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Phase relationship in the Tb–Fe–Cr ternary system at 600 °C
Journal of Alloys and Compounds 541 (2012) 198–203
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Phase relationship in the Tb–Fe–Cr ternary system at 600 °C Yan Zhong, Huai-Ying Zhou ⇑, Chao-Hao Hu, Shun-Kang Pan School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin, Guangxi 541004, PR China
a r t i c l e
i n f o
Article history: Received 12 July 2011 Received in revised form 26 June 2012 Accepted 27 June 2012 Available online 9 July 2012 Keywords: Rare earth alloys and compounds Crystal structure Phase diagrams X-ray diffraction
a b s t r a c t The phase relationships in the Tb–Fe–Cr ternary system at 600 °C have been investigated mainly by X-ray diffraction analysis and first-principles density functional theory calculations. The result shows that the isothermal section consists of 9 single-phase regions, 16 two-phase regions and 8 three-phase regions. The compound TbFe12xCrx with the ThMn12-type structure is found to have a broad solubility ranging from x = 1.4 to 2.6. The XRD patterns and total-energy calculations suggest that Tb2Fe17 crystallizes with the Th2Zn17-type rhombohedral structure under our experiment conditions. The solid solutions in this ternary system are formed by the substitution of Fe by Cr. The maximum solid solubilities of Cr in (aFe), Tb2Fe17, Tb6Fe23, and TbFe2 are about 17, 12.5, 3, and 7 at.% Cr, respectively. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Research on permanent magnet materials has led to the discovery of many ternary Fe-rich rare earth intermetallic compounds of the R–Fe–M (R = rare-earth or Yttrium; M = Al, Si, Ti, V, Cr, Nb, Mo, Ta or W) [1–3]. Currently, the R(Fe,M)12, R2(Fe,M)17, and R3(Fe,M)29 compounds have been extensively studied due to their relatively high saturation magnetization and high Curie temperature as well as strong uniaxial anisotropy [4–6]. Experimental studies have verified that the third nonmagnetic element M is necessary to stabilize these compounds and has a strong effect on the magnetic properties. Kuchin et al. [4] have synthesized the Ce2Fe17xMnx(x = 0–2.0) compounds by induction melting and found that the Curie temperature and spontaneous magnetization rise sharply with Mn content. Hao et al. [5] have also observed that a few Cr atoms substituting for Fe atoms can enhance Curie temperature of Tb2Fe17xCrx compounds obviously. To further understand the formation, solubility limit and phase relationship in the R–Fe– M systems, it is certainly worth to investigating the phase diagram of the relevant systems. In this work, the 600 °C isothermal section of the phase diagram of the Tb–Fe–Cr system was determined by combining experimental investigation and first-principles calculation. The phase diagrams of Tb–Fe, Fe–Cr, and Tb–Cr binary systems have been described in detail in the literature [7]. Four intermetallic phases occur in the Tb–Fe system: Tb2Fe17, Tb6Fe23, TbFe3, and TbFe2. All intermetallic phases form peritectically and exist at fixed compositions. Both Tb and Fe do not dissolve any noticeable
⇑ Corresponding author. E-mail address: [email protected] (H.-Y. Zhou). 0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.06.130
amount of the second component. It has been reported that there is a unique binary compound FeCr (r phase) in the Fe–Cr binary system, which forms from the bcc a phase at 820 °C around the mid-composition and decomposes eutectoidally to Fe-rich and Cr-rich bcc phases at 545 °C [8]. No intermetallic phase has been found to exist in the Tb–Cr binary system. Two ternary compounds Tb(Fe,Cr)12 (with ThMn12-type structure) and Tb3(Fe,Cr)29 (with Nd3(Fe,Ti)29-type structure) have been reported by Yang et al. [9,10], which can be derived from the CaCu5-type structure by the replacement of 1/2 and 2/5 of the Tb atoms by a pair of Fe atoms (dumb-bells). Structural data for binary and ternary phases relevant to the present study are summarized in Table 1.
