X-Ray and neutron diffraction studies of atomic scale structures of crystalline and amorphous TbFe2Dx

Journal of Alloys and Compounds 348 (2003) 167–172

L

www.elsevier.com / locate / jallcom

X-Ray and neutron diffraction studies of atomic scale structures of crystalline and amorphous TbFe 2 D x a, b b a Keiji Itoh *, Kazuyuki Kanda , Kiyoshi Aoki , Toshiharu Fukunaga a

Research Reactor Institute, Kyoto University, Kumatori-cho, Sennan-gun, Osaka 590 -0494, Japan b Kitami Institute of Technology, Koencho-165, Kitami, Hokkaido 090 -8507, Japan Received 6 May 2002; received in revised form 3 June 2002; accepted 3 June 2002

Abstract Both X-ray and neutron diffraction techniques were employed in order to elucidate short-range structures of crystalline (c-)TbFe 2 D 3.8 and amorphous (a-)TbFe 2 D x (x53.0, 2.0) prepared by deuterium absorption of the C15 Laves phase compound TbFe 2 . Interatomic distances and coordination numbers were derived from the radial distribution functions, RDF(r)s. The RDF(r)s observed by X-ray diffraction indicated that c-TbFe 2 D 3.8 adopts a rhombohedral structure, but there is a little difference in the arrangement of metal atoms between the original C15 Laves phase c-TbFe 2 and the rhombohedral c-TbFe 2 D 3.8 . In contrast, our results indicated that there is a large difference in the arrangement of metal atoms between c-TbFe 2 and a-TbFe 2 D x (x53.0, 2.0) and there are clusters of Fe and Tb atoms in a-TbFe 2 D x (x53.0, 2.0). RDF(r)s observed by the neutron diffraction indicated that the D atoms occupy tetrahedral sites consisting of 2Tb12Fe in c-TbFe 2 D 3.8 , while they occupy sites consisting of 4Tb, 3Tb11Fe and 2Tb12Fe in a-TbFe 2 D x (x53.0, 2.0).  2002 Elsevier Science B.V. All rights reserved. Keywords: Rare earth compounds; Metal hydrides; Crystal structure; X-Ray diffraction; Neutron diffraction

1. Introduction Transformation from a crystalline to an amorphous phase by hydrogen absorption is called hydrogen-induced amorphization (HIA) [1]. HIA is an interesting phenomenon, because the equilibrium crystalline alloys change to the metastable amorphous ones in contrast to usual crystallization [2]. HIA has been observed in a large number of intermetallic compounds [1], but its mechanism is still uncertain [3–5]. In order to elucidate the mechanism of HIA, it is useful and important to make the difference in the local environments around hydrogen atoms between an amorphous and a corresponding crystalline alloy. In the C15 Laves phases RFe 2 , either a crystalline or an amorphous alloy is prepared by changing the hydrogen absorption temperature [3–5], so that we can compare the local environment of D atoms in both states of alloys. One of the *Corresponding author. Tel.: 181-724-51-2423; fax: 181-724-512635. E-mail address: [email protected] (K. Itoh).

authors (Aoki) has predicted that hydrogen atoms in amorphous (a-)RFe 2 H x occupy more stable sites rather than those in crystalline (c-)RFe 2 H x through measurements of thermodynamic data [5]. However, the occupation of sites of the H atoms in a- and c-RFe 2 H x is still unclear. In this work, we investigate short-range structures of both c- and a-TbFe 2 D x prepared by deuterium (D) absorption by taking advantage of X-ray and neutron diffraction. X-Ray diffraction has the advantage of direct observation for the arrangement of Tb and Fe atoms because of the much larger scattering factors of Tb and Fe atoms rather than that of D atoms. Radial distribution functions, RDF(r)s, obtained by X-ray diffraction directly describe the short-range structure of c- and a-TbFe 2 D x . On the other hand, we can determine definitely the location of D atoms using neutron diffraction because of the equal coherent scattering length of D atoms compared to those of the metal atoms. By combining X-ray and neutron diffraction, we can obtain information on the arrangement of metal atoms and the location of D atoms in both c- and a-TbFe 2 D x .

