Effects of NiAl precipitate microstructure, loading axis and temperature on deformation behavior of Fe–Al–Ni single crystals

Intermetallics 115 (2019) 106627

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Effects of NiAl precipitate microstructure, loading axis and temperature on deformation behavior of Fe–Al–Ni single crystals Hiroyuki Y. Yasuda *, Taisuke Edahiro, Naoki Takeoka, Takashi Yoshimoto, Masataka Mizuno, Ken Cho Division of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka, 565-0871, Japan

A R T I C L E I N F O

A B S T R A C T

Keywords: Intermetallics (aluminides) Age-hardening Dislocation structure Slip system Dislocation geometry and arrangement Mechanical properties, theory

Effects of size and volume fraction of the B2-type NiAl precipitates on the deformation behavior of Fe–Al–Ni single crystals were investigated. In the crystals with different Ni contents, the fine NiAl phase was precipitated in the bcc matrix with small misfit strain. Strong precipitation hardening occurred due to the difference in primary slip system between the bcc matrix and the NiAl precipitates. Moreover, not only <111> slip but also <001> slip occurred depending on the loading axis, the precipitate morphology and the deformation temper­ ature, though the occurrence of <001> slip is generally impossible in bcc metals. The dependence of the critical resolved shear stress for <111> slip on the precipitate size was consistent with the modified precipitation hardening theory. To understand the precipitation hardening, an antiphase boundary energy of the NiAl pre­ cipitates was evaluated by first-principles calculations. Moreover, higher volume fraction of the NiAl precipitates was favorable for the activation of <001> slip. Furthermore, the activated slip system varied with deformation temperature, and therefore, the temperature dependence of the yield stress was closely related to the slip system.

1. Introduction Recently, extensive efforts have been made to develop ferritic heatresistant steels containing the NiAl precipitates with the B2 structure, since the precipitates effectively increase strength at both ambient and high temperatures [1–5]. For instance, the NiAl precipitates are known to greatly enhance the creep properties [1–4]. Some precipitation-hardened steels are also strengthened by the NiAl phase [5]. Ferritic heat-resistant steels containing the NiAl precipitates have also been developed in the last decade [6–19]. Recently, systematic studies were carried out to understand the hardening mechanism by the NiAl precipitates, using Fe–23Al–6Ni (at.%) single crystals [20,21]. Consequently, the difference in primary slip systems between the bcc matrix and the NiAl precipitates was found to be responsible for strong precipitation hardening. The primary slip systems of the bcc matrix and the NiAl precipitates are {101} <111> and {110} <001>, respectively [22,23]. If the single crystals were deformed at <149> orientation, <111> slip occurred and the NiAl precipitates were cut by a pair of 1/2<111> dislocations in the bcc matrix [20]. However, <111> slip is difficult to occur in the NiAl precipitates, which resulted in strong hardening. On the other hand, at <557> orientation, <001> slip took

place and <001> dislocations move in not only the NiAl precipitates but also the bcc matrix [20]. However, occurrence of <001> slip in bcc metals is generally impossible [24–26], also resulting in strong precip­ itation hardening. This phenomenon is called “slip frustration hardening (SFH)”, since it is caused by frustration in the slip direction between the matrix and precipitates. It is also noted that Fe–Al–Co single crystals with B2-type CoAl precipitates also exhibit SFH, since the primary slip systems of the bcc matrix and the precipitates are {101} <111> and {010} <001>, respectively [27,28]. Moreover, when {101} <111> slip occurs in Fe–Al–Co single crystals, an antiphase boundary (APB) created inside the CoAl precipitates strongly influences the hardening [27]. It is well known that precipitation hardening depends on size and volume fraction of the precipitate phase [29,30]. In fact, in Fe–Al–Co single crystals, the size and volume fraction of the CoAl precipitates strongly influence the huge hardening [27]. In the Fe–Al–Ni phase di­ agram, there exists a two-phase field composed of the bcc phase and the B2-type NiAl phase [31]. The size and volume fraction of the NiAl pre­ cipitates are dependent on annealing temperature and chemical composition. Thus, in the present study, Fe–Al–Ni single crystals with different chemical compositions were prepared and the deformation behavior was examined focusing on the size and volume fraction of the

* Corresponding author. E-mail address: [email protected] (H.Y. Yasuda). https://doi.org/10.1016/j.intermet.2019.106627 Received 26 August 2019; Received in revised form 25 September 2019; Accepted 2 October 2019 Available online 10 October 2019 0966-9795/© 2019 Elsevier Ltd. All rights reserved.

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NiAl precipitates. Temperature dependence of deformation behavior of Fe–Al–Ni single crystals with different amounts of the NiAl phase was also discussed. Moreover, an APB energy (γAPB) of the NiAl precipitates was calculated by first-principles calculations. From the Fe–Al–Ni ternary phase diagram [31], the NiAl precipitates contains small amount of Fe, and therefore, the effect of Fe on γAPB of the NiAl precipitates was discussed to understand the hardening mechanism.

atoms in NiAl is still unclear [38]. Thus, three types of Fe substitution were considered: six Fe atoms were substituted for Ni sites, Al sites and for both Ni and Al sites. The compositions of three supercells are Ni42Al48Fe6, Ni48Al42Fe6 and Ni45Al45Fe6, respectively. After substitu­ tion of six Fe atoms, half of the layers were shifted along 111 direction to introduce APB’s. As shown in Fig. 1(a)–(c), on the layers across the APB on {110} plane, one Fe atom occupies the Ni and the Al sites in Ni42Al48Fe6 (Fig. 1 (a)) and Ni48Al42Fe6 (Fig. 1 (b)), respectively. In Ni45Al45Fe6, one APB is located near one Fe atom at the Ni site and the other APB near one Fe atom at the Al site (Fig. 1 (c)). The lengths of the cells parallel to the APB are fixed to those in the B2 structure. Optimum cell lengths perpendicular to the APB were obtained by interpolation from a set of calculated results obtained with fixed cell shapes. Struc­ tural relaxations of atoms were continued until the forces on all atoms became less than 0.01 eV/Å. The supercells including the APB on {211} plane were also created, similar to that on {110} plane (Fig. 1(d)–(f)).

