge machining and fine grinding of the surfaces. The tests were performed under a constant load on a dead-weight creep machine that was constructed in-house in a protective atmosphere of dry purified. The test temperature was held constant within ±1 K for each individual test. Changes in the gauge length were measured using a linear variable displacement transducer. The samples were subjected to stepwise loading, where the load was changed after the steady-state creep rate was established for a given load. The terminal values of the true stress and the creep rate, i.e., the true compressive strain rate, were evaluated for each step. ε with the applied stress σ at different temperatures T in a double-logarithmic plot. From the figure, it is obvious that a simple power law is not able to describe the measured data even in the area of the highest temperatures. The mean value of the power n is equal to 3.8 at 1073 K and 4.6 at 1023 K, but even at these temperatures, an increase in the power at higher stresses, which is commonly referred to in the literature as a power law breakdown, is observable. A single relation that satisfies conditions for both low and high stresses is the relationship proposed by Garofalo [18,21].
where A , B and n are stress-independent parameters. Moreover, the parameter A is usually temperature dependent and this dependence can be expressed by means of Arrhenius function [22][23][24]. Equation (2) then reads where Q is the activation energy and R is the universal gas constant. The values of parameters in Equation (3) can be found by multivariable regression of the measured data ( Table 1). The analysis was performed separately for high temperatures (1023 K and 1073 K) and low temperatures (873 K, 923 K and 973 K). The resulting values are presented in ×1. It should be noted that the Garofalo equation is an empirical equation based on the evaluation of creep data of single-phase materials: (Cu, Al, Al-3Mg) and austenitic steel. However, it can also be used to describe data of multiphase materials [25]. Its use in describing rather limited present data obtained at temperatures of 923 and 973 K should be considered with caution.
Crystals 2020, 10, x FOR PEER REVIEW 4 of 9 where A′ , B and n are stress-independent parameters. Moreover, the parameter A′ is usually temperature dependent and this dependence can be expressed by means of Arrhenius function [22][23][24]. Equation (2) then reads where Q is the activation energy and R is the universal gas constant. The values of parameters in Equation (3) can be found by multivariable regression of the measured data ( Table 1). The analysis was performed separately for high temperatures (1023 K and 1073 K) and low temperatures (873 K, 923 K and 973 K). The resulting values are presented in ×1. It should be noted that the Garofalo equation is an empirical equation based on the evaluation of creep data of single-phase materials: (Cu, Al, Al-3Mg) and austenitic steel. However, it can also be used to describe data of multiphase materials [25]. Its use in describing rather limited present data obtained at temperatures of 923 and 973 K should be considered with caution.

