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

crystals

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

Ferdinand Dobeš 1, Petr Dymáˇcek 1,2 and Martin Friák 1,2,*

1 Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Žižkova 22, CZ-61662 Brno, Czech Republic; [email protected] (F.D.); [email protected] (P.D.) 2 CEITEC IPM, Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Žižkova 22, CZ-61662 Brno, Czech Republic * Correspondence: [email protected]; Tel.: +420-532-290-400

Received: 20 December 2019; Accepted: 16 January 2020; Published: 20 January 2020

Abstract: 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.

Keywords: iron aluminides; Heusler alloy; creep; stress exponent; activation energy

1. 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 [1–3]. 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 Fe2CoAl compound [12]. In the previous study, quantum-mechanical calculations were used to investigate properties of four different polymorphs of Fe2AlCo 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 Fe2AlTi-containing alloys were subjected to mechanical testing at elevated temperatures within the Fe–Al system [15–17]. The present study examines the creep behavior of a Fe2AlCo-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 Fe2AlCo 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 L21 structure as a ternary analogue of D03) because quantum-mechanical calculations showed that it is mechanically unstable [13] and the inverse-Heusler structure, cf., Figure1a, is both mechanically and thermodynamically more stable [10,13]. The inverse-Heusler is also in a better

Crystals 2020, 10, 52; doi:10.3390/cryst10010052 www.mdpi.com/journal/crystals Crystals 2020, 10, x FOR PEER REVIEW 2 of 9 Crystals 2020, 10, 52 2 of 9 high-temperature range, the arrangement of atoms may become even less ordered, exhibiting B2 and Crystals 2020, 10, x FOR PEER REVIEW 2 of 9 A2agreement lattices (Figure with experiments 1b,c). (see, e.g., Ref. [19]). In the high-temperature range, the arrangement of atomshigh-temperature may become even range, less the ordered, arrangement exhibiting of atoms B2 ma andy become A2 lattices even (Figureless ordered,1b,c). exhibiting B2 and A2 lattices (Figure 1b,c).

2 FigureFigure 1.1. SchematicSchematic 1. Schematic visualizations visualizations visualizations of atomof of atom atom conﬁgurations configurationsconfigurations in Fe in2inAlCo: FeFe2AlCo:AlCo: an inverse-Heusler an an inverse-Heusler inverse-Heusler (a), a(a partially), a(a ), a partiallyorderedpartially B2ordered (b ordered) and B2 a ( disorderedB2b) (andb) and a disordered a A2disordered (c). A A2 schematic A2 ( c(c).). A A schematicschematic of the used of of the coloringthe used used coloring ofcoloring atoms of atoms (ofd ).atoms (d). (d).

AlthoughAlthough thethe compositionthecomposition composition of of the ofthe studiedthe studied studied alloy alloyalloy is close is closeclose to the toto stoichiometric the the stoichiometric stoichiometric composition composition composition of Heusler of of Heusleralloys,Heusler we alloys, refer alloys, we to ourreferwe refer alloy to ourto asour alloy the alloy Heusler-type as as the the Heusler-type Heusler-type alloy. In alloy.alloy. accordance In In accordance accordance with with the with the more themore recentmore recent recent phase phasediagramsphase diagrams (see diagrams below), (see (see webelow), below), assume we we thatassume assume the A2 thatthat and thth B2ee latticesA2 andand coherently B2B2 lattices lattices coexistcoherently coherently at the coexist nanoscalecoexist at the at level the nanoscale level (cuboids with the size of dozens of nm embedded in a matrix) at high temperatures. nanoscale(cuboids with level the (cuboids size of with dozens the of size nm of embedded dozens of in nm a matrix)embedded at high in a temperatures.matrix) at high temperatures. 2. Materials and Methods 2. Materials Materials and and Methods Methods The alloy was prepared using vacuum induction melting and casting under argon into a The alloy was prepared using vacuum induction melting and casting under argon into a cylindrical Thecylindrical alloy castwas of prepared diameter 20using mm andvacuum exploitable induction length melting of 200 mm. and The casting nominal under composition argon ofinto a cylindricalcast ofthe diameter alloy, cast 25 of at. 20 diameter % mm Al and and 2025 exploitable at.mm % Co,and is exploitable marked length ofin parts 200lengthmm. of isothermal of The200 nominalmm. sections The composition nominalof the ternary compositionof Fe–Al– the alloy, of the25at. alloy,Co % diagram Al 25 and at. % 25 in Al at.Figure and % Co 252 ,[20]. isat. marked %The Co, grains is in marked parts are large of in isothermal andparts have of isothermalan sections elongated of sections the shape ternary with of the Fe–Al–Coa mean ternary aspect diagram Fe–Al– Coin Figurediagramratio2 of[ 4:1;20in ].Figure the The mean grains2 [20].width areThe is largeapproximately grains and are have large 250 an μandm, elongated see have Figure an shape elongated3. with ashape mean with aspect a mean ratio aspect of 4:1; ratiothe mean of 4:1; width the mean is approximately width is approximately 250 µm, see 250 Figure μm,3. see Figure 3. 40 60 40 60