2. Experimental and computational details The Tb–Fe–Cr alloy samples were prepared by arc melting using a non-consumable tungsten electrode and a water-cooled copper tray in pure argon atmosphere. Terbium, iron and chromium with purity higher than 99.9% were used as staring materials. The ingots were turned and remelted several times for better homogeneity. During the process of arc melting there is slight vaporization loss of element Tb, it is solved by compensating 1% Tb addition. The arc-melted buttons were then sealed in silica ampoules under argon for homogenization annealing. The Fe-rich alloys were first annealed at 850 °C for 20 days and then kept at 600 °C for 10 days, while the others were kept at 600 °C for 30 days followed by quenching into icewater. The alloys were characterized by X-ray powder diffraction analysis on a Rigaku D/max 2500 PC X-ray diffractometer (Cu Ka, monochromator). Some representative alloys were analyzed in an S-570 scanning electron microscope (SEM) equipped with energy dispersive X-ray spectroscopy (EDS). In addition, to determine the stable structure of Tb2Fe17 intermetallic compound in this work, its ground-state energy and simulated XRD patterns were investigated by a first-principles study. The first-principles calculations were performed by employing the Vienna ab initio simulation package (VASP) [12] within generalized gradient approximation using the Perdew–Wang 91 exchange correlation function [13]. An energy cutoff of 400 eV was used for the plane-wave basis sets and the k-point spacing smaller than 0.03 Å1 in the reciprocal space was used
199
Y. Zhong et al. / Journal of Alloys and Compounds 541 (2012) 198–203 Table 1 Crystallographic data of the initial components and compounds in the Tb–Fe–Cr ternary system. Phase
Pearson symbol
Space group
Structure type
Lattice parameters (nm)
Reference
a
c
(Tb) TbFe2
hP2 cF24
P63/mmc
Mg Cu2Mg
0.36092 0.74
0.56966
[7] [11]
NbBe3
0.511(2)
2.442(8)
[11]
Mn23Th6
1.2007
Th2Zn17
0.852
1.248
[11]
Th2Ni17 W
0.8474 0.29315
0.8327
[11] [7]
CrFe
0.87995
0.45442
[7]
W
0.2884
Mn12Th
0.8502
Fd3m TbFe3
hR12
R3m Tb6Fe23
cF116
[11]
Fm3m Tb2Fe17
hR19
R3m Tb2Fe17 (aFe)
hP38 cI2
P63/mmc
Im3m FeCr
tP30
P42 =mnm (Cr)
cI2
[7]
Im3m TbFe10Cr2
tI26
0.4769
[9]
I4=mmm
Table 2 Optimized structural parameters, together with DE0 (relative to Th2Zn17-type), of the Th2Zn17-type and Th2Ni17-type structures from first-principles calculations. Structure
Th2Zn17
ðR3mÞ
Th2Ni17 (P63/mmc)
Lattice constants (Å)
Internal atomic positions x
y
z
DE 0 (meV/f.u)
a = 8.261 (8.54) c = 12.227 (12.43)
Tb Fe1 Fe2 Fe3 Fe4
0.0000 0.0000 0.0000 0.0000 0.0069
0.0000 0.0000 0.2952 0.5000 0.5035
0.3444 0.0896 0.0000 0.5000 0.8395
0
a = 8.211 (8.451) c = 8.101 (8.298)
Tb1 Tb2 Fe1 Fe2 Fe3 Fe4
0.0000 0.3333 0.9599 0.0000 0.1683 0.3333
0.0000 0.6667 0.3304 0.5000 0.3367 0.6667
0.2500 0.7500 0.7500 0.0000 0.5106 0.1149
418.9
for all calculations in order to minimize the error from the k-point meshes. The atomic positions, lattice parameters, and cell volume were fully optimized using conjugate-gradient until total energy is converged to with 1.0 105 eV and the forces on all atoms are smaller than 0.01 eV/Å. From all these results, the phase relationships in the Tb–Fe–Cr system were determined.
3. Results and discussion 3.1. Phase analysis The Tb–Fe phase diagram was first proposed by Dariel and Holthuis [14] and later slightly revised by Okamoto et al. [7]. Similar to other Fe–R (R = Dy, Ho, Er, Tm, Lu, and Y) systems, four equilibrium intermetallic phases, Tb2Fe17, Tb6Fe23, TbFe3, and TbFe2, occur in Tb–Fe system. X-ray powder diffraction analysis confirms their
existence in this work, which is in good agreement with previous research. Tb2Fe17 exists in two polymorphic forms: Th2Zn17-type rhombohedral a-Tb2Fe17 and Th2Ni17-type hexagonal b-Tb2Fe17. However, the phase relationship between these two polymorphs is ambiguous and controversial. It was reported that the Th2Ni17-type structure forms in Fe-rich specimens and the Th2Zn17-type structure forms in Tb-rich specimens [14]. Skrabek [15] observed high-temperature hexagonal Th2Ni17-type structure in a splatcooled specimen, while the low-temperature rhombohedral Th2Zn17-type structure was observed in a specimen annealed at 1050 °C and then cooled rapidly. And besides, recent investigation of the Tb–Fe–Ga phase diagram has indicated that the coexistence of hexagonal Th2Ni17-type and rhombohedral Th2Zn17-type structures in the sample with composition of Tb2Fe17 with Th2Zn17-type structure dominates at 500 °C [16]. In present work, first-principles
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Y. Zhong et al. / Journal of Alloys and Compounds 541 (2012) 198–203
Fig. 3. Variation of the lattice parameters of TbFe12xCrx with the content of Cr.
Fig. 1. The observed and calculated XRD patterns of Tb2Fe17 from first-principles calculations. (a) The Th2Ni17-type structure; (b) the Th2Zn17-type structure; (c) the experimental data.