0925-8388 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00842-3

K. Itoh et al. / Journal of Alloys and Compounds 348 (2003) 167–172

168

OS

2. Experimental procedure

S(Q) 5 w i – j

2.1. Sample preparation

w i – j is the weighting factor defined as

TbFe 2 was prepared from Tb of 99.9% purity and Fe of 99.9% purity by arc melting in a purified argon atmosphere. The ingot was homogenized to obtain a single phase at 1073 K for 168 h in an evacuated quartz tube. The pulverized crystalline sample was reacted with high purity deuterium (99.999%) at a pressure of 1 MPa. Samples of c- and a-TbFe 2 D x were prepared by deuterium absorption for 6 h at 373 K and for 12 h at 493 K, respectively. Furthermore, in order to elucidate the effect of the D content on the structure of a-TbFe 2 D x , a-TbFe 2 D 2.0 was prepared by degassing of a-TbFe 2 D 3.0 at 473 K for 1 h in vacuum. The content D in the samples was determined at the Center for Organic Elemental Microanalysis, Kyoto University.

ci cj bi bj w i 2j 5 ]] . kbl 2

(Q),

(3)

(4)

The RDF(r) can be derived from the Fourier transformation of S(Q) as follows 2r RDF(r) 5 4p r 2 r 1 ] p

E QsS(Q) 2 1dsin Qr dQ, `

(5)

0

where r is the average number density of atoms, which was measured by Archimedes method with toluene. The RDF(r) is also written as the weighted sum of the partial radial distribution functions, RDF i – j (r) RDF(r) 5 w i 2j

2.2. Neutron and X-ray diffraction

i –j

ORDF

i2j

(r).

(6)

Detailed short-range structures of c- and a-TbFe 2 D x were investigated by X-ray and neutron diffraction techniques. The X-ray diffraction measurement was carried out using a horizontal sample goniometer (RIGAKU RINTUltima) with Mo-Ka radiation operated at 40 kV, 30 mA. After corrections for polarization, absorption and Compton scattering, the scattering intensity, I(Q), was converted to the structure factor, S(Q), where Q54psinu /l, by the generalized Krogh-Moe-Norman method [6,7]. Neutron diffraction measurement was carried out in the High Intensity Total Scattering spectrometer (HIT-II) installed at the pulsed neutron source in the High Energy Accelerator Research Organization (KEK, Tsukuba, Japan). Each alloy sample was put into a vanadium cell of inner diameter 8.0 mm with 0.025 mm wall in thickness. S(Q) was derived by applying various kinds of corrections to the background, absorption [8] and multiple scattering [9], and normalizing with an incident neutron beam profile. S(Q) is related to I(Q) by the Faber-Ziman definition [10] as follows I(Q) 2 hkb 2 l 2 kbl 2 j S(Q) 5 ]]]]]] , kbl 2

(1)

and

Oc b ,

kb 2 l 5

i

i

2 i

Oc b ,

kbl 5

i i

(2)

i

where c i and b i are the concentration and the coherent scattering length for neutron diffraction (or atomic scattering factor for X-ray diffraction) of the component atoms i (i5Tb or Fe or D), respectively. Moreover, S(Q) is written as the weighted sum of partial structure factors Si – j (Q)

Fig. 1. X-Ray diffraction patterns of TbFe 2 deuterated at different temperatures: (a) TbFe 2 , (b) c-TbFe 2 D 3.8 deuterated at 373 K for 6 h, (c) a-TbFe 2 D 3.0 deuterated at 493 K for 12 h and (d) a-TbFe 2 D 2.0 produced by desorbing D from a-TbFe 2 D 3.0 under vacuum at 473 K for 1 h.

