Thermal vacancy behavior analysis through thermal expansion, lattice parameter and elastic modulus measurements of B2-type FeAl

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Thermal vacancy behavior analysis through thermal expansion, lattice parameter and elastic modulus measurements of B2-type FeAl Mi Zhao a, Kyosuke Yoshimi a,⇑, Kouichi Maruyama a, Kunio Yubuta b a b

Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan Institute for Materials Research, Tohoku University, Sendai, Miyagi 980-8577, Japan

Received 21 August 2013; received in revised form 22 October 2013; accepted 24 October 2013 Available online 21 November 2013

Abstract Thermal vacancy behavior in B2-type FeAl was analyzed through thermal expansion, lattice parameter, and elastic modulus measurements. High-temperature X-ray diffractometry (HT-XRD) was conducted to determine the lattice parameter at elevated temperatures, and the electromagnetic acoustic resonance method was applied to investigate the temperature dependence of the elastic moduli in B2type FeAl. Using a series of in situ high-temperature techniques such as HT-XRD and dilatometry, the thermal vacancy concentration at elevated temperatures was estimated from the divergence between the changes in the sample length and the lattice parameter with temperature, giving a vacancy formation enthalpy of 0.7 and 0.6 eV for Fe–40Al and Fe–43Al (at.%), respectively. The long-range order parameter was found to increase with temperature in a high-temperature range, indicating that the Fe-atom recovery process occurs in this temperature range. The in situ high-temperature measurements suggest that at elevated temperatures, thermal vacancies have no significant influence on the lattice parameter and elastic moduli of B2-type FeAl. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Iron aluminides; Vacancies; X-ray diffraction; Lattice parameter; Elastic moduli

1. Introduction As aluminum and iron are the two most commonly used metallic resources, iron aluminides have been widely studied as structural materials because of their interesting performance at high temperature. B2-type FeAl is one such representative intermetallic compound, and the thermal vacancy behavior and positive temperature dependence of the yield strength, i.e., the so-called strength anomaly, have been the two principal research topics for B2-type FeAl in the past few decades. It is well known that this intermetallic compound contains a high concentration of thermal vacancies at high temperature and that these vacancies are easily frozen into the material upon cooling [1,2]. These quenched-in vacancies lead to “excess vacancy hardening” at room temperature. It was first reported by Rieu and ⇑ Corresponding author. Tel.: +81 22 795 7324.

E-mail address: [email protected] (K. Yoshimi).

Goux [1] that rapid quenching from an elevated temperature significantly enhanced the hardness of B2-type FeAl due to supersaturated vacancies. Nagpal and Baker [3] reported that different cooling rates had a dramatic effect on the hardness of FeAl, while Chang et al. [4] demonstrated that over a large composition range (40–51 at.% Al) the changes observed in the hardness with increasing aluminum content and quenching temperature were an indication of the relative changes in the concentration of the supersaturated vacancies in FeAl. Moreover, supersaturated vacancies cause an increase in the critical resolved shear stress and a decrease in the ductility of single crystals at room temperature [5]. Through a study on the relationship between the vacancy concentration and the yield strength of FeAl with varying aluminum contents, Xiao and Baker [6] showed that vacancies control the room-temperature mechanical properties of FeAl. The excess vacancy concentration, however, can be reduced by intermediate temperature annealing, and Nagpal and Baker