Fig. 2. XRD pattern of the TbFe12xCrx(x = 2.0) sample annealed at 600 °C for a month.
total energy calculations have been used to compare the stability of the two allotropies. The optimized structural parameters, together with the ground-state energies difference (DE0), of the Th2Zn17-type and Th2Ni17-type structures are summarized in Table 2. The optimized structural lattice parameters for the Th2Zn17-type structure are a = 8.261 Å and c = 12.227 Å, which are in good agreement with the experimental data (a = 8.54 Å and c = 12.43 Å) and the corresponding errors are only 3.27% and 1.6%, respectively. The total energy of the Th2Zn17-type structure is about 418.9 meV/f.u lower than that of the Th2Ni17-type structure, indicating that the Th2Zn17-type structure is an energetically
more favorable at ambient conditions. Furthermore, using the previous calculated crystallographic data, we can obtain the calculated XRD patterns of the Th2Zn17-type and Th2Ni17-type structures as depicted in Fig. 1a and b. It is clear that the XRD pattern of the sample with composition of Tb2Fe17 in this work is in excellent agreement with the calculated XRD pattern of the Th2Zn17-type rhombohedral a-Tb2Fe17. Thus, the Th2Zn17-type structure is adopted as the equilibrium structure of Tb2Fe17 phase at 600 °C. It is well known that the pure RFe12 is not stable and the addition of a nonmagnetic element M (M = Al, Si, Ti, V, Cr, Mo, W, Nb, or Ta) is necessary to stabilize the ThMn12 structure and form the RFe12xMx pseudobinary compounds. The inclusion of the M element has a detrimental influence on both magnetic and crystallographic properties of the RFe12xMx pseudobinary compounds [17]. To examine the smallest content of Cr needed to stabilize the TbFe12xCrx compound, samples with the composition of 7.69 at.% Tb, 82.31–71.54 at.% Fe, 10–20.77 at.% Cr have been prepared. It is found that the homogeneity range of the TbFe12xCrx compound extends from about 10.8 to 20 at.% Cr at 600 °C. Fig. 2 presents the XRD pattern of the TbFe12xCrx(x = 2.0) single phase. Yang [10] has reported that a Tb3(Fe,Cr)29 single crystal with the monoclinic Nd3(Fe,Cr)29-type structure is obtained after proper heat treatment. In order to verify the existence of Tb3(Fe,Cr)29 phase at 600 °C, the X-ray powder diffraction analyses of some alloy samples with composition of Tb3Fe29xCrx (x = 3.0, 4.0, 5.0) were conducted. The result shows that the alloy samples consist of two phases, i.e., Tb2Fe17 and (aFe). The compound of Tb3(Fe,Cr)29 does not exist as a stable phase at 600 °C, and therefore is not presented in the isothermal section of the phase diagram of the Tb– Fe–Cr system at 600 °C.
3.2. Solid solubility The homogeneity ranges of the single-phase regions are determined by using phase-disappearing method, lattice parameter method or on the basis of the movement of the XRD pattern of
Y. Zhong et al. / Journal of Alloys and Compounds 541 (2012) 198–203
201
Fig. 4. The isothermal section of the Tb–Fe–Cr ternary system at 600 °C.
Fig. 5. XRD patterns for the samples (a) Tb3Fe57Cr40 (in at.%) located in the FeCr + TbFe12xCrx two-phase region; (b) Tb30Fe68Cr2 located in the TbFe2+TbFe3 two-phase region; (c) Tb20Fe70Cr10 located in the TbFe2+Tb6Fe23 + TbFe12xCrx three-phase region and (d) Tb12Fe74Cr14 located in the Tb2Fe17 + Tb6Fe23 + TbFe12xCrx three-phase region.
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Y. Zhong et al. / Journal of Alloys and Compounds 541 (2012) 198–203
600 °C is constructed in Fig. 4. The presently determined phase relationship indicates that the isothermal section of the Tb–Fe–Cr ternary system at 600 °C consists of 9 single-phase regions (including the solid solution regions of the binary compounds), 16 twophase regions, and 8 three-phase regions. The XRD patterns for some representative samples located in some two-phase or three-phase regions are shown in Fig. 5: Fig. 5a for the sample Tb3Fe57Cr40 (in at.%) located in the FeCr + TbFe12xCrx two-phase region; Fig. 5b for the sample Tb30Fe68Cr2 located in the TbFe2+TbFe3 two-phase region; Fig. 5c for the sample Tb20Fe70Cr10 located in the TbFe2+Tb6Fe23+TbFe12xCrx three-phase region; and Fig. 5d for the sample Tb12Fe74Cr14 located in the Tb2Fe17+Tb6Fe23+TbFe12xCrx three-phase region. For the alloy Tb20Fe70Cr10, its SEM image also shows that the alloy has a clear three-phase microstructure, the dark areas are the phase TbFe12xCrx, the grey areas are Tb6Fe23, and the white areas are TbFe2 (see Fig. 6). In order to further verify these phase relationships and phase composition, EDS analyses were performed for some typical alloys located in the three-phase regions. As displayed in Table 3, we can find that the results of the EDS analysis are in good accord with the conclusions obtained by the X-ray diffraction disappearing-phase method.
Fig. 6. Micrograph of the sample Tb20Fe70Cr10. The dark areas are the phase TbFe12xCrx, the grey areas are Tb6Fe23 and the white areas are TbFe2.
the phase in the samples with different compositions. The maximum solid solubilities of Cr in (aFe), Tb2Fe17, Tb6Fe23, and TbFe2 are about 17, 12.5, 3, and 7 at.% Cr, respectively, while the maximum solid solubility of Fe in (Cr) is about 20 at.% Fe. The homogeneity range of FeCr extends from about 44.5 to 50.5 at.% Cr. The above results are similar to the finding presented in Ref. [7]. Fig. 3 shows the dependences of the lattice parameters a and c on x in TbFe12xCrx. In the single phase regime, the lattice parameters increase linearly with increasing Cr content. The homogeneity range of the single-phase TbFe12xCrx compound is determined to be 1.4 6 x 6 2.6.
