A magnetic and Mössbauer spectral study of PrFe11Ti and PrFe11TiH

Journal of Alloys and Compounds 377 (2004) 1–7

A magnetic and Mössbauer spectral study of PrFe11Ti and PrFe11TiH Cristina Piquer a,f , Fernande Grandjean a,∗ , Olivier Isnard b,c , Viorel Pop b,d , Gary J. Long e a Department of Physics, B5, University of Liège, B-4000 Sart-Tilman, Belgium Laboratoire de Cristallographie, CNRS, associé à l’Université J. Fourier, BP 166X, F-38042 Grenoble, Cedex, France c Institut Universitaire de France, Maison des Universités, 103 Boulevard Saint-Michel, F-75005 Paris, Cedex, France d Babes Bolyai University, 400084 Cluj-Napoca, Romania e Department of Chemistry, University of Missouri-Rolla, Rolla, MO 65409-0010, USA f Instituto de Ciencia de Materiales de Aragon-CSIC, University of Zaragoza, 50009 Zaragoza, Spain

b

Received 12 December 2003; accepted 6 January 2004

Abstract The lattice parameters, magnetic and Mössbauer spectral properties of PrFe11 Ti and PrFe11 TiH have been measured between 4.2 and 295 K. Both compounds crystallize in the ThMn12 -type structure. The insertion of hydrogen in PrFe11 Ti anisotropically expands the unit-cell volume by 0.4%. Both compounds are ferromagnetically ordered with Curie temperatures of 547 and 604 K, respectively. Between 4.2 and 295 K, the easy magnetization direction is within the basal plane along the [1 0 0] direction as indicated by the Mössbauer spectra which have been fit with a model taking into account both the binomial distribution of titanium near neighbors of the iron atoms and the basal orientation of the magnetic moments. © 2004 Elsevier B.V. All rights reserved. PACS: 75.50Bb; 76.80.+y; 75.20.En; 75.30.Cr Keywords: Rare earth compounds; Hydrogen absorbing materials; Gas–solid reactions; Mössbauer spectroscopy; Magnetic measurements; Transition metal compounds; Metal hydrides

1. Introduction To the best of our knowledge there have been no published papers detailing the properties of the compounds found in the iron rich corner of the Pr–Fe–Ti ternary alloy phase diagram. In contrast, the iron rich corner of the related Nd–Fe–Ti [1] and Sm–Fe–Ti [2] phase diagrams have been investigated in detail. In the most recent study [1] undertaken at 1373 K, three major phases have been identified, specifically, the Nd(Fe,Ti)12 and Nd2 (Fe,Ti)17 solid solutions and a third solid solution that was originally described as Nd2 (Fe,Ti)19 but finally identified as Nd3 (Fe,Ti)29 . The first two solid solutions crystallize with the ThMn12 and Th2 Zn17 -type structures, respectively, both of which can be derived from the CaCu5 -type structure [3]. The Nd3 (Fe,Ti)29 solid solution exhibits a more complex monoclinic structure [4,5], a structure that also may be related to the CaCu5 type structure.

∗

Corresponding author. Fax: +32-43664516. E-mail address: [email protected] (F. Grandjean).

0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2004.01.028

Hence, all three of these phases are structurally related, have very similar compositions, and present a rather broad solid solution domain for the substitution of titanium for iron. Although the Pr–Fe–Ti ternary alloy phase diagram is less well known, the presence of the Pr3 (Fe,Ti)29 , Pr2 (Fe,Ti)17 and Pr(Fe,Ti)12 solid solutions is well established. However, the latter, which is known to be difficult to prepare [6], has seldom been studied. Due to the size and electronic similarities of praseodymium and neodymium, we have based our investigation of the Pr–Fe–Ti compounds on the Nd–Fe–Ti ternary phase diagram. The goal of the present work has been the synthesis and characterization of both the highly pure Pr(Fe,Ti)12 solid solution and the resulting hydride compounds that result from the insertion of hydrogen.