1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.10.051

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[3] demonstrated that the hardness of furnace-cooled FeAl reduced after annealing at 400 °C for 118 h. Yoshimi et al. [7] also showed that after being completely annealed at 425 °C for 120 h, the hardness of Fe–48Al (at.%) was even lower than that of Fe–39Al. Due to the removal of supersaturated vacancies, exothermic peaks were observed in differential scanning calorimetry (DSC) curves of quenched FeAl [8,9]. Several studies have investigated the behavior of thermal and quenched-in vacancies to understand their effects on the mechanical properties of B2-type FeAl. Here, it is worth mentioning the “vacancy hardening” model, which was proposed by George and Baker [10] to explain the strength anomaly of B2-type FeAl at elevated temperatures. Because the vacancy formation enthalpy is much lower than the migration enthalpy [11], thermal vacancies in FeAl form easily but find it difficult to migrate. In their theory, newly generated thermal vacancies in the strength anomaly temperature range can hardly move and so impede the dislocation motion by the “solid solution” hardening mechanism. Since the positive temperature dependence of the yield strength in B2-type FeAl was found by Chang [12] in 1990, a number of mechanisms have been proposed to explain the phenomenon. In addition to the vacancy hardening model, both “glide decomposition” [13] and “local climb locking” [14] are also candidate models. However, the discussion about the strength anomaly in B2-type FeAl is far from finished. In this study, thermal expansion, lattice parameter and elastic modulus measurements were conducted to study the thermal vacancy behavior in B2-type FeAl. Several samples subjected to different thermal histories were examined at room and elevated temperatures, and the thermal vacancy concentration and its formation properties were estimated. In light of the obtained results, we discuss excess vacancy hardening and the role of thermal vacancies on the temperature dependence of the lattice parameter and elastic moduli. 2. Experimental procedures Ingots with compositions of Fe–40Al and Fe–43Al (at.%) were prepared by conventional argon arc-melting using pure aluminum (99.99 wt.%) and pure iron (99.99 wt.%). Each ingot was melted five times, flipping the ingot upside down after each melt to ensure homogeneity. The as-cast ingots were subjected to a homogenization heat treatment at 1100 °C for 24 h under vacuum conditions of better than 103 Pa and then slowly cooled to 400 °C, before being aged at the same temperature for 100 h to eliminate supersaturated vacancies. The ingots were then furnace-cooled to room temperature. All the experimental specimens were prepared from these fully annealed ingots. Powder samples for X-ray diffraction (XRD) measurements were prepared by crushing parts of these ingots in a tungsten mortar. The size of the powder particles was less

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than 46 lm in diameter. The powder was sealed in a quartz tube under vacuum conditions of better than 102 Pa and heated at 800 °C for 1 h to eliminate the residual strain followed by the excess-vacancy-elimination heat treatment at 400 °C for 100 h. All the powder samples described below were subject to this thermal history. The lattice parameters of the FeAl powder samples were measured at both room and elevated temperatures using Co Ka X-rays and a D8 ADVANCE (Bruker AXS) diffractometer equipped with a HTK1200N high-temperature furnace (Anton Paar). For the room-temperature measurements, the powder was first sealed in the quartz tube, filled with 4  104 Pa Ar gas and quenched at different temperatures. For the high-temperature measurements, the powder was kept under vacuum conditions on the order of 103 Pa at the corresponding testing temperature for 30 min before each test to avoid temperature inhomogeneities. Oxidation was not detected in the samples since no oxide peak appeared in any of the measurements up to 1000 °C. The lattice parameter values were estimated from the whole powder pattern decomposition (WPPD) method, and the integrated intensity of the diffraction peaks was calculated by the single profile fitting (SPF) method using the TOPAS4 software (Bruker AXS). The long-range order parameter was estimated from the integrated intensity ratio of the superlattice and fundamental diffractions in the XRD profiles. Several bulk specimens were also cut from the fully annealed ingots by electrodischarge machining (EDM). These specimens were used for hardness, thermal expansion and elastic modulus measurements. The thermal expansion of the 5 mm  5 mm  20 mm samples was measured by thermomechanical analysis (TMA) using a Q400 analyzer (TA Instruments Japan Inc.). Isothermal measurements were conducted by keeping the temperature of the specimens fixed for 30 min at every 100 °C interval between 100 °C and 1000 °C to provide the same heating path as that in the high-temperature XRD measurements. The dimension changes of the specimens were taken as the average of the values in the last 10 min at each temperature step. The thermal vacancy concentration was estimated from the divergence between the lattice parameter change and the thermal expansion of the samples. Moreover, the activation energy of vacancy formation was derived using the Arrhenius relationship. The temperature dependence of the elastic moduli was obtained using the electromagnetic acoustic resonance (EMAR) method using a CCII-HT instrument (Nihon Techno-Plus Co. Ltd.). As shown schematically in Fig. 1, a 5 mm  5 mm  5 mm specimen surrounded by a coil was placed between two hard magnets. Two different vibration modes were excited in the specimen by the Lorentz force when an electric pulse was sent through the coil, and the ultrasonic waves returned to the coil were transformed into digital signals. The moduli measurements were performed at room temperature to up to 800 °C over a frequency range of 350– 1200 kHz in a magnetic field of 0.5 T. The specimens were

