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Homogeneity range, crystal structure and magnetic properties of the ThMn12-type compounds Gd1−nNdn(Fe,Mo)12 (n=0–1.0)
Journal of Alloys and Compounds 316 (2001) 299–308
L
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Homogeneity range, crystal structure and magnetic properties of the ThMn 12 -type compounds Gd 12n Nd n (Fe,Mo) 12 (n50–1.0) ¨ M. Zinkevich*, N. Mattern, A. Handstein, B. Gebel, I. Bacher ¨ Festkorper¨ Institut f ur und Werkstofforschung Dresden, Postfach 27 00 16, D-01171 Dresden, Germany Received 8 November 2000; accepted 30 November 2000
Abstract The existence range, crystal structure and magnetic properties of the Gd 12n Ndn (Fe,Mo) 12 compound series (n50–1) have been studied by electron probe X-ray microanalysis, X-ray diffraction followed by Rietveld refinement, and magnetization measurements. It has been found that the tetragonal ThMn 12 -type structure is formed for Mo concentrations from 8.7 to 28.7 at.% (n50) and from 6.4 to 23.4 at.% (n51.0). The concentration of molybdenum at the borders of the homogeneity range linearly decreases with n. The structure evolution of Gd 12n Nd n (Fe,Mo) 12 upon substitution of Nd for Gd is determined by two competitive factors: the lanthanide contraction with increasing atomic number and the charge transfer effect, so that the ratio of the unit cell parameters c /a decreases. The saturation magnetization of Gd 12n Nd n (Fe,Mo) 12 with an average Mo content of 19.160.7 at.% increases with n, the Curie temperature being about 25 K higher between n¯0.2 and n¯0.8 compared to the values for n50 and n51. At the same time, the Curie temperature at the Fe-rich border of homogeneity range continuously decreases with increasing Nd concentration. 2001 Elsevier Science B.V. All rights reserved. Keywords: Magnetically ordered materials; Rare earth alloys and compounds; Crystal structure; X-ray diffraction; Magnetization
1. Introduction Ternary rare-earth iron intermetallic compounds R(Fe,M) 12 with M5Al, Ga, Si, Ti, V, Nb, Mo, W, or Re, where R5rare earth element, crystallizing in the structure type of ThMn 12 (tetragonal, space group I4 /mmm) have been widely investigated during the past 10 years since their interstitial derivatives R(Fe,M) 12 N y exhibit excellent intrinsic magnetic properties to produce permanent-magnet materials [1–6]. Among the R(Fe,M) 12 or 1:12 compounds, much attention has been given to R(Fe,Mo) 12 since these intermetallics form easier than other compounds and possess an appreciable homogeneity range [7–9]. The largest saturation magnetization has been achieved so far on Nd(Fe,Mo) 12 , whereas the highest Curie temperature was detected in Gd-based compounds [2,4,7]. Therefore, the authors have suggested that a quaternary compound containing both the Nd and Gd atoms in the lattice could have optimal characteristics at a certain composition. The crystal structure and magnetic properties of Gd(Fe,Mo) 12 within the entire homogeneity range has been recently investigated [9,10]. Among the quaternary *Corresponding author. E-mail address: [email protected] (M. Zinkevich).
Mo-based 1:12 compounds the crystallographic and magnetic properties have been previously studied only for Y 12n Dy n Fe 10.5 Mo 1.5 [11] and Nd 12n Dy n Fe 11 Mo [12]. The present work reports the existence range, structural and magnetic parameters of Gd 12n Ndn (Fe,Mo) 12 .
2. Experimental Gd 12n Nd n (Fe,Mo) 12 alloys (n50–1.0) were prepared as three series with nominal Mo concentrations of 8, 20 and 32 at.%, respectively. In the first and third series, the specified amount of the stabilizing element was chosen to obtain non single-phase alloys and thus, to determine the border of the homogeneity range of the ThMn 12 -type phase regarding the Mo concentration at different n values. In contrast, alloys of the second series should consist mainly of the ThMn 12 -type phase. Ingots of alloys were melted from 99.9% Fe and 99.99% Gd, Nd and Mo (Alfa Aesar) in an argon arc furnace, using a non-consumable tungsten electrode on a water-cooled copper hearth. The alloys were remelted four times, the ingot was inverted after each melt to promote mixing. The mass of each ingot was about 10 g. An additional amount (1 wt.%) of rare earth elements was added to compensate their loss during preparation.
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 00 )01500-0
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The ingots were wrapped in tantalum foil, annealed at 11008C for 144 h in sealed quartz ampoules under 0.15 bar purified Ar gas and then quenched in water. A part of each ingot was prepared for the metallographical examination by polishing the resin-mounted specimens with diamond pastes. The actual chemical composition of the alloys as well as that of the ThMn 12 -type phase were measured by electron probe X-ray microanalysis (EPMA) using wavelength-dispersive X-ray (WDX) spectroscopy (SEMQ, Applied Research, USA) with the correction program LOVSCOTT, employing the pure metals as standard materials. The characteristic wavelengths of FeKa, MoLa, NdLa, and GdLa were detected to determine the concentration of elements using an acceleration voltage of 20 kV. The area of the analyzing window on the specimen surface was varied from 131 mm 2 (analysis of individual phases) to 1003100 mm 2 to obtain the average chemical composition of the non single-phase alloys. The standard deviations of the element concentration were calculated from three to five independent measurements, moving a probe each time to the new position. X-ray diffraction analysis was conducted with a Phillips PW1820 Bragg–Brentano diffractometer operating at a voltage of 40 kV and a current of 40 mA (CoKa radiation), equipped with secondary monochromator and a sample spinner. The powders with a particle size of #100 mm were prepared from ingots using a hard metal mortar and pestle as well as a sieve. For the phase identification the X-ray powder patterns were recorded in a 2u range between 5 and 1208, a step size of 0.058, and a counting time of 3 s. Assignment of the particular phases to the diffraction maxima was performed with X’PERT software package (Phillips Analytical, Almelo, The Netherlands), which uses a database of the International Center for Diffraction Data (ICDD). Precise lattice parameters a and c of the tetragonal unit cell were obtained measuring the individual (550) /(710) and (004) reflections in a 2u range between 93 and 1108, a step size of 0.018, and a counting time of 25 s employing an internal standard of pure Si. For quantitative refinement of the atom positions and occupancies, full-profile Rietveld refinements of the X-ray diffraction patterns recorded in a 2u range between 15 and 1308, a step size of 0.038, and a counting time of 14 s were carried out using Phillips X’PERT PLUS software. For the investigation of magnetic properties small pieces (10 . . . .50 mg) of the annealed ingots were employed. The thermomagnetic analysis was made using a SQUID magnetometer (MPMS-5S, Quantum Design) from 5 to 340 K and a vibrating sample magnetometer operating at a frequency of 29 Hz (IFW Dresden) from 300 to 820 K in a field of m0 H 5 0.1 T. The Curie temperatures were derived by extrapolating the steepest part of the slope of the M(T ) curve to M50. The magnetization curves were measured with the SQUID magnetometer from 0 to 5 T at 10 K. The values of saturation magnetization were obtained by extrapolation of the M vs. 1 /H curves to 1 /H50.
