Available online at www.sciencedirect.com

www.elsevier.com/locate/actamat

ScienceDirect

Acta Materialia 71 (2014) 195–205

Phase stability of r-CrFe intermetallic compound under fastelectron irradiation

Satoshi Anada a, Takeshi Nagase a,b,⇑, Keita Kobayashi b, Hidehiro Yasuda b, Hirotaro Mori b

a Division of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1, Yamada-Oka, Suita, Osaka 565-0871, Japanb Research Center for Ultra-High Voltage Electron Microscopy, Osaka University, 7-1, Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Received 19 July 2013; received in revised form 31 December 2013; accepted 11 March 2014

Abstract

The phase stability of the r-CrFe intermetallic compound under fast electron irradiation was studied using high-voltage electronmicroscopy. Under MeV electron irradiation within the temperature range of 298–473 K, the r phase does not maintain its originalstructure, but instead transforms into a body-centered cubic solid solution. No changes in the topological structure are observed attemperatures below 103 K. This temperature dependence of the phase stability in r-CrFe exhibited the opposite tendency to that ofsolid-state amorphization. The dominant factor affecting the phase stability was discussed in terms of the Gibbs free energy and themicrostructural changes associated with the thermally assisted, radiation-enhanced migration of defects and/or constituent atoms.� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: In situ transmission electron microscopy (TEM); High-voltage electron microscopy; Irradiation effect; Solid-state reaction

1. Introduction

To facilitate further progress in materials science andthe development of sustainable and environmentallyfriendly advanced materials, it is important to understandthe formation of non-equilibrium as well as equilibriumphases, which are difficult to obtain by conventionalprocesses. In situ electron irradiation experiments in ahigh-voltage electron microscope (HVEM) offer a uniqueopportunity to evaluate the formation of these phasesfor the following reasons [1–5]. (i) The MeV electronirradiation method can induce the formation of non-equilibrium phases (e.g. amorphization of intermetallic

http://dx.doi.org/10.1016/j.actamat.2014.03.023

1359-6454/� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights r

⇑ Corresponding author at: Research Center for Ultra-High VoltageElectron Microscopy, Osaka University, 7-1, Mihogaoka, Ibaraki, Osaka567-0047, Japan. Tel.: +81 6 6879 7941; fax: +81 6 6879 7942.

E-mail address: t-nagase@uhvem.osaka-u.ac.jp (T. Nagase).

compound) by accumulation of irradiation defects. Con-versely, by inducing migration of constituent atoms, MeVelectron irradiation can also cause the formation of equilib-rium phases (e.g. crystallization of an amorphous phase).(ii) With an HVEM, it is possible to observe the phase tran-sition process by various transmission electron microscopy(TEM) techniques during electron irradiation. (iii) Duringelectron irradiation, it is possible to suppress contamina-tion, oxidation and increases in temperature, so that theeffects on phase transitions can be considered negligible.(In contrast, conventional techniques, such as severe plasticdeformation and mechanical milling, cannot realize theideal experimental conditions.)

To study the formation of non-equilibrium solid-solution phases under fast electron irradiation, MeV elec-tron irradiation experiments have been performed by vari-ous researchers. The results identified the following typesof phase transition paths: (i) transition from an ordered

eserved.

196 S. Anada et al. / Acta Materialia 71 (2014) 195–205

alloy to a random solid solution that is not present in thethermal equilibrium phase diagram (e.g. from L12 to aface-centered cubic (fcc) solid solution in the case of Ni3Al[6]); (ii) transition from an ordered alloy to a high-temper-ature solid-solution phase that is stable within the high-temperature region of the phase diagram (e.g. from thetI10 structure to fcc for Ni4Mo [7], from B2 to body-centered cubic (bcc) for FeAl [8], or from C11b to bccfor Cr2Al [9]); (iii) crystalline-to-amorphous-to-crystalline(C-A-C) transition, where the MeV electron irradiationcauses the formation, via an intermediate amorphousphase, of a non-equilibrium solid solution that is not pres-ent at the composition of the corresponding compound inthe phase diagram (e.g. C11b-Zr2Cu [10]); and (iv) C-A-Ctransition where an intermediate amorphous phase formsand then yields a non-equilibrium solid-solution phase thatis present at the same composition in the phase diagramwithout irradiation (e.g. C15-Cr2Ti [9]). However, little isknown about the origin of the significant difference amongthe phase transition paths leading to the formation of anon-equilibrium solid-solution phase. To elucidate thefactors controlling the irradiation-induced formation ofsolid solutions from intermetallic compounds, additionalsystematic studies are necessary.

The present study evaluates the phase transitionsinduced by MeV electron irradiation of the r-CrFe inter-metallic compound, using HVEM to clarify the formationof the solid-solution phase at various temperatures. r-CrFeis selected due to its location in the phase diagram, as dis-cussed in detail in Section 2. Another motivation for thisstudy is the fact that the drastic deterioration of many use-ful properties of stainless steels, used as major constructionmaterials in many important branches of industry, such ascivil, chemical, petrochemical, nuclear power plants andthe heavy manufacturing industry, is affected by r-CrFeintermetallic compounds [11–13]. Thus, understanding thephase transitions between r-CrFe and the corresponding

Intermetallic compounds with high te

Intermetallic compounds without hig

2 3 4 5 6 7 8

Mg

Ca Sc Ti V Cr Mn Fe

Sr Y Zr Nb Mo Tc Ru

Ba La Hf Ta W Re Os

Ce Pr Nd Pm Sm Eu

M

M

M No intemetallic compounds

Fig. 1. Features of the phase diagrams for the intermetallic compounds Cra corresponding high-temperature bcc solid-solution phase. White letters wcorresponding high-temperature bcc solid-solution phases. Black letters withcorresponding high-temperature bcc solid-solution phases. White letters with

bcc solid solution is not only a challenge to fundamentalresearch on the formation of non-equilibrium and/orequilibrium solid solution, but is also of major interest toindustry and engineering.