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where kB is the Boltzmann constant and T is the absolute temperature. In a binary system, the long-range order parameter S defined by the Bragg–Williams approximation is generally used to describe ordered and disordered conditions [17]: S ¼ r A  wB ¼ r B  wA

Fig. 1. Schematic illustration of the EMAR method showing two induced vibrational modes.

rested for 30 min between each testing temperature. The Young’s modulus, shear modulus and Poisson’s ratio were estimated at each testing temperature. 3. Data analysis The newly generated thermal vacancy concentration Dcv was evaluated based on a precise combination of the temperature-dependent changes in the bulk length DL/L0 and X-ray lattice parameter Da/a0. Because the bulk length change includes both the average lattice expansion and increased lattice site numbers due to vacancy formation, while the X-ray lattice parameter change is only capable of detecting the average lattice expansion, the relative thermal vacancy concentration can be expressed as follows [15]:   DLðT Þ DaðT Þ  Dcv ðT Þ ¼ 3 ð1Þ LðT 0 Þ aðT 0 Þ where DL(T)/L(T0) and Da(T)/a(T0) are the changes in specimen length and lattice parameter at temperature T from the reference temperature, T0, respectively. The thermal vacancy concentration estimated from the vacancy formation enthalpy and entropy [11] was less than 105 below 400 °C. Note that the constitutional vacancy concentration in FeAl with a composition of 40–45 at.% Al was too low to be detected according to Xiao and Baker [6]. In the present experiment, since the excess-vacancy-elimination heat treatment was performed at 400 °C, the vacancy concentration below 400 °C was not significant enough to be taken into consideration, and thereby the reference temperature T0 in Eq. (1) was fixed at 400 °C for estimations of the thermal vacancy concentration. Furthermore, the activation enthalpy H FV and entropy S FV of vacancy formation were calculated by [16]  F   SV H FV Dcv ¼ exp exp  ð2Þ kB kBT

ð3Þ

where ri and wi refer to the fraction of i sites occupied by the right and wrong atoms, respectively. The integrated X-ray intensity of a superlattice diffraction pattern is proportional to S2 [18], and to normalize the intensity scaling factor of different XRD profiles, the integrated intensity of the superlattice diffraction was divided by the integrated intensity of a corresponding fundamental diffraction. Thereby, the measured value of the long-range order parameter Smea is obtained as [6] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðI s =I f Þobs ð4Þ S mea ¼ ðI s =I f Þcal where Is and If are the integrated intensities of the superlattice and fundamental diffractions, respectively, (Is/If)obs is the intensity ratio of the experimentally observed superlattice and fundamental diffractions and (Is/If)cal is the intensity ratio of the ideal superlattice and fundamental diffraction obtained from a calculation of a fully ordered compound. The ideal XRD profile of the fully ordered FeAl was simulated using the CrystalDiffract software (CrystalMaker Software Ltd.). In this study, the intensities of the {1 0 0} peak (superlattice diffraction) and the {2 0 0} peak (fundamental diffraction) were used to avoid the texture effect. The EMAR method is a non-contact measurement method of the elastic moduli that uses the ultrasonic wave induced by an electric pulse. The fundamental principle in the elastic modulus analysis in the EMAR method is [19,20] Z 1 L¼ ðqx2 dij ui uj  cij ei ej ÞdV ð5Þ 2 X where L is the Lagrangian, q is the density of the sample, x is the resonance frequency, dij is a constant such that d = 1 (i = j) or d = 0 (i – j), ui and uj are displacement vectors, cij is an elastic constant and ei and ej are elastic strains. Since the Lagrangian should be zero at the resonance vibration, cij can be calculated from its relationship with x. The elastic moduli were obtained via an inverse calculation. The accuracy of the results was guaranteed by the root mean square (rms) value:

rms ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  u  u F cal F mea 2 tR F cal N