2. Experimental procedure 2.1. Calculation of APB energy γ APB of NiAl including substituted Fe atoms was calculated by firstprinciples calculations. We employed the Vienna ab initio simulation package (VASP) [32,33] with the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) [34]. Potentials based on the all-electron projector augmented wave (PAW) method were used [35, 36]. First, the equilibrium lattice parameter of NiAl was calculated. We used a kinetic-energy cutoff of 350 eV and 16 � 16 � 16 k mesh in the Monkhorst–Pack scheme. The equilibrium lattice parameter obtained in the present work is 2.8934 Å, which well reproduced the experimental value of 2.877 Å [37]. We constructed a supercell of Ni48Al48 that con­ sisted of 12 {110} planes of the B2 structure. Next, NiAl with small amount of Fe was considered. From Fe–Al–Ni phase diagram, the NiAl phase contains nearly 10%Fe [31]. However, the substitution site of Fe

2.2. Sample preparation, mechanical testing and microstructure observation Fe–21Al–2Ni, Fe–23Al–6Ni and Fe–25Al–10Ni ingots were prepared by melting high purity Fe, Al and Ni using a plasma arc furnace. These alloys seem to lie on the same tie-line in the bcc-B2 two-phase field [30]. Consequently, the volume fraction (f) of the NiAl precipitates increases with increasing Ni content such that the chemical compositions of the

Fig. 1. Atomic configuration of supercells including the APB on {110} ((a)–(c)) and {211} ((d)–(f)) planes. Six Fe atoms were substituted for (a), (d) Ni sites, (b), (e) Al sites and (c), (f) both Ni and Al sites. 2

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bcc matrix and the precipitates remain constant irrespective of Ni con­ tent. Single crystals were grown from the ingots by a floating zone method at a growth rate of 5 mm/h. After homogenization at 1373 K for 48 h, these crystals were furnace-cooled to room temperature at a cooling rate of 80 K/h (hereafter referred to as FC crystals). Some crystals were solutionized at 1123 K for 1 h and then annealed at 823 K (AG crystals, hereafter). Fe–21Al–2Ni, Fe–23Al–6Ni and Fe–25Al–10Ni crystals are denoted as 2Ni, 6Ni and 10Ni, respectively. FC crystals with 2Ni, 6Ni and 10Ni are referred to as 2Ni-FC, 6Ni-FC and 10Ni-FC, respectively. The same notation is also adopted for AG crystals with different Ni contents. Experimental procedure for the measurements of the mean particle size (r), f, dissolution temperature (Tp) and misfit strain (δ) of the NiAl precipitates were well documented in previous papers [20,27]. Rectangular compression specimens with [149] (A), [557] (B), [001] (C) and [011] (D) orientations were cut from the single crystals by spark machining. The loading axis, front and side faces of the compression specimens with dimensions of approximately 2 � 2 � 5 mm are shown in Fig. 2. Table 1 presents Schmid factors for each slip system at different loading axes. The Schmid factor for (101) [111], (110) [001] and (010) [001] slip systems at A, B and D orientations, respectively, is 0.5. In contrast, <001> slip is impossible to occur at C orientation due to its low Schmid factor. All specimens were polished mechanically and electrolytically to remove surface damage. Compression tests were performed in the temperature range between room temperature and 1023 K at a constant cross-head speed of 0.05 mm/min corresponding to an initial strain rate of 1.7 � 10 4/s. The slip planes after compression were determined by a two-surface trace analysis using an optical mi­ croscope. The microstructure and dislocation structure were observed using a transmission electron microscope (TEM) operated at 300 kV.

Table 1 Schmid factors for some {110} <111>, {211} <111>, {110} <001> and {010} <001> slip systems at A–D orientations. slip system

loading axis A

B

C

D

(101)[111]

0.50

0.35

0.41

0.41

(211)[111]

0.43

0.37

0.24

0.47

(112)[111]

0.43

0.23

0.47

0.24

(110)[001]

0.32

0.50

0

0.35

(010)[001]