4. Conclusions (1) The isothermal section of the Tb–Fe–Cr ternary system at 600 °C has been determined, which consists of 9 singlephase regions, 16 two-phase regions, and 8 three-phase regions. (2) At 600 °C, the existences of five binary compounds and a ternary compound, namely, TbFe2, TbFe3, Tb6Fe23, Tb2Fe17, FeCr, and TbFe12xCrx(1.4 6 x 6 2.6), are confirmed. The XRD patterns and total-energy calculations suggest that Tb2Fe17 crystallizes with the Th2Zn17-type rhombohedral structure in this work. (3) The solid solutions in this ternary system are formed by substitution of Fe by Cr. The maximum solid solubilities of Cr in
3.3. Isothermal section at 600°C By comparing and analyzing the XRD patterns of the presently investigated samples, supplemented with the literature [18–20], the experimental isothermal section of the Tb–Fe–Cr system at
Table 3 XRD and EDS experimental results for some typical alloys in the Tb–Fe–Cr system at 600 °C. Phase regions
Typical alloy
Alloy composition (at.%)
Phase identified by EDS (at.%)
Phase identified by XRD
Tb
Fe
Cr
Tb
Fe
Cr
Phase
1
Tb30Fe25Cr45
30
25
45
0.88 31.63 99.09
19.71 61.56 0.63
79.40 6.81 0.28
(Cr) TbFe2 (Tb)
(Cr) + TbFe2 + (Tb)
2
Tb15Fe50Cr35
15
50
35
31.45 0 8.57
61.78 18.66 71.32
6.77 81.34 20.11
TbFe2 (Cr) TbFe12xCrx
TbFe2 + (Cr) + TbFe12xCrx
3
Tb3Fe52Cr45
3
52
45
1.03 0 6.32
20.17 44.92 72.24
78.80 55.08 21.44
(Cr) FeCr TbFe12xCrx
(Cr) + FeCr + TbFe12xCrx
4
Tb3Fe67Cr30
3
67
30
1.11 0.55 8.35
54.97 82.16 72.19
43.92 17.29 19.46
FeCr (aFe) TbFe12xCrx
FeCr + (aFe) + TbFe12xCrx
5
Tb7Fe88Cr5
7
88
5
1.93 9.11 13.57
92.00 80.15 85.36
6.07 10.74 1.07
(aFe) TbFe12xCrx Tb2Fe17
(aFe) + TbFe12xCrx + Tb2Fe17
6
Tb14Fe76Cr10
14
76
10
12.65 8.16 20.48
75.04 71.82 76.52
12.31 20.02 3.00
Tb2Fe17 TbFe12xCrx Tb6Fe23
Tb2Fe17 + TbFe12xCrx + Tb6Fe23
7
Tb20Fe70Cr10
20
70
10
20.78 34.99 9.21
76.28 57.89 71.14
2.94 7.12 19.65
Tb6Fe23 TbFe2 TbFe12xCrx
Tb6Fe23 + TbFe2 + TbFe12x Crx
8
Tb25Fe71Cr4
25
71
4
33.00 24.27 19.64
60.65 75.21 77.26
6.35 0.52 3.10
TbFe2 TbFe3 Tb6Fe23
TbFe2 + TbFe3 + Tb6Fe23
Y. Zhong et al. / Journal of Alloys and Compounds 541 (2012) 198–203
(aFe), Tb2Fe17, Tb6Fe23, and TbFe2 are about 17, 12.5, 3, and 7 at.% Cr, respectively. The coefficient x of TbFe12xCrx ranges from 1.4 to 2.6.
Acknowledgements This work is supported by the National Natural Science Foundation of China (Nos. 50631040, 50961005, and 50901023), and the Key Program of Natural Science Foundation of Guangxi Province (No. GXNSFD013009). References [1] R. Vert, D. Fruchart, B. Garcia-Landa, D. Gignoux, Y. Amako, J. Alloys Compd. 275–277 (1998) 611–614. [2] C.P. Yang, Y.Z. Wang, B.P. Hu, J.L. Wang, Z.X. Wang, Z.L. Jiang, J. Alloys Compd. 290 (1999) 144–149. [3] P. Qian, N.X. Chen, J. Shen, Solid State Commun. 134 (2005) 771–776. [4] A.G. Kuchin, W. Iwasieczho, J. Alloys Compd. 509 (2011) 6763–6767.
