Structural and intrinsic magnetic material parameters of Pr3(Fe,Ti)29 and Pr3(Fe,Ti)29Nx

~ H Journalof magnetism ~

,i~ ELSEVIER

and magnetic materials

Journal of Magnetism and Magnetic Materials 153 (1996) 75-85

Structural and intrinsic magnetic material parameters of Pr3(Fe,Ti)29 and Pr3(Fe,Ti) 29Nx V. Psycharis, O. Kalogirou *, E. Devlin, M. Gjoka, A. Simopoulos, D. Niarchos Institute of Materials Science, National Center for Scientific Research 'Demokritos', 153 10 Ag. Paraskevi, Attiki, Greece Received 10 April 1995; revised 11 July 1995

Abstract We report the study of the structural and the intrinsic magnetic properties of the Pr member of the newly discovered class of R 3(Fe,Ti)29 compounds and its nitride. The X-ray powder diffraction pattern of the alloy is indexed in monoclinic symmetry with lattice parameters a = 10.647(1) ,~, b = 8.6014(7) ,~, c = 9.755(l) ,~ and /3 = 96.92(1) ° and the structure is described in the A 2 / m space group. Atomic positions and bond lengths are given. Nitrogenation results in a lattice expansion of 6.6% corresponding to ~ 4 N atoms per formula unit. The Curie temperature is 392(5) K, and the saturation magnetization, the anisotropy field and the average hyperfine field at room temperature are 135.4 A m2/kg, 3.9 and 20°3 T, respectively. A magnetic phase transition is observed at ~ 160 K. After nitrogenation the Curie temperature increases to 721(5) K, and the saturation magnetization to 174.8 A m2/kg, the anisotropy field 7.2 T and the average hyperfine field 30.1 T at room temperature. M~Sssbauer spectroscopy, X-ray powder diffraction and magnetization measurements on magnetically oriented powder samples provide evidence of the presence of an easy-cone-type magnetocrystalline anisotropy for both the parent and nitrided compounds in the temperature range 85-300 K. The cone angles calculated from the fitted M0ssbauer spectra are 34 ° for the parent compound and 36 ° for the nitrided compound.

1.

Introduction

A ternary phase o f nominal c o m p o s i t i o n R3(Fe,T)29 with a monoclinic structure has been recently identified [1-3]. Besides Nd3(Fe,Ti)29, which has been studied in a number of reports [3-12], the structure is now known to exist with R = Y [13], Ce [14-16], Pr [14,15,17,18], Sm [19], Gd [15] and Tb [20], and T = V [21], Cr, Mn [5,14] and Mo [12]. This new phase can easily absorb N atoms [12,15,16,22,23] and H and C atoms [22,24], with the phase Sm3(Fe,Ti)29N x having the most

* Corresponding author. Fax: +30-1-651-9430; email: [email protected].

promising magnetic properties for permanent magnet applications [23,25-28]. The introduction of N, H or C atoms results in a considerable enhancement of the magnetic properties of the compounds as in the related S m 2 F e l 7 N 3_ ~ [29] and Nd(Fe,Ti)I2N l _ ~ [30] phases. The structure of R3(Fe,Ti)29 is intermediate between the well known rhombohedral Th2Znj7 and tetragonal ThMnl2 structures. In a recent work [12] we showed that the Nd3(Fe,Ti)29-type structure can be described more accurately in the A 2 / m space group than in the P2 l / c proposed in Refs. [4,6], and that the nature of the magnetocrystalline anisotropy of Nd3(Fe,Ti)29 and Nd3(Fe,Ti)29Nx is that of an easy-cone type. The number of nitrogen sites in the 3:29 nitrided phase is four nitrogen atoms per chemical formula [12,22].

0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 5 4 0 - 4

76

v. Psycharis et al./ Journal of Magnetism and Magnetic Materials 153 (1996) 75-85

In the present work, we synthesized the Pr3(Fe,Ti)29 alloys and Pr3(Fe,Ti)29Nx nitrides and studied their structural and magnetic properties in detail. In particular, we report a study of the nature of the magnetocrystalline anisotropy by means of M6ssbauer spectroscopy, X-ray powder diffraction and magnetization measurements. A model for calculating the easy-cone angle from the intensity of the 2,5 lines of the MiSssbauer spectra is presented.