0.37

0.35

0

0.50

and 744.8 mJ/m2, respectively, which is slightly smaller than that ob­ tained by other calculations ({110}: 760–815 mJ/m2, {211}: 995 mJ/ m2) [39–41]. On the other hand, the substitution of Fe atoms for Al sites reduces γ APB in Ni48Al42Fe6, while that for Ni sites increases it in Ni42Al48Fe6. The change in γ APB by the substitution for Al sites is more significant than that for Ni sites, and therefore, the substitution of Fe for both Al and Ni sites slightly decrease γ APB in Ni45Al45Fe6, as shown in Table 2. In addition, in Ni48Al42Fe6, γ APB on {211} plane is slightly lower than that on {110} plane, in contrast to binary Ni48Al48. 3.2. Microstructure of Fe–Al–Ni alloys Fig. 3 shows the selected area electron diffraction patterns (SAED) and dark-field images (DFI) of 2Ni-FC, 6Ni-FC and 10Ni-FC crystals. In the SAED, 001 superlattice reflection can be seen in these crystals (Fig. 3 (d)–(f)). In the DFI taken with 001 reflection, there exists fine NiAl precipitates of which r is less than 10 nm (Fig. 3(a)–(c)). Thus, the NiAl precipitates with the B2 structure is precipitated in the bcc matrix satisfying the cube-on-cube orientation relationship. Note that the NiAl precipitates are so fine that the image of the precipitates is overlapped due to truncation effect of TEM samples. Table 3 represents r, f, Tp and δ of 2Ni-FC, 6Ni-FC and 10Ni-FC crystals. r and f increase with increasing Ni concentration whereas Tp and δ remain almost constant regardless of Ni content. In particular, δ is determined to be 0.24% and is independent of Ni content. Fig. 4 shows DFI of 6Ni-AG crystals annealed at 823 K. r of the NiAl precipitates increases gradually with an increase in annealing time up to 24 h and then saturated at r ¼ 5 nm, while f remains almost constant at 0.11.

3. Results 3.1. Calculation of APB energy The calculated γ APB for {110} and {211} planes of NiAl with or without small amount of Fe is listed in Table 2. In the present study, γAPB of binary NiAl on {110} and {211} planes are calculated to 723.9 mJ/m2

3.3. Deformation behavior at room temperature Fig. 5 shows stress-strain (S–S) curves of 2Ni-FC, 6Ni-FC and 10Ni-FC crystals compressed with A–D orientations at room temperature. Strong precipitation hardening occurs by the NiAl precipitates. In particular, the yield stress (σ y) of 6Ni-FC and 10Ni-FC crystals exceeds 1000 MPa at all orientations tested. Note that σ y of 2Ni-FC crystals depends on the loading axis; σ y and the Schmid factor for {101} <111> slip or {211} <111> slip increases and decreases, respectively, in the following order: A→C→D→B (Table 1). This means that <111> slip occurs in 2Ni-FC crystals, independent of loading axis. In contrast, in 6Ni-FC and 10NiFC crystals, the increasing order of σy is D→B→A→C, suggesting that the activated slip system varies with the loading axis. Fig. 6 shows slip markings of 2Ni-FC and 10Ni-FC crystals compressed with A–D Table 2 Calculated APB energies on {110} and {211} planes. APB energy, γAPB (mJ/m2) Ni48Al48 Ni42Al48Fe6 Ni48Al42Fe6 Ni45Al45Fe6

Fig. 2. Compression axes of [149] (A), [557] (B), [001] (C) and [011] (D) orientations selected in the present study, marked by ○. Normals of the front and side faces of the compression specimens for A–D orientations are marked by ▴ and ■, respectively. 3

{110}

{211}

723.9 740.7 614.3 671.3

744.8 820.2 613.6 705.3

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Fig. 3. DFI with g ¼ 001 (a)–(c) and SAED with a beam direction (BD) of [110] (d)–(f). (a),(d) 2Ni-FC, (b),(e) 6Ni-FC, (c),(f) 10Ni-FC. Table 3 Parameters characterizing microstructure of 2Ni-FC, 6Ni-FC and 10Ni-FC crystals. samples

2Ni-FC

6Ni-FC

10Ni-FC

average radius, r (nm) volume fraction, f misfit strain with the bcc matrix, δ (%) dissolution temperature, Tp (K)

2.9 0.038 0.24 938

7.4 0.116 0.24 943

9.4 0.227 0.24 951

Fig. 5. S–S curves of 2Ni-FC, 6Ni-FC and 10Ni-FC crystals compressed with A–D orientations at room temperature.

slip traces associated with the occurrence of <111> slip can also be seen at C orientation at which the Schmid factor for <001> slip is 0 (Fig. 6 (k), (o)). It is also noted that at C orientation, slips occur preferentially on {110} and {211} planes in 2Ni-FC and 10Ni-FC crystals, respectively. In contrast, slip planes at A, B and D orientations are determined to be {hk0}, (110) and (010), respectively, though the Schmid factor for (101) [111] slip is 0.5 at A orientation (Fig. 6 (i), (j), (l), (m), (n), (p)). Note that {hk0} is an intermediate plane between {010} and {110} planes and {hk0} <001> slip was observed to occur in NiAl single phase [23]. In this case, the index of {hk0} at A orientation is nearly {130}. More­ over, (110) and (010) slip traces are observed at B and D orientations at which the Schmid factor for (110) [001] and (010) [001] slips are 0.5, respectively, as shown in Fig. 6 (j), (n), (l), (p). These results suggest that <001> slip occurs at A, B and D orientations in 10Ni-FC crystals. Dislocation structures in 2Ni-FC and 10Ni-FC crystals compressed with A and B orientation at room temperature were observed using TEM, as shown in Fig. 7. In 2Ni-FC crystals deformed at A orientation, disloca­ tions are visible with g ¼ 101 (Fig. 7 (a)), while are out of contrast with g ¼ 121 and 011 (Fig. 7(b) and (c)). This means that the Burgers vector of dislocations is parallel to [111]. It is also noted that the dislocations with a screw character make a pair in the weak-beam dark field image (WBDFI); the separation distance between the dislocations is approxi­ mately 10 nm (Fig. 7 (d)). When the dislocations cut the NiAl pre­ cipitates, 1/2[111] dislocations make a pair not to create the APB inside the precipitates [20]. It is also noted that the dislocation arrangement is