ð6Þ

where N refers to the total number of resonance peaks, Fmea is the measured resonance frequency and Fcal is the resonance frequency calculated using the Rayleigh–Litz method from the sample dimension, density and an

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assumed cij. This assumed cij value was adopted only if rms < 1%. In the present study, c11 and c44 were obtained directly from the measurements. Furthermore, the Young’s modulus E and shear modulus G were calculated as follows:    1 2 1 ¼  U E c11  c12 c44     1 2 1 þ þ ð7aÞ 3 c11  c12 c11 þ 2c12    1 2 1 1 ¼2 ð7bÞ  Uþ G c11  c12 c44 c44 A¼

2c44 c11  c12

ð7cÞ

where U is the orientation function and A is an anisotropy factor [21]. Since the polycrystalline samples used in this study were assumed to be isotropic, the anisotropy ratio A was set to 1. Thus, the Young’s modulus, shear modulus and Poisson’s ratio m can be calculated using     1 1 2 1 0 ¼ þ ð7a Þ E 3 c11  c12 c11 þ 2c12 G ¼ c44 m¼

E 1 2G

0

ð7b Þ 0

ð7c Þ

4. Results 4.1. Recovery behavior of the as-crushed powders The recovery behavior of the as-crushed powders was analyzed by a preliminary XRD measurement. Fig. 2 shows the high-temperature XRD profiles of the as-crushed Fe–40Al and Fe–43Al powders. At room temperature, when the powders contained the highest level of residual strain, the XRD profiles show extremely broad peaks, but with increasing temperature, all the peaks become sharp, and the {1 0 0} B2 superlattice diffraction peak becomes clearer. This behavior indicates the removal of residual strain. Fig. 3 shows the change in the full width at half maximum (FWHM) of the {1 1 0} peak as well as the change in the long-range order parameter S over a temperature range of 400–800 °C. The errors in the figure are smaller than ±0.001° for FWHM and are ±0.001 for the longrange order parameter, so that error bars are invisible on the scale of the diagram as presented. The FWHM decreased drastically before reaching a stable level of 0.08° at a certain temperature (500 °C for Fe–40Al and 600 °C for Fe–43Al). The opposite tendency was found for the change in S, indicating that Fe and Al atoms in the as-crushed powder tend to be well ordered at a higher temperature. At 800 °C, which was chosen as the temperature for the residual-strain-elimination heat treatment, both the FWHM and S reached equilibrium values,

Fig. 2. XRD profiles of as-crushed powders of (a) Fe–40Al and (b) Fe– 43Al as a function of the testing temperature “f” or “s” subscripted to the Miller indices indicates fundamental reflection or superlattice reflection, respectively.

Fig. 3. FWHM of the {1 1 0} peak and the long-range order parameter S of the Fe–40Al and Fe–43Al as-crushed powders as a function of the measuring temperature. Error bars are invisible on the scale of the diagram.

indicating that 800 °C was high enough and reasonable for removing the residual strain. Therefore, the powders used for the lattice parameter measurements were guaranteed to be free of residual strain.

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Fig. 4. Vickers hardness of Fe–40Al and Fe–43Al as a function of the quenching temperature.

Fig. 5. Lattice parameter of Fe–40Al and Fe–43Al as a function of the quenching temperature. Error bars are within the symbol size and are thus invisible.

