I. INTRODUCTION
The binary compound RFe3 (R=rare-earth metal) usually crystallizes in two closely related structures depending on the heat treatments: a hexagonal CeNi3-type structure (α phase) with space group P63/m m c and a rhombohedral PuNi3-type structure (β phase) with space group R3¯m (Buschow, Reference Buschow1971, Reference Buschow1977; Kirchmayr and Poldy, Reference Kirchmayr and Poldy1978). A unit cell of the PuNi3-type structure consists of 9 f.u. (z=9) with R occupying two nonequivalent Wyckoff sites 3a (R I) and 6c (R II) and the transition atom (T) at the 3b (T I), 6c (T II), and 18h (T III) sites. The RFe3 compound maintains the PuNi3-type structure when Fe is substituted by Ni or Co. Thus, the so-called pseudobinary compounds R(Fe,Ni)3 and R(Fe,Co)3 are formed, and their chemical and physical properties are only slightly different from those of Fe-Ni and Fe-Co binary compounds. In a unit cell of the CeNi3 structure with 6 f.u., R also occupies two nonequivalent Wyckoff sites of 2c (R I) and 4f (R II) and T occupies four nonequivalent sites of 2a (T I), 2b (T II), 2d (T III), and 12k (T IV). Although there is some ambiguity in the literature, it is generally found that the α phase represents a high-temperature modification while the β phase tends to become stable towards lower temperatures. This appears to be related with the degree of disordered substitution in the compounds. In general, substitution with a third component (Al) seems to play a role similar to temperature in establishing structural changes in the pure binary compounds. Considerable influence of rare-earth metal on the magnetic and structural properties of RFe3 compounds was observed when Al was substituted for Fe (Oesterreicher and Pitts, Reference Oesterreicher and Pitts1973; Oesterreicher, Reference Oesterreicher1976; Oesterreicher and Mcneely, Reference Oesterreicher and Mcneely1977a; Burzo, Reference Burzo and Seitabla1982, Reference Burzo1983; Plusa, Reference Plusa1985; Wang et al., Reference Wang, Wu, Jin, Chuang and Li1995; Pfranger and Plusa, Reference Pfranger and Plusa1996). A large substitution of Al for Fe leads to a structural transition of DyFe3 to the CeNi3-type structure at room temperature. Plusa (Reference Plusa1985) reported that the unit-cell parameters of the hexagonal phase did not follow Vegard’s law (Vegard, Reference Vegard1921) since the lattice constants a decreased and c increased with increasing Al substitution. However, the results of Oesterreicher and Mcneely (Reference Oesterreicher and Mcneely1977b) indicated that both the lattice
Figure 1. (Color online) XRD patterns of DyFe3−xAlx: (a) x=0–1.0 and (b) enlarged patterns for x=0.5 and 0.67.
parameters a and c increased with increasing Al. This paper reports the structural transitions caused by Al substitution for Fe.
II. EXPERIMENTAL
Alloys of DyFe3−xAlx (x=0, 0.2, 0.33, 0.4, 0.45, 0.5, 0.67, 0.8, 1.0, 1.1, and 1.2) were prepared by arc melting the raw materials in a water-cooled copper crucible under high-purity argon atmosphere. The purities of the starting materials were 99.95% for Dy, 99.98% for Fe, and 99.9% for Al. The ingots were turned over and remelted several times to ensure homogeneity. As-cast samples used for structural characterization by powder X-ray diffraction (XRD) analysis were prepared directly from the ingots without other heat treatments.
XRD patterns of the as-cast samples were collected at room temperature using a Rigaku D/Max-2500 X-ray diffractometer with Cu K α radiation (45 kV and 250 mA) and a diffracted-beam graphite monochromator. The scan range was from 10° to 120° 2θ with a step size of 0.02° 2θ and a sampling time of 1 s/step.
III. RESULTS AND DISCUSSION
A. Crystalline phase
XRD patterns of the samples with x≥1.0 are depicted in Figure 1. It shows that DyFe3 crystallizes in the PuNi3-type structure. No appreciable change can be observed in the XRD patterns of DyFe3−xAlx compounds with x=0.2, 0.33,
Figure 2. Changes of unit-cell parameters a and c, unit-cell volume V, and average volume per atom V¯ with the composition x for DyFe3−xAlx.
TABLE I. Unit-cell parameters for DyFe3−xAlx.