Fig. 4. DFI of 6Ni-AG crystals annealed at 823 K for 0.25 h (a), 1 h (b), 24 h (c) and 100 h (d); g ¼ 001.

orientations at room temperature, while those of 6Ni-FC crystals are available in a previous paper [20]. In 2Ni-FC crystals, the slip plane is always {101} and/or {211} regardless of the loading axis, suggesting that only <111> slip occurs (Fig. 6(a)–(h)). In 10Ni-FC crystals, {211} 4

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Fig. 6. Slip traces of 2Ni-FC ((a)–(h)) and 10Ni-FC ((i)–(p)) crystals compressed with A ((a), (e), (i), (m)), B ((b), (f), (j), (n)), C ((c), (g), (k), (o)) and D ((d), (h), (l), (p)) orientations at room temperature. (a)–(d), (i)–(l) front face, (e)–(h), (m)–(p) side face.

planar, compared with the bcc metals, which is caused by the interaction between the dislocations and the NiAl precipitates [42,43]. Paired 1/2 [111] dislocations are also observed in 2Ni-FC crystals at B orientation (Fig. 7(e)–(h)). In contrast, in 10Ni-FC crystals compressed at A orien­ tation, the dislocation visible with g ¼ 101 (Fig. 7 (i)) cannot be seen with g ¼ 200 and 110 (Fig. 7(j) and (k)), suggesting that the Burgers vector is [001]. In the high magnification image (Fig. 7 (l)), the dislo­ cation shows a zigzag line probably due to the elastic anisotropy and/or pinning effect of the NiAl precipitates. 10Ni-FC crystals with B orien­ tation also deform by [001] dislocations (Fig. 7 (m)–(p)). The activated slip systems at room temperature, determined by two-surface slip trace and TEM analyses, are summarized in Table 4. The data for 6Ni-FC are taken from a previous paper [20]. As presented in Table 4, <111> slip occurs in 2Ni-FC crystals irrespective of the loading axis. On the other hand, in 6Ni-FC crystals, <111> slip occurs at A and C orientations, whereas <001> slip takes place at B and D orientations. On the other hand, in 10Ni-FC crystals, <001> slip is activated except C orientation where the Schmid factor for <001> slip is 0. This suggests that the activated slip system at room temperature depends on f, since f increases with increasing Ni content. Higher f at higher Ni content is favorable for the activation of <001> slip. In order to understand the effect of r on the deformation behavior of Fe–Al–Ni single crystals, 6Ni-FC crystals were annealed at 823 K after solutionization. As a result, the NiAl precipitates with different r at f �

0.11 could be formed, as shown in Fig. 4. Effect of r on the precipitation hardening was quantitatively examined for Fe–18Al–18Co single crys­ tals containing the B2-type CoAl precipitates and is well documented in a previous paper [27]. In general, shear stress increase (Δτ) by fine pffiffiffi shearable precipitates is proportional to fr or r1.5/l where l is the mean particle center-to-center spacing along dislocation and is given by Refs. [29,30], sffiffiffiffiffi ! 2π l¼ r (1) 3f Thus, Δτ of 6Ni-AG crystals compressed with A orientation at room temperature were obtained from the difference in σ y between the sol­ utionized and AG crystals at 823 K and is plotted against r1.5/l in Fig. 8. Not that (101) [111] slip occurred in 6Ni-AG crystals annealed at 823 K for up to 10 h. For comparison, the data for Fe–18Al–18Co single crystals with the CoAl precipitates are also shown in Fig. 8 [27]. In both cases, Δτ increases linearly with increasing r1.5/l. It should be noted that the slope of the line corresponds to the hardening ability of the precipitates. The slope of the line for 6Ni-AG crystals is lower than that of Fe–18Al–18Co crystals. This means that the hardening ability of the NiAl precipitates in 6Ni-AG crystals is lower than that of the CoAl precipitates in Fe–18Al–18Co crystals. It is also noted that further increase in r1.5/l in Fe–18Al–18Co single crystals results in the activation of <001> slip or 5

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Fig. 7. TEM micrographs of 2Ni-FC (a)–(h) and 10Ni-FC (i)–(p) crystals compressed with A ((a)–(d), (i)–(l)) or B ((e)–(h), (m)–(p)) orientation at room temperature; BD � [101] ((a), (b), (d)), [101] ((e), (f), (h)), [111] ((c), (g)), [010] ((i), (j), (l)), [110] ((k), (m), (n), (p)) and [130] (o), (a)–(c), (e)–(g), (i)–(k), (m)–(o) bright-field images (BFI), (d), (h), (l), (p) WBDFI, g/4 g condition. Arrows in (d), (h) show separation of paired dislocations.

formation of Orowan loops [27]. However, in the case of 6Ni-AG crys­ tals, the growth rate of the NiAl precipitates at 823 K is so slow that neither <001> dislocations nor Orowan loops can be observed. In order to understand the effect of f on the deformation behavior, CRSS for <111> and <001> slips were calculated from the data for the FC crystals and the CRSS are plotted in Fig. 9. The CRSS for <111> and <001> slips increases and decreases with increasing f, respectively, though the data for <001> slip cannot be obtained from 2Ni-FC crystals.