K. Itoh et al. / Journal of Alloys and Compounds 348 (2003) 167–172 Table 1 Weighting factors, w i – j , for c-TbFe 2 D 3.8 and a-TbFe 2 D x (x50.3, 0.2) calculated by Eq. (4) for X-ray and neutron diffraction w Fe – D

w Tb – D

wD–D

w Fe – Fe

w Fe – Tb

w Tb – Tb

X-Ray c-TbFe 2 D 3.8 a-TbFe 2 D 3.0 a-TbFe 2 D 2.0

0.0271 0.0216 0.0147

0.0339 0.0271 0.0184

0.0010 0.0006 0.0003

0.1853 0.1872 0.1909

0.4632 0.4693 0.4774

0.2895 0.2942 0.2983

Neutron c-TbFe 2 D 3.8 a-TbFe 2 D 3.0 a-TbFe 2 D 2.0

0.3594 0.3526 0.3212

0.1404 0.1382 0.1254

0.2412 0.1869 0.1134

0.1339 0.1664 0.2275

0.1047 0.1304 0.1778

0.0204 0.0255 0.0347

Fig. 2. Structure factors, S(Q), observed by X-ray diffraction for (a) c-TbFe 2 D 3.8 , (b) a-TbFe 2 D x (x: 3.0, 2.0).

169

3. Results and discussion Fig. 1 shows X-ray diffraction (XRD) patterns of the original c-TbFe 2 and c- and a-TbFe 2 D x prepared by deuterium absorption. The XRD pattern of c-FeTb 2 is indexed on the basis of the C15 Laves phase structure. Deuteration of TbFe 2 at 373 K for 6 h gives rise to the formation of c-TbFe 2 D 3.8 whose diffraction pattern is ] indexed on the basis of a rhombohedral structure (R3m). In contrast, Bragg peaks disappear in TbFe 2 deuterated at 493 K for 12 h and a halo pattern characteristic of an amorphous phase becomes dominant. It is noteworthy that a-TbFe 2 D 3.0 is formed at a higher deuteration temperature and its D concentration is lower than that of c-TbFe 2 D 3.8 . According to Eqs. (3) and (6), S(Q) and RDF(r) for TbFe 2 D x can be described as the weighted sum of six partial pair correlations (Fe–D, Tb–D, D–D, Fe–Fe, Fe– Tb and Tb–Tb). The weighting factors, w i – j , for cTbFe 2 D 3.8 and a-TbFe 2 D x (x53.0, 2.0) calculated by Eq. (4) are listed in Table 1. Since the atomic scattering factor of the D atom is much smaller than those of the Fe and Tb atoms for the X-ray diffraction, w i – j of Fe–D, Tb–D and D–D pair correlations are less than those of metal–metal pair correlations (Fe–Fe, Fe–Tb and Tb–Tb). Consequently, S(Q) and RDF(r) observed by X-ray diffraction mainly describe the distribution of metal atoms. Fig. 2(a) and (b) shows S(Q)s observed by the X-ray diffraction for c-TbFe 2 D 3.8 and a-TbFe 2 D x (x53.0, 2.0), respectively. The Bragg peaks associated with the rhombohedral structure are clearly visible for c-TbFe 2 D 3.8 . The large difference in S(Q)s between crystalline and amorphous deuterides leads us to anticipate a great difference in real space. Indeed, a large difference in the RDF(r) plots for c-TbFe 2 D 3.8 and a-TbFe 2 D x (x53.0, 2.0) is observed as shown in Fig. 3. In RDF(r)s, broken lines indicate the peaks of three pair correlations for Fe–Fe, Fe–Tb and Tb–Tb by approximating with a Gaussian distribution function. The nearest neighbor coordination number, Ni – j , and the interatomic distance, r 1 , which have been derived from the Gaussian peaks in the RDF(r) for c-TbFe 2 D 3.8 and a-TbFe 2 D x (x53.0, 2.0) are summarized along with the Goldschmidt diameter in Table 2. NFe – Fe (NFe – Tb , NTb – Tb ) denotes the coordination number of the nearest neighbor Fe (Tb, Tb) atoms around an Fe (Fe, Tb) atom. On the other hand, r Fe – Fe , r Fe – Tb and r Tb – Tb denote the interatomic distance for Fe–Fe, Fe–Tb and Tb–Tb atom pairs, respectively. The value of r Fe – Fe for c-TbFe 2 is larger than that of the Goldschmidt diameter of Fe, but the value of r Tb – Tb is smaller than that of the Goldschmidt diameter of Tb. These experimental results are quite reasonable, because the small Fe atoms expand and the large Tb atoms contract so as to construct the C15 Laves structure when the atomic size ratio R Tb /R Fe is larger than the ideal value, 1.225 [4]. NFe – Fe , NFe – Tb and NTb – Tb for c-TbFe 2 D 3.8 are almost identical with those for c-TbFe 2 .