2. Experimental On the basis of the Nd–Fe–Ti phase diagram, we have synthesized several Pr–Fe–Ti compounds with different iron to titanium ratios. These compounds have been synthesized

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C. Piquer et al. / Journal of Alloys and Compounds 377 (2004) 1–7

in a water-cooled copper crucible by melting 99.95% pure praseodymium and titanium and 99.99% pure iron in a high frequency induction furnace. The resulting ingots were wrapped in tantalum foil, annealed for 5 days at 1373 K in quartz tubes under an argon atmosphere, and quenched in water. On the basis of X-ray diffraction and thermomagnetic results, a sample of actual stoichiometry PrFe11.04 Ti0.96 was selected for study. Only the tetragonal ThMn12 phase was observed in the X-ray diffraction pattern and the sample was found to be single phase with only a small trace of ␣-iron a trace that was only detectable by thermomagnetic analysis. The hydrogen insertion has been carried out at 300 K under 20 bar of hydrogen gas after a 10 min thermal activation at 580 K, an activation that initiates the hydrogen insertion. The presence of one hydrogen per formula unit was determined by measuring the gain in mass and is accurate to ±0.1 hydrogen. The two compounds studied herein will be refered to as PrFe11 Ti and PrFe11 TiH. X-ray diffraction patterns have been recorded with a Guinier-Hägg focusing camera with 1.9373 Å iron K␣1 radiation; silicon powder was used as an internal standard. The lattice parameters have been refined from 24 observed Bragg reflections. The Curie temperatures were measured on a Faraday balance through measurements between 300 and 800 K with a heating and cooling rate of 5 K/min. The sample was sealed in an evacuated silica tube to avoid oxidation upon heating. The magnetic properties were also measured between 4 and 300 K by using the extraction method in a field of up to 9 T. During these measurements the microcrystalline powder was free to rotate in the applied field. The saturation magnetization, MS , values have been obtained by extrapolation of the isothermal magnetization to zero field. The low temperature ac magnetic susceptibilities have been obtained on a computer controlled mutual inductance susceptometer at an exciting field of 10−4 T and a frequency of 1 kHz. The temperature dependence of the real component, χ , has been measured in order to determine the temperatures of the magnetic phase transitions. The real part of the ac susceptibility is predominately influenced by the changes in both the magnetic anisotropy energy and the domain wall energy. The Mössbauer spectra have been measured between 4.2 and 295 K on a constant-acceleration spectrometer which utilized a rhodium matrix cobalt-57 source and was calibrated at room temperature with ␣-iron foil. The Mössbauer spectral absorbers contained 35 mg/cm2 of powdered sample which had been sieved to a 0.045 mm or smaller

diameter particle size. The spectra were measured in a Janis Super–Varitemp cryostat and the temperature was controlled with a Lakeshore Cryogenics temperature controller with an accuracy better than 1% of the observed temperature. The resulting spectra have been fit as discussed below and the estimated errors are at most ±0.2 T for the hyperfine fields and their incremental changes, ±0.01 mm/s for the isomer shifts, and ±0.02 mm/s for the quadrupole shifts. The observed line widths in the magnetic spectra were typically 0.36 ± 0.02 mm/s for both PrFe11 Ti and PrFe11 TiH.