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[5] Y.M. Hao, Y. Zhou, M. Zhou, J. Funct. Mater. 7 (2005) 1045–1047. [6] M. Sorescu, T.H. Xu, F. Pourarian, L. Barreiro, Intermetallics 19 (2011) 644–650. [7] T.B. Massalski, H. Okamoto, P.R. Subramanian, L. Kacprzak, Binary Alloy Phase Diagrams, ASM International, Materials Park, 1990. [8] V.P. Itkin, in: H. Okamoto (Ed.), Phase Diagram of Binary Iron Alloys, ASM International, Materials Park, OH, 1993, pp. 102–129. [9] F.M. Yang, Q.A. Li, R.W. Zhao, J.P. Kuang, F.R. de Boer, J.P. Liu, J. Alloys Compd. 177 (1991) 93–100. [10] C.P. Yang, Y.Z. Wang, G.H. Wu, B.P. Hu, J. Du, X.F. Han, Solid State Commun. 111 (1999) 247–252. [11] P. Villars, A. Prince, H. Okamoto, Handbook of Ternary Alloy Phase Diagrams, 1995, pp. 899-900. [12] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169–11186. [13] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244–13249. [14] M.P. Dariel, J.P. Holthuis, M.R. Pickus, J. Less-Common Met. 45 (1976) 91–101. [15] K.H.J. Buschow, J. Less-Common Met. 11 (1966) 204–208. [16] J.Q. Li, M. Ouyang, D.C. Liu, F.S. Liu, W.Q. Ao, Intermetallics 17 (2009) 733–737. [17] K.H.J. Buschow, J. Magn. Magn. Mater. 100 (1991) 79–89. [18] Q.R. Yao, H.L. Wang, W. Zhan, H.Y. Zhou, S.K. Pan, J. Alloys Compd. 475 (1–2) (2009) 286–288. [19] W. He, X.H. Wang, J.M. He, J.X. Wen, M.H. Yu, L.M. Zeng, J. Alloys Compd. 502 (1) (2010) 87–91. [20] Q.R. Yao, H.Y. Zhou, S.K. Pan, Z.M. Wang, J. Alloys Compd. 509 (5) (2011) 1579– 1581.
Contents lists available at SciVerse ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Phase relationship in the Tb–Fe–Cr ternary system at 600 °C Yan Zhong, Huai-Ying Zhou ⇑, Chao-Hao Hu, Shun-Kang Pan School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin, Guangxi 541004, PR China
a r t i c l e
i n f o
Article history: Received 12 July 2011 Received in revised form 26 June 2012 Accepted 27 June 2012 Available online 9 July 2012 Keywords: Rare earth alloys and compounds Crystal structure Phase diagrams X-ray diffraction
a b s t r a c t The phase relationships in the Tb–Fe–Cr ternary system at 600 °C have been investigated mainly by X-ray diffraction analysis and first-principles density functional theory calculations. The result shows that the isothermal section consists of 9 single-phase regions, 16 two-phase regions and 8 three-phase regions. The compound TbFe12xCrx with the ThMn12-type structure is found to have a broad solubility ranging from x = 1.4 to 2.6. The XRD patterns and total-energy calculations suggest that Tb2Fe17 crystallizes with the Th2Zn17-type rhombohedral structure under our experiment conditions. The solid solutions in this ternary system are formed by the substitution of Fe by Cr. The maximum solid solubilities of Cr in (aFe), Tb2Fe17, Tb6Fe23, and TbFe2 are about 17, 12.5, 3, and 7 at.% Cr, respectively. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Research on permanent magnet materials has led to the discovery of many ternary Fe-rich rare earth intermetallic compounds of the R–Fe–M (R = rare-earth or Yttrium; M = Al, Si, Ti, V, Cr, Nb, Mo, Ta or W) [1–3]. Currently, the R(Fe,M)12, R2(Fe,M)17, and R3(Fe,M)29 compounds have been extensively studied due to their relatively high saturation magnetization and high Curie temperature as well as strong uniaxial anisotropy [4–6]. Experimental studies have verified that the third nonmagnetic element M is necessary to stabilize these compounds and has a strong effect on the magnetic properties. Kuchin et al. [4] have synthesized the Ce2Fe17xMnx(x = 0–2.0) compounds by induction melting and found that the Curie temperature and spontaneous magnetization rise sharply with Mn content. Hao et al. [5] have also observed that a few Cr atoms substituting for Fe atoms can enhance Curie temperature of Tb2Fe17xCrx compounds obviously. To further understand the formation, solubility limit and phase relationship in the R–Fe– M systems, it is certainly worth to investigating the phase diagram of the relevant systems. In this work, the 600 °C isothermal section of the phase diagram of the Tb–Fe–Cr system was determined by combining experimental investigation and first-principles calculation. The phase diagrams of Tb–Fe, Fe–Cr, and Tb–Cr binary systems have been described in detail in the literature [7]. Four intermetallic phases occur in the Tb–Fe system: Tb2Fe17, Tb6Fe23, TbFe3, and TbFe2. All intermetallic phases form peritectically and exist at fixed compositions. Both Tb and Fe do not dissolve any noticeable
⇑ Corresponding author. E-mail address: [email protected] (H.-Y. Zhou). 0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.06.130
amount of the second component. It has been reported that there is a unique binary compound FeCr (r phase) in the Fe–Cr binary system, which forms from the bcc a phase at 820 °C around the mid-composition and decomposes eutectoidally to Fe-rich and Cr-rich bcc phases at 545 °C [8]. No intermetallic phase has been found to exist in the Tb–Cr binary system. Two ternary compounds Tb(Fe,Cr)12 (with ThMn12-type structure) and Tb3(Fe,Cr)29 (with Nd3(Fe,Ti)29-type structure) have been reported by Yang et al. [9,10], which can be derived from the CaCu5-type structure by the replacement of 1/2 and 2/5 of the Tb atoms by a pair of Fe atoms (dumb-bells). Structural data for binary and ternary phases relevant to the present study are summarized in Table 1.