K. Itoh et al. / Journal of Alloys and Compounds 348 (2003) 167–172

170

Fig. 3. Radial distribution functions, RDF(r), observed by X-ray diffraction for c-TbFe 2 D 3.8 and a-TbFe 2 D x (x: 3.0, 2.0). Broken curves are the Gaussian functions corresponding to the Fe–Fe, Fe–Tb and Tb–Tb pair correlations.

In contrast, r Fe – Fe , r Fe – Tb and r Tb – Tb for c-TbFe 2 D 3.8 are larger than those for c-TbFe 2 . These experimental results indicate that deuterium absorption gives rise to a large lattice expansion, but only to a small difference in the atomic arrangement. The expansion of the lattice parameters due to the hydrogen (deuterium) absorption for

ErFe 2 H 3.5 (D) samples has also been reported [12]. A large difference is detected not only between the shape of the RDF(r) of c-TbFe 2 D 3.8 and a-TbFe 2 D x (x53.0, 2.0), but also between the coordination numbers NFe – Fe , NFe – Tb , and NTb – Tb . The coordination number for the same kind of metals, i.e. NFe – Fe and NTb – Tb of a-TbFe 2 D 3.8 is larger than those of c-TbFe 2 . In contrast, the coordination number for different kinds of metals, i.e. NFe – Tb of a-TbFe 2 D 3.8 is smaller than that of c-TbFe 2 . These experimental results suggest that Fe and Tb atoms do not distribute homogeneously, but form clusters in these amorphous alloys. Similar results have been reported for a-GdFe 2 [13,14] and a-GdFe 2 H 3.0 [6]. The distance r Tb – Tb in a-TbFe 2 D x (x5 3.0, 2.0) is larger than that in c-TbFe 2 , c-TbFe 2 H 3.8 and the Goldschmidt diameter of Tb, which indicates that the D atoms occupy positions between the Tb atoms. S(Q)s and RDF(r)s obtained by neutron diffraction give a different insight in the structure, because D has a coherent scattering length equal to that of Fe or Tb atoms. The values of w i – j of Fe–D, Tb–D and D–D pair correlations listed in Table 1 are fairly large compared with those of the metal–metal pair correlations. Consequently, S(Q) and RDF(r) obtained by neutron diffraction give us information on the local environment around a D atom. Fig. 4 shows S(Q)s of c-TbFe 2 D 3.8 and a-TbFe 2 D x (x53.0, 2.0) observed by neutron diffraction. The corresponding RDF(r)s evaluated from S(Q)s in Fig. 4 are shown in Fig. 5. The well-resolved first peak in the RDF(r) for c-TbFe 2 D 3.8 and a-TbFe 2 D x (x53.0, 2.0) seems to correspond to the Fe–D pair correlation if a hard sphere model with Goldschmidt radii for Fe and D atoms is applied. The second peak in the RDF(r) of c-TbFe 2 D 3.8 consists of two peaks, which are expected to be Tb–D and D–D pair correlations. In contrast, the second peak in the RDF(r) of a-TbFe 2 D x consists not only of Tb–D and D–D pair correlations, but also of metal–metal correlations. In order to discuss the local environment around the D atoms, we have tried to divide it into partial correlations by approximating with Gaussian distribution functions. The metal–metal pair correlations for a-TbFe 2 D x (x53.0, 2.0) inferred from r 1 and Ni – j are listed in Table 2. This allows us to deduce the nearest neighbor atomic distance and the coordination number for the Fe–D, Tb–D, Fe–Fe, D–D,

Table 2 Nearest neighbor coordination number, Ni – j , and interatomic distances, r 1 , of metal atoms in c-TbFe 2 D 3.8 and a-TbFe 2 D x (x50.3,0.2) calculated from the RDF(r)s observed by X-ray diffraction Fe–Fe