3. Results and discussion
3.1. Existence range Table 1 presents the elemental chemical composition and phase constitution of investigated samples Nd–Gd– Fe–Mo, where a symbol in square brackets means the atomic concentration of the respective element in the alloy. Each specimen is identified with its series number (i.e. I, II or III) and a serial number. The results of the phase analysis are those combined from X-ray diffraction and EPMA experiments. The principal impurity phases in the series I and III were (Fe), which stands for a solid solution of Mo in the bcc-Fe and Fe 3 Mo 2 , respectively, whereas the samples of the series II were almost single-phase (the sum of additional phases was ,5 wt.%). This is in agreement with the idea employed in alloy preparation, so that the series I and III are outside, and the series II is inside the homogeneity region of the ThMn 12 -type phase with respect to Mo content. All other impurity phases indicated in Table 1 present only in trace amounts. The chemical composition of the 1:12 phase in the alloy series under study as determined by EPMA and Rietveld refinement is given in Table 2. The outline of a homogeneity region of the ThMn 12 -type phase Gd 12n Nd n (Fe,Mo) 12 is represented in Fig. 1. A range of the Mo concentrations providing the stability of 1:12 phase is wider for Gd-rich compounds, being shifted, however, to the higher values. The concentration of molybdenum at the Fe- and Mo-rich borders of homogeneity range increases linearly by |2 and |5 at.%, respectively, from n51 to n50. The existence range is related to the Gibbs energy functions of the individual phases in equilibrium, which are the thermodynamic origin of the phase diagrams. The crystal structure of ThMn 12 -type contains four atomic positions in the asymmetric unit: 2a, 8f, 8j and 8i. Taking into account that Mo atoms can only occupy the 8i crystallographic site and rare-earth atoms are expected in 2a positions [3,9], the Gibbs energy of (Gd,Nd)(Fe,Mo) 12 phase can be expressed in terms of the generalized sublattice formalism [13,14] G 1:12 5 y Fe y Gd GGd:Fe:Fe 1 y Mo y Gd GGd:Fe:Mo 1 y Fe y Nd GNd:Fe:Fe 1 y Mo y Nd GNd:Fe:Mo 1 1 8RT [y Fe ln ( y Fe ) 1 y Mo ln ( y Mo )] 1 2RT [y Gd ln ( y Gd ) 1 y Nd ln ( y Nd )] 1 y Fe y Mo y Gd 0 LGd:Fe:Fe,Mo 1 1 y Fe y Mo y Nd 0 LNd:Fe:Fe,Mo 1 y Gd y Nd y Fe 0 LGd,Nd:Fe:Fe 0
1 y Gd y Nd y Mo LGd,Nd:Fe:Mo
(1)
where y i are the site fractions of the constituents on each sublattice, GGd:Fe:Fe and GNd:Fe:Fe are the Gibbs energy of the hypothetical compounds GdFe 12 and NdFe 12 , respec-
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301
Table 1 Chemical composition and phase constitution of Gd 12n Nd n (Fe,Mo) 12 ID
Phase constitution a
Elemental composition of alloy (at.%)
I.1 I.2 I.3 I.4 I.5 I.6 I.7 II.1 II.2 II.3 II.4 II.5 II.6 II.7 III.1 III.2 III.3 III.4 III.5 III.6 III.7
[Fe]
[Gd]
[Mo]
[Nd]
Major
Impurity phases
84.760.3 84.760.3 85.060.5 84.560.8 84.860.1 85.060.3 85.661.0 72.960.5 73.460.4 74.360.4 74.660.4 73.060.3 75.560.3 72.661.0 63.161.0 60.060.9 63.160.8 62.161.1 64.660.3 61.960.7 61.060.8
0.0760.06 1.5660.05 2.260.3 3.860.4 4.8760.06 5.9760.06 9.460.5 #0.1 1.5060.07 2.6260.11 3.860.2 5.1460.11 5.760.3 8.560.5 #0.1 1.7860.05 2.860.3 3.960.4 5.560.2 6.360.4 9.360.3
6.460.2 6.960.2 7.3360.05 7.660.4 7.8760.15 7.560.3 5.060.5 18.660.3 19.060.8 17.960.6 17.360.3 19.060.3 17.460.1 18.960.3 30.760.8 31.860.6 29.461.3 29.361.3 27.460.5 30.461.1 29.760.6
8.9460.13 6.8060.07 5.560.3 4.260.2 2.560.1 1.5360.06 0 8.560.3 6.160.4 5.1260.13 4.360.3 2.960.2 1.460.1 0 6.260.3 6.460.3 4.760.6 4.860.5 2.5660.11 1.560.2 0
1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12
(Fe), 2:17 (Fe), 2:17 (Fe), 2:17 (Fe), 2:17, Fe 2 (Gd,Nd) (Fe), 2:17 (Fe), 2:17 2:17 Fe 3 Mo 2 , Fe 2 Mo, Nd Fe 3 Mo 2 Fe 3 Mo 2 (Mo), Fe 3 Mo 2 Fe 3 Mo 2 – Fe 2 Gd, Fe 23 Gd 6 Fe 3 Mo 2 , Nd, FeMo Fe 3 Mo 2 , Nd Fe 3 Mo 2 , Fe 2 Mo, Nd Fe 3 Mo 2, d(Gd,Nd) Gd, Fe 3 Mo 2 Gd, (Mo), Fe 3 Mo 2 (Mo), Fe 2 Gd
a
1:12 stands for ThMn 12 -type phase, 2:17 refers to the (Gd,Nd) 2 (Fe,Mo) 17 compounds with Th 2 Zn 17 type of structure; (Fe) and (Mo) are symbols for the bcc solid solutions based on Fe and Mo, respectively; d (Gd,Nd) stands for the ordered Sm-type phase.
tively, GGd:Fe:Mo and GNd:Fe:Mo correspond to the Gibbs energy of phases, where the 8i sublattice is fully filled with Mo atoms, R equals the gas constant, and T is the absolute temperature. 0 LGd:Fe:Fe,Mo and 0 LNd:Fe:Fe,Mo are the interaction parameters of Fe and Mo atoms in the 8i sublattice when the 2a site is filled with Gd and Nd atoms,
0
LGd,Nd:Fe:Fe and 0 LGd,Nd:Fe:Mo are the interaction parameters of Gd and Nd atoms in the 2a sublattice when the 8i site is filled with Fe and Mo atoms, respectively. A free energy diagram of the (Gd,Nd)(Fe,Mo) 12 system, which is in qualitative agreement with the homogeneity region plotted in Fig. 1 is shown in Fig. 2. The curves are
Table 2 Homogeneity range, crystallographic and magnetic properties of the ThMn 12 -type compounds Gd 12n Nd n (Fe,Mo) 12 ; [Mo] is the concentration of molybdenum in compounds; a and c are lattice constants; T C is the Curie temperature and MS is the saturation magnetization at 10 K expressed in Am 2 / kg ID
n
[Mo] (at.%)
a (nm)
c (nm)
V (nm 3 )
T C (K)
MS
I.1 I.2 I.3 I.4 I.5 I.6 I.7 II.1 II.2 II.3 II.4 II.5 II.6 II.7 III.1 III.2 III.3 III.4 III.5 III.6 III.7
1.0 0.81 0.71 0.50 0.34 0.20 0.0 1.0 0.80 0.66 0.52 0.36 0.20 0.0 1.0 0.78 0.62 0.55 0.32 0.19 0.0
6.460.2 6.960.2 7.3360.05 7.361.0 7.8760.15 7.560.3 8.761.0 18.660.3 19.060.8 20.061.0 18.160.8 19.060.7 19.860.5 18.960.3 23.460.8 24.760.2 24.360.7 26.460.4 27.060.8 28.260.1 28.761.0
0.85815(9) 0.85736(2) 0.85691(6) 0.85609(1) 0.85551(5) 0.85493(5) 0.85442(5) 0.86221(5) 0.86122(2) 0.86068(4) 0.85987(1) 0.85967(1) 0.85944(3) 0.85916(2) 0.86391(4) 0.86296(6) 0.86284(3) 0.86287(7) 0.86295(3) 0.86355(1) 0.86358(5)
0.47795(4) 0.47793(1) 0.47800(1) 0.47806(1) 0.47809(1) 0.47812(1) 0.47865(6) 0.48176(1) 0.48135(2) 0.48132(2) 0.48107(5) 0.48125(2) 0.48148(1) 0.48190(1) 0.48332(1) 0.48379(7) 0.48412(4) 0.48460(3) 0.48505(4) 0.48596(3) 0.48653(6)
0.35197(9) 0.35131(2) 0.35099(6) 0.35037(1) 0.34991(4) 0.34947(5) 0.34942(6) 0.35814(5) 0.35702(3) 0.35654(5) 0.35569(4) 0.35566(2) 0.35564(3) 0.35572(3) 0.36072(3) 0.36027(9) 0.36042(5) 0.36080(8) 0.36121(6) 0.36239(2) 0.36284(9)
496611 – – 51365 – 52465 – 317610 34165 34366 359610 342610 343610 322610 – – – – – – –
– – – – – – – 98.6 84.2 79.5 79.3 62.5 51.7 42.0 – – – – – – –
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Fig. 1. Outline of a homogeneity region of the 1:12 compound in the system Gd 12n Nd n (Fe,Mo) 12 .
Figs. 3–5. The number near each data point indicates the concentration of dissolved Mo (Table 2). The numerical values of a, c and V are given in Table 2. Fig. 3 represents the evolution of the lattice constants at Fe-rich border of the homogeneity range (series I) with increasing fraction of Nd atoms at 2a crystallographic site. The lattice parameter a increases almost linearly with n as could be expected since the ionic radius of Nd is greater than that of Gd due to the lanthanide contraction with increasing atomic number. However, the parameter c changes in the opposite direction, mostly between n50 and n50.2 and hardly varies at all in the range 0.2,n#1.0 (Fig. 3a). The possible misinterpretation of the concentration dependence of the unit cell constant c due to the different Mo content in alloys can be ruled out, as there is no correlation between the percentage of Mo within the series I and the value of lattice parameter c. An exception is the sample I.7 (n50), where the Mo concentration is about 1.5 at.%
calculated according to Eq. (1) with GNd:Fe:Fe ,GGd:Fe:Fe , GNd:Fe:Mo .GGd:Fe:Mo , and 0 LGd:Fe:Fe,Mo 5 0 LNd:Fe:Fe,Mo 50. Using the common tangent construction it is easy to demonstrate that the homogeneity range of Gd(Fe,Mo) 12 will be shifted towards higher Mo contents relative to Nd(Fe,Mo) 12 (Fig. 2). It is thus possible to conclude that Nd-rich compounds are more stable than Gd-rich ones at low Mo concentrations, whereas the opposite is true at high Mo contents. Furthermore, the Nd and Gd atoms should form a nearly ideal solution in the 2a sublattice (i.e. both the interaction parameters 0 LGd,Nd:Fe:Fe and 0 LGd,Nd:Fe:Mo are zero) as suggested by the linearly changing borders of the homogeneity range for the intermediate compositions.
3.2. Crystal structure The unit cell parameters a, c and the unit cell volume V of Gd 12n Nd n (Fe,Mo) 12 compounds are plotted versus n in
Fig. 2. Schematic free energy diagram of the (Gd,Nd)(Fe,Mo) 12 system vs. site fraction of Mo in 8i crystallographic site.
Fig. 3. Unit cell parameters of Gd 12n Nd n (Fe,Mo) 12 (series I). The number near each data point indicates a concentration of dissolved Mo.
M. Zinkevich et al. / Journal of Alloys and Compounds 316 (2001) 299 – 308
303
Fig. 4. Unit cell parameters of Gd 12n Nd n (Fe,Mo) 12 (series II). The number near each data point indicates a concentration of dissolved Mo.