3. Structural and magnetic results The lattice parameters and some of the magnetic properties of PrFe11 Ti and PrFe11 TiH are summarized in Table 1. A small but significant anisotropic unit cell expansion, resulting in an increase in the c/a ratio, occurs upon hydrogen insertion into the PrFe11 Ti lattice. Both PrFe11 Ti and PrFe11 TiH order ferromagnetically below Curie temperatures of 547 and 604 K, respectively. Although the increase in unit-cell volume upon hydrogenation is smaller than in the analogous RFe11 Ti compounds [7], the increase in Curie temperature is substantial. Further, the saturation magnetization increases slightly upon hydrogen insertion into the lattice. A similar increase has been reported for other RFe11 Ti compounds, in which the iron sublattice magnetization has also been found to increase [7,8]. In both PrFe11 Ti and PrFe11 TiH a slightly reduced saturation magnetization is observed at 5 K than at 300 K, a reduction that may originate from an imperfect ferromagnetic alignment of the iron and praseodymium moments due to crystalline electric field effects at low temperature. For a better understanding of this phenomenon a neutron diffraction investigation will be undertaken. The ac susceptibility of PrFe11 Ti and PrFe11 TiH, see Fig. 1, confirms [7] the absence of any magnetic transition between 4 and 300 K. Furthermore, no anomaly has been observed above 300 K in the thermomagnetic analysis. Hence, the easy magnetization axis in both compounds does not change between 4.2 K and their Curie temperature. In PrFe11 Ti, the easy magnetization direction lies within the basal plane [9] between 4.2 and the Curie temperature, because the planar praseodymium sublattice anisotropy dominates the uniaxial iron sublattice anisotropy. Previous investigations of the RFe11 TiHx compounds have demonstrated that hydrogen insertion occurs in the rare-earth environment [7,8] and induces a significant modification in the crystalline electric field gradient at the

Table 1 The lattice parameters, Curie temperatures, and saturation magnetizations of PrFe11 Ti and PrFe11 TiH Compound

a (Å)

c (Å)

c/a

V (Å3 )

TC (K)

MS5 K (␮B )

MS300 K (␮B )

PrFe11 Ti PrFe11 TiH

8.609(2) 8.610(2)

4.798(1) 4.817(1)

0.55732(22) 0.55947(24)

355.6 357.1

547(4) 604(6)

16.8(2) 19.3(2)

19.2(2) 20.5(2)

C. Piquer et al. / Journal of Alloys and Compounds 377 (2004) 1–7

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rare-earth site and, consequently, modifies the magnetic anisotropy. Indeed, an increase in the crystal electric field gradient at the gadolinium site in GdFe11 Ti has been demonstrated by Gd-155 Mössbauer spectroscopy [10]. Hence, hydrogen insertion reinforces the rare-earth contribution to the magnetocrystalline anisotropy and, in agreement with the temperature dependence of the ac susceptibility of PrFe11 TiH, no spin reorientation occurs in this compound which also exhibits planar magnetic anisotropy. This conclusion is in perfect agreement with the Mössbauer spectral results discussed below.

4. Mössbauer spectral measurements

Fig. 1. The temperature dependence of the ac magnetic susceptibility in PrFe11 Ti, solid line, and PrFe11 TiH, dashed line.

The Mössbauer spectra of PrFe11 Ti and PrFe11 TiH obtained between 4.2 and 295 K are shown in Figs. 2 and 3, respectively. The Mössbauer spectra for both compounds show the same overall shape and correspond to a magnetic phase

Fig. 2. The Mössbauer spectra of PrFe11 Ti obtained between 4.2 and 295 K.

Fig. 3. The Mössbauer spectra of PrFe11 TiH obtained between 4.2 and 295 K.

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Table 2 Mössbauer spectral hyperfine parameters for PrFe11 Ti Parameter

T (K)

8f

8i1

H0 (H) (T)

295 225 155 85 4.2

24.8 26.9 27.6 27.8 28.0

δ0 (δ) (mm/s)a

295 225 155 85 4.2

−0.144 −0.084 −0.027 −0.022 −0.022

(−0.029) (−0.019) (−0.009) (−0.007) (−0.006)

−0.075 0.020 0.069 0.091 0.106

(0.086) (0.088) (0.091) (0.088) (0.087)

ε0 (ε) (mm/s)

295 225 155 85 4.2

−0.011 −0.018 0.021 −0.009 −0.006

(0.019) (−0.001) (−0.004) (−0.001) (−0.005)

0.016 −0.036 −0.055 0.016 −0.066

(0.100) (0.106) (0.121) (0.092) (0.092)

(−1.8) (−1.8) (−1.8) (−1.8) (−1.8)

34.0 37.2 38.3 39.2 39.2

8i2 (−2.3) (−2.3) (−2.3) (−2.3) (−2.3)