2. Experimental

Ingots with the starting composition of Pr:Fe:Ti = 9.4:85:4.6, corresponding to nominal stoichiometry Pr3(Fel_yTiy)29, y = 0.05, were prepared by argonarc-melting of high purity elemental constituents ( > 99.9%). The ingots were then wrapped in tantalum foil, heat treated in evacuated sealed tubes at 1323 K for 72 h and water quenched. The annealed samples were ground to fine powder ( < 37 Ixm) and were nitrided by heating in high-purity nitrogen at 4 atm for 12 h at 673 K. The samples were characterized by means of X-ray powder diffraction (XRD) using Cu K s radiation and Rietveld analysis. The magnetic properties of the

alloys were studied using thermomagnetic analysis (TMA), a Quantum Design SQUID magnetometer (applying a field up to 5 T and at temperatures of 5-300 K), M~Sssbauer spectroscopy, and ac susceptibility measurements. The 57Fe M6ssbauer spectra were obtained at 85 and 300 K on a conventional constant acceleration spectrometer with a 57Co(Rh) source moving at RT while the absorber was at the desired temperature. The magnetization measurements were performed on magnetically oriented powders fixed in epoxy resin. The ac susceptibility measurements were made using a home-made ac susceptometer with a driving coil and two secondary coils wound in opposition, and the usual lock-in detection of the signal. XRD, M6ssbauer spectroscopy, and magnetization measurements on magnetically aligned powders were carried out to study the magnetocrystalline anisotropy of the materials.

3. Results and discussion 3.1. Structure and phase constitution

The X-ray pattern of Pra(Fe,Ti)29 plotted in Fig. 1 is typical of the Nda(Fe,T)E9-type compounds. The

0q

Pra(Fe,Ti)29

© mmllmm

20

L

I

I

I

I

30

40

50

60

70

2-thet,

a

Fig. 1. XRD spectrumof Pr3(Fe,Ti)29 refined by the Rietveldmethod.

80

V. Psycharis et al. / Journal of Magnetism and Magnetic Materials 153 (1996) 75-85 Table 1 Crystallographic data for Pr3(Fe,Ti)29 compound (space group No. 12 A 2 / m ) . Unit cell dimensions: a = 10.647(1) ,~, b = 8.6014(7) ,~, c = 9.7550(9) A, /3 = 96.92(1) ° and V = 886.86 ,~3. Agreement indices (R-factors): R p = 6 . 7 4 , Rwp= 10.95, R B = 5.95, Rexp = 2.60% Atom

Site

x

y

z

Pr I Pr 2 Fe I Fe 2 Fe 3 Fe 4 Fe 5 Fe 6 Fe 7 Fe 8 Fe 9 F%o Fell

2a 4i 2c 4i 4i 8j 8j 4g 4i 8j 4i 8j 4e

0.0 0.5983(5) 0.5 0.136(2) 0.250(2) 0.797(1) 0.623(1) 0.0 0.889(1) 0.801(1) 0.706(2) 0.404(1) 0.0

0.0 0.0 0.0 0.0 0.0 0.7783(8) 0.643(1) 0.354(2) 0.0 0.249(2) 0.0 0.750(1) 0.25

0.0 0.1849(6) 0.5 0.297(2) 0.522(2) 0.090(1) 0.184(1) 0.0 0.282(2) 0.346(2) 0.914(2) 0.063(1) 0.25

annealed alloys were single phase, apart from a small amount of tx-Fe impurity. The ot-Fe content as calculated by Rietveld analysis was 4.6 wt% and by MSssbauer spectroscopy 2 wt%. As we showed in Ref. [12], the Nd3(Fe,T)29-type compounds crystallize in the monoclinic space group A 2 / m . Thus, the crystal structure refinement was performed using this space group. The starting parameters were taken from Ref. [12] for Nd3(Fe,Ti)29. Table 1 gives the final values of the calculated atomic positions. The bond distances are given in Table 2. Fig. 1 shows plots of the Rietveld diffraction pattems (observed, calculated and difference pattem). Nitrogenation results in a lattice expansion of 6.6%, which corresponds to eight nitrogen atoms per unit cell, as we showed in Ref. [12]. XRD and thermomagnetic analysis (TMA) measurements showed that the samples were fully nitrided. The et-Fe content did not increase considerably (5.9 wt%) but the formation of the nitrided 1:12 phase was detected (12.2 wt%). The cell parameters of Pr3(Fe,Ti)29Nx are a = 10.939(5),~, b = 8.797(4) A, c = 9.919(5) A, ~ = 97.82(1) ° and the unit cell volume V = 945.62 ,~3.