Fig. 11 shows optical micrographs of slip traces in 2Ni-FC and 10Ni-FC crystals compressed with A or B orientation at 823 K. In 2Ni-FC crystals, slip plane is {101}, suggesting that <111> slip is activated (Fig. 11(a), (b), (e), (f)). On the other hand, in 10Ni-FC crystals, {hk0} or (110) slip traces are observed at A and B orientations, respectively (Fig. 11 (c), (d), (g), (h)). This means that <001> slip occurs in 10Ni-FC crystals at the orientations. For instance, [001] dislocations are observed in 6Ni-FC crystals compressed with B orientation even at 823 K, as shown in Fig. 12. In this way, the activated slip systems of Fe–Al–Ni crystals with different Ni contents, loading axes and deformation temperature were examined and are presented in Table 4. A part of the data for 6Ni-FC is taken from a previous paper [20]. In 2Ni-FC crystals, <111> slip is al­ ways activated, though the slip plane is {101} and/or {211} depending on the loading axis and deformation temperature. On the other hand, in the 6Ni-FC and 10Ni-FC crystals, not only <111> slip but <001> slip occur. For instance, <111> slip always takes place at C orientation since the Schmid factor for <001> slip is 0. In contrast, 6Ni-FC crystals compressed at A orientation deform by <111> slip at and below 823 K while {hk0} <001> slip occurs at 923 K. Moreover, in 10Ni-FC crystals, <001> slip occurs over the wide temperature range even at A orienta­ tion, though the orientation is suitable for <111> slip. In addition, B and D orientations are obviously favorable for <001> slip both in 6Ni-FC and 10Ni-FC crystals. Furthermore, at D orientation, a transition in slip plane from {010} to {hk0} takes place at 823 K. It is also noted that in 10Ni-FC crystals at A, B and D orientations, <001> slip also occurs at

3.4. Deformation behavior at high temperatures Fig. 10 shows the temperature dependence of σy of 2Ni-FC, 6Ni-FC and 10Ni-FC crystals compressed at A–D orientations. In any case tested, σ y shows a high value at and below 823 K, especially in 6Ni-FC and 10NiFC crystals. However, further increase in deformation temperature re­ sults in a decrease in σ y, especially around Tp where the NiAl precipitates dissolve into the bcc matrix. In 2Ni-FC crystals, σ y at B orientation is the highest among the orientations due to its low Schmid factor for <111> slip (Fig. 10 (a)). On the other hand, in 6Ni-FC crystals, σy at B and D orientations is lower than that at A and C orientations (Fig. 10 (b)). It is also noted that a decrease in σy with temperature at B and D orientations is more significant than that at A and C orientations. Moreover, in 10NiFC crystals compressed with C orientation, σy remains almost constant up to 823 K, whereas σy at A, B and D orientations decreases gradually with increasing deformation temperature, as shown in Fig. 10 (c). 6

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Table 4 Activated slip systems in 2Ni-FC, 6Ni-FC and 10Ni-FC crystals compressed with A–D orientations at different temperatures. sample

Loading axis

Temperature (K) RT

723

823

923

1023

2Ni-FC

A

{101}< 111> {101}/ {211}< 111> {101}< 111> {211}< 111> {101}< 111> {110}< 001> {101}/ {211}< 111> {010}< 001> {hk0}< 001> {110}< 001> {211}< 111> {010}< 001>

{101}< 111> {101}/ {211}< 111> {101}< 111> {211}< 111> {101}< 111> {110}< 001> {101}/ {211}< 111> {010}< 001> {hk0}< 001> {110}< 001> {211}< 111> {010}< 001>

{101}< 111> {101}< 111>

{101}< 111> {101}< 111>

{101}< 111> {101}< 111>

{211}< 111> {211}< 111> {101}< 111> {110}< 001> {101}/ {211}< 111> {hk0}< 001> {hk0}< 001> {110}< 001> {211}< 111> {hk0}< 001>

{211}< 111> {211}< 111> {hk0}< 001> {110}< 001> {101}/ {211}< 111> {hk0}< 001> {hk0}< 001> {110}< 001> {211}< 111> {hk0}< 001>

{211}< 111> {211}< 111> {101}< 111> {101}< 111> {101}/ {211}< 111> {hk0}< 001> {hk0}< 001> {110}< 001> {211}< 111> {hk0}< 001>

B C D 6Ni-FC

A B C D

10NiFC

A B C D

Fig. 9. Variation of the CRSS for <111> and <001> slip at room temperature with f. A–D means the loading axis.

