Neutron diffraction in Ti1.2Mn1.8 deuteride: Structural and magnetic aspects

Journal

of the Less-Common

Metals,

99 (1984)

307

307

- 319

NEUTRON DIFFRACTION IN Tilv,Mnle8 DEUTERIDE: AND MAGNETIC ASPECTS

STRUCTURAL

D. FRUCHART Laboratoire de Cristallographie, 166X, 38042 Grenoble Ce’dex

Centre (France)

National

de la RechercheScientifique

de Grenoble,

J. L. SOUBEYROUX Insfitut

Laue-Langevin,

156X,

38042

Grenoble

CPdex

(France)

R. HEMPELMANN lnstitut (Received

fiir Festkb’rperforschung, November

Kernforschungsanlage

Jiilich,

517

Jiilich

(F.R.G.)

13,1983)

Summary

The hydrogen storage compound Til,zMnl.s is an off-stoichiometric hexagonal Laves phase (C14) where the excess titanium atoms are inserted in the manganese sublattice and are located exclusively on the 2a sites. This leads to the formation of TisMn tetrahedra which do not exist in stoichiometric TiMn,?. Our neutron diffraction study revealed that the three deuterium atoms per formula unit do not enter TiMns or Mn, sites but are distributed among the Ti,Mnz and the TisMn sites, where the latter have an increased occupancy because of their higher hydrogen affinity. An exclusive volume exists around each deuterium atom; owing to the high deuterium concentration this results in liquid-like short-range order with the first and second coordination spheres at about 2.1 i% and 2.8 A respectively. The manganese atoms on the 6h sites in the magnetically ordered state of Til.2Mn,.,Ds form ferromagnetic layers, whereas the other manganese atoms and the titanium atoms remain non-magnetic.

1. Introduction

Since its discovery as a hydrogen storage material in 1976 by a Japanese group [l, 21 the off-stoichiometric variant Ti,.,Mn,.s of the hexagonal Laves phase TiMn, (which itself does not form a hydride under “normal” conditions) has been the subject of many investigations of both its technological applications and its fundamental properties. The technological studies have included the determination of its thermodynamic [l, 21 and kinetic properties [ 31, its long-term hydrogen storage capacity [ 41 and its resistance to impurities in the fuel gas [5] and the development of an economical and reproducible large-scale production process [6]. Multicomponent pseudo0022-5088/84/$3.00

@ Elsevier

Sequoia/Printed

in The Netherlands

308

binary derivatives of TiMn*, such as Ti0.8Zr0.~Cr0sMn1.2 [7], Tio.sZr,.1Vo.2Cr0.4Mnl.4 [8l,TLdr0.~CrMn [91 and Ti~.~8Zr~.~2V0.4~Feo.lCro.o,Mn,.4 [101, have been suggested. The more fundamental investigations have been concentrated on the parent Tii.zMni.s -H system and have included studies of the magnetic properties [ll, 121, the hydrogen absorption and diffusion rates [ 131, the microscopic details of hydrogen diffusion [ 141 and the surface effects due to the activation process [15, 161 as well as tritium tracer experiments [ 171. The representation TiMn,.5 proposed by the Japanese group [l, 21 implies that the deviation from the AB;! stoichiometry is due to vacancies in the B sublattice. This contrasts with the results of density measurements performed by Waterstrat et al. [ 181 which indicated that the excess titanium atoms occupy manganese sites. With respect to the type of substitution, recent Miissbauer effect measurements [12, 191 have shown that the excess titanium atoms preferentially occupy one of the two non-equivalent manganese sites of the hexagonal Laves phase. In contrast, Mayer et al. [20] have claimed that vanadium atoms, manganese atoms and vacancies are statistically distributed among the B sites in the closely related isostructural of compound TiVo.YsMni.i2. Thus we decided to check the off-stoichiometry Tii.*Mni_s by neutron diffraction examination. The distribution of the deuterium atoms among the available interstitial sites in a hexagonal Laves phase was first determined by Didisheim et al. [21] for ZrMnzDJ, and we shall refer to this work later. The major difference observed in our system (Til.l Mn,.sD,) is the off-stoichiometry. In view of the substitution of manganese atoms by titanium atoms in the stoichiometric Laves phase we expect considerable changes in the occupation of certain interstitial sites because of the substantially higher hydrogen affinity of titanium compared with manganese. Neutron diffraction techniques can be used to measure magnetic as well as geometric structures, and Til.zMnl,s -H is also an interesting system in this respect. Whereas the parent inter-metallic is a Pauli paramagnet, at least at temperatures above 1.5 K, the hydride orders ferromagnetically below the Curie temperature of 213 K [ll, 121. A classification of the ferromagnetic ordering as localized or itinerant ferromagnetism according to the RhodesWohlfarth plot [22] showed that the Ti-Mn Laves phase hydride tends to exhibit localized moments which should give rise to magnetic neutron scattering. The existence of these moments was investigated in the present work.