3.2. Magnetic properties Thermomagnetic analysis (TMA) confirmed that the annealed alloy was of single phase apart from the

77

small amount of tx-Fe impurity. The Curie temperature, determined with a heating rate of 5°C/min, was 392(5) K, in agreement with the value reported in Ref. [14], 393 K. Magnetization measurements at 5 and 300 K parallel and perpendicular to the magnetic field were carried out on powder samples magnetically oriented in epoxy resin at room temperature using a 2 T applied field (Fig. 2). The saturation magnetization was deduced from the law of approach to saturation (LAS) and was found to be 169.1 A m2/kg at 5 K and 135.4 A m2/kg at 300 K. By extrapolating the MII- M± versus H plots the anisotropy fields were found to be 7.4 T at 5 K and 3.9 T at 300 K. These values, M s and H A, are close to those found for Nd3(Fe,Ti)29 [12]. The thermal dependence of the magnetization at a constant field of 0.01 T is shown in Fig. 3. The zero-field-cooled Table 2 Bond lengths (,~) for the compound Pr3(Fe,Ti)29 Pr I - F e 2 X 2 -Fe 4 X4 -Fe 6 X 2 -Fe 7 X2

3.08(2) 3.09(1) 3.04(2) 3.12(2)

Prl-Fe 3 X 1 - F e 4 X2 -Fe 5 X2 -Fe 5 X2 -Fe 7 X 1 -Fe 9 X 1 -Felo X 2

3.11(2) 3.07(1) 3.08(1) 3.07(1) 3.13(1) 3.00(2) 3.12(1)

Fei-Fe 3 X2 -Fe 5 × 4 -Felo X 4

2.70(2) 2.426(9) 2.490(9)

Fe 2 - F e 3 X 1 - F % X2 - F e 5 X2 -Fe 6 x 2 -Fe 7 X 1 -F% X 2 -Fe 9 X 1 -Fell X 2

2.38(2) 2.70(1) 2.83(2) 2.88(2) 2.62(2) 2.70(2) 2.81(3) 2.60(2)

Fe 3-Fe 4 x 2 -Fe 5 x 2 -Fe 6 × 2 -Fe 7 X 1 -Fe s X 2 -Felo X 2

2.65(1) 2.83(2) 2.93(2) 2.55(3) 2.59(2) 2.70(2)

F%-Fe s x 1 -Fe 6 X 1 -Fe 7 x 1 -Fe 8 x 1 -Feg x 1 -Fe 9 X 1 -Felo x 1 -Fejj × 1

2.46(1) 2.68(1) 2.77(2) 2.50(2) 2.40(2) 2.67(2) 2.47(1) 2.52(1)

Fes-Fe s X 1 -Fe 8 × 1 -Fe 9 X 1 -Felo X 1 -Fel0 X 1 -Felo × 1

2.46(1) 2.50(I) 2.62(2) 2.65(1) 2.56(1) 2.68(1)

Fe6-Fe 6 × 1 -Fe 7 x 2 -Fe s x 2 - F e l l X2

2.51(2) 2.62(2) 2.60(2) 2.598(6)

Fe 7 - F e 8 × 2 -Felt X2

2.45(2) 2.491(7)

Fes-Fe 9 X 1 -Feto x 1 -Fell X 1

2.51(2) 2.45(2) 2.42(1)

Fe9-Felo X2

2.47(1)

Felo-Felo X 1

2.51(2)

V. Psycharis et al. / Journal of Magnetism and Magnetic Materials 153 (1996) 75-85

78 1601

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N

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Field

0.10

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4

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(T)

I 50

I 100

,

I t I , 150 200 Temperature (K)

I 250

I 300

Fig. 2. Magnetization curves along and perpendicular to the orientation direction at 5 and 300 K of Pr3(Fe,Ti)z9.