2. Experimental and computational details The Tb–Fe–Cr alloy samples were prepared by arc melting using a non-consumable tungsten electrode and a water-cooled copper tray in pure argon atmosphere. Terbium, iron and chromium with purity higher than 99.9% were used as staring materials. The ingots were turned and remelted several times for better homogeneity. During the process of arc melting there is slight vaporization loss of element Tb, it is solved by compensating 1% Tb addition. The arc-melted buttons were then sealed in silica ampoules under argon for homogenization annealing. The Fe-rich alloys were first annealed at 850 °C for 20 days and then kept at 600 °C for 10 days, while the others were kept at 600 °C for 30 days followed by quenching into icewater. The alloys were characterized by X-ray powder diffraction analysis on a Rigaku D/max 2500 PC X-ray diffractometer (Cu Ka, monochromator). Some representative alloys were analyzed in an S-570 scanning electron microscope (SEM) equipped with energy dispersive X-ray spectroscopy (EDS). In addition, to determine the stable structure of Tb2Fe17 intermetallic compound in this work, its ground-state energy and simulated XRD patterns were investigated by a first-principles study. The first-principles calculations were performed by employing the Vienna ab initio simulation package (VASP) [12] within generalized gradient approximation using the Perdew–Wang 91 exchange correlation function [13]. An energy cutoff of 400 eV was used for the plane-wave basis sets and the k-point spacing smaller than 0.03 Å1 in the reciprocal space was used
199
Y. Zhong et al. / Journal of Alloys and Compounds 541 (2012) 198–203 Table 1 Crystallographic data of the initial components and compounds in the Tb–Fe–Cr ternary system. Phase
Pearson symbol
Space group
Structure type
Lattice parameters (nm)
Reference
a
c
(Tb) TbFe2
hP2 cF24
P63/mmc
Mg Cu2Mg
0.36092 0.74
0.56966
[7] [11]
NbBe3
0.511(2)
2.442(8)
[11]
Mn23Th6
1.2007
Th2Zn17
0.852
1.248
[11]
Th2Ni17 W
0.8474 0.29315
0.8327
[11] [7]
CrFe
0.87995
0.45442
[7]
W
0.2884
Mn12Th
0.8502
Fd3m TbFe3
hR12
R3m Tb6Fe23
cF116
[11]
Fm3m Tb2Fe17
hR19
R3m Tb2Fe17 (aFe)
hP38 cI2
P63/mmc
Im3m FeCr
tP30
P42 =mnm (Cr)
cI2
[7]
Im3m TbFe10Cr2
tI26
0.4769
[9]
I4=mmm
Table 2 Optimized structural parameters, together with DE0 (relative to Th2Zn17-type), of the Th2Zn17-type and Th2Ni17-type structures from first-principles calculations. Structure
Th2Zn17
ðR3mÞ
Th2Ni17 (P63/mmc)
Lattice constants (Å)
Internal atomic positions x
y
z
DE 0 (meV/f.u)
a = 8.261 (8.54) c = 12.227 (12.43)
Tb Fe1 Fe2 Fe3 Fe4
0.0000 0.0000 0.0000 0.0000 0.0069
0.0000 0.0000 0.2952 0.5000 0.5035
0.3444 0.0896 0.0000 0.5000 0.8395
0
a = 8.211 (8.451) c = 8.101 (8.298)
Tb1 Tb2 Fe1 Fe2 Fe3 Fe4
0.0000 0.3333 0.9599 0.0000 0.1683 0.3333
0.0000 0.6667 0.3304 0.5000 0.3367 0.6667
0.2500 0.7500 0.7500 0.0000 0.5106 0.1149
418.9
for all calculations in order to minimize the error from the k-point meshes. The atomic positions, lattice parameters, and cell volume were fully optimized using conjugate-gradient until total energy is converged to with 1.0 105 eV and the forces on all atoms are smaller than 0.01 eV/Å. From all these results, the phase relationships in the Tb–Fe–Cr system were determined.
3. Results and discussion 3.1. Phase analysis The Tb–Fe phase diagram was first proposed by Dariel and Holthuis [14] and later slightly revised by Okamoto et al. [7]. Similar to other Fe–R (R = Dy, Ho, Er, Tm, Lu, and Y) systems, four equilibrium intermetallic phases, Tb2Fe17, Tb6Fe23, TbFe3, and TbFe2, occur in Tb–Fe system. X-ray powder diffraction analysis confirms their
existence in this work, which is in good agreement with previous research. Tb2Fe17 exists in two polymorphic forms: Th2Zn17-type rhombohedral a-Tb2Fe17 and Th2Ni17-type hexagonal b-Tb2Fe17. However, the phase relationship between these two polymorphs is ambiguous and controversial. It was reported that the Th2Ni17-type structure forms in Fe-rich specimens and the Th2Zn17-type structure forms in Tb-rich specimens [14]. Skrabek [15] observed high-temperature hexagonal Th2Ni17-type structure in a splatcooled specimen, while the low-temperature rhombohedral Th2Zn17-type structure was observed in a specimen annealed at 1050 °C and then cooled rapidly. And besides, recent investigation of the Tb–Fe–Ga phase diagram has indicated that the coexistence of hexagonal Th2Ni17-type and rhombohedral Th2Zn17-type structures in the sample with composition of Tb2Fe17 with Th2Zn17-type structure dominates at 500 °C [16]. In present work, first-principles
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Fig. 3. Variation of the lattice parameters of TbFe12xCrx with the content of Cr.