8j1

32.6 35.4 36.7 36.7 37.0

(−2.7) (−2.7) (−2.7) (−2.7) (−2.7)

26.6 30.1 31.2 31.4 31.8

8j2 (−1.8) (−1.8) (−1.8) (−1.8) (−1.8)

−0.100 −0.017 0.045 0.051 0.059

– – – – – −0.077 −0.017 −0.055 −0.179 −0.062

(−0.284) (−0.265) (−0.266) (−0.266) (−0.264)

0.010 0.019 0.063 0.024 0.131

(−0.041) (−0.049) (−0.053) (−0.049) (−0.050) (0.120) (0.104) (0.098) (0.094) (0.101)

27.6 29.8 30.7 31.4 31.4

Wt. av. (−2.4) (−2.4) (−2.4) (−2.4) (−2.4)

−0.107 −0.027 0.032 0.043 0.050

– – – – – −0.021 −0.017 −0.065 −0.069 −0.079

25.8 28.4 29.4 29.7 29.9

(−0.097) (−0.091) (−0.091) (−0.080) (0.101)

−0.047 −0.062 −0.030 −0.033 −0.039

The numbers in parentheses are the incremental hyperfine parameters for one Ti near neighbor. a Relative to room temperature ␣-iron foil.

in which the easy magnetic direction is contained within the basal plane of the tetragonal structure. The Mössbauer spectra have been analyzed by using a model which takes into account both the distribution of titanium atoms in the near-neighbor environment of the three crystallographically distinct iron sites and the planar direction of the magnetization in these compounds. Further, the model assumes a linear dependence of the hyperfine parameters upon the number of titanium nearest neighbors. The same model has been described in detail and successfully applied in the analysis of the Mössbauer spectra of several different RFe11 TiHx compounds [11–15]. The random occupation of the 8i sites by the titanium atoms creates a distribution of near-neighbor environments for the 8f, 8i, and 8j iron sites. If this distribution is assumed to be binomial, the iron 8i sites contribute to the total spectra three sextets with 6.47, 10.79, and 9.58% areas, and the iron 8f and iron 8j sites each contribute three sextets with 11.51, 15.34, and 9.38% areas. For each site these sextets represent iron atoms with zero, one, and two or more titanium near neighbors, respectively. A further subdivision of these nine spectral components is necessary when the compound exhibits planar magnetic behavior [11,13–15]. For PrFe11 Ti and PrFe11 TiH the best fit of the Mössbauer spectra is achieved when we assume that the magnetization lies along the [1 0 0] direction. In this case, because of the relative orientations of the hyperfine magnetic field and the principal axis of the electric field gradient, Vzz , there is a further magnetic subdivision of the 8i and 8j sextets. Each 8i and 8j sextet is subdivided into two sextets of equal relative areas with identical isomer shift but different quadrupole shifts and slightly different hyperfine fields; these components have been labeled 8i1 , 8i2 , 8j1 , and 8j2 . Consequently, the Mössbauer spectra have been fit with fifteen sextets, which include 26 hyperfine parameters, one line width, and one total absorption area. As is shown in Figs. 2 and 3, all

the fits are very good. The resulting hyperfine parameters for PrFe11 Ti and PrFe11 TiH are given in Tables 2 and 3, respectively. The weighted average given in the last column of these tables are computed with the binomial distribution. It should be noted that the presence of 7% of ␣-iron has been observed in the spectra of both compounds; this ␣-iron has been fit with a sextet with hyperfine parameters constrained to the known hyperfine parameters of ␣-iron. The above model contains a large number of variables and, as a consequence, one would think that it should be easy to obtain good fits but that the resulting fits might be far from unique. To avoid this problem, in the next section we discuss the temperature dependencies of the hyperfine parameters and indicate how they provide confidence to our spectral analysis, its physical meaning, and the extent of its uniqueness. Extensive experience indicates that finding good fits to the observed spectra it is less easy than might be expected, especially when physically viable changes with temperature of the hyperfine parameters are imposed upon the model. Indeed, we have not been able to find an alternative model that both provided better fits and viable variations in the hyperfine parameters with temperature, but such an undiscovered model may, of course, exist. However, fits with an axial model or with an alternative basal magnetization model were always substantially poorer than those shown in Figs. 2 and 3.