Fig. 4. Temperature dependence of the ac magnetic susceptibility of Pr3(Fe,Ti)29.

curve indicates domain wall motion and no other magnetic transition is observed in this temperature range. In Fig. 4 the ac-magnetic susceptibility against temperature is plotted. A relative broad peak is observed at about 160 K. This kind of magnetic transition has been observed in the ac susceptibility curve of Nd3(Fe,Ti)29 [7] and Tb3(Fe,Ti)29 [20], both at the same temperature, and has been interpreted as

a first-order magnetization process (FOMP) of the Al-type in uniaxial systems. As will be discussed below, M6ssbauer spectroscopy on magnetically oriented powders at 85 and 300 K showed that there is no change in the easy magnetization direction in this temperature range. Thus, we believe that the magnetic transition observed in the ac susceptibility should not be attributed to a spin reorientation phenomenon. In other words, it is not related to a change in the different anisotropy contributions of the Pr and the Fe sublattices with temperature, but is perhaps associated with a magnetic phase transition of as yet unknown character. After nitrogenation, the Curie temperature of the nitrided compound increased by 330 K and reached 721(5) K. The presence of the 1:12 nitride secondary phase could not be detected since the Curie temperature of this phase is very close to that value. Magnetization measurements on magnetically oriented powder samples at 5 and 300 K, parallel and perpendicular to the field, are plotted in Fig. 5. The values of the saturation magnetization, determined from the law of approach to saturation, were 184.3 and 174.8 A m2/kg, and those of the anisotropy fields were found to be 13.9 and 7.2 T at 5 and 300 K, respectively. The magnetization against temperature measurements at a field of 0.01 T applied parallel to the

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Fig. 3. Zero-field-cooled (ZFC) and field-cooled (FC) M versus T curves of Pr3(Fe,Ti)29 at a field of 0.01 T.

V. Psycharis et al./ Journal of Magnetism and Magnetic Materials 153 i1996) 75-85 200

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3.3. Magnet©crystalline anisotropy

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The type of the magnet©crystalline anisotropy of Pr3(Fe,Ti)29 and Pr3(Fe,Ti)29N x was studied using three different experimental techniques: X-ray powder diffraction, M6ssbauer spectroscopy and magnetization isotherms on magnetically oriented samples. As discussed below, it was concluded that there is strong experimental evidence from all of these techniques that the nature of the magnet©crystalline anisotropy in Pr3(Fe,Ti)29 and Pr3(Fe,Ti)29Nx is that of an easy-cone type in the temperature range 85-300 K. Similar results were reported in Ref. [12] for Nd3(Fe,Ti)29 and Nd3(Fe,Ti)29N x.

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Pr 3 (Fe,T029 N x

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Magnetic Field (T)

3.3.1. MOssbauer spectroscopy

Fig. 5. Magnetization curves of Pr3(Fe,Ti)29N ~ along and perpendicular to the orientation direction at 5 and 300 K.

orientation direction are shown in Fig. 6. The zerofield-cooled curve reveals behavior typical of domain wall motion. In the ac susceptibility measurements no magnetic transition of any kind was observed in the temperature range 77-300 K.

29

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28

I

~00•

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Pr 3 (Fe,Ti)29 N x

O

FC

t"q

27 •

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ZFC

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25 I

24 0

100

,

I

i

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200 300 Temperature (K)

,

400

Fig. 6. Zero-field-cooled (ZFC) and field-cooled (FC) M versus T curves of Pr3(Fe,Ti)29Nx at a field of 0.01 T.

Fig. 7 shows the 57Fe M~Sssbauer spectra of Pr3Fe27.5Til. 5 and Pr3Fe27.sTil.sNx, respectively, at 85 and 300 K. In the A 2 / m space group the 3:29 structure is described by 11 crystallographically inequivalent iron sites. A careful examination of the site environments led us to divide the 11 sites into four groups. For this purpose, we applied a Wigner-Seitz cell analysis. A detailed description of this approach will be published elsewhere. According to this analysis there are three main groups with respect to the number of the nearest neighbors (nn), i.e. 9, 10, 13 nn (see Table 2). In order to determine the number of the nearest neighbors the occupancy of some of the iron sites by Ti was also taken into account. Based on neutron diffraction data for Nd3(Fe,Ti)29, Hu et al. [I0] reported that in the P21/c description of the 3:29 structure the iron sites 4e 3, 4e 4, and 4e14 are occupied by Ti 30.45%, 21.4% and 10.3% (total site occupancy), respectively. In our description these sites correspond to Fe 2, Fe 3 and Fe6, which in both descriptions are the dumb-bell sites. It is characteristic that in the transformation 3:29 ~ 1:12 these sites coincide with the 8i site of the 1:12 phase, which is preferentially occupied by Ti [31]. The iron sites were therefore finally divided in three groups with average numbers of Fe nearest neighbors 8.75, 9.4 and 12.3 respectively. However, the M~Sssbauer spectra indicate that a minimum of four subspectra are in fact required. An examination of the largest iron group (Fe 1, Fe 4, Fes, Fe 7, Fe 8, F e ~ ) with 9.4 nn shows that it has two separate