2. Sample preparation and experimental details The intermetallic compounds were prepared by arc melting and subsequent annealing in an argon atmosphere. The resulting brittle Ti-Mn samples were charged with deuterium from the gas phase. The ratios of titanium to manganese were obtained by assuming that the melting losses which occurred

309

during the arc melting process were entirely due to the evaporation of compositions, which were determined from manganese [ 181; the “exact” the relation between the lattice constants and the titanium-to-manganese ratio [ll, 181, were Ti,.OzMn,.,s and Ti1.2sMn1.77. The deuterium content was determined gas volumetrically by hot extraction. A special deactivation technique was used to seal the surface of the fine powder (particle diameter, about 1 pm) in such a way that deuterium was not desorbed at room temperature even in a vacuum. Therefore, despite the high deuterium equilibrium pressure, a simple thin-walled vanadium tube could be used as the sample holder. The details of the sample preparation and characterization have already been described previously in connection with the magnetic measurements [ 111. The neutron diffraction experiment was performed at the high flux reactor of the Institut Laue-Langevin, Grenoble, using the DlB powder diffractometer which was equipped with a large position-sensitive detector (PSD). Diffractograms were recorded for three Ti-Mn samples in the homogeneity range of the Ti-Mn Laves phase (TiMn*, Ti,.,Mni.s and at room temperature and for Til.,Mn,.sDs at various temperaTi i.ssMn,.,,) tures between 80 and 300 K. Unfortunately the Til.,,Mnl.,, sample contained an admixture of another phase which prevented a quantitative evaluation of the diffraction intensities of the Laves phase. To minimize the overlap of the Bragg peaks the large neutron wavelength h = 2.5205 A was used and the angular domain (30” < 28 S 150”) was covered by two overlapping positions of the PSD. 3. Results The data are summarized in Fig. 1. Figure l(a) shows the diffractogram for Til.zMnl.s. Only lines characteristic of the hexagonal Laves phase were observed. The lattice constants are a0 = 4.862(3) A and co = 7.969(3) A. The diffraction pattern of the stoichiometric specimen TiMn* is identical with this pattern apart from a slight angular shift of the peaks (the lattice constants are a0 = 4.820(2) A and co = 7.915(3) A). The starting point for the crystallographic refinement of the structure in the Cl4 space groupP6,/mmc was chosen on the basis of Mijssbauer measurements [12] which indicated that the excess titanium atoms substitute manganese atoms on 2a sites only. The integrated intensity method and the profile refinement method gave the same result without significant differences. The overlapping part of each spectrum (low angle and high angle regions of the PSD) was adequately averaged. The unit cell (four formula units) and the position parameters are given in Table 1. The diffractogram of Tila2Mn i.s deuteride is shown in Fig. l(b). It also exhibits the characteristic diffraction pattern of the Cl4 Laves phase, i.e. no reduction in symmetry has to be considered. However, the peak positions are markedly shifted (there is a large lattice expansion compared with the parent intermetallic alloy) and the peak intensities are very different.

310 0

20

LO

60

80

Fig. 1. Neutron diffractograms of Ti r.zMnr.s and its deuteride: (a) Tir.2Mnr.s (T = 295 K); (b) Tir.2Mnr.sDa (7’ = 240 K); (c) Ti r_zMnr,sDs (difference plot between spectra at 80 K and 240 K).