Fig. 1. The observed and calculated XRD patterns of Tb2Fe17 from first-principles calculations. (a) The Th2Ni17-type structure; (b) the Th2Zn17-type structure; (c) the experimental data.
Fig. 2. XRD pattern of the TbFe12xCrx(x = 2.0) sample annealed at 600 °C for a month.
total energy calculations have been used to compare the stability of the two allotropies. The optimized structural parameters, together with the ground-state energies difference (DE0), of the Th2Zn17-type and Th2Ni17-type structures are summarized in Table 2. The optimized structural lattice parameters for the Th2Zn17-type structure are a = 8.261 Å and c = 12.227 Å, which are in good agreement with the experimental data (a = 8.54 Å and c = 12.43 Å) and the corresponding errors are only 3.27% and 1.6%, respectively. The total energy of the Th2Zn17-type structure is about 418.9 meV/f.u lower than that of the Th2Ni17-type structure, indicating that the Th2Zn17-type structure is an energetically
more favorable at ambient conditions. Furthermore, using the previous calculated crystallographic data, we can obtain the calculated XRD patterns of the Th2Zn17-type and Th2Ni17-type structures as depicted in Fig. 1a and b. It is clear that the XRD pattern of the sample with composition of Tb2Fe17 in this work is in excellent agreement with the calculated XRD pattern of the Th2Zn17-type rhombohedral a-Tb2Fe17. Thus, the Th2Zn17-type structure is adopted as the equilibrium structure of Tb2Fe17 phase at 600 °C. It is well known that the pure RFe12 is not stable and the addition of a nonmagnetic element M (M = Al, Si, Ti, V, Cr, Mo, W, Nb, or Ta) is necessary to stabilize the ThMn12 structure and form the RFe12xMx pseudobinary compounds. The inclusion of the M element has a detrimental influence on both magnetic and crystallographic properties of the RFe12xMx pseudobinary compounds [17]. To examine the smallest content of Cr needed to stabilize the TbFe12xCrx compound, samples with the composition of 7.69 at.% Tb, 82.31–71.54 at.% Fe, 10–20.77 at.% Cr have been prepared. It is found that the homogeneity range of the TbFe12xCrx compound extends from about 10.8 to 20 at.% Cr at 600 °C. Fig. 2 presents the XRD pattern of the TbFe12xCrx(x = 2.0) single phase. Yang [10] has reported that a Tb3(Fe,Cr)29 single crystal with the monoclinic Nd3(Fe,Cr)29-type structure is obtained after proper heat treatment. In order to verify the existence of Tb3(Fe,Cr)29 phase at 600 °C, the X-ray powder diffraction analyses of some alloy samples with composition of Tb3Fe29xCrx (x = 3.0, 4.0, 5.0) were conducted. The result shows that the alloy samples consist of two phases, i.e., Tb2Fe17 and (aFe). The compound of Tb3(Fe,Cr)29 does not exist as a stable phase at 600 °C, and therefore is not presented in the isothermal section of the phase diagram of the Tb– Fe–Cr system at 600 °C.
3.2. Solid solubility The homogeneity ranges of the single-phase regions are determined by using phase-disappearing method, lattice parameter method or on the basis of the movement of the XRD pattern of
Y. Zhong et al. / Journal of Alloys and Compounds 541 (2012) 198–203
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Fig. 4. The isothermal section of the Tb–Fe–Cr ternary system at 600 °C.
Fig. 5. XRD patterns for the samples (a) Tb3Fe57Cr40 (in at.%) located in the FeCr + TbFe12xCrx two-phase region; (b) Tb30Fe68Cr2 located in the TbFe2+TbFe3 two-phase region; (c) Tb20Fe70Cr10 located in the TbFe2+Tb6Fe23 + TbFe12xCrx three-phase region and (d) Tb12Fe74Cr14 located in the Tb2Fe17 + Tb6Fe23 + TbFe12xCrx three-phase region.