5. Results and discussion 5.1. Hyperfine fields The assignment and temperature dependence of the three hyperfine fields for zero titanium near neighbor and their weighted average for PrFe11 Ti and PrFe11 TiH are shown in Fig. 4a and b, respectively. The reader should note that this

C. Piquer et al. / Journal of Alloys and Compounds 377 (2004) 1–7

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Table 3 Mössbauer spectral hyperfine parameters for PrFe11 TiH Parameter

T (K)

8f

8i1

H0 (H) (T)

295 225 155 85 4.2

26.5 27.4 28.3 28.8 29.1

δ0 a (δ) (mm/s)

295 225 155 85 4.2

−0.112 −0.068 −0.033 −0.020 −0.015

(−0.023) (−0.023) (−0.023) (−0.024) (−0.004)

0.095 0.148 0.198 0.222 0.225

(−0.036) (−0.036) (−0.033) (−0.023) (−0.023)

ε0 (ε) (mm/s)

295 225 155 85 4.2

0.175 0.110 0.114 0.130 0.099

(−0.120) (−0.120) (−0.120) (−0.116) (−0.115)

0.019 0.056 −0.044 −0.058 0.014

(−0.060) (−0.080) (−0.038) (−0.036) (−0.036)

(−2.1) (−2.1) (−2.1) (−2.1) (−2.1)

34.8 36.8 38.1 38.4 39.0

8i2 (−1.2) (−1.2) (−1.2) (−1.2) (−1.2)

31.5 32.7 34.2 35.4 36.1

8j1 (−1.6) (−1.6) (−1.3) (−1.3) (−1.3)

28.2 30.3 31.4 32.0 32.4

– – – – – −0.095 −0.041 −0.112 −0.118 −0.082

(−0.029) (−0.050) (−0.012) (−0.015) (−0.015)

8j2 (−2.4) (−2.4) (−2.2) (−2.2) (−2.2)

−0.118 −0.066 −0.029 0.022 0.022

(0.029) (0.029) (0.030) (0.015) (0.014)

−0.038 0.008 −0.078 −0.088 −0.082

(−0.175) (−0.185) (−0.196) (−0.197) (−0.197)

29.2 30.3 31.4 31.9 32.4

Wt. av. (−2.0) (−2.0) (−2.0) (−2.0) (−2.0)

– – – – – 0.233 (−0.097) 0.235 (−0.087) 0.270 (−0.131) 0.300 (−0.132) 0.172 (−0.0132)

27.2 28.6 29.7 30.2 30.7 −0.067 −0.018 0.023 0.058 0.060 −0.023 −0.047 −0.050 −0.030 −0.052

The numbers in parentheses are the incremental hyperfine parameters for one Ti near neighbor. a Relative to room temperature ␣-iron foil.

weighted average is different from that given in Tables 2 and 3, because it does not take into account the decremental field, H. A Wigner–Seitz cell analysis of the three inequivalent iron sites in RFe11 Ti and RFe11 TiH indicates that the 8i site has 11.75 iron near-neighbors, the largest average number of iron near neighbors, whereas the 8f and 8j iron sites both have nine iron near neighbors [16]. Consequently, the sextets with the largest hyperfine field, H0 , have been assigned to the 8i site, on the basis of both its percentage contribution to the spectral absorption area and its iron near-neighbor environment, an assignment that is further supported by the observed isomer shift values, see below. Because of both their identical constrained percentage spectral areas and their iron near-neighbor environments, it is not possible to unequivocally assign the 8f and 8j sextets on the basis of their fields and their assignment is based on their isomer shifts, see below.