V. Psycharis et al./Journal of Magnetism and Magnetic Materials 153 (1996) 75-85

80

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99.5

99.0 e~

i~

98.5

Pr3(Fe,Ti)29

•

°

'~ 100.0 [.-,

~ 99.8 a) 99.6 I

-10

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-15

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5

I0

Velocity (mm/s) I

I

100.0

I

99.5

~- - 99.0

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.0 .~ 98.5 98.0

Pr3(Fe,Ti)29Nx

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b)

99.7 99.6 ,

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ranges of bond lengths (see Table 2) which naturally subdivide this component. Thus, we split this iron group into two subgroups: one of Fe 4, Fe 5. Fe 7 with the longer average bond lengths of 2.589 A, and one with Fel, Fe 8, Fel~ with the shorter average bond lengths of 2.515 A. The fit was then made with four components with an area ratio of 1:2:t.5:1.2 corresponding to the populations of these iron site groups, taking into account the Ti occupancy of the sites mentioned above. A fifth component was introduced for et-Fe. During the fitting the relative subspectral areas were kept constrained to be in the same ratio for all spectra (parent and nitrided samples). A small amount of line broadening was allowed for each component to simulate the distribution of environments within each component. The fits with four subspectra yielded average 57Fe hyperfine fields of 28.5 and 20.3 T at 85 and 300 K, respectively, for the parent compound, and 32.3 and 30.1 T at 85 and 300 K for the nitride, respectively. The substantial increase in the average hyperfine field of the Pr3(Fe,Ti)29N x sample reflects the enhancement of the Curie temperature by 330 K after nitrogenation and is typical of the rare-earth intermetallic compounds. A more detailed analysis of the MiSssbauer spectra is beyond the scope of this paper, and will be discussed in a future publication. Here, we elaborate on the spectral intensities of the aligned absorbers in order to study the magnetocrystalline anisotropy of the materials at different temperatures. In MSssbauer spectroscopy the line intensities of a magnetically split spectrum depend on the angle 0 between the magnetic moment and the ",/-rays. The intensities of the three components are given by

10

Velocity (mm/s) Fig. 7. Fitted Mbssbauer spectra at 85 and 300 K of magnetically aligned powder samples of(a) Pr3(Fe,Ti)z9 and (b) Pr3(Fe,Ti)29N x with the ~,-rays parallel to the alignment direction.

A M = -T-1

3(1 + cos20)

lines 1,6;

AM = 0 AM = + 1

4 sin20 1 + cos20

lines 2,5; lines 3,4.

Thus, for the cases of 0 = 90 ° a ratio of 3:4:1 is obtained, and for 0 = 0 °, 3:0:1. For a random distribution of moments the intensity ratios are obtained by integrating the above expressions over a sphere and the ratio 3:2:1 is deduced. For a system with an easy-cone anisotropy the grains in a magnetic field perpendicular to the sample holder are aligned within the cone, resulting in a configuration with the axes of each individual easy cone forming a cone with the

V. Psycharis et al. / Journal of Magnetism and Magnetic Materials 153 (1996) 75-85 perpendicular to the sample with an angle equal to the angle of the easy cone 0c (Fig. 8). In this case, after removing the magnetic field, the magnetic moments are equally distributed within a cone of angle 2 0c in a perfectly aligned sample, as depicted in Fig. 8. Thus, when the direction of the "y-rays is parallel to the alignment direction, to get the intensity ratios the above expressions are again integrated but only over the solid angle of the cone. That means that the following calculation is limited to cone angles 0 < 0c < 45 °, i.e. 0 < 2 0c < 90 °. Integrating the intensity equation, we obtain the following expressions: For A M = -T-1 (lines 1,6):

A

zo L

I

'

I

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/' /

1.6 "c-raysI/H

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

3 fo2~ f020~ ( 1 + cos2O)sin 0 d0dqo I = S--A

'

81

0

20

40 60 20c (degrees)

80

100

4 - 3 cos 0~ - coS30c

(1)

=

1 -

c o s 0~

B 4.0~,,.~

i

,

I

,

I

'

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3.8 where S A is the solid angle of the cone 2 0c. The intensity of A M = +__1 (lines 3,4) is just one-third of this value. For A M = 0 (lines 2,5)

4 £2~r£ZO~sin3OdOdq ° 1 = S--A

3.6 3.4 3.2 3.0 2.8

=

s 1 - cos oc (1 + 3

sin 0c)

(2)

1 - cos 0c

2.6 2.4

U s i n g t h e s e f u n c t i o n s the d e p e n d e n c e o f IaM=T.l/laM= o on 0c can be obtained (Fig. 9). Fitting the intensities o f aligned samples can lead to an accurate determination o f the cone angle in a well aligned sample. To test the method of alignment, and

C

0 C Fig. 8. Configuration of moment distribution in a magnetically aligned sample with easy-cone anisotropy; (A) easy-cone axis, (B) alignment direction, and (C) ~,-ray direction.