2. Cr–Fe alloy system

The formation of irradiation-induced solid solutions hasbeen investigated in detail, particularly in Cr-containingintermetallic compounds of Cr2Ti and Cr2Al, belongingto the Cr–Ti and Cr–Al alloy systems [9], and it waspointed out that the existence of a high-temperature bccsolid-solution phase is an important factor for the forma-tion of bcc solid-solution phase under irradiation. Of thevarious Cr–M binary alloy systems known (M = elementsfrom groups 2–14), intermetallic compounds that have cor-responding high-temperature bcc solid-solution phasesexist only for Cr–X (X = Ti, Mn, Fe, Os, Co and Al) alloysystems (see Fig. 1). In the present study, we selected theCr–Fe alloy system for investigation because of its indus-trial importance as well as the similarity of its phase dia-gram to those of the Cr–Ti and the Cr–Al alloy systemspreviously studied.

Fig. 2(a) shows the binary phase diagram of the Cr–Fealloy system [14], while Fig. 2(b) is a schematic illustrationof a unit cell of the r-CrFe intermetallic compound. The r-CrFe is the only intermetallic compound possible in theCr–Fe system. It can be seen from the phase diagram thatthe bcc solid solution exists as an equilibrium phase in thehigh-temperature region at the composition range of r-CrFe, whereas at temperatures below 793 K a two-phasemixture of bcc solid solutions with different compositionsappears as a thermodynamically stable microstructure. Ascan be seen from Fig. 2(b), the r-CrFe has a tetragonalunit cell (space group P42/mnm) that comprises 30 atomsdivided into five nonequivalent sublattices (A2, B4, C8, D8

and E8, with the subscript indices denoting the site

mperature bcc solid solution

h temperature bcc solid solution

9 10 11 12 13 14

Al Si

Co Ni Cu Zn Ga Ge

Rh Pd Ag Cd In Sn

Ir Pt Au Hg Tl Pb

Gd Tb Dy Ho Er Tm

–M (M = group 2–14 elements) from the viewpoint of the existence ofith a red background: the existence of intermetallic compounds anda yellow background: the existence of intermetallic compounds without

a blue background: intermetallic compounds do not exist.

Fig. 2. (a) Equilibrium phase diagram for the Cr–Fe system [14] and (b)the tetragonal unit cell of r-CrFe, where A, B, C, D and E indicatecrystallographically nonequivalent sublattices.

Cal

cula

ted

stru

ctur

e fa

ctor

s

6050403020

q [nm-1]

(a) referred from Pearson's handbook

(b) fully disordered σ phase

Fig. 3. Calculated structure factor of the various structures in the r-CrFephase. (a) A r phase taken from Pearson’s Handbook [18] and (b) a fullydisordered r phase.

S. Anada et al. / Acta Materialia 71 (2014) 195–205 197

multiplicities) [15–17]. This structure may be constructedby stacking Kagome tile planes (at z = 0 and 1/2 in the unitcell) and sublattice E planes (z � 1/4 and 3/4) alternately.

Fig. 3 shows the calculated structure factor of r-CrFeintermetallic compounds for two different site occupancies:(a) a r phase taken from Pearson’s Handbook [18] and (b) afully disordered r phase. The Cr site occupancies (at.% ofCr) of the sublattices (A, B, C, D, E) are (a) (12, 75, 62,16, 66) and (b) (50, 50, 50, 50, 50), respectively. As can beseen in Fig. 3, there is almost no difference in the structurefactors between (a) and (b). This was due to the small differ-ence of the atomic scattering factor between the constituentFe and Cr atoms. This indicates that the site occupancydependence of the structure factors of the r-CrFe is

too small for the changes in chemical disorder of the r-CrFeto be detected under irradiation by in situ TEM.

3. Experimental procedures

The composition of Cr48.5Fe51.5 is indicated in Fig. 2(a)by a vertical black arrow and a vertical dotted line. Thiscomposition was selected because of the wide temperaturerange of r-CrFe in the phase diagram. The preparation ofr-CrFe single-phase specimen from high-purity base met-als will be reported in detail in another paper [19]. The fol-lowing process was adopted in the present study. (1) Amaster ingot of a Cr48.5Fe51.5 alloy (at.%) was preparedby melting the appropriate amounts of Cr (99.99 wt.% pur-ity; Mitsuwa Pure Chemical Co. Ltd.) and Fe (99.99 wt.%purity, carbon impurity 5 40 ppm; Toho Zinc Co. Ltd.) inan arc furnace in an atmosphere of highly purified Ar. (2)The prepared ingot was cold rolled. (3) The rolled speci-mens were annealed at 973 K for 3.6 � 104 s in a vacuumquartz tube with Ti as an oxygen getter. The constituentphases of these annealed samples were identified by X-raydiffraction (XRD; RINT2000, Rigaku Co. Ltd) analysisat room temperature using Cu Ka radiation. Thin filmsfor TEM and MeV electron irradiation were prepared byion thinning using Ar ions. The accelerating voltage waskept constant at 4.5 kV and a temperature of 298 K.Damage to the thin films during ion thinning wasconsidered negligible.