TbFe 2 [11] c-TbFe 2 D 3.8 a-TbFe 2 D 3.0 a-TbFe 2 D 2.0 Goldschmidt radii

Fe–Tb

Tb–Tb

NFe – Fe (atoms)

r1 (nm)

NFe – Tb (atoms)

r1 (nm)

NTb – Tb (atoms)

r1 (nm)

6 6.07 8.61 8.41 –

0.2597 0.290 0.251 0.248 0.254

6 5.98 2.44 2.38 –

0.3045 0.336 0.305 0.300 0.304

4 3.92 8.00 7.62 –

0.3181 0.349 0.362 0.357 0.354

K. Itoh et al. / Journal of Alloys and Compounds 348 (2003) 167–172

171

Fig. 4. Structure factors, S(Q), observed by neutron diffraction for c-TbFe 2 D 3.8 and a-TbFe 2 D x (x: 3.0, 2.0).

Fe–Tb and Tb–Tb pairs. The best fit is depicted in Fig. 5, where the dotted lines indicate Fe–D and Tb–D pair correlations and the broken lines indicate metal–metal correlations. The nearest neighbor coordination number of Fe and Tb atoms around a D atom, ND – Fe and ND – Tb , calculated from the area under the Gaussian peaks in the RDF(r)s are listed in Table 3 together with the interatomic distances, r 1 , for the Fe–D and Tb–D pair correlations. ND – Fe and ND – Tb for c-TbFe 2 D 3.8 are nearly 2 and the total number of them is 4, which indicates that the D atoms occupy tetrahedral sites consisting of 2Fe12Tb atoms. Three kinds of tetrahedral site exist, i.e. 2R12Fe, 1R1 3Fe, and 4Fe in the C15 Laves phases RFe 2 [5]. The present work clearly shows that only 2R12Fe type sites are occupied by D atoms. In contrast, it has been predicted that five kinds of tetrahedral site exist, i.e. 4R, 3R11Fe, 2R12Fe, 1R13Fe, and 4Fe in the corresponding amorphous a-RFe 2 [5]. Among these sites, D may occupy 4R, 3R11Fe and 2R12Fe sites because of the large formation enthalpy of the rare earth metal deuteride. The occupation of these sites was confirmed by the present neutron diffraction analysis as follows. ND – Fe and ND – Tb for aTbFe 2 D 3.0 is approximately 1 and 3, respectively, but the total number of them is still nearly 4. These experimental results imply that the D atoms do not occupy only 3Tb1 1Fe tetrahedral sites, but occupy 4Tb, 3Tb11Fe and 2Tb12Fe tetrahedral sites in a-TbFe 2 D x . The reason is

Fig. 5. Radial distribution functions, RDF(r), observed by neutron diffraction for c-TbFe 2 D 3.8 and a-TbFe 2 D x (x: 3.0, 2.0). Dotted lines are the Gaussian function corresponding to the Fe–D, Fe–D and D–D pair correlations. Broken lines for amorphous samples indicate the metal– metal correlations referred from the r 1 and Ni – j listed in Table 2.

that if they occupy only 3Tb11Fe sites, ND – Fe and ND – Tb for a-TbFe 2 D x must be independent of the D content. However, the present neutron diffraction experiment showed that ND – Fe and ND – Tb for a-TbFe 2 D x is reduced to 0.62 and increased to 3.3, respectively, by heating of a-TbFe 2 D 3.0 at 473 K for 1 h in vacuum. This result Table 3 Nearest neighbor coordination number, Ni – j , and interatomic distances, r 1 , in c-TbFe 2 D 3.8 and a-TbFe 2 D x (x50.3, 0.2) calculated from RDF(r)s observed by neutron diffraction D–Fe

c-TbFe 2 D 3.8 a-TbFe 2 D 3.0 a-TbFe 2 D 2.0

D–Tb

Tb–Tb

ND – Fe (atoms)

r1 (nm)

ND – Tb (atoms)

r1 (nm)

ND – Fe 1ND – Tb (atoms)