Fig. 5. Unit cell parameters of Gd 12n Nd n (Fe,Mo) 12 (series III). The number near each data point indicates a concentration of dissolved Mo.
higher than the mean value of all other samples of series I. However, the results of Yang et al. [7], which are plotted in Fig. 3 for comparison suggest that an unusually high value of the parameter c at n50 is not only due to the greater Mo content. Furthermore, one can see that the unit cell constant c of GdFe 11.2 Mo 0.8 is higher than the corresponding parameter of NdFe 11.2 Mo 0.8 , whereas it takes an intermediate values in the Gd 12n Nd n (Fe,Mo) 12 (0,n,1) compounds of series I. The unit cell volume of series I shows the concentration dependence on n to be similar to that of the lattice parameter a (compare Fig. 3a and 3b), while only very little increase is observed between n50 and n50.2. This is due to the anomalously high parameter c. The c /a ratio, however, decreases continuously with n (Fig. 3b). The values of the unit cell volume at n50 and n51 are in very good agreement with those in [7]. The composition dependence of the unit cell parameters of the series II is more complex (Fig. 4). On the curve
corresponding to the parameter a, two straight lines with different slopes intersecting at n¯0.5 can be isolated, whereas the parameter c shows a minimum at this composition (Fig. 4a). Note that the lattice constant a steadily increases with n while the values of the lattice constant c at n50 and n51 are almost equal. The enhancement of both the lattice constants at n50.66 resulting in a slight deviation from the linear dependence is perhaps due to the higher Mo content in the sample. Also, the sharp minimum of the parameter c at n¯0.5 could be due to a somewhat lower Mo concentration with respect to the mean value. These deviations do not however, change the overall picture. The observed behaviour, on the one hand, can indicate that upon increasing the Mo concentration in Gd 12n Nd n (Fe,Mo) 12 the structure of the Gd-rich phase, which exists at n,0.5 differs from that of the Nd-rich phase, which is formed at n.0.5, whereas at n50.5 these two phases become indistinguishable. On the other hand, the composition n50.5 can be considered as a critical
304
M. Zinkevich et al. / Journal of Alloys and Compounds 316 (2001) 299 – 308
point where the lattice expansion due to the larger size of the Nd ion is compensated by the contraction owing to another effect (see below). These two possible explanations are not necessarily contradictory. The opposite composition dependence of the unit cell parameters a and c in the range n,0.5 leads to somewhat unexpected behaviour of the unit cell volume, so that it remains constant in the Gd-rich region (Fig. 4b). In spite of this anomaly, the c /a ratio decreases monotonously with n similarly to that of series I. Within the series III (Mo-rich border of the homogeneity range), the compositional dependence of the unit cell parameters on Nd concentration is superimposed with the obvious lattice expansion due to higher Mo content in Gd-rich samples (Fig. 5). The Nd-rich region (n$0.62) is characterized by an increase of parameter a with n, whereas for the Gd-rich compounds (n#0.19) a slight decrease is observed. In the intermediate composition range the unit cell parameter a is approximately constant, although there is a weak minimum at n50.62 (Fig. 5a). Note, that the corresponding value at n50 is only a little smaller than that at n51, while it becomes much lower in the middle. The lattice parameter c as well as the c /a ratio decrease continuously with n (Fig. 5). At the same time, there is a minimum in the compositional dependences of the unit cell volume, which is to be attributed to the compensation of the lattice shrinking with increasing fraction of Gd by the enlargement of the unit cell because of the growing Mo content (Fig. 5b). In general, there are two regularities, which control the structure of 1:12 phase Gd 12n Nd n (Fe,Mo) 12 in alloys of the series I–III: • the decrease of the lattice parameter c with increasing Nd concentration, whereas the lattice parameter a simultaneously increases; • the non-monotonous concentration dependence of the unit cell parameters throughout the whole composition range. The anisotropy in change of the lattice parameters a and c of the ThMn 12 -type structure R(Fe,M) 12 along the rareearth series (R5Ce . . . .Lu) is known from the literature [2,4,7,12,15]. However, only a little attention has been paid to this matter. To understand the somewhat surprising behaviour of the unit cell parameters, Rietveld refinements of the powder diffraction patterns of the series II samples, which contain the largest amount of the 1:12 phase, has been done. The results are given in Table 3 and Figs. 6 and 7. Note, that it was not possible to refine the occupancy in 2a site, since the X-ray scattering factors of Nd and Gd are only a little different. The common observation for all samples is that 8f and 8j crystallographic sites are only partially filled with Fe atoms as it has been also found previously for ThMn 12 -type phases Gd 11m Fe 122p2q Mo p h q (h5vacancy) [9]. The corresponding occupancies vary
Table 3 Refined structure parameters of the ThMn 12 -type compounds Gd 12n Nd n (Fe,Mo) 12 with an average Mo content of 19.160.7 at.% (series II). For the definition of residuals see [16] Atom
Site
y
z
Residuals (%) R exp : 4.5 1.000 0.000000 0.95(2) 0.250000 0.92(2) 0.2784(3) 0.32(3) 0.3600(1) 0.68(3) 0.3600(1)
0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.2 (n50.80) Residuals (%) R p : 4.8 R wp : 6.1 R exp : 4.8 Nd 2a 0.80 0.000000 Gd 2a 0.20 0.000000 Fe 8f 0.98(2) 0.250000 Fe 8j 0.95(2) 0.2764(3) Fe 8i 0.29(3) 0.3600(2) Mo 8i 0.71(3) 0.3600(2)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.3 (n50.66) Residuals (%) R p : 3.9 R wp : 5.0 R exp : 4.4 Nd 2a 0.66 0.000000 Gd 2a 0.34 0.000000 Fe 8f 0.95(2) 0.250000 Fe 8j 0.95(2) 0.2764(3) Fe 8i 0.33(3) 0.3601(2) Mo 8i 0.67(3) 0.3601(2)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.4 (n50.52) Residuals (%) R p : 4.7 R wp : 6.1 R exp : 4.1 Nd 2a 0.52 0.000000 Gd 2a 0.48 0.000000 Fe 8f 0.95(2) 0.250000 Fe 8j 0.89(2) 0.2768(3) Fe 8i 0.41(3) 0.3598(2) Mo 8i 0.59(3) 0.3598(2)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.5 (n50.36) Residuals (%) R p : 5.0 R wp : 6.5 R exp : 4.7 Nd 2a 0.36 0.000000 Gd 2a 0.64 0.000000 Fe 8f 0.91(2) 0.250000 Fe 8j 0.91(2) 0.2769(3) Fe 8i 0.34(3) 0.3593(2) Mo 8i 0.66(3) 0.3593(2)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.6 (n50.20) Residuals (%) R p : 4.4 R wp : 6.0 R exp : 3.8 Nd 2a 0.20 0.000000 Gd 2a 0.80 0.000000 Fe 8f 0.92(2) 0.250000 Fe 8j 0.90(2) 0.2803(3) Fe 8i 0.38(3) 0.3591(1) Mo 8i 0.62(3) 0.3591(1)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.7 (n50.0) R p : 4.3 R wp : 5.7 Gd 2a Fe 8f Fe 8j Fe 8i Mo 8i
0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.1 (n51.0) R p : 4.3 R wp : 5.7 Nd 2a Fe 8f Fe 8j Fe 8i Mo 8i
Occupancy
x
Residuals (%) R exp : 3.6 1.000 0.000000 0.92(2) 0.250000 0.92(1) 0.2806(2) 0.42(2) 0.3582(1) 0.58(2) 0.3582(1)
M. Zinkevich et al. / Journal of Alloys and Compounds 316 (2001) 299 – 308
Fig. 6. Fractional atomic x-coordinate of 8j and 8i sites in the lattice of ThMn 12 -type phase Gd 12n Nd n (Fe,Mo) 12 versus Nd concentration n at an average Mo content of 19.160.7 at.% (series II).
between 0.90 and 0.97 (Table 3) showing no clear dependence on Nd content. At the same time, the fractional atomic coordinate x of 8j and 8i sites, which is not determined by symmetry and space group, exhibit more or less systematic changes as the fraction of neodymium in 2a position increases (Table 3, Fig. 6). The x coordinate of the 8j site remains almost constant when n in
305
Gd 12n Nd n (Fe,Mo) 12 increases from 0 to 0.20, abruptly decreases between n50.20 and n50.36, and then remains unchanged up to n50.80, increasing again in the pure Nd compound. The x coordinate of the 8i crystallographic site grows continuously up to n50.52 and then comes close to the saturation. Note that the relative change of the coordinate of the 8i position is smaller. Such behaviour cannot be expected on the basis of the simple substitutional model. Thus, the displacement of atoms in the 8i and 8j crystallographic sites with n shown in Fig. 6 indicates that a charge transfer within the 2a coordination shell depends on what atom (Gd or Nd) occupies this position. Fig. 7 shows a variation of the interatomic distances in the ThMn 12 -type structure of series II samples with the Nd concentration n. The distances are grouped together according to the coordination shell and their numerical values. All the distances in the 2a coordination shell increase with n, whereas the 2a–8j spacing is approximately constant at n $ 0.36. The 2a–8f distance shows a similar dependence as the parameter a in Fig. 4a. The 8i–8i spacings are decreasing taking a minimum value at n50.6–0.7. A little composition dependence has been observed for the 8j–8i distances, although they exhibit somewhat lowered values on the plateau between n50.36 and n50.80. The 8j–8j spacing behaves like the 2a–8j one, while the distance 8f –8f reflects the composition dependence of the parameter c in Fig. 4a. The length
Fig. 7. Interatomic distances in the lattice of ThMn 12 -type phase Gd 12n Nd n (Fe,Mo) 12 versus Nd concentration n at an average Mo content of 19.160.7 at.% (series II).