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600 °C is constructed in Fig. 4. The presently determined phase relationship indicates that the isothermal section of the Tb–Fe–Cr ternary system at 600 °C consists of 9 single-phase regions (including the solid solution regions of the binary compounds), 16 twophase regions, and 8 three-phase regions. The XRD patterns for some representative samples located in some two-phase or three-phase regions are shown in Fig. 5: Fig. 5a for the sample Tb3Fe57Cr40 (in at.%) located in the FeCr + TbFe12xCrx two-phase region; Fig. 5b for the sample Tb30Fe68Cr2 located in the TbFe2+TbFe3 two-phase region; Fig. 5c for the sample Tb20Fe70Cr10 located in the TbFe2+Tb6Fe23+TbFe12xCrx three-phase region; and Fig. 5d for the sample Tb12Fe74Cr14 located in the Tb2Fe17+Tb6Fe23+TbFe12xCrx three-phase region. For the alloy Tb20Fe70Cr10, its SEM image also shows that the alloy has a clear three-phase microstructure, the dark areas are the phase TbFe12xCrx, the grey areas are Tb6Fe23, and the white areas are TbFe2 (see Fig. 6). In order to further verify these phase relationships and phase composition, EDS analyses were performed for some typical alloys located in the three-phase regions. As displayed in Table 3, we can find that the results of the EDS analysis are in good accord with the conclusions obtained by the X-ray diffraction disappearing-phase method.
Fig. 6. Micrograph of the sample Tb20Fe70Cr10. The dark areas are the phase TbFe12xCrx, the grey areas are Tb6Fe23 and the white areas are TbFe2.
the phase in the samples with different compositions. The maximum solid solubilities of Cr in (aFe), Tb2Fe17, Tb6Fe23, and TbFe2 are about 17, 12.5, 3, and 7 at.% Cr, respectively, while the maximum solid solubility of Fe in (Cr) is about 20 at.% Fe. The homogeneity range of FeCr extends from about 44.5 to 50.5 at.% Cr. The above results are similar to the finding presented in Ref. [7]. Fig. 3 shows the dependences of the lattice parameters a and c on x in TbFe12xCrx. In the single phase regime, the lattice parameters increase linearly with increasing Cr content. The homogeneity range of the single-phase TbFe12xCrx compound is determined to be 1.4 6 x 6 2.6.
4. Conclusions (1) The isothermal section of the Tb–Fe–Cr ternary system at 600 °C has been determined, which consists of 9 singlephase regions, 16 two-phase regions, and 8 three-phase regions. (2) At 600 °C, the existences of five binary compounds and a ternary compound, namely, TbFe2, TbFe3, Tb6Fe23, Tb2Fe17, FeCr, and TbFe12xCrx(1.4 6 x 6 2.6), are confirmed. The XRD patterns and total-energy calculations suggest that Tb2Fe17 crystallizes with the Th2Zn17-type rhombohedral structure in this work. (3) The solid solutions in this ternary system are formed by substitution of Fe by Cr. The maximum solid solubilities of Cr in
3.3. Isothermal section at 600°C By comparing and analyzing the XRD patterns of the presently investigated samples, supplemented with the literature [18–20], the experimental isothermal section of the Tb–Fe–Cr system at
Table 3 XRD and EDS experimental results for some typical alloys in the Tb–Fe–Cr system at 600 °C. Phase regions
Typical alloy
Alloy composition (at.%)
Phase identified by EDS (at.%)
Phase identified by XRD
Tb
Fe
Cr
Tb
Fe
Cr
Phase
1
Tb30Fe25Cr45
30
25
45
0.88 31.63 99.09
19.71 61.56 0.63
79.40 6.81 0.28
(Cr) TbFe2 (Tb)
(Cr) + TbFe2 + (Tb)
2
Tb15Fe50Cr35
15
50
35
31.45 0 8.57
61.78 18.66 71.32
6.77 81.34 20.11
TbFe2 (Cr) TbFe12xCrx
TbFe2 + (Cr) + TbFe12xCrx
3
Tb3Fe52Cr45
3
52
45
1.03 0 6.32
20.17 44.92 72.24
78.80 55.08 21.44
(Cr) FeCr TbFe12xCrx
(Cr) + FeCr + TbFe12xCrx
4
Tb3Fe67Cr30
3
67
30
1.11 0.55 8.35
54.97 82.16 72.19
43.92 17.29 19.46
FeCr (aFe) TbFe12xCrx
FeCr + (aFe) + TbFe12xCrx
5
Tb7Fe88Cr5
7
88
5
1.93 9.11 13.57
92.00 80.15 85.36
6.07 10.74 1.07
(aFe) TbFe12xCrx Tb2Fe17
(aFe) + TbFe12xCrx + Tb2Fe17
6
Tb14Fe76Cr10
14
76
10
12.65 8.16 20.48
75.04 71.82 76.52
12.31 20.02 3.00
Tb2Fe17 TbFe12xCrx Tb6Fe23
Tb2Fe17 + TbFe12xCrx + Tb6Fe23
7
Tb20Fe70Cr10
20
70
10
20.78 34.99 9.21
76.28 57.89 71.14
2.94 7.12 19.65
Tb6Fe23 TbFe2 TbFe12xCrx
Tb6Fe23 + TbFe2 + TbFe12x Crx
8
Tb25Fe71Cr4
25
71
4
33.00 24.27 19.64
60.65 75.21 77.26
6.35 0.52 3.10
TbFe2 TbFe3 Tb6Fe23
TbFe2 + TbFe3 + Tb6Fe23
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(aFe), Tb2Fe17, Tb6Fe23, and TbFe2 are about 17, 12.5, 3, and 7 at.% Cr, respectively. The coefficient x of TbFe12xCrx ranges from 1.4 to 2.6.
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