4.2. Quenched-in vacancies The Vickers hardness of FeAl at room temperature was increased by elevating the quenching temperature, as shown in Fig. 4. The solid symbols correspond to data obtained from quenched samples, and open symbols correspond to data obtained from fully annealed samples, which are plotted for comparison. Each hardness value is the average of 16 measurements. Quenching from 400 °C had no significant effect on the hardness values of both Fe– 40Al and Fe–43Al. However, if the quenching temperature was increased (500–800 °C), a rapid increase in the hardness was detected. Within this quenching temperature range, the hardness of Fe–43Al was much higher than that of Fe–40Al. Fig. 5 shows the relationship between the lattice parameter and quenching temperature. The errors in the lattice ˚ , which are parameter are on the order of ±1.0  105 A within the symbol size and thus invisible. The difference between Fe–40Al and Fe–43Al is apparent in this figure: For Fe–43Al, the lattice parameter was relatively constant up to 600 °C but then rapidly decreased due to a significant increase in the concentration of supersaturated vacancies [22]. For Fe–40Al, however, although the lattice parameter decreased slightly for quenching temperatures above 600 °C, the change was not as evident as that for Fe– 43Al. This is consistent with the observations of Kogachi and Haraguchi [22]. 4.3. Thermally equilibrated thermal vacancies (thermal vacancies) Fig. 6 shows the XRD profiles of Fe–40Al and Fe–43Al at different measuring temperatures. We note that no oxide peak is present in any of the profiles (even up to 1000 °C), which guaranteed the accuracy of the profile analysis because the composition was not disturbed by oxidation during the high-temperature measurements. Fig. 7 shows the lattice parameters of the two samples as a function of the measuring temperature obtained by analyzing the

Fig. 6. XRD profiles of (a) Fe–40Al and (b) Fe–43Al as a function of the measuring temperature “f” or “s” subscripted to the Miller indices indicates fundamental reflection or superlattice reflection, respectively.

XRD profiles. The goodness of fitness (GOF) value of the WPPD method was below 1.1, and the experimental ˚ , which are comerrors were on the order of ±1.0  104 A parable to the size of the corresponding symbols and thus invisible. The solid lines are a fit to a quadratic relationship between the lattice parameter and temperature. The lattice

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Fig. 7. Lattice parameter of Fe–40Al and Fe–43Al as a function of the testing temperature. Error bars are comparable to the size of the corresponding symbols and are thus invisible.

˚ is related to the temperature T parameter a(T) in A through aðT Þ ¼ 2:8816 þ 5:7815  105 T þ 5:3461  109 T 2

ð8aÞ

aðT Þ ¼ 2:8899 þ 5:2467  105 T þ 6:3613  109 T 2 ð8bÞ where Eqs. (8a) and (8b) are for Fe–40Al and Fe–43Al, respectively. The small coefficients of the T2 terms indicate an approximately linear increase in the lattice parameter with increasing temperature, and this is consistent with the results of Kogachi et al. [23]. The lattice expansion coefficient a,   1 da a¼ ð9Þ a dT 2

was obtained by neglecting the T terms and yielded values of a = 2.3232  105 K1 for Fe–40Al and a = 2.2494  105 K1 for Fe–43Al. Fig. 8 shows the thermal expansion of both Fe–40Al and Fe–43Al. Fig. 8a presents the change over time of the specimen dimension and temperature. The far left-hand sides of each plateau of the dimension change have a rounded-corner shape, indicating that the dimension change is delayed to a small extent against the temperature change. This is also notable in Fig. 8b, where small nodes on the dimension change curves are seen at each temperature step, especially in the lower temperature range (marked by arrows). Therefore, to exclude the delay in the dimension change, the dimension changes were averaged over the values in the last 10 min of each temperature step for which the specimens appeared to have attained an equilibrium length. The divergence between the change in the specimen length and the X-ray lattice parameter is apparent in Fig. 9. The errors in the Da/a values in both Fig. 9a and b are on the order of the symbol size. This divergence results from the newly generated atomic sites accompanied

Fig. 8. Thermal expansion of Fe–40Al and Fe–43Al measured every 100 °C. (a) Dimension and temperature changes as a function of time. (b) Dimension change as a function of temperature.

by the formation of thermal vacancies. Using Eq. (1), the thermal vacancy concentration was estimated and plotted as a function of temperature in Fig. 10. It is clear in Fig. 10a that Fe–43Al has a higher vacancy concentration than Fe–40Al at elevated temperatures, which is consistent with the room-temperature hardness changes by quenching from elevated temperatures as shown in Fig. 4. The increase in the thermal vacancy concentration had an exponential relationship with temperature, and Arrhenius plots (Fig. 10b) allowed the activation enthalpy and entropy of vacancy formation in Eq. (2) to be calculated: For Fe–40A1;