precipitates at and below 823 K and the deformation behavior, espe­ cially the activated slip system depended on the loading axis, the pre­ cipitate morphology and the deformation temperature. The hardening mechanism by the NiAl precipitates and the selection rule of the acti­ vated slip system are discussed. 4.1. Calculation of APB energy The γ APB of binary NiAl, calculated in the present study, is slightly smaller than that obtained by other calculations (Table 2) [39–41]. One of the possible reasons for this discrepancy is the difference in the GGA. The equilibrium lattice parameters calculated using the GGA by PBE employed in the present study tend to be slightly longer than those obtained by the use of the GGA by PW91 [44] employed in the previous studies. The longer lattice parameter is expected to reduce the energy penalty by the formation of Al–Al bonds at the APB, as discussed below. Another possible reason is the effect of the volume optimization. While we optimized the cell length perpendicular to the APB on {110} plane, the γAPB of 760 mJ/m2 was obtained at the fixed supercell volume [40]. We reproduced the γAPB of 758.7 mJ/m2 using the GGA by PW91 at the fixed supercell volume, which is close to 760 mJ/m2 reported by Lazar and Podloucky [40]. The substitution of Fe atoms for Al sites reduces the γ APB in Ni48Al42Fe6, while that for Ni sites increases it in Ni42Al48Fe6. Let us discuss the effect of Fe substitution on γAPB on {110} plane, focusing on the electronic structure. To examine the change in the electronic structure induced by the substitution of Fe atoms, the density of states (DOS) of the Fe atom in Ni42Al48Fe6 and Ni48Al42Fe6 are shown in Fig. 13. Although the Fe atom in the matrix of Ni42Al48Fe6 does not exhibit a significant spin polarization, a spin polarization is induced at the Fe atom on the APB in Ni42Al48Fe6 because of the interaction with neighboring Ni atoms (Fig. 13 (a)). As a result, a large peak appears around the Fermi level in the minority-spin DOS at the Fe atom on the APB. This large peak is caused by the anti-bonding interaction with the Ni atom and contributes to an energy loss. Therefore, the Fe atom at the Ni site on the APB increases γAPB. In the case of Ni48Al42Fe6 in which Fe atoms substitute Al sites, a larger spin polarization is observed at the Fe atom both in the matrix and on the APB (Fig. 13 (b)). In the lower valence band, the majority and minority-spin band is shifted to a higher energy at the Fe atom on the APB in comparison with the Fe atom in the matrix. This is due to the decrease in the number of neighboring Ni atoms at the Fe atom on the APB. Focusing on the DOS around the Fermi level, the Fermi level lies at local minimum both in the matrix and on the APB, while the minority-spin band just below the Fermi level slightly increases on the APB. Therefore, the change in the electronic structure of

Fig. 8. Variation in Δτ with r1.5/l for 6Ni-AG crystals annealed at 823 K and then compressed with A orientation at room temperature. The data for Fe–18Al–18Co crystals are also shown. Fitting parameter, γAPB is set to 570 mJ/ m2 and 750 mJ/m2 for 6Ni-AG and Fe–18Al–18Co crystals, respectively.

1023 K at which the NiAl precipitates dissolve into the matrix. 4. Discussion In the present study, systematic studies were carried out to under­ stand the deformation behavior of Fe–Al–Ni single crystals with the B2type NiAl precipitates, focusing on r and f of the precipitates. The γ APB of NiAl with small amount of Fe was also calculated to understand the hardening mechanism. Strong hardening occurred by the NiAl 7

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Fig. 10. Temperature dependence of σy in 2Ni-FC (a), 6Ni-FC (b) and 10Ni-FC (c) crystals compressed at different loading axes.

Fig. 11. Slip traces of 2Ni-FC (a), (b), (e), (f) and 10Ni-FC (c), (d), (g), (h) crystals compressed with A (a), (c), (e), (g) or B (b), (d), (f), (h) orientations at 823 K. (a)– (d) front face, (e)–(h) side face.

Fig. 12. Dislocation structure of 6Ni-FC crystals compressed with B orientation at 823 K. (a), (b), (d) BD � [110], (c) BD � [010], (d) WBDFI, g/4 g condition.

Fig. 13. Partial DOS of the Fe atom in the matrix and on the APB on {110}. (a) The Fe atom was substituted for the Ni site. (b) The Fe atom was substituted for the Al. 8

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the Fe atom on the Al site is less significant than that on the Ni site. The instability of the APB arises partly from the lattice strain in the vicinity of the APB. The structures of the APB on {110} plane are shown in Fig. 14. In the case of binary NiAl, the Al atoms move outward from the APB to accommodate the difference in the distance between Al–Al and Ni–Ni bonds that are formed across the APB (Fig. 14 (a)). In Ni48Al42Fe6 in which Fe atoms substitute Al sites, the Fe atom on the APB forms the Fe–Al bonds across the APB, as shown in Fig. 14 (c). The distance of the Fe–Al bond formed across the APB in Ni48Al42Fe6 is shorter than that of the Al–Al bond in Ni48Al48. As a result, the distance of Al–Fe bond becomes comparable to that of the Ni–Ni bond, which contributes to reducing the APB energy. On the one hand, the distance of the Fe–Ni bond formed across the APB in Ni42Al48Fe6 is comparable to that of the Ni–Ni bond in Ni48Al48 (Fig. 14 (b)). Therefore, the difference in the distance between the Al–Al and Ni–Fe is not reduced by the substitution of Fe atoms for Ni sites. Regarding the difference in γAPB between {110} and {211} planes, the decrease in γ APB for {211} plane by the substitution of Fe atoms for Al sites in Ni48Al42Fe6 is more significant than that for {110} plane. This is mainly due to the difference in the number of neighboring Ni atoms: the Fe atom on the APB for {211} plane has three neighboring Ni atoms, while there are two neighboring Ni atoms around the Fe atom on the APB for {110} plane (Fig. 1). As a result, γAPB for {211} plane of Ni48Al42Fe6 becomes slightly lower than that for {110} plane by the substitution of Fe atoms for Al sites (Table 2).