The solid lines in Fig. 4 are the result of a least-squares fit with the equation [17],
 3/2  5/2  T T H = H0 1 − B3/2 − C5/2 , TC TC where H0 and TC are the saturation field and magnetic ordering temperature, respectively. The T3/2 term in this equation has its origin in the excitation of long-wavelength spin waves [18]. For the PrFe11 Ti compound, B3/2 is 0.0, and C5/2 is ∼0.85, for all three sites and their weighted average. For the hydride, B3/2 and C5/2 are ∼0.10 and ∼0.30, respectively. The average hyperfine field in PrFe11 Ti increases upon hydrogenation, although the increase results only from increases of ∼0.5 T in the 8j and 8f hyperfine fields. This small increase in hyperfine field as compared to the increases observed in other RFe11 TiHx compounds [11–15,19] may

40

40 (a)

8i

36

hyperfine field (T)

hyperfine field (T)

8i

avg.

32

8j 28

(b)

36 avg. 32

8j 8f

28

8f 24

24 0

50

100 150 200 250 temperature (K)

300

0

50

100 150 200 250 temperature (K)

300

Fig. 4. The temperature dependence of the maximum site average hyperfine fields, H0 , at the three iron sites, and their weighted average, in PrFe11 Ti, (a), and PrFe11 TiH, (b).

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result from the small increase in unit-cell volume and consequently a small increase in the iron-iron near-neighbor distances. The changes in the hyperfine field per titanium near neighbor are between −1.8 and −2.7 T for PrFe11 Ti and between −1.2 and −2.4 T for PrFe11 TiH. These observed decreases in the hyperfine fields upon the replacement of one iron by one titanium near neighbor are very similar to those observed in the other RFe11 Ti compounds and their hydrides [11–15,19], and are within the range of −1.1 to −6 T observed in a spinel oxide [20] and in Nd2 Fe16 Ti, respectively, [21]. In both PrFe11 Ti and PrFe11 TiH, substantial differences in the maximum hyperfine fields assigned to the pair of magnetically inequivalent sites, 8i1 and 8i2 are observed, see Tables 2 and 3. These differences range from 1.5 to 2.5 T for PrFe11 Ti, and from 3.0 to 4.0 T for PrFe11 TiH. In contrast, the differences in the maximum hyperfine fields arising from the subdivided pairs of sextets, 8j1 and 8j2 are smaller and range from 0.0 to 1.0 T for both PrFe11 Ti and PrFe11 TiH. This difference is mainly due to the different orbital contributions to the hyperfine field. The anisotropy in the orbital field results from an incomplete quenching of the orbital moment as a consequence of the anisotropy in the spin-orbit coupling [22,23]. Hence, the stronger anisotropy observed in the 8i hyperfine field indicates that in PrFe11 Ti and PrFe11 TiH the incomplete quenching of the orbital moment by the crystallographic surroundings is more effective in the 8i sites than in the 8j sites. Different contributions to the anisotropy of the orbital field and, hence, to the magnetization, from different crystallographic sites have also been reported in Y2 Fe17 [22].

for PrFe11 Ti and PrFe11 TiH are shown in Fig. 5a and b, respectively. In agreement with the Wigner–Seitz cell analysis [16] of the three inequivalent iron sites, the sequence of decreasing isomer shifts, 8i > 8j > 8f , follows the sequence of Wigner–Seitz cell volumes. A similar correlation between the isomer shifts and the Wigner–Seitz cell volumes has been observed in many RFe11 Ti, R6 Fe13 X, and R2 Fe17 compounds [11–15,19,24–26]. However, the changes in the average isomer shift upon hydrogenation are different for the inequivalent iron sites. The 8i and 8f isomer shifts remain practically unchanged upon hydrogenation, whereas the 8j isomer shift shows a maximum increase of ca. 0.025 mm/s. In the RFe11 TiH compounds the iron 8j site is the only iron site with a hydrogen near neighbor, specifically a hydrogen near-neighbor on the 2b site [8]. As a result the isomer shift of the 8j site exhibits the most change upon hydrogenation. The total increase in the isomer shift upon hydrogenation is ca. 0.012 mm/s, a value which is also slightly reduced from that found in other RFe11 TiHx compounds, [11–15,19] a reduction that may result from the smaller increase in the unit-cell volume upon hydrogenation. The temperature dependence of the weighted average isomer shifts shown in Fig. 5a and b has been fit with the Debye model for the second order Doppler shift [27,28]. For both compounds the resulting effective vibrating mass [27] is, as expected, 57 g/mol and the effective Mössbauer temperature is 350±10 K. Similar Debye temperatures, typical of intermetallic compounds [29,30], have been found for other RFe11 TiHx compounds [11–15,19].