a) 873 K b) 923 K 40 60 40 60 50 50 50 50 a) 873 K B2 b) 923 K B2 50 50 5060 50 40 60 40 a a e t e t. . F F B2 D0 % B2 % 3 % C % C . . t 70 40 30 o t 70 60 4030 o a 60 a a a 0 3 e t e D t. . F + F % D0 A2 % 3 % 2 C % C . 80 B 20 80. 20 t 70 2+ 30 o t 70 30 o a A 2 a A2+B2 +B0 3 A2D 2+ 90 A 10 90 10 B2 80 2+ 20 80 20 A2A 2 B2+B2* B2 A2 A2+B2 B2 +B B2+B2* B2* 2 100 A A2+B2* 0 100 0 90 10 90 10 0 102030405060 0 102030405060 A2 at. %B2+B2* Al B2 A2 at. % Al B2 B2+B2* B2* 100 A2+B2* 0 100 0 Figure 2. Details of the isothermal sections of the Fe–Al–Co system at (a) 873 K, calculated, and (b) 9230 K, experimental, 102030405060 according to Kozakai et al. [20]. 0 102030405060 at. % Al at. % Al

Figure 2. Details ofof thethe isothermal isothermal sections sections of of the the Fe–Al–Co Fe–Al–Co system system at (a at) 873 (a) K,873 calculated, K, calculated, and ( band) 923 (b K,)

923experimental, K, experimental, according according to Kozakai to Kozakai et al. [20 et]. al. [20].

Crystals 2020, 10, 52 3 of 9 Crystals 2020, 10, x FOR PEER REVIEW 3 of 9

FigureFigure 3. BackscatteredBackscattered electron electron micrograph micrograph of meta metallographicllographic section of the uncrept alloy.

Creep tests were performed in uniaxial compressioncompression on samples with a gauge length of 10 mm 2 and a cross-section of 5 × 5 mm2.. The The compressive compressive testing testing allows allows creep creep deformation deformation not not affected affected by × the onset of fracture processes to bebe studied.studied. On On the the other hand, because of of the need for a specificspecific compressive cage (reversible grips), the test arra arrangementngement does not allow rapid cooling of the test specimen, and not even cooling under the eeffectffect of load. Effective Effective observation of the microstructure after creep is, therefore,therefore, limited.limited. The The samples were prepared by travelling wire electro-discharge machining and fine fine grinding of the surfaces. The tests were performed under a constant load on a dead-weight creepcreep machine machine that that was was constructed constructed in-house in-house in a protectivein a protective atmosphere atmosphere of dry purified. of dry Thepurified. test temperatureThe test temperature was held constantwas held within constant1 wi K forthin each ±1 K individual for each individual test. Changes test. in Changes the gauge in ± thelength gauge were length measured were usingmeasured a linear using variable a linear displacement variable displacement transducer. transducer. The samples The were samples subjected were to subjectedstepwise loading,to stepwise where loading, the load where was changedthe load after was thechanged steady-state after the creep steady-state rate was established creep rate forwas a establishedgiven load. for The a terminal given load. values The of terminal the true values stress andof the the true creep stress rate, and i.e., the truecreep compressive rate, i.e., the strain true compressiverate, were evaluated strain rate, for eachwere step.evaluated for each step.