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between 8f and 8i sites steadily increases with n, but the 8f –8j distance shows a flat minimum between n50.36 and n50.52. The anomalous behaviour of parameter c with increasing Nd concentration is thus correlated with the composition dependence of the interatomic distances 8f – 8f, 8f –8j, 8i–8i, and 8j–8i (Fig. 7). The coordination shell of the 2a site in the ThMn 12 -type structure is shown in Fig. 8. The iron atoms occupying 8f sites form the tetragonal environment around the central rare-earth atom. Upon substitution of Nd for Gd one could expect two opposite effects influencing the unit cell parameters: the size effect owing to the larger ionic radius of Nd, and the chemical effect, which reflects the charge transfer between species of different electronegativity. Although the Pauling’s electronegativity of Nd (EN51.14) is only a bit smaller than that of Gd (EN51.20), one should take into account that the Gd 31 ion has a more stable electron configuration (4f 7 ) than Nd 31 ion (4f 3 ). Thus, in the presence of such electronegative elements as Mo (EN52.16) the Nd 31 ions are expected to be polarized more easily than Gd 31 . This should result in a decrease of the actual ionic radius and hence, could result even in the lattice contraction as the fraction of Nd increases. However, the attracting forces do not act uniformly, but by means of hybridization of atomic orbitals, which is an origin of the anisotropic crystal deformation. In the case of Gd 12n Nd n (Fe,Mo) 12 the chemical effect gives rise particularly to reduction of the interatomic spacings 8f –8f, 8f –8j, which appear to be responsible for the decrease of unit cell parameter c (Fig. 8). The bonding between atoms in 2a and 8f sites probably increases too, but it seems to be compensated by a size effect. No more detailed conclusions can be drawn without electronic structure calculations. In the series I and probably III the evolution of the unit cell parameter c of Gd 12n Nd n (Fe,Mo) 12 with n is obviously controlled by chemical effect (Figs. 3a and 5a), however in the series II the size effect dominates at n.0.5 (Fig. 4a).
Fig. 8. Coordination shell of 2a site in the ThMn 12 -type structure.
3.3. Magnetic properties The dependence of the Curie temperature (T C ) and the saturation magnetization (MS ) on Nd content n for the compounds Gd 12n Nd n (Fe,Mo) 12 is shown in Fig. 9. The corresponding numerical values are listed in Table 2. It can be seen that MS of the compounds with an average Mo concentration of 19.160.7 at.% (series II) increases from 42.0 A?m 2 ?kg 21 for n50 to 98.6 A?m 2 ?kg 21 for n51.0, whereas the gain of the saturation magnetization in the range 0#n#0.52 is about two times larger than that between n50.52 and n51.0 (Fig. 9a). Note a correlation between MS and the lattice parameter a (Fig. 4a). The increase of the saturation magnetization with n can be understood, since the magnetic moments of Fe and Gd are coupled antiferromagnetically, while the ferromagnetic
Fig. 9. Saturation magnetization MS at 10 K and Curie temperature T C of Gd 12n Nd n (Fe,Mo) 12 (series I and II) versus Nd concentration n.
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ordering exists in the case of Fe and Nd. The curve, which represents a dependence of the saturation magnetization shows a deviation from the simple linear dependence, which could be expected if the magnetic moments were collinear. According to [4], the easy magnetization direction (EMD) in NdFe 10 Mo 2 changes to a cone due to a spin reorientation below 147 K, whereas in GdFe 10 Mo 2 it is parallel to the c axis in the whole temperature range of magnetic ordering. Fig. 9a suggests that the angle between EMD and the c axis in Gd 12n Nd n (Fe,Mo) 12 (0,n,1) is different from zero, since neither Gd-rich, nor Nd-rich samples show a linear dependence of MS on n. The Curie temperature of series II alloys exhibits a maximum at n50.52 (Fig. 9b) and, hence, correlates with the parameter c (see Fig. 4a). Although the enhancement of T C (and also of MS ) at this composition could be due to the lower Mo content in the sample, the Curie temperature unambiguously increases by 20–25 K at the intermediate compositions compared to the values for n50 and n51 (Fig. 9b). A non-monotonous change of T C upon substitution in 2a site has not been reported so far [11,12]. At the same time, T C of Gd 12n Nd n (Fe,Mo) 12 at the Fe-rich border of homogeneity range (series I) decreases continuously upon substitution of Nd for Gd. The Curie temperature of Nd(Fe,Mo) 12 , where [Mo]56.4 at.% agrees well with the literature value [7]. There are also values of MS and T C for the ternary compound GdFe 9.5 Mo 2.5 [17], in which the Mo content is close to that of series II studied in the present work. No investigations of the analogous Nd phase have been performed. The saturation magnetization MS 538 A?m 2 ? kg 21 is in fair agreement with the present study, but the Curie temperature reported in [17] is much higher (405 K compared to 322 K). Many investigators have studied T C of NdFe 10 Mo 2 [2,4,7,18–20] and GdFe 10 Mo 2 [2,4,7,17– 21]. The scatter between the results of different authors, being as large as DT570 K, probably indicates that the measured Curie temperatures are strongly affected by small changes in the ratio of Fe to Mo atoms as well as the by the experimental technique used and method of the data treatment. The value of T C 5405 K for n50 [17] is therefore not shown in Fig. 9b. Following the curves in Fig. 9b one can conclude that the behaviour of the Curie temperature correlates with the compositional dependence of the unit cell parameters. Indeed, the monotonous changes were observed for T C , a, c, and V within the series I (compare Fig. 9b and Fig. 3), whereas the Curie temperature and the lattice parameters of Gd 12n Nd n (Fe,Mo) 12 with an average Mo concentration of 19.160.7 at.% (series II) have different compositional dependences in the regions of n,0.5 and n.0.5 (compare Fig. 9b and Fig. 4). Apart from the relative orientation of the magnetic moments in the R and Fe sublattices, which mainly affects the saturation magnetization, two other factors are known to govern the T C of the R(Fe,M) 12
307
intermetallics: the unit cell volume and the strength of Fe–Fe, R–Fe, and R–R interactions. In general, the Fe–Fe interactions are dominant and the R–R interactions are negligible. The enhancement of the Curie temperature due to the volume expansion (for example, if the interstitial compounds with H, N or C are formed) is known as the magnetovolume effect. However, a comparison of Fig. 9b with Figs. 3b and 4b shows that the variation of the unit cell volume with composition (n) cannot be accounted for the observed changes of T C . At the same time, several Fe–Fe interatomic distances (8j–8i, 8i–8i and 8f –8j) pass through a minimum upon increasing Nd content in compounds of the series II (Fig. 7). This appears to result in stronger interactions between the corresponding magnetic moments and hence, enhanced T C values of Gd 12n Nd n (Fe,Mo) 12 with an average Mo concentration of 19.160.7 at.% at 0,n,1.
4. Summary The compounds Gd 12n Nd n (Fe,Mo) 12 crystallize with the tetragonal ThMn 12 -type structure for n50–1. Their existence range is limited by a Mo concentration from 8.7 to 28.7 at.% (n50) and from 6.4 to 23.4 at.% (n51.0). The concentration of Mo at the Fe- and Mo-rich borders of the homogeneity range linearly decreases with n. The Nd and Gd atoms can be mixed together in the 2a sublattice without appreciable enthalpy change, the Nd-rich compounds being more stable at low Mo concentrations, whereas the Gd-rich phases are energetically preferred at high Mo contents. The structure evolution of Gd 12n Ndn (Fe,Mo) 12 upon substitution of Nd for Gd is controlled by two competitive factors: the lanthanide contraction with increasing atomic number and the charge transfer effect, so that the a /c ratio decreases. At constant Mo content a always rises with increasing Nd concentration. The lattice parameter c commonly decreases with n, although it can also change in opposite direction in a certain range of composition. The saturation magnetization of Gd 12n Nd n (Fe,Mo) 12 with an average Mo content of 19.160.7 at.% increases with n and shows a deviation from the straight-line interpolation, indicating the non-collinear alignment of magnetic moments of Gd and Nd. The Curie temperature of these compounds between n50.20 and n50.80 is about 25 K higher compared to the values for n50 and n51. This enhancement originates probably from the increased strength of magnetic Fe–Fe interaction due to the shortening of the interatomic distances 8j–8i, 8i–8i and 8f –8j in the intermediate range of n. At the same time, the Curie temperature at the Fe-rich border of homogeneity range continuously decreases with increasing Nd concentration. The behaviour of Curie temperature is thus correlated with the compositional dependence of the unit cell parameters.
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Acknowledgements The authors wish to express their thanks to B. Opitz, A. Weckbrodt, and K. Pittruff for technical assistance. Financial support of the Deutsche Forschungsgemeinschaft DFG (project Ma1531 / 5) is gratefully acknowledged.
References [1] D.B. de Mooij, K.H.J. Buschow, J. Less-Common Met. 136 (1988) 207. [2] A.S. Yermolenko, E.V. Shcherbakova, G.V. Ivanova, E.V. Belozerov, Phys. Met. Metall. 70 (1990) 52. [3] K.H.J. Buschow, J. Magn. Magn. Mater. 100 (1992) 79. ¨ [4] X.C. Kou, R. Grossinger, G. Wiesinger, J.P. Liu, F.R. de Boer, I. ¨ Kleinschroth, H. Kronmuller, Phys. Rev. B. 51 (1995) 8254. [5] R.H. Richman, W.P. McNaughton, J. Electronic Mater. 26 (1997) 415. [6] Ph. Oleinek, Ph.D. Thesis, University of Technology, Dresden, 1999. [7] J. Yang, S. Dong, W.H. Mao, P. Xuan, Z. Liu, Y. Sun, Y.C. Yang, S.L. Ge, J. Appl. Phys. 78 (1995) 1140.