Electron irradiation was performed at 22–473 K usingthe Hitachi H-3000-type HVEM at Osaka University,which was operated at an acceleration voltage of 2 MV.The dose rate ranged from 1.2 � 1024 to 2.1 � 1024 m�2 s�1,with the longest irradiation period being 1.2 � 103 s.Changes in the microstructure of the samples during

100

80

60

40

20

0

Cro

ss s

ectio

n [b

arns

]

3.02.52.01.51.00.50.0

Acceleration voltage [MV]

Cr, Ed=24 eV

Fe, Ed=20 eV

Fig. 4. The cross-section of atomic displacement of pure Cr and Fecalculated using the McKinley–Feshbach formula [20–22]. At 2.0 MeV,the cross-sections of Cr and Fe by fast electron were roughly estimated at48 and 73 barns, respectively.

Fig. 5. (a) XRD patterns of the rolled samples before and after they wereannealed at 973 K for 3.6 � 104 s and (b) TEM images of the rolledsamples annealed at 973 K for 3.6 � 104 s before being irradiated.

198 S. Anada et al. / Acta Materialia 71 (2014) 195–205

electron irradiation were observed by in situ TEM per-formed at 2 MV by capturing bright-field (BF) imagesand selected-area diffraction (SAD) patterns. The cross-sections of atomic displacement of pure Cr and Fe wereestimated using the McKinley–Feshbach formula [20–22];the results are shown in Fig. 4. At 2.0 MeV, the cross-sec-tions of atomic displacement of Cr and Fe by fast electronswere roughly estimated to be 48 and 73 barns, respectively[5]. These values corresponded to a damage rate that rangedfrom 5.8 � 10�3 to 1.0 � 10�2 dpa s�1 for Cr and from8.8 � 10�3 to 1.5 � 10�2 dpa s�1 for Fe, respectively. Thethreshold energies of atomic displacement of Cr and Fe inthe r-CrFe intermetallic compound could not be estimatedaccurately because there are no reliable theories for the eval-uation of atomic displacement of constituent elements incompounds. In the present work, then, it is assumed thata cross-section of atomic displacement of 61 barns,obtained from the linear mixture rule for pure Cr and Fe,holds good in r-CrFe, and this value was employed to esti-mate practical dpa rates. Although the threshold energy foratomic displacement is known to depend slightly upon thetemperature (i.e. it becomes smaller at higher temperatures[2,23]), the dependence was ignored in the estimation of thedpa rate.

4. Results

4.1. Microstructure of r single-phase samples

Fig. 5(a) shows the XRD pattern for the rolled samplesbefore and after annealing at 973 K for 3.6 � 104 s. In theCr48.5Fe51.5 alloy, the r phase can exist over the tempera-ture range from 833 to 1043 K as a thermal equilibriumphase, as shown in the phase diagram (Fig. 2(a)). As can

be seen from Fig. 5(a), only bcc-related peaks were visiblein the XRD pattern for the as-rolled sample, indicatingthat a single bcc phase was formed, with the formationof the r phase not being evident. On the other hand, inthe case of the rolled samples annealed at 973 K, the mainconstituent phase was r-CrFe, and the bcc phase-relatedpeaks disappeared completely. Fig. 5(b) shows a BF imageand the corresponding SAD pattern of the rolled specimenannealed at 973 K for 3.6 � 104 s. A coarse-grained r-CrFephase was observed as a main constituent phase in theannealed sample; no bcc phase could be observed usingTEM. These results show that a r-CrFe single-phase sam-ple with a coarse grain size suitable for MeV electron irra-diation was obtained by cold rolling and subsequentannealing at 973 K. MeV electron irradiation was then per-formed on these samples.

4.2. MeV electron irradiation on r-CrFe

Fig. 6 shows the irradiation-induced changes in theintermetallic compound r-CrFe at 298 K at a dose rate

Fig. 6. In situ TEM images showing the changes induced in the structureof the intermetallic compound r-CrFe by irradiation with MeV electronsat 298 K at a dose rate of 2.1 � 1024 m�2 s�1. (a) The r-CrFe specimenbefore being irradiated, and after being irradiated for (b) 60 s, (c) 300 sand (d) 600 s. The arrows in the BF images mark the same position.

S. Anada et al. / Acta Materialia 71 (2014) 195–205 199

of 2.1 � 1024 m�2 s�1. Fig. 6(a) shows the BF image andthe corresponding SAD pattern before irradiation. TheSAD pattern could be consistently indexed as the ½12�1�net pattern of the r-CrFe. After irradiation for 60 s(Fig. 6(b)), the BF image of the sample appeared to havea black dot contrast in the central portion of the irradiatedarea. In contrast, no significant change in the correspond-ing SAD pattern was observed. The fact that Debye ringsdid not appear in the SAD pattern indicated that the blackdot contrast in the BF image corresponded not to the for-mation of a nanocrystalline phase but to the accumulation

of defects. The black dot contrast spread over a larger areawith increasing irradiation time (Fig. 6(b) and (c)). The dis-appearance of the black dot contrast and the appearance ofa crystalline contrast (i.e. faint bend contours) could beobserved in the central portion of the irradiated area afterirradiation for 600 s (Fig. 6(d)). At the same time, a signif-icant change in the SAD pattern was observed, whereinmost of the diffraction spots attributable to the r-CrFephase disappeared.