3. Results . Figure 44 showsshows thethe variation of creep rate εε with withthe the appliedapplied stressstress σσ atat didifferentfferent temperatures T in a double-logarithmic double-logarithmic plot. plot. From From the the figure, figure, it itis isobvious obvious that that a simple a simple power power law law is not is not able able to describeto describe the the measured measured data data even even in in the the area area of of the the highest highest temperatures. temperatures. The The mean mean value value of of the power nn0′is is equal equal to to 3.8 3.8 at at 1073 1073 K K and and 4.6 4.6 at at 1023 1023 K, K, but but even even at theseat these temperatures, temperatures, an increasean increase in the in powerthe power at higher at higher stresses, stresses, which which is commonly is commonl referredy referred to in the to literature in the asliterature a power as law a breakdown,power law breakdown,is observable. is A observable. single relation A single that satisfies relation conditions that satisfies for conditions both low and for high both stresses low and is thehigh relationship stresses is proposedthe relationship by Garofalo proposed [18, 21by]. Garofalo [18,21]. . n ε = A00 σ 0 (1) n′ ε = A′′σ (1)

Crystals 2020, 10, x FOR PEER REVIEW 4 of 9

ε = ′[]()σ n Crystals 2020, 10, 52  A sinh B 4 of(2) 9 where A′ , B and n are stress-independent parameters. Moreover, the parameter A′ is usually . n temperature dependent and this dependenceε = Acan0[sinh be (expressedBσ)] by means of Arrhenius function [22–(2) 24]. Equation (2) then reads where A0, B and n are stress-independent parameters. Moreover, the parameter A0 is usually temperature dependent and this dependence can be expressed by means of Arrhenius function [22–24]. Equation (2)  − Q  n then reads ε = Aexp []sinh()Bσ . Q (3) ε = A exp −RT [sinh(Bσ)]n (3) RT where Q isis thethe activationactivation energyenergy andand RR isis thethe universaluniversal gasgas constant.constant. The valuesvalues ofof parametersparameters in Equation (3)(3) cancan bebe found found by by multivariable multivariable regression regression of theof the measured measured data data (Table (Table1). The 1). analysisThe analysis was performedwas performed separately separately for high for high temperatures temperatures (1023 (1023 K and K 1073 and K)1073 and K) low and temperatures low temperatures (873 K, (873 923 K, K and923 K 973 and K). 973 The K). resulting The resulting values arevalues presented are presented in 1. It in should ×1. It beshould noted be that noted the Garofalothat the equationGarofalo × isequation an empirical is an empirical equation equation based on based the evaluation on the eval ofuation creep dataof creep of single-phase data of single-phase materials: materials: (Cu, Al, Al-3Mg)(Cu, Al, andAl-3Mg) austenitic and austenitic steel. However, steel. itHowever, can also beit usedcan also to describe be used data to describe of multiphase data of materials multiphase [25]. Itsmaterials use in describing[25]. Its use rather in describing limited present rather limited data obtained present at data temperatures obtained at of temperatures 923 and 973 K of should 923 and be considered973 K should with be considered caution. with caution.

-3 10

TEMPERATURE -4 10 1073 K 1023 K

-5 973 K 10 923 K 873 K -6 10

-7 10

-8 CREEP RATE (1/s) 10

-9 10

-10 10 10 100 1000 APPLIED STRESS (MPa)

Figure 4. Dependence of thethe creepcreep raterate onon appliedapplied stress.stress. SolidSolid lines:lines: GarofaloGarofalo Equationequation (3), dashed lines: power power functions. Table 1. Calculated values of parameters in Equation (3). Table 1. Calculated values of parameters in Equation (3). T [K] A [1/s] Q [kJ/mol] B [1/MPa] n T [K] A [1/s] Q [kJ/mol] B [1/MPa] n 873–973 23.16 322.0 0.0045 4.23 1023–1073873–973 48.3823.16 322.0 544.6 0.0045 0.0096 4.23 3.41 1023–1073 48.38 544.6 0.0096 3.41

4. 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 Crystals 2020, 10, 52 5 of 9 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 [29–31]. 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 26Al 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

" . # ∂ ln ε Q = (4) − ∂(1/RT) σ

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 Figure2). 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. Figures5 and6 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. Recently, a ferritic alloy strengthened by coherent hierarchical precipitates has been developed [8,9]. Its excellent creep properties are due to the presence of Heusler-phase-based precipitates, which themselves contain coherent nano-scaled B2 zones. Crystals 2020,, 1010,, 52x FOR PEER REVIEW 6 of 9 Crystals 2020, 10, x FOR PEER REVIEW 6 of 9