[8] C.P. Yang, Y.Z. Wang, B.P. Hu, J.L. Wang, Z.X. Wang, Z.L. Jiang, C.L. Ma, J. Zhu, J. Alloys Compd. 290 (1999) 144. [9] M. Zinkevich, N. Mattern, B. Wolf, K. Wetzig, Phys. Stat. Sol. A 178 (2000) 671. [10] M. Zinkevich, Ph.D. Thesis, University of Technology, Dresden, 1999. [11] C.P. Yang, Y.Z. Wang, B.P. Hu, W.Y. Lai, Z.X. Wang, J. Alloys Compd. 278 (1998) 34. [12] C.P. Yang, Y.Z. Wang, B.P. Hu, J.L. Wang, Z.X. Wang, F.R. de Boer, Physica B 266 (1999) 146. ˚ [13] B. Sundman, J. Agren, J. Phys. Chem. Solids 42 (1981) 297. [14] U.R. Kattner, JOM 49 (1997) 14. [15] M. Gueramian, K. Yvon, F. Hulliger, J. Less-Common Met. 175 (1991) 321. [16] R.A. Young (Ed.), The Rietveld Method, Oxford University Press, New York, 1993. [17] R. Vert, D. Fruchart, B. Garcia-Landa, D. Gignoux, Y. Amako, J. Alloys Compd. 275–277 (1998) 611. [18] X. Xu, S.A. Shaheen, J. Appl. Phys. 76 (1994) 6754. [19] T. Zhao, X.C. Kou, Z.D. Zhang, X.K. Sun, Y.C. Chuang, F.R. de Boer, J. Phys. Condens. Matter 8 (1996) 8923. ¨ [20] C. Christides, A. Kostikas, X.C. Kou, R. Grossinger, D. Niarchos, J. Phys. Condens. Matter 5 (1993) 8611. [21] C. Christides, A. Kostikas, D. Niarchos, A. Simopoulos, J. Phys. Colloq., 49 (1988) 539 (C8, Proc. Int. Congr. Magn., 1988, Pt. 1).
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Homogeneity range, crystal structure and magnetic properties of the ThMn 12 -type compounds Gd 12n Nd n (Fe,Mo) 12 (n50–1.0) ¨ M. Zinkevich*, N. Mattern, A. Handstein, B. Gebel, I. Bacher ¨ Festkorper¨ Institut f ur und Werkstofforschung Dresden, Postfach 27 00 16, D-01171 Dresden, Germany Received 8 November 2000; accepted 30 November 2000
Abstract The existence range, crystal structure and magnetic properties of the Gd 12n Ndn (Fe,Mo) 12 compound series (n50–1) have been studied by electron probe X-ray microanalysis, X-ray diffraction followed by Rietveld refinement, and magnetization measurements. It has been found that the tetragonal ThMn 12 -type structure is formed for Mo concentrations from 8.7 to 28.7 at.% (n50) and from 6.4 to 23.4 at.% (n51.0). The concentration of molybdenum at the borders of the homogeneity range linearly decreases with n. The structure evolution of Gd 12n Nd n (Fe,Mo) 12 upon substitution of Nd for Gd is determined by two competitive factors: the lanthanide contraction with increasing atomic number and the charge transfer effect, so that the ratio of the unit cell parameters c /a decreases. The saturation magnetization of Gd 12n Nd n (Fe,Mo) 12 with an average Mo content of 19.160.7 at.% increases with n, the Curie temperature being about 25 K higher between n¯0.2 and n¯0.8 compared to the values for n50 and n51. At the same time, the Curie temperature at the Fe-rich border of homogeneity range continuously decreases with increasing Nd concentration. 2001 Elsevier Science B.V. All rights reserved. Keywords: Magnetically ordered materials; Rare earth alloys and compounds; Crystal structure; X-ray diffraction; Magnetization
1. Introduction Ternary rare-earth iron intermetallic compounds R(Fe,M) 12 with M5Al, Ga, Si, Ti, V, Nb, Mo, W, or Re, where R5rare earth element, crystallizing in the structure type of ThMn 12 (tetragonal, space group I4 /mmm) have been widely investigated during the past 10 years since their interstitial derivatives R(Fe,M) 12 N y exhibit excellent intrinsic magnetic properties to produce permanent-magnet materials [1–6]. Among the R(Fe,M) 12 or 1:12 compounds, much attention has been given to R(Fe,Mo) 12 since these intermetallics form easier than other compounds and possess an appreciable homogeneity range [7–9]. The largest saturation magnetization has been achieved so far on Nd(Fe,Mo) 12 , whereas the highest Curie temperature was detected in Gd-based compounds [2,4,7]. Therefore, the authors have suggested that a quaternary compound containing both the Nd and Gd atoms in the lattice could have optimal characteristics at a certain composition. The crystal structure and magnetic properties of Gd(Fe,Mo) 12 within the entire homogeneity range has been recently investigated [9,10]. Among the quaternary *Corresponding author. E-mail address: [email protected] (M. Zinkevich).
Mo-based 1:12 compounds the crystallographic and magnetic properties have been previously studied only for Y 12n Dy n Fe 10.5 Mo 1.5 [11] and Nd 12n Dy n Fe 11 Mo [12]. The present work reports the existence range, structural and magnetic parameters of Gd 12n Ndn (Fe,Mo) 12 .
2. Experimental Gd 12n Nd n (Fe,Mo) 12 alloys (n50–1.0) were prepared as three series with nominal Mo concentrations of 8, 20 and 32 at.%, respectively. In the first and third series, the specified amount of the stabilizing element was chosen to obtain non single-phase alloys and thus, to determine the border of the homogeneity range of the ThMn 12 -type phase regarding the Mo concentration at different n values. In contrast, alloys of the second series should consist mainly of the ThMn 12 -type phase. Ingots of alloys were melted from 99.9% Fe and 99.99% Gd, Nd and Mo (Alfa Aesar) in an argon arc furnace, using a non-consumable tungsten electrode on a water-cooled copper hearth. The alloys were remelted four times, the ingot was inverted after each melt to promote mixing. The mass of each ingot was about 10 g. An additional amount (1 wt.%) of rare earth elements was added to compensate their loss during preparation.
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 00 )01500-0
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The ingots were wrapped in tantalum foil, annealed at 11008C for 144 h in sealed quartz ampoules under 0.15 bar purified Ar gas and then quenched in water. A part of each ingot was prepared for the metallographical examination by polishing the resin-mounted specimens with diamond pastes. The actual chemical composition of the alloys as well as that of the ThMn 12 -type phase were measured by electron probe X-ray microanalysis (EPMA) using wavelength-dispersive X-ray (WDX) spectroscopy (SEMQ, Applied Research, USA) with the correction program LOVSCOTT, employing the pure metals as standard materials. The characteristic wavelengths of FeKa, MoLa, NdLa, and GdLa were detected to determine the concentration of elements using an acceleration voltage of 20 kV. The area of the analyzing window on the specimen surface was varied from 131 mm 2 (analysis of individual phases) to 1003100 mm 2 to obtain the average chemical composition of the non single-phase alloys. The standard deviations of the element concentration were calculated from three to five independent measurements, moving a probe each time to the new position. X-ray diffraction analysis was conducted with a Phillips PW1820 Bragg–Brentano diffractometer operating at a voltage of 40 kV and a current of 40 mA (CoKa radiation), equipped with secondary monochromator and a sample spinner. The powders with a particle size of #100 mm were prepared from ingots using a hard metal mortar and pestle as well as a sieve. For the phase identification the X-ray powder patterns were recorded in a 2u range between 5 and 1208, a step size of 0.058, and a counting time of 3 s. Assignment of the particular phases to the diffraction maxima was performed with X’PERT software package (Phillips Analytical, Almelo, The Netherlands), which uses a database of the International Center for Diffraction Data (ICDD). Precise lattice parameters a and c of the tetragonal unit cell were obtained measuring the individual (550) /(710) and (004) reflections in a 2u range between 93 and 1108, a step size of 0.018, and a counting time of 25 s employing an internal standard of pure Si. For quantitative refinement of the atom positions and occupancies, full-profile Rietveld refinements of the X-ray diffraction patterns recorded in a 2u range between 15 and 1308, a step size of 0.038, and a counting time of 14 s were carried out using Phillips X’PERT PLUS software. For the investigation of magnetic properties small pieces (10 . . . .50 mg) of the annealed ingots were employed. The thermomagnetic analysis was made using a SQUID magnetometer (MPMS-5S, Quantum Design) from 5 to 340 K and a vibrating sample magnetometer operating at a frequency of 29 Hz (IFW Dresden) from 300 to 820 K in a field of m0 H 5 0.1 T. The Curie temperatures were derived by extrapolating the steepest part of the slope of the M(T ) curve to M50. The magnetization curves were measured with the SQUID magnetometer from 0 to 5 T at 10 K. The values of saturation magnetization were obtained by extrapolation of the M vs. 1 /H curves to 1 /H50.