0.4, and 0.45, indicating the formation of the DyFe3 based solid solution. Alloys with x=0.5 and 0.67 are composed of the PuNi3-type structure and a new phase of CeNi3 type structure, whereas the DyFe3−xAlx alloys with x=0.8 and 1.0 have the CeNi3-type structure. Therefore, the substitution of the third component (Al) for Fe leads to a structure change (from PuNi3- to CeNi3-type) of the pure binary compound. It should be noted that the structure change in DyFe3−xAlx from the PuNi3- to CeNi3-type structure can also be obtained by a heat treatment. Normally, the CeNi3-type structure represents a high-temperature phase, while the PuNi3-type tends to become stable at low temperatures. However, Al substitution for Fe may not be directly comparable with an increase in temperature. It is the CeNi3 (α phase) which is stabilized by a substitution of Al for Fe in DyFe3. Incidentally, the samples with high Al substitutions (i.e., x=1.1 and 1.2) were each found to be a mixture of more than two phases.
Figure 3. (Color online) Projection of 12 layers of rhombus parallel to the a-b plane of the DyFe3 structure.
Figure 4. (Color online) Projection of eight-layer rhombus on the a-b plane of the DyFe2Al structure.
B. Unit-cell parameters
As shown in Figure 2 and Table I, both the a and c unit-cell parameters, unit-cell volume V, and average volume per atom in unit-cell V¯ increase almost linearly with increasing Al concentration. It must be pointed out that the unit-cell parameters of the DyFe3 and DyFe2Al based solid solutions in the two-phase region change linearly with the compositions of the alloys, which are different from usual two-phase equilibrium. Normally, the unit-cell parameters of each phase remain unchanged in a two-phase equilibrium. However, in the two-phase DyFe3−xAlx system, the unit-cell parameters change linearly with the composition.
C. Crystal structure
DyFe3 (Dariel and Erez, Reference Dariel and Erez1970) crystallizes in the rhombohedral PuNi3-type structure with space group R3¯m and unit-cell parameters of a=5.1203(8) and c=24.521(3) Å. The formula unit per unit cell is Z=9; i.e., there are 9 Dy and
Figure 5. (Color online) Experimental and refined XRD patterns for DyFe2.67Al0.33.
TABLE II. Structure parameters for DyFe3−xAlx with x=0, 0.2, 0.33, 0.4, and 0.45.
27 Fe atoms in a unit cell. The 9 Dy atoms occupy two Wyckoff sites: 3a (0, 0, 0) and 6c (0,0,z∼1/6); 27 Fe atoms occupy three sites: 3b (0, 0, 1/2), 6c (0,0,z∼1/3), and 18h (x∼1/2, y=x¯∼1/2, z∼1/12). The crystal structure of DyFe3 can be considered to be built up by 12 layers of rhombuses stacking along the c axis (see Figure 3), and the four sides of each rhombus have the same length of 5.1203(8) Å.
DyFe2Al (Oesterreicher and Mcneely, Reference Oesterreicher and Mcneely1977b) has the hexagonal CeNi3-type structure with space group P63/m m c and unit-cell parameters of a=5.2183(4) and c=16.732(1) Å. The formula unit per unit cell is Z=6; i.e., there are 6 Dy+12 Fe+6 Al atoms in a unit cell. The 6 Dy atoms occupy two Wyckoff sites: 2c (1/3, 2/3, 1/4) and 4f (1/3, 2/3, z∼0); 18(Fe, Al) atoms occupy four sites: 2a (0, 0, 0), 2b (0, 0, 1/4), 2d (1/3, 2/3, 3/4), and 12k (x∼5/6, y=2x∼2/3, z∼1/8). The stacking period of this compound is an eight-layer period along the z axis. The layer structures of the eight-layer rhombus parallel to the a-b plane are shown in Figure 4.
In order to determine the correct positions of the Al atoms in DyFe3−xAlx for both PuNi3- and CeNi3-type structures, the XRD intensities with Al at different Wyckoff sites were calculated. Taking DyFe2Al, for example, three forms of occupations for the six Al atoms were calculated. The first one was carried out corresponding to the statistical distribution of Fe and Al at the 12k site and Fe solely occupying the 2a, 2b, and 2d sites (ordering 1); the second was a complete statistical distribution of Fe and Al at transition metal sites (ordering 2); and the third was set as 6 Al atoms at three 2a, 2b, and 2d sites and Fe on the 12k site (ordering 3). The intensity calculation for ordering 1 shows a good agreement with the experimental results, while orderings 2 and 3 agree less well with the experimental results, which is consistent with that reported by Oesterreicher and Mcneely (Reference Oesterreicher and Mcneely1977b). The calculated intensities of the compound DyFe3−xAlx with x=0.8 are in good agreement with the experimental results with Fe and Al occupying the 12k sites and Fe solely at the 2a, 2b, and 2d sites. For DyFe3−xAlx with x=0.2, 0.33, 0.4, and 0.45, the calculation for statistical distributions of Fe and Al on the 18h site and Fe solely occupying the 3b and 6c sites agrees well with the experimental results.