The d~fraction pattern is superimposed on two broad diffuse peaks: the first is centred at 8 = 37” which corresponds to d = 2.1 8, and the second is centred at 8 = 65” which corresponds to d = 1.4 8. A list of the possible tetrahedral interstitial sites used to locate the deuterium atoms is given in TABLE 1 Metal atom positions in the intermetallic compounds Ti1.zMnr.s (space group, P63/mmc (no. 194) [23])

TiMnz and

Atom

Position

TiMnz

Til.zMnl.8

Ti

4f

2 = 0.435(l) 3 = 1.5(6) Mn onty B = 0.6(6) x =0.827(l) B = 0.7(4)

B = 1.4(6) 0.3 Mn + 0.2 Ti B = 0.8(6) x = 0.833(l) B = 1.3(5)

Reliability factor 5.3%

4.8%

Lattice constants a0 = 4.820 a co = 7.915 a

a0 = 4.862 .k co=7.969a

Mn+Ti

2a

Mn

6h

2 =

0.439(l)

311 TABLE

2

Possible

hydrogen

Site

sites in the hexagonal

Laves phase hydride

Til.zMnI_sH3

Environment

Tetrahedron

Crystallographic

position

1 (Mn + Ti) (Xa) 1 Mn (6h) 2 Ti (4f)

TizMnz or TisMn

241;~ = 0.041;~ z = 0.563

= 0.33;

2 Mn 2 Ti

(6h) (4f)

TizMnz

12kl;x = 0.458; y = 2x z = 0.628

2 Mn 2 Ti

(6h) (4f)

TizMnz

6h,;x = 0.461;y z = l/4

= 2x;

2Mn 2 Ti

(6h) (4f)

TizMnz

6hz;x = 0.206;~ z = l/4

= 2x;

1 (Mn+ Ti) (2a) 2 Mn (6h) 1 Ti (4f)

TiMn3 or TizMnl

12k2;x = 0.132;~ z = 0.138

3 Mn 1 Ti

TiMn3

4f;x = 113;~ = 213; z = 0.665

TiMn3 or Mn4

4e;x=O;y

(6h) (4f)

1 (Mn + Ti) (Za) 3 Mn (6h)

=O;z

= 2x

=0.188

Table 2 which is based on the study of the isotypic compound ZrMntDs performed by Didisheim et al. [21]. The results of the refinement are reported in Table 3 and the interatomic distances are given in Table 4. The main features are (i) a continuous shift with temperature of the Mn(Gh)Mn(6h) distances, (ii) a decrease in the filling of the 241 tetrahedra with decreasing temperature which is correlated with an increase in the filling of the 12kr tetrahedra (about 0.25 deuterium atoms per formula unit progressively change their location) and (iii) very slight but continuous displacements of the mean deuterium positions in these sites (the atomic distances are reported in Table 4). The decrease in the 241 occupation is accompanied by a significant decrease in the mean distance D(241)-Mn(6h), whereas the reverse tendency is observed in the neighbourhood of the 12k, metal atom. The reliability factors are fairly good for the data recorded at 240,190 and 170 K (R < 0.03). Small magnetic contributions affect the result at 80 K where R = 0.076. A comparison of the diffractograms obtained at 240 and 80 K (the difference plot in Fig. l(c)) reveals modifications in the intensities of several diffraction peaks. At 80 K most of these variations appear as small increases, but slight decreases are also observed (even for large 0 values). Both nuclear and magnetic effects are assumed to contribute to these modifications. There are good reasons (see Section 4.4) for assuming that the titanium atoms on the 4f sites and both atoms on the mixed site (Za) are non-magnetic. The saturation magnetization at 4.2 Kis 16.18 Am* kg-’ [12]. on the 6h sites. We iteratively made This corresponds to 0.3 pg (Mn atom)-’

312 TABLE

3

Metal and deuterium atom positions and deuterium occupancies n and m per site and per formula unit respectively in Til.zMnI_sD3.1 (space group, P63lmmc) Atom