3. Results and discussion
3.1. Existence range Table 1 presents the elemental chemical composition and phase constitution of investigated samples Nd–Gd– Fe–Mo, where a symbol in square brackets means the atomic concentration of the respective element in the alloy. Each specimen is identified with its series number (i.e. I, II or III) and a serial number. The results of the phase analysis are those combined from X-ray diffraction and EPMA experiments. The principal impurity phases in the series I and III were (Fe), which stands for a solid solution of Mo in the bcc-Fe and Fe 3 Mo 2 , respectively, whereas the samples of the series II were almost single-phase (the sum of additional phases was ,5 wt.%). This is in agreement with the idea employed in alloy preparation, so that the series I and III are outside, and the series II is inside the homogeneity region of the ThMn 12 -type phase with respect to Mo content. All other impurity phases indicated in Table 1 present only in trace amounts. The chemical composition of the 1:12 phase in the alloy series under study as determined by EPMA and Rietveld refinement is given in Table 2. The outline of a homogeneity region of the ThMn 12 -type phase Gd 12n Nd n (Fe,Mo) 12 is represented in Fig. 1. A range of the Mo concentrations providing the stability of 1:12 phase is wider for Gd-rich compounds, being shifted, however, to the higher values. The concentration of molybdenum at the Fe- and Mo-rich borders of homogeneity range increases linearly by |2 and |5 at.%, respectively, from n51 to n50. The existence range is related to the Gibbs energy functions of the individual phases in equilibrium, which are the thermodynamic origin of the phase diagrams. The crystal structure of ThMn 12 -type contains four atomic positions in the asymmetric unit: 2a, 8f, 8j and 8i. Taking into account that Mo atoms can only occupy the 8i crystallographic site and rare-earth atoms are expected in 2a positions [3,9], the Gibbs energy of (Gd,Nd)(Fe,Mo) 12 phase can be expressed in terms of the generalized sublattice formalism [13,14] G 1:12 5 y Fe y Gd GGd:Fe:Fe 1 y Mo y Gd GGd:Fe:Mo 1 y Fe y Nd GNd:Fe:Fe 1 y Mo y Nd GNd:Fe:Mo 1 1 8RT [y Fe ln ( y Fe ) 1 y Mo ln ( y Mo )] 1 2RT [y Gd ln ( y Gd ) 1 y Nd ln ( y Nd )] 1 y Fe y Mo y Gd 0 LGd:Fe:Fe,Mo 1 1 y Fe y Mo y Nd 0 LNd:Fe:Fe,Mo 1 y Gd y Nd y Fe 0 LGd,Nd:Fe:Fe 0
1 y Gd y Nd y Mo LGd,Nd:Fe:Mo
(1)
where y i are the site fractions of the constituents on each sublattice, GGd:Fe:Fe and GNd:Fe:Fe are the Gibbs energy of the hypothetical compounds GdFe 12 and NdFe 12 , respec-
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Table 1 Chemical composition and phase constitution of Gd 12n Nd n (Fe,Mo) 12 ID
Phase constitution a
Elemental composition of alloy (at.%)
I.1 I.2 I.3 I.4 I.5 I.6 I.7 II.1 II.2 II.3 II.4 II.5 II.6 II.7 III.1 III.2 III.3 III.4 III.5 III.6 III.7
[Fe]
[Gd]
[Mo]
[Nd]
Major
Impurity phases
84.760.3 84.760.3 85.060.5 84.560.8 84.860.1 85.060.3 85.661.0 72.960.5 73.460.4 74.360.4 74.660.4 73.060.3 75.560.3 72.661.0 63.161.0 60.060.9 63.160.8 62.161.1 64.660.3 61.960.7 61.060.8
0.0760.06 1.5660.05 2.260.3 3.860.4 4.8760.06 5.9760.06 9.460.5 #0.1 1.5060.07 2.6260.11 3.860.2 5.1460.11 5.760.3 8.560.5 #0.1 1.7860.05 2.860.3 3.960.4 5.560.2 6.360.4 9.360.3
6.460.2 6.960.2 7.3360.05 7.660.4 7.8760.15 7.560.3 5.060.5 18.660.3 19.060.8 17.960.6 17.360.3 19.060.3 17.460.1 18.960.3 30.760.8 31.860.6 29.461.3 29.361.3 27.460.5 30.461.1 29.760.6
8.9460.13 6.8060.07 5.560.3 4.260.2 2.560.1 1.5360.06 0 8.560.3 6.160.4 5.1260.13 4.360.3 2.960.2 1.460.1 0 6.260.3 6.460.3 4.760.6 4.860.5 2.5660.11 1.560.2 0
1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12 1:12
(Fe), 2:17 (Fe), 2:17 (Fe), 2:17 (Fe), 2:17, Fe 2 (Gd,Nd) (Fe), 2:17 (Fe), 2:17 2:17 Fe 3 Mo 2 , Fe 2 Mo, Nd Fe 3 Mo 2 Fe 3 Mo 2 (Mo), Fe 3 Mo 2 Fe 3 Mo 2 – Fe 2 Gd, Fe 23 Gd 6 Fe 3 Mo 2 , Nd, FeMo Fe 3 Mo 2 , Nd Fe 3 Mo 2 , Fe 2 Mo, Nd Fe 3 Mo 2, d(Gd,Nd) Gd, Fe 3 Mo 2 Gd, (Mo), Fe 3 Mo 2 (Mo), Fe 2 Gd
a
1:12 stands for ThMn 12 -type phase, 2:17 refers to the (Gd,Nd) 2 (Fe,Mo) 17 compounds with Th 2 Zn 17 type of structure; (Fe) and (Mo) are symbols for the bcc solid solutions based on Fe and Mo, respectively; d (Gd,Nd) stands for the ordered Sm-type phase.
tively, GGd:Fe:Mo and GNd:Fe:Mo correspond to the Gibbs energy of phases, where the 8i sublattice is fully filled with Mo atoms, R equals the gas constant, and T is the absolute temperature. 0 LGd:Fe:Fe,Mo and 0 LNd:Fe:Fe,Mo are the interaction parameters of Fe and Mo atoms in the 8i sublattice when the 2a site is filled with Gd and Nd atoms,
0
LGd,Nd:Fe:Fe and 0 LGd,Nd:Fe:Mo are the interaction parameters of Gd and Nd atoms in the 2a sublattice when the 8i site is filled with Fe and Mo atoms, respectively. A free energy diagram of the (Gd,Nd)(Fe,Mo) 12 system, which is in qualitative agreement with the homogeneity region plotted in Fig. 1 is shown in Fig. 2. The curves are
Table 2 Homogeneity range, crystallographic and magnetic properties of the ThMn 12 -type compounds Gd 12n Nd n (Fe,Mo) 12 ; [Mo] is the concentration of molybdenum in compounds; a and c are lattice constants; T C is the Curie temperature and MS is the saturation magnetization at 10 K expressed in Am 2 / kg ID
n
[Mo] (at.%)
a (nm)
c (nm)
V (nm 3 )
T C (K)
MS
I.1 I.2 I.3 I.4 I.5 I.6 I.7 II.1 II.2 II.3 II.4 II.5 II.6 II.7 III.1 III.2 III.3 III.4 III.5 III.6 III.7
1.0 0.81 0.71 0.50 0.34 0.20 0.0 1.0 0.80 0.66 0.52 0.36 0.20 0.0 1.0 0.78 0.62 0.55 0.32 0.19 0.0
6.460.2 6.960.2 7.3360.05 7.361.0 7.8760.15 7.560.3 8.761.0 18.660.3 19.060.8 20.061.0 18.160.8 19.060.7 19.860.5 18.960.3 23.460.8 24.760.2 24.360.7 26.460.4 27.060.8 28.260.1 28.761.0
0.85815(9) 0.85736(2) 0.85691(6) 0.85609(1) 0.85551(5) 0.85493(5) 0.85442(5) 0.86221(5) 0.86122(2) 0.86068(4) 0.85987(1) 0.85967(1) 0.85944(3) 0.85916(2) 0.86391(4) 0.86296(6) 0.86284(3) 0.86287(7) 0.86295(3) 0.86355(1) 0.86358(5)
0.47795(4) 0.47793(1) 0.47800(1) 0.47806(1) 0.47809(1) 0.47812(1) 0.47865(6) 0.48176(1) 0.48135(2) 0.48132(2) 0.48107(5) 0.48125(2) 0.48148(1) 0.48190(1) 0.48332(1) 0.48379(7) 0.48412(4) 0.48460(3) 0.48505(4) 0.48596(3) 0.48653(6)
0.35197(9) 0.35131(2) 0.35099(6) 0.35037(1) 0.34991(4) 0.34947(5) 0.34942(6) 0.35814(5) 0.35702(3) 0.35654(5) 0.35569(4) 0.35566(2) 0.35564(3) 0.35572(3) 0.36072(3) 0.36027(9) 0.36042(5) 0.36080(8) 0.36121(6) 0.36239(2) 0.36284(9)
496611 – – 51365 – 52465 – 317610 34165 34366 359610 342610 343610 322610 – – – – – – –
– – – – – – – 98.6 84.2 79.5 79.3 62.5 51.7 42.0 – – – – – – –
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Fig. 1. Outline of a homogeneity region of the 1:12 compound in the system Gd 12n Nd n (Fe,Mo) 12 .
Figs. 3–5. The number near each data point indicates the concentration of dissolved Mo (Table 2). The numerical values of a, c and V are given in Table 2. Fig. 3 represents the evolution of the lattice constants at Fe-rich border of the homogeneity range (series I) with increasing fraction of Nd atoms at 2a crystallographic site. The lattice parameter a increases almost linearly with n as could be expected since the ionic radius of Nd is greater than that of Gd due to the lanthanide contraction with increasing atomic number. However, the parameter c changes in the opposite direction, mostly between n50 and n50.2 and hardly varies at all in the range 0.2,n#1.0 (Fig. 3a). The possible misinterpretation of the concentration dependence of the unit cell constant c due to the different Mo content in alloys can be ruled out, as there is no correlation between the percentage of Mo within the series I and the value of lattice parameter c. An exception is the sample I.7 (n50), where the Mo concentration is about 1.5 at.%
calculated according to Eq. (1) with GNd:Fe:Fe ,GGd:Fe:Fe , GNd:Fe:Mo .GGd:Fe:Mo , and 0 LGd:Fe:Fe,Mo 5 0 LNd:Fe:Fe,Mo 50. Using the common tangent construction it is easy to demonstrate that the homogeneity range of Gd(Fe,Mo) 12 will be shifted towards higher Mo contents relative to Nd(Fe,Mo) 12 (Fig. 2). It is thus possible to conclude that Nd-rich compounds are more stable than Gd-rich ones at low Mo concentrations, whereas the opposite is true at high Mo contents. Furthermore, the Nd and Gd atoms should form a nearly ideal solution in the 2a sublattice (i.e. both the interaction parameters 0 LGd,Nd:Fe:Fe and 0 LGd,Nd:Fe:Mo are zero) as suggested by the linearly changing borders of the homogeneity range for the intermediate compositions.