To investigate the structural change in the r-CrFe dur-ing severe electron irradiation, a detailed study of the newlyappeared crystalline structure was carried out throughSAD pattern analysis by using conventional TEM withan acceleration voltage of 200 kV. The results are shownin Fig. 7. The BF image of a sample irradiated at 298 Kfor 1.2 � 103 s (Fig. 7(a)) shows a coarse crystalline region(indicated by index A) surrounded by the r-CrFe phase(represented by the black dot contrast and indicated byindex B). The difference in the microstructure of the irradi-ated region between indices A and B can be explained bythe characteristics of the electron flux profile, which exhib-its an approximately Gaussian distribution [24]. The cen-tral area shown by index A corresponds to an area witha relatively high electron dose, whereas the peripheral areashown by index B corresponds to an area with a relativelylow electron dose. The SAD patterns taken from thecoarse-grained area indicated by index A are shown inFig. 7(b), (c) and (d), together with the key diagrams(Fig. 7(b0), (c0) and (d0)). These SAD patterns wereobtained by changing the direction of the incident electronbeam, and can be indexed, respectively, as the [001], [110]and [111] net patterns of a bcc structure with a lattice con-stant of 0.29 nm. No irradiation-induced changes in thecomposition of the sample were detected by TEM–energy-dispersive spectroscopy analyses. Similar resultswere obtained on samples irradiated at 373 and 473 K.These results clearly indicate that the r-CrFe did not main-tain its original structure after being irradiated at or above298 K, and that the intermetallic compound transformedinto the bcc solid solution.

Next, the orientation relationship between the originalr-CrFe phase and the irradiation-produced bcc phasewas studied using a sample irradiated at 373 K, and theresults obtained are illustrated in Fig. 8. Fig. 8(a) is a BFimage showing an area of irradiation-produced bcc phase(the central, round area) surrounded by the r-CrFe phase.Fig. 8(b) is a SAD pattern taken from a rather wide area inFig. 8(a) containing both the bcc and r-CrFe phases. Allthe diffraction spots in the SAD in Fig. 8(b) can be indexedas the superposition of the bcc [010] and r-CrFe [010] netpatterns, as shown in Fig. 8(c). In detail, the 002bcc and�101bcc spots are located close to the 203r and �202r spots,respectively, and the bcc [010] net pattern is rotated clock-wise by approximately 2� against the r-CrFe [010] net pat-tern, as shown in Fig. 8(c). Simple vector analysis thenshows that the �103bcc spot is present in a position closeto the 005r spot but is rotated clockwise by approximately

Fig. 7. Phase identification of a crystalline phase formed in the r-CrFeafter being irradiated at 298 K for 1.2 � 103 s. (a) BF image of theirradiated area; (b–d) the SAD patterns obtained from the irradiated areaby changing the direction of the incident electron beam; and (b0–d0) thekey diagrams of [001], [110] and [111] of a bcc structure.

200 S. Anada et al. / Acta Materialia 71 (2014) 195–205

2� around the common axis of the [010]bcc (or the [010]r,which is identical with the reverse of the incident electronbeam direction), as depicted in Fig. 8(c). In a similarway, by using the 1 01bcc (the 401r) and 200bcc (the60�1r) spots, it is shown that the 30 1bcc spot is present ina position close to the 10 00r spot but is rotated clockwiseby approximately 2� around the common axis, as depictedin Fig. 8(c). These analyses indicate that the followingorientation relationship is present between the originalr-CrFe phase and the irradiation-produced bcc phase:

the [010]bcc and the [01 0]r directions are parallel to eachother, and the [301]bcc direction is nearly parallel to the[10 0]r direction but is rotated clockwise approximately2� around the common axis of the [010]bcc (or [010]r)direction. A schematic illustration of the above orientationrelationship expressed in the real space is presented inFig. 8(d), where both the bcc (dotted lines) and r-CrFe(solid lines) lattices extend from the common origin, 0,and both are viewed along the common axis of the[01 0]bcc (or [010]r) direction. With regard to the bcc lat-tice, a lattice constant, a, of 0.290 nm was employed. Withregard to the r-CrFe lattice, two unit cells are stacked inthe [001]r direction. This is because the stacking of theð�1 03Þ plane in bcc is repeated in units of 10 ð�103Þ layersand this unit requires a height equal to the length of thea½�10 3� vector, i.e. 0.917 nm, which is close to the lengthof 2cr (i.e. 0.912 nm). Further discussions are presentedin Section 5.