5.2. Isomer shifts

The quadrupole shifts, ε0 of the three inequivalent iron sites observed in the Mössbauer spectra of PrFe11 Ti and PrFe11 TiH are small and lie between −0.2 and 0.3 mm/s. These small quadrupole shifts are expected because

The assignment and the temperature dependence of the three site average isomer shifts, and their weighted average,

5.3. Quadrupole shifts

Fig. 5. The temperature dependence of the three site average isomer shifts and their weighted average in PrFe11 Ti, (a), and PrFe11 TiH, (b).

C. Piquer et al. / Journal of Alloys and Compounds 377 (2004) 1–7

Mössbauer spectral studies [15,31] at 295 K of some related paramagnetic RFe11 Ti and RFe11 Mo compounds yield quadrupole splittings of at most 0.7 mm/s. It should be noted that the total averaged quadrupole shift in both compounds is ca. −0.040 mm/s, a value very similar to that found in the RFe11 TiHx compounds with planar magnetic anisotropy [13–15]. The quadrupole shifts for the magnetically inequivalent sites, 8i1 and 8i2 , and 8j1 and 8j2 are in the ratio of (3 cos2 θ− 1), where θ is the angle between the easy magnetization direction and the principal axis of the electric field gradient tensor, Vzz . For a planar magnetization, θ is 0◦ and 90◦ for the pair of inequivalent magnetic sites and a ratio of 2 to −1 is expected for their quadrupole shifts. Unfortunately, this ratio is not observed, a failure that no doubt results from the different assumptions made in our model and their resulting inadequacies in representing the titanium distribution. Indeed, the fitted linewidths of 0.36 ± 0.02 mm/s for both compounds are larger than the experimental calibration linewidth of 0.28 mm/s. This broadening indicates the inability of our model to adequately account both for changes in quadrupole shifts resulting from the presence of one or more atoms of titanium, for any possible titanium spatial inhomogeneity, and for different relative orientations of the easy magnetization direction relative to Vzz .

6. Conclusions The magnetic phase diagram for PrFe11 Ti and PrFe11 TiH has been investigated by combined ac magnetic susceptibility, thermomagnetic, and iron-57 Mössbauer spectral measurements. Our combined ac magnetic susceptibility, thermomagnetic, and iron-57 Mössbauer spectral measurements of PrFe11 Ti and PrFe11 TiH reveal the absence of any spin reorientation below its ordering temperature and are consistent with a planar magnetic anisotropy for both compounds. The Mössbauer spectra are consistent with the alignment of the iron magnetic moments along the [1 0 0] direction within the basal plane of the tetragonal unit cell. From a microscopic point of view, the insertion of hydrogen increases the iron hyperfine fields and the 8j isomer shift. However, the observed increases in the hyperfine parameters are slightly smaller than those found in the related RFe11 TiHx compounds, in which R is a heavy rare earth, and result from a smaller increase in unit-cell volume upon hydrogenation.

Acknowledgements The financial support of the University of Liège through grant number 2850006 is acknowledged with thanks. F.G. thanks the “Fonds National de la Recherche Scientifique,

7

Belgium,” for grant number 9.456595. This work was partially supported by the US National Science Foundation through grants DMR95-21739 and INT-9815138, and the “Centre National de la Recherche Scientifique, France” through grant action initiative number 7418.

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