3.2. Crystal structure The unit cell parameters a, c and the unit cell volume V of Gd 12n Nd n (Fe,Mo) 12 compounds are plotted versus n in
Fig. 2. Schematic free energy diagram of the (Gd,Nd)(Fe,Mo) 12 system vs. site fraction of Mo in 8i crystallographic site.
Fig. 3. Unit cell parameters of Gd 12n Nd n (Fe,Mo) 12 (series I). The number near each data point indicates a concentration of dissolved Mo.
M. Zinkevich et al. / Journal of Alloys and Compounds 316 (2001) 299 – 308
303
Fig. 4. Unit cell parameters of Gd 12n Nd n (Fe,Mo) 12 (series II). The number near each data point indicates a concentration of dissolved Mo.
Fig. 5. Unit cell parameters of Gd 12n Nd n (Fe,Mo) 12 (series III). The number near each data point indicates a concentration of dissolved Mo.
higher than the mean value of all other samples of series I. However, the results of Yang et al. [7], which are plotted in Fig. 3 for comparison suggest that an unusually high value of the parameter c at n50 is not only due to the greater Mo content. Furthermore, one can see that the unit cell constant c of GdFe 11.2 Mo 0.8 is higher than the corresponding parameter of NdFe 11.2 Mo 0.8 , whereas it takes an intermediate values in the Gd 12n Nd n (Fe,Mo) 12 (0,n,1) compounds of series I. The unit cell volume of series I shows the concentration dependence on n to be similar to that of the lattice parameter a (compare Fig. 3a and 3b), while only very little increase is observed between n50 and n50.2. This is due to the anomalously high parameter c. The c /a ratio, however, decreases continuously with n (Fig. 3b). The values of the unit cell volume at n50 and n51 are in very good agreement with those in [7]. The composition dependence of the unit cell parameters of the series II is more complex (Fig. 4). On the curve
corresponding to the parameter a, two straight lines with different slopes intersecting at n¯0.5 can be isolated, whereas the parameter c shows a minimum at this composition (Fig. 4a). Note that the lattice constant a steadily increases with n while the values of the lattice constant c at n50 and n51 are almost equal. The enhancement of both the lattice constants at n50.66 resulting in a slight deviation from the linear dependence is perhaps due to the higher Mo content in the sample. Also, the sharp minimum of the parameter c at n¯0.5 could be due to a somewhat lower Mo concentration with respect to the mean value. These deviations do not however, change the overall picture. The observed behaviour, on the one hand, can indicate that upon increasing the Mo concentration in Gd 12n Nd n (Fe,Mo) 12 the structure of the Gd-rich phase, which exists at n,0.5 differs from that of the Nd-rich phase, which is formed at n.0.5, whereas at n50.5 these two phases become indistinguishable. On the other hand, the composition n50.5 can be considered as a critical
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point where the lattice expansion due to the larger size of the Nd ion is compensated by the contraction owing to another effect (see below). These two possible explanations are not necessarily contradictory. The opposite composition dependence of the unit cell parameters a and c in the range n,0.5 leads to somewhat unexpected behaviour of the unit cell volume, so that it remains constant in the Gd-rich region (Fig. 4b). In spite of this anomaly, the c /a ratio decreases monotonously with n similarly to that of series I. Within the series III (Mo-rich border of the homogeneity range), the compositional dependence of the unit cell parameters on Nd concentration is superimposed with the obvious lattice expansion due to higher Mo content in Gd-rich samples (Fig. 5). The Nd-rich region (n$0.62) is characterized by an increase of parameter a with n, whereas for the Gd-rich compounds (n#0.19) a slight decrease is observed. In the intermediate composition range the unit cell parameter a is approximately constant, although there is a weak minimum at n50.62 (Fig. 5a). Note, that the corresponding value at n50 is only a little smaller than that at n51, while it becomes much lower in the middle. The lattice parameter c as well as the c /a ratio decrease continuously with n (Fig. 5). At the same time, there is a minimum in the compositional dependences of the unit cell volume, which is to be attributed to the compensation of the lattice shrinking with increasing fraction of Gd by the enlargement of the unit cell because of the growing Mo content (Fig. 5b). In general, there are two regularities, which control the structure of 1:12 phase Gd 12n Nd n (Fe,Mo) 12 in alloys of the series I–III: • the decrease of the lattice parameter c with increasing Nd concentration, whereas the lattice parameter a simultaneously increases; • the non-monotonous concentration dependence of the unit cell parameters throughout the whole composition range. The anisotropy in change of the lattice parameters a and c of the ThMn 12 -type structure R(Fe,M) 12 along the rareearth series (R5Ce . . . .Lu) is known from the literature [2,4,7,12,15]. However, only a little attention has been paid to this matter. To understand the somewhat surprising behaviour of the unit cell parameters, Rietveld refinements of the powder diffraction patterns of the series II samples, which contain the largest amount of the 1:12 phase, has been done. The results are given in Table 3 and Figs. 6 and 7. Note, that it was not possible to refine the occupancy in 2a site, since the X-ray scattering factors of Nd and Gd are only a little different. The common observation for all samples is that 8f and 8j crystallographic sites are only partially filled with Fe atoms as it has been also found previously for ThMn 12 -type phases Gd 11m Fe 122p2q Mo p h q (h5vacancy) [9]. The corresponding occupancies vary
Table 3 Refined structure parameters of the ThMn 12 -type compounds Gd 12n Nd n (Fe,Mo) 12 with an average Mo content of 19.160.7 at.% (series II). For the definition of residuals see [16] Atom
Site
y
z
Residuals (%) R exp : 4.5 1.000 0.000000 0.95(2) 0.250000 0.92(2) 0.2784(3) 0.32(3) 0.3600(1) 0.68(3) 0.3600(1)
0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.2 (n50.80) Residuals (%) R p : 4.8 R wp : 6.1 R exp : 4.8 Nd 2a 0.80 0.000000 Gd 2a 0.20 0.000000 Fe 8f 0.98(2) 0.250000 Fe 8j 0.95(2) 0.2764(3) Fe 8i 0.29(3) 0.3600(2) Mo 8i 0.71(3) 0.3600(2)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.3 (n50.66) Residuals (%) R p : 3.9 R wp : 5.0 R exp : 4.4 Nd 2a 0.66 0.000000 Gd 2a 0.34 0.000000 Fe 8f 0.95(2) 0.250000 Fe 8j 0.95(2) 0.2764(3) Fe 8i 0.33(3) 0.3601(2) Mo 8i 0.67(3) 0.3601(2)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.4 (n50.52) Residuals (%) R p : 4.7 R wp : 6.1 R exp : 4.1 Nd 2a 0.52 0.000000 Gd 2a 0.48 0.000000 Fe 8f 0.95(2) 0.250000 Fe 8j 0.89(2) 0.2768(3) Fe 8i 0.41(3) 0.3598(2) Mo 8i 0.59(3) 0.3598(2)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.5 (n50.36) Residuals (%) R p : 5.0 R wp : 6.5 R exp : 4.7 Nd 2a 0.36 0.000000 Gd 2a 0.64 0.000000 Fe 8f 0.91(2) 0.250000 Fe 8j 0.91(2) 0.2769(3) Fe 8i 0.34(3) 0.3593(2) Mo 8i 0.66(3) 0.3593(2)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.6 (n50.20) Residuals (%) R p : 4.4 R wp : 6.0 R exp : 3.8 Nd 2a 0.20 0.000000 Gd 2a 0.80 0.000000 Fe 8f 0.92(2) 0.250000 Fe 8j 0.90(2) 0.2803(3) Fe 8i 0.38(3) 0.3591(1) Mo 8i 0.62(3) 0.3591(1)
0.000000 0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.7 (n50.0) R p : 4.3 R wp : 5.7 Gd 2a Fe 8f Fe 8j Fe 8i Mo 8i
0.000000 0.250000 0.500000 0.000000 0.000000
0.000000 0.250000 0.000000 0.000000 0.000000
Sample II.1 (n51.0) R p : 4.3 R wp : 5.7 Nd 2a Fe 8f Fe 8j Fe 8i Mo 8i
Occupancy
x
Residuals (%) R exp : 3.6 1.000 0.000000 0.92(2) 0.250000 0.92(1) 0.2806(2) 0.42(2) 0.3582(1) 0.58(2) 0.3582(1)
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Fig. 6. Fractional atomic x-coordinate of 8j and 8i sites in the lattice of ThMn 12 -type phase Gd 12n Nd n (Fe,Mo) 12 versus Nd concentration n at an average Mo content of 19.160.7 at.% (series II).
between 0.90 and 0.97 (Table 3) showing no clear dependence on Nd content. At the same time, the fractional atomic coordinate x of 8j and 8i sites, which is not determined by symmetry and space group, exhibit more or less systematic changes as the fraction of neodymium in 2a position increases (Table 3, Fig. 6). The x coordinate of the 8j site remains almost constant when n in
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Gd 12n Nd n (Fe,Mo) 12 increases from 0 to 0.20, abruptly decreases between n50.20 and n50.36, and then remains unchanged up to n50.80, increasing again in the pure Nd compound. The x coordinate of the 8i crystallographic site grows continuously up to n50.52 and then comes close to the saturation. Note that the relative change of the coordinate of the 8i position is smaller. Such behaviour cannot be expected on the basis of the simple substitutional model. Thus, the displacement of atoms in the 8i and 8j crystallographic sites with n shown in Fig. 6 indicates that a charge transfer within the 2a coordination shell depends on what atom (Gd or Nd) occupies this position. Fig. 7 shows a variation of the interatomic distances in the ThMn 12 -type structure of series II samples with the Nd concentration n. The distances are grouped together according to the coordination shell and their numerical values. All the distances in the 2a coordination shell increase with n, whereas the 2a–8j spacing is approximately constant at n $ 0.36. The 2a–8f distance shows a similar dependence as the parameter a in Fig. 4a. The 8i–8i spacings are decreasing taking a minimum value at n50.6–0.7. A little composition dependence has been observed for the 8j–8i distances, although they exhibit somewhat lowered values on the plateau between n50.36 and n50.80. The 8j–8j spacing behaves like the 2a–8j one, while the distance 8f –8f reflects the composition dependence of the parameter c in Fig. 4a. The length
Fig. 7. Interatomic distances in the lattice of ThMn 12 -type phase Gd 12n Nd n (Fe,Mo) 12 versus Nd concentration n at an average Mo content of 19.160.7 at.% (series II).