2.05 0.98 0.62

0.172 0.173 0.172

2.01 3.03 3.33

0.221 0.223 0.223

4.06 4.01 3.95

172

K. Itoh et al. / Journal of Alloys and Compounds 348 (2003) 167–172

indicates that the weakly trapped D atoms in 2Tb12Fe sites escape when heating. As a result, ND – Fe for aTbFe 2 D 2.0 is reduced, but ND – Tb for a-TbFe 2 D 2.0 is increased. The occupation of the more stable sites by D atoms has been reported in the rapidly quenched amorphous NiZr–D alloys [15]. The present work clearly demonstrates that D (or H) atoms in amorphous a-TbFe 2 D x are much more strongly bound than those in the corresponding crystalline c-TbFe 2 D x . If the crystalline alloy is heated to the temperature where the Tb and Fe atom can move over a short distance, rearrangements can occur to reduce the total free energy of the system, which is HIA.

4. Conclusion The short-range structures for c-TbFe 2 D 3.0 and aTbFe 2 D x (x53.0, 2.0) prepared by deuterium absorption were investigated by combining X-ray and neutron diffraction techniques. The coordination numbers for the metal– metal pair correlations in a-TbFe 2 D x suggest that there are clusters of Fe and Tb atoms. The neutron diffraction experiment indicates that the D atoms occupy tetrahedral sites in both the crystalline and the amorphous alloys. The tetrahedral sites occupied by D atoms in c-TbFe 2 D 3.8 consist of 2Tb12Fe. In contrast, D atoms in a-TbFe 2 D x occupy the tetrahedral sites consisting of 4Tb, 3Tb11Fe and 2Tb12Fe. When c-TbFe 2 D 3.8 is heated up to 473 K where both Tb and Fe atoms can move over short distances, rearrangements occur so as to reduce the total free energy of the system and this leads to HIA.

Acknowledgements The authors express their thanks to the Booster Synchrotron Utilization Facility at KEK for providing us

the opportunity of the neutron scattering experiment. This work was supported in part by a Grant-in-Aid for Scientific Research on Priority Areas A of ‘New Protium Function’, Grant-in-Aid for Scientific Research (B), Grant-in-Aid for Exploratory Research and Grant-in-Aid for Encouragement of Young Scientists from the Ministry of Education, Science, Sports and Culture.

References [1] K. Aoki, T. Masumoto, J. Alloys Comp. 231 (1995) 20. [2] X.G. Li, A. Chiba, K. Aoki, T. Masumoto, Intermetallics 5 (1997) 387. [3] K. Aoki, T. Yamamoto, Y. Satoh, K. Fukamichi, T. Masumoto, Acta Metall. 35 (1987) 2465–2470. [4] K. Aoki, X.-G. Li, T. Masumoto, Acta Metall. Mater. 40 (1992) 1717–1726. [5] K. Aoki, X.-G. Li, T. Hirata, E. Matsubara, Y. Waseda, T. Masumoto, Acta Metall. Mater. 41 (1993) 1523–1530. [6] Y. Waseda, The Structure of Non-Crystalline Materials, McGrawHill, New York, 1980. [7] C.N.J. Wagner, H. Ocken, M.L. Joshi, Z. Naturforsch. 20a (1965) 325. [8] H.H. Paalman, C.J. Pings, J. Appl. Phys. 33 (1965) 2635. [9] I.A. Blech, B.L. Averbach, Phys. Rev. 137 (1965) 1113. [10] T.E. Faber, J.M. Ziman, Phil. Mag. 11 (1985) 153. [11] P. Villars, L.D. Calvert:, Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, American Society for Metals, 1985. [12] G.E. Fish, J.J. Rhyne, S.G. Sankar, W.E. Wallace, J. Appl. Phys. 50 (1979) 2003. [13] G.S. Cargill, Solid State Phys. 30 (1975) 289. [14] M. Saito, Y. Waseda, E. Matsubara, X.-M. Wang, T. Aihara, K. Aoki, J. Non-Cryst. Solids 205–207 (1996) 721. [15] K. Suzuki, N. Hayashi, Y. Tomitsuka, T. Fukunaga, K. Kai, N. Watanabe, J. Non-Cryst. Solids 61 / 62 (1982) 637.