Discussion
The determination of the rate-controlling creep mechanism is usually based on a comparison of the measured value of power n with the theoretical models published in the literature. Models predict that n = 1 corresponds to diffusional creep, n = 2 to grain boundary sliding and n between 3 and 7 to dislocation creep [26]. Values of the power of n, whether obtained directly from logarithmic dependencies or using Equation (3), indicate that creep is controlled by dislocation motion. The estimated activation energies at both high and low temperatures are higher than the activation enthalpy of the diffusion of iron in the B2 phase (270 kJ/mol [27], 234 kJ/mol [28]). The effective activation enthalpy for diffusion in a multicomponent alloy can be assessed by various approaches [29][30][31]. Their detailed discussion is beyond the scope of the present contribution. A weighted average of the enthalpies of the individual elements can be used as an approximate estimate of the effective activation enthalpy. The activation enthalpy of Co diffusion in B2 Fe-Co is 247 kJ/mol [32]. Problems associated with the availability of the isotope 26 Al lead to the recommendation of 214 kJ/mol as a suitable value for the activation enthalpy of aluminum diffusion in B2 [33]. The effective activation enthalpy then ranges from 232 to 250 kJ/mol. Even higher values of activation energy of creep (780 kJ/mol) can be determined over a temperature range from 973 K to 1023 K using the usual formula The detected activation energies are, therefore, to be considered rather apparent values, resulting from the fact that neither the crystal lattice nor the microstructure are temperature-independent. As far as the crystal lattice is considered, the ternary phase diagram is known only for lower temperatures (see Figure 2). For higher temperatures, there is only an approximate estimate of the boundary between a single-phase and a two-phase structure [20]. At 1000 K, this boundary lies close to the chemical composition of the studied alloy. It is, therefore, likely that at 1023 and 1073 K, our alloy is single-phased and has a crystal lattice of type B2, or possibly, at the highest temperature, of type A2. Thus, a change from a single-phase to a two-phase structure and switching the crystal lattice from type B2 to an even more ordered type (an inverse-Heusler phase with possibly some disorder in some of the sublattices) when the temperature is reduced from the high-temperature to low-temperature region is likely to cause the high apparent activation energy of 780 kJ/mol. The more ordered inverse-Heusler phase is more resistant to deformation than a less-ordered B2 lattice or a disordered A2 lattice. Similarly, a two-phase structure is more resistant to deformation than a single-phase structure. Thus, changes in the creep rate as the temperature increases are not only due to the increase of the diffusion coefficient but also to the material weakening resulting from the changing microstructure and lattice disordering. Consequently, the apparent activation energy of creep is greater than the enthalpy of diffusion. Figures 5 and 6 show a comparison of the stress dependence of the creep rate in the present alloy and a binary Fe-25 at. % alloy [34] at 873 K and 1073 K, respectively. The addition of cobalt significantly improves the creep resistance, particularly at the lower temperature. The comparison is complemented by the results of creep research in ternary alloys of Fe-Al-Ti, where the Heusler phase is also formed [16,35,36]. The data used for comparison were also obtained by the compressive testing. The data point of the alloy with 25 at. % Al and 20 at. % Ti at 873 K [35] was obtained by extrapolating the data at 1073 K using the appropriate activation energy and stress exponent. Evidently, at 1073 K, the effect of titanium additions on creep is somewhat more pronounced than the effect of cobalt addition. On the other hand, at a temperature of 873 K, the effects of the addition of both elements are approximately equal. This observation may be related to the position of both elements in the periodic table.
It is well-known that there are two non-equivalent positions for iron atoms in the Fe 3 Al compound ordered into the L2 1 lattice: one with eight iron atoms as closest neighbors, the other with four iron atoms and four aluminum atoms as closest neighbors. The alloying elements to the left of Fe in the periodic table, such as Ti, preferentially occupy the former positions, whereas elements to the right of Fe (i.e., Co) occupy the latter positions [37,38]. The preference of positions has an influence on the stability of the L2 1 lattice. The addition of titanium leads to the stabilization, which results in an increase in the L2 1 -B2 transition temperature [39]. The situation in the inverse-Heusler lattice is more complicated (due to the existence of four sublattices) but the Co atoms are expected [19] to occupy the sublattice at locations where the second nearest neighbors are only the Fe and Co atoms (and not the Al atoms). It was also shown previously by quantum-mechanical calculations of Heusler-based Fe 2 AlCo polymorphs, that the ordered full-Heusler structure is mechanically unstable and thermodynamically less stable than the inverse-Heusler lattice [13]. The energy differences between different polymorphs were found to be so small that partly disordered B2 and completely disordered A2 structures are predicted for elevated and high temperatures. The formation of polymorphs with disordered sublattices is thus probable with increasing temperatures similarly as phase-composition changes, i.e., a transition from a two-phase material to a single-phase one.

Conclusions
The creep of Fe-25 at. % Al-25 at. % Co alloy was studied in the temperature range from 873 K to 1073 K. The stress and temperature dependence of the creep rate was described by a combined Garofalo (sinh) and Arrhenius equation. The following conclusions regarding the creep resistance of the alloy can be drawn:

•
The whole temperature range investigated can be divided into two regions with different values of the stress exponent and activation energy.

•
The estimated activation energies at both high and low temperatures are higher than the effective activation enthalpy of diffusion resulting from the weighted average of enthalpies of individual components. An even greater value of the apparent activation energy was found in the transition between the two regions.

•
The division into different regions can be explained by changes in the microstructure and crystal lattice ordering.

•
The addition of cobalt significantly improves the creep resistance of the binary alloy Fe-25 at. % Al. However, at 1073 K, the effect of cobalt is less than that of titanium addition. At 873 K, the effects of both elements are comparable.   Figure 1 was visualized using the VESTA package [40].

Conflicts of Interest:
The authors declare no conflict of interest.