H FV ¼ 0:7 eV; S FV ¼ 1:4k B

ð10aÞ

For Fe–43A1;

H FV ¼ 0:6 eV; S FV ¼ 1:0k B

ð10bÞ

The lower vacancy formation enthalpy of Fe–43Al indicates that the generation of thermal vacancies was more frequent than that in Fe–40Al. Activation enthalpy values have been reported previously: for example, 0.91 eV for Fe–40 at.% Al and 0.83 eV for Fe–44 at.% Al, determined by electric-resistivity measurements after quenching [24]; Wu¨rschum et al. [11] reported an activation enthalpy of 0.98 eV for Fe–39 at.% Al from a positron lifetime analysis; Morris et al. [25] obtained a value of 0.73 eV for Fe–39 and

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Fig. 9. Comparison of the lattice parameter and sample length changes of (a) Fe–40Al and (b) Fe–43Al as a function of temperature.

Fe–43 at.% Al from hardness measurements of quenched samples; and Kerl et al. [26] found values of 0.92 eV for the B2(l) phase and 0.51 eV for the B2(h) phase of Fe– 43 at.% Al from differential dilatometry measurements. All these values are in good agreement considering the differences in the measurement methods. The dashed line in Fig. 10b shows the Fe–39Al data between 387 and 467 °C obtained by Wu¨rschum et al. [11]. The slope of this line is slightly different from that of the Fe–40Al data of the present study, but these two lines coincide by extrapolating to 500 °C. These results suggest that thermal vacancies are generated more easily in the higher-temperature range as a result of the lower vacancy formation energy. The long-range order parameter S estimated from the XRD profiles of the high-temperature tested samples is shown by the open symbols in Fig. 11. This parameter gradually increased with temperature and peaked at 800–900 °C for Fe–40Al and 700–800 °C for Fe–43Al. The positive temperature dependence of S in the immediate temperature range would be due to a rearrangement of Fe and Al atoms. In early studies, the triple defect (TRD) model was proposed to interpret the thermodynamic properties of several B2-type intermetallic systems [27]. In the TRD model, additional thermal defects created in the alloy due to elevating temperatures are thought to consist of two

Fig. 10. (a) Thermal vacancy concentration as a function of temperature and (b) Arrhenius plots of the thermal vacancy concentration of Fe–40Al and Fe–43Al.

Fig. 11. Long-range order parameter as a function of the testing or quenching temperature.

vacancies and one anti-site atom, i.e., for the case of Ferich FeAl, two vacancies at the Fe-site and one anti-site Fe atom at an Al site. According to Fig. 11, in the temperature range where S increased, the anti-site Fe atoms tended to return to their own correct sublattice sites. Simultaneously, vacancies at Al sites formed via

M. Zhao et al. / Acta Materialia 64 (2014) 382–390

FeAl þ 2V Fe ! FeFe þ V Fe þ V Al

ð11Þ

where FeFe and FeAl indicate Fe atoms at the Fe and Al sites, and VFe and VAl are vacancies at the Fe and Al sites, respectively. This is the so-called Fe-atom recovering (Fe-R) process [23]. Therefore, in the present work, Fig. 11 suggests that the number of Al-site vacancies increases at elevated temperatures since the proportion of anti-site Fe atoms shows a gradual decrease.The longrange order parameters of the quenched samples were also plotted with solid symbols in Fig. 11. Basically, they were always lower than those obtained by the in situ high-temperature measurements. Furthermore, the gap of the values between the quenching and the high-temperature in situ measurements was much larger for Fe–40Al than for Fe– 43Al. Although vacancies can be frozen into the material by quenching, this result suggests that disordering occurs upon cooling. In the vacancy elimination process, long-distance migration of atoms is needed, while the ordering–disordering process can simply result from nearby atom exchanges. The quenching process is capable of inducing disorder but not vacancy elimination, which is why disordering occurred upon quenching.