2.2 2.0

0

20

40 60 20c (degrees)

80

100

Fig. 9. Dependence of the intensity x of lines 2,5 from the cone-angle 0c (a) with the ~/-raysparallel to the alignment direction, and (b) perpendicular to the alignment direction ( x = 31aM=o/laM=~:l).

also our model, an aligned sample of Nd2Fe~4B was prepared at room temperature and then the spectra at room temperature and at 85 K were obtained (Fig. 10). The negligible intensity of lines 2,5 at room temperature indicates that there is nearly perfect alignment o f the easy-axis moments. A n estimate o f the degree of alignment using a distribution of the form cos~0, as proposed by Coey et al. [32], yields a value of n = 8, i.e. a rather good alignment. At 85 K

82

V. Psycharis et al./Journal of Magnetism and Magnetic Materials 153 (1996) 75-85

the intensity ratio is 3:0.7:1, giving a 20 c angle of 52 °, i.e. 0~ = 26°, very close to the known easy-cone angle of Nd2Fel4B at this temperature, 30° [33]. Fig. 7 shows a comparison of the M5ssbauer spectra of the parent and nitrided aligned samples at 85 and 300 K. The intensities of the lines 2,5 of the aligned samples are reduced in both the parent and nitrided compounds and remain the same at both temperatures. We believe that this is the strongest experimental evidence that Pr3(Fe,Ti)29 and Pr3(Fe,Ti)29Nx present easy-cone-type anisotropy in the temperature range 85-300 K. The fitted curves yielded intensity ratios of 3:1.35:1 for the parent compound and 3:1.45:1 for the nitride, which remain constant with temperature in both cases. These values give a cone angle 0~ = 34 ° for Pr3(Fe,Ti)29 and 0~ = 36 ° for Pr3(Fe,Ti)29N~. However, as shown in Ref. [16], this behavior of the 2,5 line intensity could be also interpreted as planar anisotropy with in-plane preference directions of the easy magnetization. In order to clarify this point we prepared another aligned sample of the parent Pr3(Fe,Ti)29. This time the magnetic field was

i

i

100.0 99.8 99.6

I

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I .

.

°'.

.'1

•"

Pr3 (Fe'Ti)29

U

! T = 300 K

96.0 -10

I

I -5

I 0 Velocity (mm/s)

I 5

I

10

Fig. 11. Fitted MiSssbauerspectrum at 300 K of a magnetically aligned powder sample of Pr3(Fe,Ti)29 with the ~-rays perpendicular to the alignment direction.

applied parallel to the plane of the sample holder and the measurement was carded out with the direction of the ",/-rays perpendicular to the sample holder, i.e. perpendicular to the alignment direction. In this case, to get the intensity ratios the integration should be done over the angle -rr/2 - 2 0c to the angle r r / 2 + 2 0c (see Fig. 8). By analogy to the above mentioned calculation, the intensity ratio laM=:~JIaM= o is now given by the following expression: I~M=.y_, -

I~M=0

3 1 + lsin20 =

4 1 -- 3sin20 '

(3)

the dependence of IAM= -V-l/IaM=O on 0c is given in Fig. 9(b). In such a configuration a system having in-plane anisotropy is expected to present an intensity ratio of 3:2:1. The fitted curve (Fig. 11) yielded an intensity ratio of 3:2.25:1, which corresponds to a cone angle 0c = 35 °, which is in very good agreement with the value obtained when the 7-ray direction was applied parallel to the alignment direction.

Nd2FelgB

100.0 99.8

99.6 99.4 -10

' .

.~' ~~ ,.,o° i 97.0 98.0

x =

99.0

.I .

99.0

-

= 85 K

'

"" .

~

3

99.4 o= 99.2

..