Position

Ti

4f

0.2Ti 0.3Mn Mn

2a 6h

D(1)

241

D(2)

12k,

D(3)

6hl

D(4)

6h2

Parameters

only)

80 K (nuclear + magnetic)

x=0.826(1) B = 2.3(5) x =0.0397(4) y =0.343(l) %=0.552(l) B =4.7(5) n=0.223(4) m = 1.34 x=0.462(1) z = 0.625(l) B = 4.4(5) n = 0.386(8) m = 1.16 x=0.451(1) B = 3.1(5) n = 0.220(5) m = 0.33 x=0.214(1) B = 3.5(5)

x=0.840(1) B = 1.7(5) x =0.0400(4) x =0.0397(4) y =0.333(2) y = 0.324(2) z =0.552(l) z = 0.552(l) B =4.4(5) B =4.1(5) n =0.200(6) n = 0.193(6) m = 1.20 m =1.16 x=0.466(1) x=0.468(1) z =0.614(l) .z= 0.609(l) B=4.1(5) B = 3.8(5) n =0.392(S) n =0.400(8) m =1.18 m =1.20 x=0.451(1) x =0.451(l) B=3.1 3 = 3.1 n =0.236(4) n = 0.240(4) m = 0.35 m = 0.36 x=0.214(1) x=0.214(1) B = 3.5 B=3.5

n = 0.204(4) m = 0.30

n = 0.188(4) m = 0.28

n = 0.188(4) m = 0.28

B=3.5 n = 0.204(4) m = 0.30

n = 0.184 m = 0.27

3.01

3.00

3.02

3.13

R = 2.0

R = 2.9

R =7.6

R = 3.1

5.258 8.577

5.257 8.576

5.254 8.572

5.254 8.572

Reliability

factor

R (%) R = 2.3

CO

80K (nuclear

t=0.439(1) B =2.1(5) B = 1.8(8)

per formula 3.13

constants

170K

z =0.442(Z) B = 2.4(5) 3 =2.1(S)

atoms

00

temperatures

190 K

240 K

Deuterium

Lattice

for the following

z = 0.436(l) B = l&(5) B = 1.4(8)

x=0.834(1)

B = 2.0(5)

2=0.438(4) z = 0.4357(14) B = 2.4(7) B=l.Q B = 2.0(1.0) B = 2.1 x=0.846(2) B = 2.318) x =0.053(10) y =0.307(6) z = 0.543(6) B = 4.7(7) n = 0.179(7) m = 1.02 x = 0.470(3) z = 0.602(3) B = 4.4(7) n = 0.458(14) m =I.37 x=0.451(1) B =3.1 n = 0.224(4) m = 0.33 x=0.214(1)

x =0.8433(8) 3=1.9 x =0.0492(34) y = 0.3093(21) z =0.5478(24) B = 4.8 n = 0.183(6) m = 1.10 x=0.4700(9) z =0.6050(13) B =4.7 n =0.456(12) m =1.37 x=0.451 n = 0.260 m = 0.39

x =0.214

unit

(8)

5.271 8.579

the following assumptions in calculating the magnetic intensities of the diffraction lines: (i) the moments of the manganese atoms on the 6h sites are directed along the c axis; (ii) the moments of the manganese atoms on the 6h sites lie in the (001) planes (the direction of the spins in the basal plane cannot be determined from powder diffractogram data). We subtracted these intensities (renormalized to the nuclear contribution) from the total measured intensities at 80 K. The refinement of the difference intensities (Table 3, last column) gives a better result when the magnetic moments are assumed

313 TABLE

4

Interatomic

Ti1.2Mn1.8

Ti (4f) Ti+Mn

Mn (6h) Til.2Mn1.sD3 Ti (4f) Ti + Mn (2a) Mn (6h)

distances (A) for the following sites

Interatomic

distances

Ti (4f)

Ti + Mn (2a)

Mn (6h)