crystals, {101} <111> slip starts to be activated at 1184 MPa at A orientation at which the Schmid factor for the slip is 0.5, though the law does not strictly hold in bcc metals. On the other hand, {hk0} <001> slip occurred at σy ¼ 1095 MPa in 10Ni-FC crystals at A orientation (Fig. 5), and therefore, <001> slip took place even at the orientation, instead of <111> slip. Moreover, the slip plane selected in 10Ni-FC crystals at A orientation is {hk0} (Fig. 6 (i), (m)). As mentioned earlier, {hk0} is an intermediate plane between {010} and {110} planes [23]. As a result, at A orientation, the Schmid factor for {hk0} <001> slip is higher than that for {010} <001> and {110} <001>, resulting in the activation of {hk0} <001> slip in 10Ni-FC crystals. The CRSS for <111> slip in 6Ni-AG crystals is proportional to r1.5/l, which is similar to that of Fe–18Al–18Co single crystals with the CoAl precipitates (Fig. 8). In the case of Fe–Al–Co crystals, high γAPB of the CoAl precipitates is found to play an important role on the hardening on <111> slip [27]. Moreover, as mentioned earlier, the slope of the line in Fig. 8, corresponds to the hardening ability of the precipitates. Thus, the hardening ability of the NiAl precipitates was lower than that of the CoAl precipitates. Let us consider the difference in hardening ability. If the ordered precipitates are sheared by dislocations, APB is created in the precipitates, which leads to strong precipitation hardening [29,30]. This type of precipitation hardening is termed as order hardening. Ardell et al. [30,45,46] proposed the modified theory for the order hardening, in which precise shape of bowing-out dislocations is taken into consid­ eration as follows: Δτorder ¼

4.2. Deformation behavior at room temperature 2Ni-FC crystals with low f deformed by <111> slip at room tem­ perature, irrespective of the orientation, as shown in Figs. 6 and 7. Moreover, σ y was in good agreement with the Schmid factor for <111> slip (Fig. 5, Table 1). In contrast, the activated slip system of 6Ni-FC and 10Ni-FC crystals at room temperature varied with the loading axis. In 6Ni-FC crystals, <111> slip occurred at A and C orientations whereas <001> slip was activated at B and D orientations (Figs. 6 and 7). Furthermore, in 10Ni-FC crystals, <001> slip occurred even at A orientation, though <111> slip took place at C orientation where the Schmid factor for <001> slip is 0 (Figs. 6 and 7). In general, the occurrence of <001> slip is impossible in bcc metals [24–26]. However, the NiAl precipitates significantly increased the CRSS for <111> slip (Figs. 8 and 9), which resulted in the activation of <001> slip, especially at B and D orientations at which the Schmid factor for <001> slip is high. Moreover, high f in 10Ni-FC crystals is obviously favorable for <001> slip, since the CRSS for <001> slip decreases with increasing f (Fig. 9). In fact, CRSS for <001> slip of binary NiAl is about 100 MPa, much lower than that of 10Ni-FC crystals [22]. For instance, the CRSS for <111> slip of 10Ni-FC crystals is calculated to be 592 MPa from σy at C orientation (Fig. 9). If the Schmid law is assumed to hold in the

u¼

B¼

γAPB u 2b

� �1=2 4B þ B2 3 2ð1 B=6Þ

(2) B

3π2 γAPB fr 32T

(3) (4)

where T is the line tension of dislocation and is given by Ref. [30], � � � � μ b2 1 þ ν 3νsin2 ξ Λ T¼ m ln (5) 1 ν r0 4π where μm is the shear modulus of the bcc matrix, ν is Poisson’s ratio, ξ is the angle between the dislocation line and the Burgers vector, and Λ and r0 are outer and inner cut-off distances used in calculating the line en­ ergy. ν is assumed to be 1/3. 1/2<111> screw dislocations are dominant (Fig. 7), and therefore, ξ ¼ 0. In addition, ln (Λ/r0) is assumed to be 4 [30]. When {101} <111> slip occurs in bcc metals, μm for the slip is written as [47], 1 3

μm ¼ ðC11 þ C44

C12 Þ

(6)

Fig. 14. Structures in the vicinity of the APB on {110} plane. (a) No Fe atom was substituted. (b) The Fe atom was substituted for the Ni site. (c) The Fe atom was substituted for the Al site. 9

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Intermetallics 115 (2019) 106627

transition from {010} <001> to {hk0} <001> due to the stronger temperature dependence of {hk0} slip, which is similar to 6Ni-FC crystals (Table 4). It should also be noted that the NiAl precipitates dissolve into the matrix at 1023 K and the B2 single phase is stable at the temperature. Thus, the activation of <001> slip at 1023 K in 6Ni-FC and 10Ni-FC crystals deformed at D orientation is not surprising (Table 4).