The crystal structure of DyFe3−xAlx (x=0.2, 0.33, 0.4, and 0.45), with Al occupying the 18h site, uses the atomic positions of PuNi3 (Cromer and Olsen, Reference Cromer and Olsen1959) as initial parameters and was refined using the pseudo-Voigt profile function and the Rietveld method (Rietveld, Reference Rietveld1967, Reference Rietveld1969) using the program FULLPROF. The observed and calculated residuals of the XRD patterns of DyFe3−xAlx with x=0.33 are shown in Figure 5 as an example. The Rietveld refinement results are listed in Table II. The R p values are relatively high (see Table II), and this may be owing to the as-cast samples having asymmetric peak shapes and strong background intensities.
DyFe3−xAlx (x=0.8 and 1.0), with the Al atoms occupying the 12k site and using atomic positions of Oesterreicher and Mcneely (Reference Oesterreicher and Mcneely1977b) as initial parameters, was also refined using the Rietveld method. The Rietveld refinement results are listed in Table III.
The maximum number of the substituted Al atoms is 6 in each unit cell of the CeNi3-type structure. In other words, only half of the 12 Fe atoms at the 12k site are replaced by the Al atoms. Multiphase will be formed if the Al atoms exceed 6.
D. Essential of two-phase region
As shown in Figure 6, all the DyFe3−xAlx compounds have three stacking layers with different atoms parallel to the a-b plane of a unit cell: (A) 2Dy+Fe, (B) 3 (Fe,Al), and (C) Dy+2 Fe for DyFe3 and DyFe2Al. Furthermore, the stack order of both structures is the same, i.e., 2Dy+Fe---3(Fe,Al)---Dy+2Fe---3(Fe,Al)---2Dy+Fe⋯. As shown in Figures 3 and 4, the orientation of atom arrangement for each stacking layer is different. There are three
TABLE III. Structure parameters for DyFe3−xAlx with x=0.8 and 1.0.
Figure 6. (Color online) Three stacking layers parallel to the a-b plane of DyFe3−xAlx.
TABLE IV. Refined results for DyFe2.33Al0.67 alloy with both CeNi3 and PuNi3 phases.
kinds of orientations for each layer: A(1) A(2) A(3), B(1) B(2) B(3), and C(1) C(2) C(3) (see Figure 6). By translating the atoms along the a-b plane, three orientations can coincide in the same stacking layer. The rearrangement between the layers formed two different structures.
According to the diffraction data of the DyFe2.33Al0.67 alloy, the XRD pattern of the alloy has been refined with nominal composition x=0.67. In order to reduce the number of the refinement parameters, we fixed the temperature factors B according to those for the single-phase compounds. Using atomic positions of DyFe2.55Al0.45 and DyFe2.2Al0.8 as initial parameters of the two phases, we have refined the occupancies of Al on the 18h and 12k sites. The results are listed in Table IV. Finally, we obtained the values of x=0.580 and 0.588 for the PuNi3- and CeNi3-type structures, respectively. Since the difference between the refined results of these two phases is small, the compositions of two phases are practically the same. This is in contrast to the composition of normally equilibrated two phases in a two-phase region. We conclude that these two phases in the two-phase region have the same composition but different stacking arrangements.
IV. CONCLUSION
The structural behavior and phase relationships of DyFe3−xAlx alloys have been studied. XRD results show that DyFe3 based solid solutions (x≤0.45) crystallize in the rhombohedral PuNi3-type structure and DyFe2Al based solid solutions (0.8≤x<1.0) have a hexagonal CeNi3-type structure. Both structures consist of the same atom arrangements in each layer and can be achieved by a shift of the atoms parallel to the a-b plane. So the changes in the crystal structure involve stacking variations along the c axis. For the 0.45<x<0.8 case, both structures coexist in the two-phase region and the unit-cell parameters increase linearly with increasing Al concentration. For DyFe3 based solid solutions, the calculated results with Dy at the 3a and 6c sites, statistical distribution of Fe and Al at the 18h site, and Fe solely occupying the 3b and 6c sites agree well with the experimental results. For DyFe2Al based solid solutions, the calculated intensities agree with the experimental results with the Dy at the 2c and 4f sites, Fe and Al disordering at the 12k site, and Fe at the 2a, 2b, and 2d sites. The refinement results of two-phase region show that it does not follow the phase equilibrium lever rule. The two phases in the two-phase region are formed by the same composition but different stacking arrangements, so it leads to the unit-cell parameters that change linearly with the compositions of the alloys.
ACKNOWLEDGMENTS
This work was supported by the National Basic Research Program of China (Grant Nos. 2006CB601101 and 2006CB605101) and by the National Natural Science Foundation of China (Grant No. 50631040).