2.971 3.012

2.849

2.849 2.860

2.849

3.985 4.862

2.437

2.849 2.860

2.337

2.431 2.431

3.003 3.294

3.077

3.015 3.106

3.077

4.289 5.259

2.667

2.667

2.514 2.745

D (241)

D (12kl)

1.883 1.938 1.766 2.787 1.835 2.787 2.836 2.981 1.386 1.861; 2.013;

1.951 1.959

(T = 240 K)

3.015 3.106

D (241)

2.861 1.711 2.834

1.928 2.094

2.821 2.904 2.966

3.198 Ti + Mn (2a) Mn (6h)

D (241)

3.083 3.134 3.074

3.083

3.134 3.074

4.286 4.254

2.573

2.573

2.522 2.785

2.935 2.976 D (12k1)

2.744 2.790 2.807 2.815

1.826 1.911

1.969 2.081 1.570 2.792 1.821 2.733 2.825 3.101 1.110 1.723; 2.262;

1.858

2.927 1.882 2.156 2.487 3.102

D (12kl)

Til.2 Mnl.8 03 (T = 80 K) Ti (4f) 3.226

1.133; 2.025

2.793 1.919 3.113

1.886 2.448

1.234; 1.980 2.586 2.704 2.716 2.965 1.822 2.156 2.487

1.801

314

to lie in the (001) planes. The R factor of this nuclear fit is 3% which is significantly better than that of the fit obtained without taking the magnetic contributions into account. 4. Discussion 4.1. Substitution scheme in the inter-metallic compound Neutron diffraction is generally a powerful tool for studying the ordering and relative positions of metals in intermetallic compounds, particularly in those cases where X-ray diffraction fails because the different metals have a similar number of electrons (similar nuclear charge). For the hexagonal Laves phase Ti,.,Mn,.s either a vacancy or a substitutional type of offstoichiometry is possible. The first case would correspond to the formula which is rather improbable because no examples of metallic TiMn&0.5 alloys with such a large vacancy concentration have been reported in the literature. We also easily excluded this possibility by performing a structure refinement with the assumption that vacancies were present in the B sublattice. The vacancies were assumed to be distributed homogeneously among the 2a and 6h sites, preferentially on the 2a sites or preferentially on the 6h sites, and R values of about 25% were obtained in all three cases. These values are much higher than those obtained in this work (see Section 3) and clearly indicate that this structure proposal must be wrong. Mayer et al. [20] obtained similar high R values in a structure refinement of TiVa.,,Mn 1.r2 with the assumption of vacancies on the B sublattice; in our opinion a substitutional type of off-stoichiometry also holds for this compound. Two modes of the excess titanium distribution on the 2a and 6h sites must be considered: a statistical distribution between both sites or preferential substitution on one site only. Unfortunately, neither X-ray nor neutron diffraction data enable a definitive choice to be made between these modes because the scattering lengths of titanium and manganese are very similar (AZ/Z = 0.12; Ah/b = 0.055). However, according to experience with other off-stoichiometric Laves phases [24, 251 and results obtained for 57Fe-doped Til.zMnI.s by Mijssbauer spectroscopy [12,19], which appears to be the only technique suitable for elucidating the substitution scheme, the excess titanium atoms are not uniformly distributed between the two non-equivalent manganese sites but enter the 2a sites. The low R value of about 5% which was obtained in the structure refinement using our neutron diffraction data strongly supports this structure. We can definitely reject a vacancy type of off-stoichiometry in the Ti-Mn hexagonal Laves phase, but on the basis of our neutron diffraction data we cannot completely exclude other modes for the distribution of the excess titanium although they are comparatively unlikely. 4.2. Interstitial occupancies in the deuteride The Laves phase structures can be considered as a close-packed arrangement of atoms of different sizes and, as is well known, only occur if the