where Cij is the elastic stiffness constants. If γ APB on {110} plane in the NiAl precipitates is set to be 570 mJ/m2, Eqs. (2)–(4) is in quantitatively good agreement with the data plot for 6Ni-AG crystals in Fig. 8. Ardell [46] obtained γ APB ¼ 500 mJ/m2 based on the experimental study by Taillard et al. [1], which is similar to our experimental results. However, γ APB on {110} plane of NiAl with small amount of Fe, obtained from first-principles calculations (Table 2), is slightly higher than that experimentally obtained from Eqs. (2)–(4) and Fig. 8. The NiAl pre­ cipitates are so small that the chemical composition of the precipitates is difficult to be evaluated, which results in the small difference in γ APB between the first-principles calculations and the experimental results. For instance, if Fe atoms substitute for Al site in Al-deficient NiAl, the γ APB on {110} plane is 614 mJ/m2 (Table 2), close to the experimental value. Therefore, one can conclude that high γ APB inside the NiAl pre­ cipitates is mainly responsible for strong precipitation hardening for <111> slip. It is also noted that high CRSS for <111> slip in NiAl single phase is also related to high γ APB [22]. On the other hand, the data for Fe–Al–Co single crystals with the CoAl crystals agree with γ APB ¼ 750 mJ/m2 [27]. Thus, lower γ APB of the NiAl precipitates results in lower hardening ability of the NiAl precipitates, compared with CoAl (Fig. 8). It is also noted that the CRSS for <111> slip in 6Ni-FC crystals is similar to that in 10Ni-FC crystals (Fig. 9). At C orientation and room temperature, {211} <111> slip preferentially occurred in 10Ni-FC crystals, in contrast to 2Ni-FC and 6Ni-FC crystals (Fig. 6, Table 4). From Table 2, γAPB on {211} plane in Ni48Al42Fe6 is effectively reduced by Fe substitution, compared with that on {110} plane. From Eqs. (2)– (4), lower γAPB results in lower CRSS, which results in the activation of {211} <111> slip in 10Ni-FC crystals. Thus, systematic studies using the single crystals are an effective way to clarify the hardening mechanism. On the other hand, it is not easy to express CRSS for <001> slip by formula. Further study should be needed to understand it.

5. Conclusions Deformation behavior of Fe–Al–Ni single crystals with B2-type NiAl precipitates was examined focusing on the size and volume fraction of the precipitates. The following conclusions are reached. (1) The calculated results indicate that the Fe atom on the Al site reduces γAPB, while that on the Ni site increases it. This is because the electronic structure of the Fe atom on the Al site is relatively insensitive to the formation of the APB. The Fe atom on the Al site also contributes to reducing the local strain in the vicinity of the APB. (2) In Fe–Al–Ni crystals, fine NiAl phase with the B2 structure is precipitated in the bcc matrix satisfying the cube-on-cube orientation relationship with small misfit strain. The size and volume fraction of the NiAl precipitates increase with increasing Ni concentration. (3) In 2Ni-FC crystals, <111> slip always occurs while not only <111> but <001> slips take place in 6Ni-FC and 10Ni-FC crys­ tals, depending on the loading axis, precipitate morphology and deformation temperature. (4) When <111> slip occurs at room temperature, the NiAl pre­ cipitates strongly suppress the motion of 1/2<111> dislocations in the bcc matrix, since the primary slip system of the NiAl phase is {110} <001>. This leads to strong precipitation hardening. In particular, the shear stress increase for <111> slip in 6Ni-AG crystals compressed with A orientation at room temperature is in quantitatively good agreement with the modified precipitation hardening theory. γAPB of the NiAl precipitates plays an important role on the hardening. However, hardening ability of the NiAl precipitates is lower than that of the CoAl precipitates due to their lower γ APB. (5) Higher volume fraction of the NiAl precipitates is favorable for the activation of <001> slip. (6) The CRSS for <001> slip, especially {hk0} <001> slip is more temperature dependent than that for <111> slip, which results in the slip transition from <111> to <001> slip with increasing deformation temperature. Moreover, the slip plane for <001> slip varies with the loading axis and deformation temperature.

4.3. Temperature dependence of deformation behavior

σ y of the FC crystals exhibited a high value at and below 823 K, and then decreased thereafter, as shown in Fig. 10. The temperature dependence of σ y is closely related to the activated slip system. In 2Ni-FC crystals, <111> slip was always activated and the orientation depen­ dence of σy agreed well with the Schmid factor (Table 4). When <111> slip occurred in the crystals, the NiAl precipitates acted as a strong obstacle to the motion of 1/2<111> dislocations, resulting in high strength. In 6Ni-FC crystals, <111> slip also occurred at C orientation over the wide temperature range due to low Schmid factor for <001> slip (Table 4). On the other hand, at A orientation, the slip transition from {101} <111> to {hk0} <001> occurred at 923 K (Table 4). When <001> slip occurred at B and D orientations, σy decreased more rapidly with increasing temperature, compared with <111> slip at A and C orientations (Fig. 10 (b)). According to Yamaguchi and Umakoshi [26], the core structure of <001> dislocation in bcc metal is complicated, which led to the strong temperature dependence of the CRSS of <001> slip. Therefore, at A orientation, <001> slip took place at 923 K instead of <111> slip. It is also noted that the slip transition from {010} <001> to {hk0} <001> also occurred at 823 K at D orientation (Table 4). D orientation is more favorable for {010} <001> slip than {hk0} <001> according to the Schmid factor (Table 1). However, the CRSS for {hk0} <001> slip in NiAl decreases more rapidly with increasing temperature than {010} <001> slip [23]. This resulted in the activation of {hk0} <001> at and above 823 K at D orientation. In 10Ni-FC crystals, {112} <111> slip occurred at C orientation at all temperatures tested, since the Schmid factor for <001> slip is 0 (Table 4). On the other hand, <001> slip was activated at A, B and D orientations up to 1023 K. Higher f of 10Ni-FC crystals are favorable for the activation of <001> slip even at high temperatures. Moreover, primary slip plane at A and B orientations are {hk0} and {110}, respectively, corresponding to the Schmid factor. In addition, 10Ni-FC crystals also demonstrated slip

Declaration of competing interest Authors have no conflict of interest to declare. Acknowledgements This work was supported by a Grant-in Aid for Scientific Research (B) (Grant No. 26289259) from the Japan Society for the Promotion of Science (JSPS). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.intermet.2019.106627.

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