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between 8f and 8i sites steadily increases with n, but the 8f –8j distance shows a flat minimum between n50.36 and n50.52. The anomalous behaviour of parameter c with increasing Nd concentration is thus correlated with the composition dependence of the interatomic distances 8f – 8f, 8f –8j, 8i–8i, and 8j–8i (Fig. 7). The coordination shell of the 2a site in the ThMn 12 -type structure is shown in Fig. 8. The iron atoms occupying 8f sites form the tetragonal environment around the central rare-earth atom. Upon substitution of Nd for Gd one could expect two opposite effects influencing the unit cell parameters: the size effect owing to the larger ionic radius of Nd, and the chemical effect, which reflects the charge transfer between species of different electronegativity. Although the Pauling’s electronegativity of Nd (EN51.14) is only a bit smaller than that of Gd (EN51.20), one should take into account that the Gd 31 ion has a more stable electron configuration (4f 7 ) than Nd 31 ion (4f 3 ). Thus, in the presence of such electronegative elements as Mo (EN52.16) the Nd 31 ions are expected to be polarized more easily than Gd 31 . This should result in a decrease of the actual ionic radius and hence, could result even in the lattice contraction as the fraction of Nd increases. However, the attracting forces do not act uniformly, but by means of hybridization of atomic orbitals, which is an origin of the anisotropic crystal deformation. In the case of Gd 12n Nd n (Fe,Mo) 12 the chemical effect gives rise particularly to reduction of the interatomic spacings 8f –8f, 8f –8j, which appear to be responsible for the decrease of unit cell parameter c (Fig. 8). The bonding between atoms in 2a and 8f sites probably increases too, but it seems to be compensated by a size effect. No more detailed conclusions can be drawn without electronic structure calculations. In the series I and probably III the evolution of the unit cell parameter c of Gd 12n Nd n (Fe,Mo) 12 with n is obviously controlled by chemical effect (Figs. 3a and 5a), however in the series II the size effect dominates at n.0.5 (Fig. 4a).
Fig. 8. Coordination shell of 2a site in the ThMn 12 -type structure.
3.3. Magnetic properties The dependence of the Curie temperature (T C ) and the saturation magnetization (MS ) on Nd content n for the compounds Gd 12n Nd n (Fe,Mo) 12 is shown in Fig. 9. The corresponding numerical values are listed in Table 2. It can be seen that MS of the compounds with an average Mo concentration of 19.160.7 at.% (series II) increases from 42.0 A?m 2 ?kg 21 for n50 to 98.6 A?m 2 ?kg 21 for n51.0, whereas the gain of the saturation magnetization in the range 0#n#0.52 is about two times larger than that between n50.52 and n51.0 (Fig. 9a). Note a correlation between MS and the lattice parameter a (Fig. 4a). The increase of the saturation magnetization with n can be understood, since the magnetic moments of Fe and Gd are coupled antiferromagnetically, while the ferromagnetic
Fig. 9. Saturation magnetization MS at 10 K and Curie temperature T C of Gd 12n Nd n (Fe,Mo) 12 (series I and II) versus Nd concentration n.
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ordering exists in the case of Fe and Nd. The curve, which represents a dependence of the saturation magnetization shows a deviation from the simple linear dependence, which could be expected if the magnetic moments were collinear. According to [4], the easy magnetization direction (EMD) in NdFe 10 Mo 2 changes to a cone due to a spin reorientation below 147 K, whereas in GdFe 10 Mo 2 it is parallel to the c axis in the whole temperature range of magnetic ordering. Fig. 9a suggests that the angle between EMD and the c axis in Gd 12n Nd n (Fe,Mo) 12 (0,n,1) is different from zero, since neither Gd-rich, nor Nd-rich samples show a linear dependence of MS on n. The Curie temperature of series II alloys exhibits a maximum at n50.52 (Fig. 9b) and, hence, correlates with the parameter c (see Fig. 4a). Although the enhancement of T C (and also of MS ) at this composition could be due to the lower Mo content in the sample, the Curie temperature unambiguously increases by 20–25 K at the intermediate compositions compared to the values for n50 and n51 (Fig. 9b). A non-monotonous change of T C upon substitution in 2a site has not been reported so far [11,12]. At the same time, T C of Gd 12n Nd n (Fe,Mo) 12 at the Fe-rich border of homogeneity range (series I) decreases continuously upon substitution of Nd for Gd. The Curie temperature of Nd(Fe,Mo) 12 , where [Mo]56.4 at.% agrees well with the literature value [7]. There are also values of MS and T C for the ternary compound GdFe 9.5 Mo 2.5 [17], in which the Mo content is close to that of series II studied in the present work. No investigations of the analogous Nd phase have been performed. The saturation magnetization MS 538 A?m 2 ? kg 21 is in fair agreement with the present study, but the Curie temperature reported in [17] is much higher (405 K compared to 322 K). Many investigators have studied T C of NdFe 10 Mo 2 [2,4,7,18–20] and GdFe 10 Mo 2 [2,4,7,17– 21]. The scatter between the results of different authors, being as large as DT570 K, probably indicates that the measured Curie temperatures are strongly affected by small changes in the ratio of Fe to Mo atoms as well as the by the experimental technique used and method of the data treatment. The value of T C 5405 K for n50 [17] is therefore not shown in Fig. 9b. Following the curves in Fig. 9b one can conclude that the behaviour of the Curie temperature correlates with the compositional dependence of the unit cell parameters. Indeed, the monotonous changes were observed for T C , a, c, and V within the series I (compare Fig. 9b and Fig. 3), whereas the Curie temperature and the lattice parameters of Gd 12n Nd n (Fe,Mo) 12 with an average Mo concentration of 19.160.7 at.% (series II) have different compositional dependences in the regions of n,0.5 and n.0.5 (compare Fig. 9b and Fig. 4). Apart from the relative orientation of the magnetic moments in the R and Fe sublattices, which mainly affects the saturation magnetization, two other factors are known to govern the T C of the R(Fe,M) 12
307
intermetallics: the unit cell volume and the strength of Fe–Fe, R–Fe, and R–R interactions. In general, the Fe–Fe interactions are dominant and the R–R interactions are negligible. The enhancement of the Curie temperature due to the volume expansion (for example, if the interstitial compounds with H, N or C are formed) is known as the magnetovolume effect. However, a comparison of Fig. 9b with Figs. 3b and 4b shows that the variation of the unit cell volume with composition (n) cannot be accounted for the observed changes of T C . At the same time, several Fe–Fe interatomic distances (8j–8i, 8i–8i and 8f –8j) pass through a minimum upon increasing Nd content in compounds of the series II (Fig. 7). This appears to result in stronger interactions between the corresponding magnetic moments and hence, enhanced T C values of Gd 12n Nd n (Fe,Mo) 12 with an average Mo concentration of 19.160.7 at.% at 0,n,1.
4. Summary The compounds Gd 12n Nd n (Fe,Mo) 12 crystallize with the tetragonal ThMn 12 -type structure for n50–1. Their existence range is limited by a Mo concentration from 8.7 to 28.7 at.% (n50) and from 6.4 to 23.4 at.% (n51.0). The concentration of Mo at the Fe- and Mo-rich borders of the homogeneity range linearly decreases with n. The Nd and Gd atoms can be mixed together in the 2a sublattice without appreciable enthalpy change, the Nd-rich compounds being more stable at low Mo concentrations, whereas the Gd-rich phases are energetically preferred at high Mo contents. The structure evolution of Gd 12n Ndn (Fe,Mo) 12 upon substitution of Nd for Gd is controlled by two competitive factors: the lanthanide contraction with increasing atomic number and the charge transfer effect, so that the a /c ratio decreases. At constant Mo content a always rises with increasing Nd concentration. The lattice parameter c commonly decreases with n, although it can also change in opposite direction in a certain range of composition. The saturation magnetization of Gd 12n Nd n (Fe,Mo) 12 with an average Mo content of 19.160.7 at.% increases with n and shows a deviation from the straight-line interpolation, indicating the non-collinear alignment of magnetic moments of Gd and Nd. The Curie temperature of these compounds between n50.20 and n50.80 is about 25 K higher compared to the values for n50 and n51. This enhancement originates probably from the increased strength of magnetic Fe–Fe interaction due to the shortening of the interatomic distances 8j–8i, 8i–8i and 8f –8j in the intermediate range of n. At the same time, the Curie temperature at the Fe-rich border of homogeneity range continuously decreases with increasing Nd concentration. The behaviour of Curie temperature is thus correlated with the compositional dependence of the unit cell parameters.
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Acknowledgements The authors wish to express their thanks to B. Opitz, A. Weckbrodt, and K. Pittruff for technical assistance. Financial support of the Deutsche Forschungsgemeinschaft DFG (project Ma1531 / 5) is gratefully acknowledged.
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