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4.4. Temperature dependence of the elastic moduli Fig. 12a shows the temperature dependence of Young’s modulus and the shear modulus of Fe–40Al and Fe–43Al. The majority of the errors are on the order of the symbol size. There appears to be a linear relationship between the elastic moduli and temperature for both compositions. Poisson’s ratio as a function of temperature is shown in Fig. 12b, which was, in general, 0.3 although there was a slight increase with increasing temperature. In the lower temperature range, Fe–43Al has a lower Poisson’s ratio compared with Fe–40Al, but with increasing temperature, the difference in the Poisson’s ratios becomes smaller. The slope indicates that the Poisson’s ratio of Fe–43Al was more sensitive to temperature compared with that of Fe–40Al. 5. Discussion 5.1. Excess vacancy hardening at room temperature It is worth mentioning the different tendencies in the change of hardness and the room-temperature lattice parameter with increasing quenching temperature. After quenching from 500 °C and 600 °C, the lattice parameters were relatively stable for both samples. In contrast, the hardness monotonically increased over the whole quenching temperature range. The hardness seems to be much more sensitive to changes in the vacancy concentration. Munroe and Kong [28] studied solid-solution hardening in fully annealed FeAl by adding a third element, and according to their work, ternary alloys, i.e., Fe49Al50X (X = Cu, Co, Mn, Cr and V) were slightly harder than binary alloys (Fe–49Al or Fe–50Al). However, the hardening effect was very small, with an increase in the Vickers hardness of less than 50 Hv after a 1% addition of the third element [28]. This is in contrast to the present study, which, judging from Figs. 4 and 10a, found that a vacancy concentration of 1% is capable of increasing the hardness by nearly 400 Hv. Therefore, vacancies make a significant contribution to the hardening of FeAl. This also provides a reasonable interpretation of why the hardness of Fe–43Al is higher than that of Fe–40Al after quenching from elevated temperatures. Since the former contained a larger number of supersaturated vacancies, the excess vacancy hardening effect was more significant. 5.2. The role of thermal vacancies in changes to the lattice parameter and elastic moduli at elevated temperatures

Fig. 12. (a) Young’s modulus, shear modulus and (b) Poisson’s ratio of Fe–40Al and Fe–43Al as a function of temperature.

At high temperatures, the lattice parameter of FeAl will be determined mainly by (1) thermal expansion and (2) the reduction in the unit cell volume due to the formation of thermal vacancies [23]. The size effect of vacancies would contribute to the latter. The reduction in the unit cell volume caused by the creation of vacancies can be estimated from the change in the lattice parameter as a function of

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quenching temperature, as shown in Fig. 5. Even for Fe– 43Al in a temperature range of 600–800 °C, where a reduction was clearly visible, the slope of Da/a was 1.6503  106 K1. Compared with the lattice expansion coefficients a (2.3232  105 K1 for Fe–40Al and 2.2494  105 K1 for Fe–43Al), the magnitude of the volume reduction caused by the creation of vacancies is one order smaller. Thus, the volume reduction effect due to vacancy formation could be negligible compared with the lattice expansion at elevated temperatures. The linear relationship between the elastic moduli and temperature in Fig. 12a coincided with that found in an earlier study, in which the elastic constants were expressed as [29] s ð12Þ cij ¼ cij ð0Þ  T t where cij(0) is the elastic constant value at 0 K, and s and t are constants. As estimated, the thermal vacancy concentration in FeAl exponentially increases with increasing temperature, whereas the linear relationship between the elastic moduli and temperature was well maintained. In other words, newly generated thermal vacancies are not capable of causing anomalous behavior to the temperature dependence of the elastic moduli. 6. Conclusions In this study, several properties of the vacancy behavior in B2-type FeAl were investigated through quenching experiments and in situ high-temperature measurements. Thermal vacancy concentrations as a function of temperature were estimated for Fe–40Al and Fe–43Al, and their formation enthalpy and entropy values were derived, which were reasonable in comparison with earlier studies. It was found that the room-temperature hardness of FeAl was extremely sensitive to the supersaturated vacancy concentration, but at elevated temperature, the thermal vacancies show no significant influence on the lattice parameter and

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