Fig. 9 shows the response of the intermetallic compoundr-CrFe to irradiation at 103 K. The BF image of the sam-ple taken before irradiation showed conventional crystal-line contrast, and the corresponding SAD pattern couldbe indexed as the ½12�1� net pattern of r-CrFe (Fig. 9(a)).After irradiation for 1.2 � 103 s (Fig. 9(b)), a high densityof black dot contrast appeared in the BF image. However,no significant change in the SAD pattern of the sample wasobserved. At 103 K, the BF image and SAD pattern do notexhibit further changes with increasing irradiation time,indicating that no irradiation-induced topological changestake place in the crystalline structure of the r-CrFe phase.It should be noted, however, that this does not necessarilyexclude the possibility of irradiation-induced chemical dis-ordering within the r-CrFe lattice, as described in Section 2with regard to Fig. 3. At 22 K, the response of r-CrFe toelectron irradiation was similar to that at 103 K. Theseresults indicate that the stability of the r-CrFe phaseagainst the irradiation depends to a large extent on temper-ature; the stability increases when the irradiation tempera-ture is below 103 K.

As described above, no significant structural changes inthe intermetallic compound r-CrFe were observed afterirradiation at 103 K (Fig. 9) and 22 K, while transition toa bcc solid solution occurred under irradiation at 298 K(Fig. 6), 373 K and 473 K. Fig. 10 summarizes the temper-ature dependence in the phase stability of r-CrFe againstirradiation. In this figure, the mark h denotes a situationwhere the formation of bcc phase was confirmed at the cen-tral part of irradiated area, while the mark � denotes a sit-uation where no such formation was observed. Here theconfirmation of bcc phase formation was carried out inthe following manner: during irradiation, formation of aphase different from r-CrFe was detected at the centralpart of irradiated area at a certain dose by in situ BF imag-ing in HVEM, and subsequently, after the irradiationexperiment was finished, the irradiated area was examinedin detail with a transmission electron microscope operatedat 200 kV and the phase formed at the dose was identified

000

401σ

000

100nm

(a)

σ (subl.A)bcc

(b)

(d)

2cσ

= 0.

912

nm

[001]σ

[100]σ

7/10

9/101

8/10

z = 01/10 ((103)bcc)2/103/104/105/106/10

(c)

10 00σ

601σ

100σ

001σ

203σ

005σ

202σ

200bcc

101bcc101bcc

0

σ [010]+bcc [010]

103bcc

002bcc

301bcc

aσ = 0.880 nm

Fig. 8. Orientation relationship between the r-CrFe matrix and the bcc phase formed by 2 MeV electron irradiation at 373 K for 1.2 � 103 s. (a) BF imageshowing an area of irradiation-produced bcc phase (the central, round area) surrounded by the original r-CrFe phase; (b) SAD pattern taken from a widearea in Fig. 8(a) containing both the bcc and the r-CrFe phases; (c) key diagram of the SAD pattern shown in (b); and (d) schematic illustration of theorientation relationship between the r and bcc phases in the real space.

Fig. 9. In situ TEM images showing the changes induced in theintermetallic compound r-CrFe after being irradiated with MeV electronsat 103 K at a dose rate of 1.2 � 1024 m�2 s�1. The r-CrFe specimen (a)before it was irradiated and (b) after it was irradiated for 1.2 � 103 s.

20

15

10

5

0

Tota

l dos

e [d

pa]

500400300200100

Temperature [K]

Compound(σ)

Solid solution(bcc)

Fig. 10. The temperature dependence of the phase stability of interme-tallic compound r-CrFe under 2 MeV electron irradiation. h, presence ofbcc phase confirmed by TEM; �, absence of bcc phase (see text).

S. Anada et al. / Acta Materialia 71 (2014) 195–205 201

202 S. Anada et al. / Acta Materialia 71 (2014) 195–205

to be the bcc phase by SAD analyses. Thus, the borderbetween situations marked h and � can be regarded as aline that separates a region where r-CrFe is stable underirradiation from that where a r to bcc transition is broughtabout under irradiation. Namely, the line corresponds tothe critical dose required for the formation of bcc solidsolution from r-CrFe (i.e. see a broken line in Fig. 10).It is clear that the critical dose decreased with increasingtemperature. This temperature dependence in the phasestability will be discussed below.

Fig. 11. Schematic illustration of the Gibbs free energy diagram of theCr–Fe alloy system for temperatures below 793 K.

Table 1The estimated difference in Gibbs free energy among the single phase ofbcc solid solution, the two-phase mixture of bcc solid solutions withdifferent compositions, r-CrFe and liquid of Cr48.5Fe51.5 alloy (see textand Fig. 11).

Temperature (K) Gibbs free energy difference, DG (kJ mol�1)

DGA DGB � DGA DGA + DGC DGB DGC

22 2.1 15 5.1 17.1 3.0103 1.9 15 4.4 16.9 2.5298 1.5 14 2.8 15.5 1.3373 1.4 14 2.2 15.4 0.8473 1.2 13 1.4 14.2 0.2

5. Discussion

Over the temperature range from 298 to 473 K, r-CrFewas rendered into the bcc solid solution without formingan intermediate amorphous, whereas irradiation did notaffect the crystalline structure of r-CrFe within the temper-ature range of 22–103 K. The irradiation-induced solidsolution formation behavior of Cr-containing intermetalliccompounds has previously been evaluated, and theresponses of Cr2Ti [9], Cr2Al [9] and r-CrFe to fast elec-tron irradiation are clarified and summarized as follows.(i) All intermetallic compounds transformed to the bccsolid-solution phase; however, the formation path of thebcc solid solution differed among the compounds. (ii) OnlyCr2Ti formed an intermediate amorphous state, undergo-ing a C-A-C transition. (iii) In the case of Cr2Al, a high-temperature bcc phase was gradually formed directlythrough chemical disordering of Cr2Al without alterationof the fundamental crystalline structure. (iv) In the caseof r-CrFe, the bcc solid solution was formed directly fromthe compound at a temperature of 298 K or higher.