100.0

3.3.2. X-ray powder diffraction i

/

-5

,

I

*

0 5 Velocity (mm/s)

10

Fig. 10. Fitted MSssbauerspectra at 85 and 300 K of magnetically aligned powder samples of Nd2Fe 14B.

Fig. 12 shows the XRD spectra of the parent Pr compound (Fig. 12a) and the corresponding nitride (Fig. 12b) from non-aligned and magnetically aligned powders, with the magnetic field normal and parallel to the sample holder under a magnetic field of 2 T at

V. Psycharis et a l . / Journal of Magnetism and Magnetic Materials 153 (1996) 75-85

A

Pr ~(Fe,Ti) 29

EJ

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28

30

B

32

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38

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42

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50

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Pr 3(Fe,Ti) 29N,

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30

32

34

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38

2-theta

Fig. 12. XRD spectra of (a) the parent Pr3(Fe,Ti)29 compound from non-aligned and magnetically aligned powders with the magnetic field normal and parallel to the plane of the sample holder, and (b) of the nitrided Pr3(Fe,Ti)29N x compound from non-aligned and magnetically aligned powders with the magnetic field normal and parallel to the plane of the sample holder.

300 K. The most dramatic changes can be seen in the reflections ( 4 0 - 2 ) , (040) and (204). It is worth noting that the directions normal to these planes are not casual. The [ 4 0 - 2 ] direction is related to the c-axis of the 1:12 phase and the [204] direction to the c-axis of the 2:17 phase [12]. In the case of the parent compound and when the field is applied normal to the plane of the holder, the (40 - 2 ) and (204) reflections decrease and the (040) reflection increases (Fig. 12a). The opposite behavior was observed for the same group of reflections when the field was applied parallel to the sample holder (Fig. 12a). The fact that there are no significant changes in the intensities of the general reflections for the two kinds of alignment indicates that neither planar nor easy-axis anisotropy but rather an easy-cone-type anisotropy should be expected for this compound at

83

room temperature. In the case of the nitrided sample the ( 0 4 0 ) and ( 2 0 4 ) reflections decrease and the ( 4 0 - 2 ) reflection increases slightly when the field is applied normal to the sample holder (Fig. 12b). The opposite behavior for the corresponding group of reflections is observed if the field is applied parallel to the sample holder (Fig. 12b). As in the case of the non-nitrided compound there are no changes in the intensities of the general reflections, which again indicate the presence of an easy-cone-type anisotropy, but probably with a different cone axis, considering the differences between the patterns of the two aligned samples. These results are in agreement with those obtained from the M~Sssbauer spectra as discussed above. Nevertheless, a prediction of the possible cone axes for both the parent and the nitrided compound, cannot be done based simply on these data. It is worth noting that in Sm3(Fe,Ti)29, which is uniaxial, the easy magnetization direction lies along the [40 -2] direction [19], whereas in Sm3(Fe,Ti)29N x (nitride) [23] and Sm3(Fe,Ti)29C x (carbide) [24] it lies along the [2 0 4] direction. As already mentioned, the [ 4 0 - 2 ] direction is related to the c-axis of the 1:12 phase and the [2 0 4] direction to the c-axis of the 2:17 phase.

3.3.3. Magnetization measurements So far, the magnetocrystalline anisotropy has not been described in terms of anisotropy constants for systems with monoclinic symmetry. However, the structure of the 3:29 phase can be described as consisting of layers perpendicular to the [2 0 4] direction with a hexagonal configuration in the Fe containing layers. Thus, an extrapolation of the anisotropy theory describing hexagonal systems provides an approximation in the study of the anisotropy of the 3:29 phase. Such an approximation was used in Ref. [12] for Nd-3:29, as well as by other authors for Nd- [8] and Tb-3:29 [20]. To calculate the anisotropy constants K 1 and K 2 we used the Sucksmith-Thompson formula to plot H / M versus M 2 [34]. Fitting this curve in the case of Pr3(Fe,Ti)29 the following values for the anisotropy constants were obtained: K~ = - 5.6 M J / m 3, K 2 = 3 . 7 M J / m 3 at 5 K, and K 1 = - 1 . 3 M J / m 3, K z= 1.6 M J / m 3 at 300 K. From the relations K I < 0, K 2 > 0 and K I + 2 K 2 > 0 it is deduced that the

V. Psycharis et al. / Journal of Magnetism and Magnetic Materials 153 (1996) 75-85

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magnetocrystalline anisotropy should be that of an easy cone. In the case of the easy-cone anisotropy the anisotropy field can be calculated from the formula [35] (4)

H A = 2KJM~.