-2 10-2 10 Fe - 25 at. % Al -3 Fe - 25 at. % Al 10-3 873 K [34] 10 873 K [34]

-4 10-4 10

-5 10-5 10

-6 10-6 10

-7 10-7 10 This work Al/CoThis (at.work %) Al/Co (at. %) Al/Ti (at. %) -8 25/25 Al/Ti (at. %) 10-8 25/25 25/10 [34] 10 25/10 [34] 25/20 [35] -9 25/20 [35] CREEP RATE, STRAIN RATE (1/s) STRAIN RATE CREEP RATE, 10-9 27.5/15 [16] CREEP RATE, STRAIN RATE (1/s) STRAIN RATE CREEP RATE, 10 27.5/15 [16] 27.5/25 [16] 27.5/25 [16] -10 10-10 10 100 1000 100 1000 APPLIED STRESS (MPa) APPLIED STRESS (MPa) Figure 5. Comparison of creep rate/strain rate variation with applied stress for the present alloy, Figure 5.5. ComparisonComparison of of creep creep rate rate/strain/strain rate rate variation variatio withn with applied applied stress stress for the for present the present alloy, binaryalloy, binary Fe–Al alloy and Fe–Al–Ti alloys at 873 K. Fe–Albinary alloyFe–Al and alloy Fe–Al–Ti and Fe–A alloysl–Ti at alloys 873 K. at 873 K.

-2 10-2 10 1073 K Fe - 25 at. % Al 1073 K Fe - 25 at. % Al -3 10-3 [34] 10 [34]

-4 10-4 10

-5 10-5 10 This work Al/CoThis (at.work %) -6 Al/Co (at. %) 10-6 25/25 10 25/25 Al/Ti (at. %) Al/Ti (at. %) -7 10-7 25/10 [34] 10 25/10 [34] 22/16.7 [36] 22/16.7 [36] -8 25/20 [35] -8 25/20 [35]

CREEP RATE, STRAIN RATE (1/s) CREEP RATE, STRAIN 10

CREEP RATE, STRAIN RATE (1/s) CREEP RATE, STRAIN 10 22.6/22.0 [36] 22.6/22.0 [36]

-9 10-9 10 10 100 1000 10 100 1000 APPLIED STRESS (MPa) APPLIED STRESS (MPa) Figure 6.6. ComparisonComparison of of creep creep rate rate/strain/strain rate rate variation variatio withn with applied applied stress stress for the for present the present alloy, binaryalloy, Figure 6. Comparison of creep rate/strain rate variation with applied stress for the present alloy, Fe–Albinary alloyFe–Al and alloy Fe–Al–Ti and Fe–A alloysl–Ti at alloys 1073 at K. 1073 K. binary Fe–Al alloy and Fe–Al–Ti alloys at 1073 K.

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Comparison of the creep data of this novel progressive alloy shows that the present laboratory alloy is slightly inferior as far as compressive testing at 973 K is concerned: Creep rates were 1.7 10 8 s 1 × − − at 202 MPa and 1.5 10 7 at 220 MPa [8] vs. 1.7 10 8 s 1 at 170 MPa and 3.8 10 7 s 1 at 211 MPa × − × − − × − − (present alloy). It is well-known that there are two non-equivalent positions for iron atoms in the Fe3Al compound ordered into the L21 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 L21 lattice. The addition of titanium leads to the stabilization, which results in an increase in the L21–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 Fe2AlCo 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.

5. 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.

Author Contributions: Conceptualization: F.D.; Formal analysis: P.D.; Funding acquisition: M.F.; Methodology: F.D.; Resources: M.F.; Validation: F.D. and P.D.; Visualization: F.D. and M.F.; Writing—original draft: F.D.; Writing—review & editing: F.D., P.D. and M.F. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Czech Science Foundation, grant number 17-22139S (F.D., P.D., M.F.). Acknowledgments: Authors wish to thank Y. Jirásková (IPM Brno, Czech Republic) for the supply of the experimental alloys. This research has been financially supported by the Ministry of Education, Youth and Sports of the Czech Republic under the project m-IPMinfra (CZ.02.1.01/0.0/0.0/16_013/0001823) and under the project CEITEC 2020 (LQ1601). Figure1 was visualized using the VESTA package [40]. Conflicts of Interest: The authors declare no conflict of interest. Crystals 2020, 10, 52 8 of 9

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