Herein, the irradiation-induced structural transforma-tion of r-CrFe is discussed from the viewpoints of theGibbs free energy (Sections 5.1–5.3), of the absence ofamorphous phase formation during the bcc solid solutionformation processes (Section 5.2) and of the temperaturedependence of the stability against irradiation (Section 5.3).

5.1. Differences in Gibbs free energy of Cr48.5Fe51.5 alloy

among different phases

Fig. 11 shows a schematic illustration of the Gibbs freeenergy difference in relation to the irradiation-inducedphase change of r-CrFe. Table 1 summarizes the differ-ences between the Gibbs free energy of r-CrFe and the sin-gle phase of bcc solid solution (DGA), between r-CrFe andthe amorphous phase (DGB), and between r-CrFe and atwo-phase mixture of bcc solid solutions with differentcompositions (DGC), along with some other relevant quan-tities such as (DGB � DGA) and (DGA + DGC). The calcula-tion methods are as follows. The values of DGA wereestimated from empirical thermodynamic properties ofthe Cr–Fe system [25–28]. The quantity DGB � DGA wasestimated from the energy difference between the bcc solidsolution and the liquid [29–31]. The quantity DGA + DGC

was derived from a regular solid solution model [32].The values of the Gibbs free energy differences, DGB andDGC, were obtained from DGA, DGB � DGA and DGA +DGC.

5.2. Absence of amorphous phase formation in r-CrFe under

irradiation

Among the Cr2Ti, Cr2Al and r-CrFe compounds underfast electron irradiation, only Cr2Ti forms an intermediateamorphous phase prior to transforming into the bcc solidsolution [9]. The difference in the Gibbs free energy ofthe intermetallic compound and the corresponding amor-phous phase (DGam.-im) is an important factor that deter-mines whether an amorphous phase will form under fastelectron irradiation. A larger value of DGam.-im indicatesa lower probability of solid-state amorphization upon irra-diation. The value of DGam.-im at 103 K was estimated to be�17 kJ mol�1 for r-CrFe (see DGB in Table 1) and10 kJ mol�1 for Cr2Ti [9]. The large value of DGam.-im

(i.e. DGB) for r-CrFe compared to that for Cr2Ti explainswhy r-CrFe does not form an amorphous phase.

35

30

25

20

15

10

5

0

Crit

ical

dos

e [d

pa]

200150100

Temperature [K]

35

30

25

20

15

10

5

0

Crit

ical

dos

e [d

pa]

3002001000

Temperature [K]

Compound

Crystalline phase

(b) Amorphous-to-Crystal transition

(a) Crystal-to-Amorphous transition

Amorphous

Amorphous

Fig. 12. Typical examples of the temperature dependence of the phasestability of (a) intermetallic compounds against irradiation-induced solid-state amorphization and (b) the amorphous phase against irradiation-induced crystallization. (a) shows experimental data regarding the criticaldose required for amorphization of Co3B [34]. (b) shows the criticalirradiation dose required to induce crystallization of the Fe88Zr9B3

amorphous phase, where bcc solid solution is a main constituent of thecrystalline structure [35].

S. Anada et al. / Acta Materialia 71 (2014) 195–205 203

5.3. Temperature dependence of the phase stability against

irradiation, and transition path from r-CrFe to the bcc solid

solution

Two possibilities exist for the pathway to forming thebcc solid solution from r-CrFe system under fast electronirradiation. The first involves the formation of a single-phase bcc solid solution with the composition Cr48.5Fe51.5.This path may correspond to DGA in Fig. 11. This value ofDGA is estimated to be approximately 2 kJ mol�1 (Table 1),which is rather small compared to the difference betweenthe Gibbs free energies of Cr2Ti and its amorphous phase(10 kJ mol�1 at 103 K) [9], and between the Gibbs freeenergies of Cr2Al and its high-temperature bcc solid solu-tion (8 kJ mol�1 at 103 K) [9]. The present experimentsshow that the bcc solid solution was not formed at 22and 103 K (Figs. 9 and 10), indicating that the increase inthe Gibbs free energy of r-CrFe under fast electron irradi-ation may be smaller than DGA and may be insufficient toinduce the r to bcc transition. In other words, the pathindexed by DGA in Fig. 11 does not occur. Evidently, morework is needed to make clear the reason for the insufficientincrease in the Gibbs free energy in r by irradiation, butone possibility is that the atomic sizes of Cr and Fe arequite similar to each other and the nearest-neighbor effec-tive interaction energy (or ordering energy) in r-CrFehas been reported to be as low as 0–3 mRy [33].