Using this formula, we found values of 8.6 and 3.2 T at 5 and 300 K, respectively, which are in good agreement with those determined by extrapolation of the M I I - M . versus H curves, i.e. 7.4 and 3.9 T, respectively. The cone angles calculated from the formula [34] 0c = arcsin~/-

KJ2K

2 ,

(5)

are 59 ° and 53 ° at 5 and 300 K, respectively. Following the same procedure for the nitrided compound the anisotropy constants obtained were: K l = - 9 . 1 M J / m 3, K 2 = 6 . 5 M J / m 3 at 5 K and K 1= - 4 . 9 M J / m 3, K 2 = 4 . 1 M J / m 3 at 300 K. These values also fulfil the conditions for the presence of easy-cone magnetocrystalline anisotropy. The anisotropy field values calculated using K 1 are 13.6 and 7.7 T at 5 and 300 K, respectively, in good agreement with those determined by extrapolation of the Mll - M± versus H curves, i.e. 13.9 and 7.2 T, respectively. The cone angles calculated from Eq. (4) are 56 ° and 51 ° at 5 and 300 K, respectively. The cone-angle values obtained from the Sucksmith and Thompson formula are larger than those calculated from M~Sssbauer spectroscopy for both the parent and the nitrided compounds. Durst et al. [36] showed that the application of the SucksmithThompson model on polycrystalline oriented samples introduces errors especially of K 2 due to the fact that grain misalignments produce similar curvatures of the magnetization curve as a higher anisotropy constant K 2 which is used to calculate the cone-angle. Moreover, this uncertainty becomes larger from the fact that this model has been developed for systems with hexagonal symmetry. We suggest that the values obtained from the M~Sssbauer spectroscopy are probably closer to reality.

[12]. The addition of nitrogen leads to a significant increase in the Curie temperature, saturation magnetization, average hyperfine field, i.e. iron moment, and the anisotropy field as in the case of the 2:17 and 1:12 rare-earth-iron alloys. The intrinsic magnetic properties of the material are similar to those of Nd3(Fe,Ti)29 [3,12], in particular the nature of the magnetocrystalline anisotropy, as expected from the fact that both rare-earths have negative second-order crystal field coefficients. M~Sssbauer data of oriented samples of Ce3(Fe,Ti)29, with the non-magnetic Ce atom, have provided evidence that the anisotropy of the iron sublattice of the 3:29 phase could be planar [16]. In the present study Mbssbauer spectroscopy, X-ray powder diffraction and magnetization measurements on magnetically oriented powder samples give strong evidence that the magnetic structure of Pr3(Fe,Ti)29 and Pr3(Fe,Ti)29Nx is noncollinear over the whole temperature range 85-300 K. This may be due to the peculiar structure of the 3:29 phase, which is intermediate between the rhombohedral Th2Znl7 and the tetragonal ThMnl2 structures. It seems that nitrogenation results in a spin reorientation of the easy-cone axis though the easy-cone angle remains the same, ~ 35 °. The study of Pr3(Fe,Ti)29 and Pr3(Fe,Ti)29Nx can provide a better understanding of the behavior of the anisotropy in Nd3(Fe,Ti)29. For the latter it has been reported that a spin reorientation occurs at ~ 230 K from planar to easy-cone anisotropy [7]. On the other hand, from neutron diffraction data at room temperature, Hu et al. predicted that the moments could be found to lie along the a axis, although the possibility of a small component in the b direction was not excluded [10]. This supports our results, derived from magnetization measurements, that Nd3(Fe,Ti)29 presents easy-cone anisotropy over the whole temperature range 85-300 K [ 12]. This assumption was confirmed by MSssbauer spectroscopy on magnetically oriented Nd3(Fe,Ti)29 powder samples [37], which present the same behavior in the temperature range 85-300 K as that of Pr3(Fe,Ti)29 reported in this work.

4. Conclusions The ternary alloy Pr3(Fe,Ti)29 and its nitride were synthesized. The structure refinement obtained from X-ray powder diffraction confirms the monoclinic A 2 / m space group earlier reported for Nd3(Fe,Ti)29

Acknowledgements This work was partially supported by the B / E CT91-405 project of the EU. We are grateful to V. Vlessides for careful SQUID measurements.

V. Psycharis et al./Journal of Magnetism and Magnetic Materials 153 (1996) 75-85

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