The second path involves forming a two-phase mixtureof bcc solid solutions with different compositions, andmay correspond to DGC in Fig. 11. Although it was difficultto directly confirm the formation of Fe-rich and Cr-richregions by analyzing SAD patterns in Figs. 6–8 due tothe similarity between the lattice parameters of bcc Crand bcc Fe, the observed temperature dependence (Figs. 6–10) offers useful information about the pathway to the bccsolid solution. At and above 298 K, the bcc solid solutionforms (Figs. 6 and 7) under irradiation, and the criticalirradiation dose required for bcc solid solution formationdecreases as the irradiation temperature increases(Fig. 10). In general, the temperature dependence of thecritical dose depends strongly on the path of the irradia-tion-induced structural change. Fig. 12 shows typicalexamples of the temperature dependence of the criticaltotal dose in relation to the fast electron irradiation-induced structural change: (a) solid-state amorphizationof Co3B with an increase in the Gibbs free energy [34]and (b) crystallization of the Fe88Zr9B3 melt-spun amor-phous phase accompanied by a decrease in the Gibbs freeenergy [35]. In the case of solid-state amorphization(Fig. 12(a)), the intermetallic compounds tend to more eas-ily transform into the amorphous phase at lower tempera-tures under MeV electron irradiation because thesuppression of thermal recovery causes point defects toaccumulate more efficiently at lower temperatures. Thisphenomenon is common to the irradiation-induced phasechange of intermetallic compounds with an increase inthe Gibbs free energy. In contrast, the stability of the

amorphous phase against irradiation shows the oppositetemperature dependence (Fig. 12(b)). Generally, irradia-tion-induced crystallization forms a crystalline phase froman amorphous phase [5,35–38], and the critical doserequired for this transformation is smaller at higher tem-peratures. This temperature dependence is consistent witha phase transition assisted by thermal recovery and accom-panied by a decrease in the Gibbs free energy under irradi-ation. Because the amorphous phase is not at thermal

204 S. Anada et al. / Acta Materialia 71 (2014) 195–205

equilibrium, the radiation-enhanced migration of defectsand/or atoms may cause the crystallization of the amor-phous phase. With regard to the temperature dependenceof the stability of the r-CrFe phase against irradiation,the obtained experimental results shown in Fig. 10 werein conflict with the tendency shown in Fig. 12(a), and weresimilar to those in Fig. 12(b). This strongly suggests thatthe thermally assisted, radiation-enhanced migration ofdefects and/or atoms plays an essential role in the r-CrFeto bcc phase transition under irradiation, and that ther-CrFe changes to a two-phase mixture of bcc solid solu-tions with different compositions along the energy pathindexed by DGC in Fig. 11.

Finally, a brief discussion is given on the possible struc-tural path for the r-CrFe to bcc phase transition underirradiation. As described in Section 4.2, the bcc phase pro-duced by irradiation has such an orientation relationshipwith the matrix of r as that illustrated in Fig. 8(d). As seenfrom this figure, a rectangular parallelepiped within the bcclattice with corners at a[000] a[301], a[030], a[331],a½�103�, a[204], a½�1 33� and a[234] possesses three orthogo-nal edges with dimensions of 0.917 (a[30 1]), 0.870 (a[030])and 0.917 nm ða½�103�Þ and a volume of 0.732 nm3, whichare close to those of the rectangular parallelepiped com-posed of the two-stacked unit cells of r, namely, with edgesof 0.880 (a[10 0]r), 0.880 (a[010]r) and 0.912 nm (2c[001]r)and a volume of 0.706 nm3. In addition, these two rectan-gular parallelepipeds contain the same number of atoms,namely 60 atoms each. Such structural features seem tobe primarily responsible for the observed orientation rela-tionship between the r and the bcc phases. The practicalatom displacements that occur in r to form the bcc regularatomic arrangement are not clear at present. However, it isworth noting that rearrangements of atoms in r along sucha line as described in Appendix A make it possible to formthe bcc structure [39]. It is considered that the extension ofatom rearrangements along such a line by radiation-enhanced migration of defects and/or atoms may beresponsible for the r to bcc transition.

6. Conclusions

In the present study, an HVEM was used to investigatethe phase stability of the r-CrFe phase against fast electronirradiation, and the irradiation-induced structural changesin the r-CrFe intermetallic compound. The conclusions areas follows:

(1) r-CrFe cannot maintain its original crystalline struc-ture under MeV electron irradiation at 298–473 K,but instead transforms into a bcc solid-solutionphase.

(2) No significant changes in the fundamental structureof r-CrFe were observed after it had been irradiatedat 103 or 22 K. Namely, the r-CrFe phase becamemore resistant to the irradiation with a decrease intemperature.

(3) The temperature dependence of the r-CrFe phasestability suggests that thermally assisted, radiation-enhanced migration of defects and/or atoms playsan essential role in the transition from r-CrFe tosolid-solution phase under irradiation, and r-CrFechanges to a two-phase mixture of bcc solid solutionswith different compositions with the decrease in theGibbs free energy under irradiation.

Acknowledgements

This work was supported in part by Grants for ExcellentGraduate Schools, the Ministry of Education, Culture,Sports, Science and Technology (MEXT), Japan.

Appendix A. A possible line along which rearrangements of

atoms in r occur to form the bcc structure

The atomic plane in r at z = 0r in Fig. 2(b) (the heightposition corresponds to z ¼ 0½�103�bcc in Fig. 8(d)) contains atotal of 11 atoms. These 11 atoms are divided into threegroups: seven atoms are displaced on the same plane atz = 0r to form a ð�101Þbcc layer at z ¼ 0½�103�bcc composedof six atoms on the regular lattice points with one atomat an interstitial site; two other atoms undergo downwarddisplacements with a z-component of Dz = �1/5r to forma ð�301Þbcc layer at z ¼ 9=10½�103�bcc composed of six atomson the regular lattice points, in combination with fouratoms which are from the atomic plane in r at z = 3/4r;and the remaining two atoms undergo upward displace-ments with a z-component of Dz = 1/5r to form að�3 01Þbcc layer at z ¼ 1=10½�103�bcc composed of six atoms onthe regular lattice points, in combination with four atomswhich come from the atomic plane in r at z = 1/4r. Onthe other hand, the 11 atoms on the atomic plane in r atz = 1/2r in Fig. 2(b) (the height position corresponds toz ¼ 2:5=10½�103�bcc in Fig. 8) are divided into two groups:six atoms undergo upward displacements with a z-compo-nent of Dz = 1/10r to form a ð�301Þbcc layer atz ¼ 3=10½�103�bcc composed of six atoms on the regular latticepoints, while the remaining five atoms undergo downwarddisplacements with a z-component of Dz = �1/10r to forma ð�301Þbcc layer at z ¼ 2=10½�103�bcc composed of five atomson the six regular lattice points with one vacancy. Atomrearrangements along this line are considered to be onepossible way to bring about the r to bcc structural transi-tion under irradiation. It is noted here that in the atomrearrangements it is possible to limit the displacements ofall the atoms reaching the regular bcc lattice points far lessthan the shortest nearest-neighbor distance in r [39].

References

[1] Fujita H. J Electron Microsc Technol 1986;3:243.[2] Seeger A. J Electron Microsc 1999;48:301.[3] Fujita H. Proc Jpn Acad Ser B 2005;48:141.

S. Anada et al. / Acta Materialia 71 (2014) 195–205 205

[4] Mori H. J Electron Microsc 2011;60:S189.[5] Nagase T. In: Kakeshita T, editor. Progress in advanced structural

and functional materials design. Tokyo: Springer; 2013.[6] Carpenter GJC, Schulson EM. Scripta Metall 1981;15:549–54.[7] Banerjee S, Urban K, Wilkens M. Acta Metall 1984;32:299.[8] Mukai T, Kinoshita C, Kitajima S. Philos Mag A 1983;47:255.[9] Anada S, Nagase T, Yasuda H, Mori H. J Alloys Compd

2013;579:646.[10] Nagase T, Umakoshi Y. Scripta Mater 2003;48:1237.[11] Hall EO, Algie SH. Metall Rev 1966;11:61.[12] Grobner PJ. Metall Trans 1973;4:251.[13] Sahu JK, Krupp U, Ghosh RN, Christ H-J. Mater Sci Eng A

2009;508:1.[14] Chen SL, Zhang JY, Lu XG, Chou KC, Chang YA. J Phase Equilib

Diffus 2006;27:121.[15] Yakel HL. Acta Crystallogr B 1983;39:20.[16] Cieslak J, Reissner M, Dubiel S, Wernish J, Steiner W. J Alloys

Compd 2008;460:20.[17] Dubiel SM, Cieslak J. Crit Rev Solid State Mater Sci 2011;36:191.[18] Villars P. Pearson’s handbook of crystallographic data for interme-

tallic phases, vol. 3, 2nd ed.. Materials Park (OH): ASM Interna-tional; 1991.

[19] Anada S, Nagase T, Yasuda H, Mori H. in preparation.[20] Seitz F, Koehler JS. In: Seitz F, Tumbull D, editors. Solid state

physics, vol. 2. New York: Academic Press; 1956.

[21] Corbett JW. Electron radiation damage in semiconductors andmetals. New York: Academic Press; 1966.

[22] Oen OS. Nucl Instrum Methods Phys Res Sect B 1988;33:744.[23] Hohenstein M, Seeger A, Sigle W. J Nucl Mater 1989;169:33.[24] Yasuda H, Furuya K. Philos Mag A 2000;80:2355.[25] Dench WA. Trans Faraday Soc 1963;59:1279.[26] Backhurst I. J Iron Steel Inst 1958;189:124.[27] Martens H, Duwez P. J Met 1956;8:614.[28] Kornilov II, Matveeva NM. Russ J Inorg Chem 1960;5:671.[29] Chen Q, Sundom B. J Phase Equilib 2001;22:631.[30] Hertzman S, Sundom B. CALPHAD 1982;6:67.[31] Andersson JO, Sundom B. CALPHAD 1987;11:83.[32] Koyama T. Zairyo-Sekkei-Keisan-Kogaku, Uchida Rokakuho; 2011.[33] Kabliman E, Blaha P, Schwarz K. Phys Rev B 2011;84:184206.[34] Sakata T, Mori H, Fujita H. J Ceram Soc Jpn Int 1989;97:1382.[35] Nagase T, Umakoshi Y. Mater Sci Eng A 2003;347:136.[36] Nagase T, Sanda T, Nino A, Qin W, Yasuda H, Mori H, et al. J Non-

Cryst Solids 2012;358:502.[37] Brimhall JL. J Mater Sci 1984;19:1818.[38] Doi M, Yoshida M, Nonoyama M, Imura T, Masumoto T, Yashiro

Y. Mater Sci Eng 1976;23:169.[39] Anada S, Nagase T, Kobayashi K, Yasuda H, Mori H. in

preparation.