315

stoichiometry corresponds to AB2 and the ratio of the atomic radii is 3?2i/2 = 1.225 (small deviations from both criteria are allowed). Since all interstices are formed by tetrahedra of chemically variable composition and crystallographically variable regularity, these structures are characterized as tetrahedrally close packed [26]. For hydrogen absorption to occur under “normal conditions” of pressure and temperature, at least one of the constituent metals must be a “hydride former” as is generally the case for intermetallic hydrides [27]. The various interstitial sites are filled with hydrogen according to the following criteria. (i) Under the chemical criteria A2B2, AB, and B4 sites are available and we distinguish the cases when only A has a high hydrogen affinity (e.g. in ZrMn,D,) and hence only A2B2 sites are occupied [21], and when both metal atoms attract hydrogen (e.g. in ThZr2H, and ThTi,H, [28] or in ZrV2H, [29,30]) and hence a correspondingly higher hydrogen content is reached. Efforts have been made to quantify these ideas (Miedema model [311h (ii) The geometrical criteria include the exclusion rule proposed by Shoemaker and Shoemaker [26] which states that “two tetrahedra with a face in common may not both contain hydrogen atoms at their centres” and Westlake’s criteria of the minimum hole size (0.40 A) and the minimum H-H distance (2.1 A) [32]. Electronic effects are also important and in some sense contribute to criteria (i) and (ii), but to the best of our knowledge neither simple rules nor extended band structure calculations exist for Laves phases. Therefore we shall restrict ourselves to chemical and geometrical points of view. A discussion in terms of the Miedema model is unlikely to be helpful because this model cannot distinguish between crystallographically different interstitial sites with the same chemical environment, e.g. between the four A2B2 sites in Cl4 structure compounds. Our diffraction data indicate that only the 241, 12k,, 6h, and 6h2 sites are occupied by deuterium in Ti 1.2Mn1.8D3. In the stoichiometric case all these sites are composed of two titanium and two manganese atoms. Thus the deuterium atoms are distributed among 48 sites in the unit cell. The substitution of manganese by titanium on the 2a positions (40%) implies that some of the Ti2Mn2 tetrahedra are transformed to TisMn, some of the TiMns tetrahedra are transformed to Ti2Mn2 and some of the Mn4 tetrahedra are transformed to TiMns (see Table 2). Thus, as can be seen in Fig. 2, 40% of the 241 sites are transformed to TisMn on substitution. This substitution does not lead to a reduction in the overall symmetry, so we can only determine an average occupancy of the 241 sites which is clearly higher than that in the stoichiometric case (compare Table 2 with ref. 21, Table 1). Some of the 12k, sites improve their hydrogen affinity on substitution and are transformed to Ti2Mn, (see Table 2). However, these 12k2 sites have a triangular face in common with two already filled 241 sites of the composition Ti,Mn. Therefore, according to the exclusion principle, the 12k2 sites cannot be effectively filled.

316

Fig. 2. Schematic representation of the structure of Tit_&nf,sD~ showing two tetrahedra around D(l), two tetrahedra around D(2) and one tetrahedron around D(3 ): @, titanium ; manganese and titanium; 0, manganese; O, D(1) (0.223); B, D(2) (0.386); A, D(3) 0, (0.220); V, D(4) (0.204). The occupation numbers of the various deuterium sites are given in parentheses.

The total number of interstitial sites available for hydrogen in Til.ZMni,s therefore remains 48 and is not changed on substitution. Although some of the 241 sites are transformed to Ti3Mn sites, they are not the most attractive for hydrogen; the k1 sites have a substantially higher occupancy which increases further, mainly at the expense of the 241 sites, as the temperature is decreased. These sites act as traps for diffusing hydrogen atoms. A recent quasi-elastic neutron scattering (QNS) study of hydrogen diffusion in Ti,.,MnxasHs by Hempelmann et cd. [ 141 took account of energetically nonequivalent interstitial sites and revealed different motional states for the protons: the “free state” where the hydrogen atoms propagate over energetically higher accessible sites and the “trapped state” where the hydrogen atoms are located in structural traps. In the qu~tit~tive treatment of the QNS data the fraction of the trap sites was a free parameter which was evaluated to be 24.4% ;t 6.4% in perfect agreement with the fraction of 12ki sites which represent 25% of all interstices. Thus the hydrogen trapping in Ti1.2Mn1.8H3 does not appear to be due to the excess titanium atoms, in accordance with the observation of trapping phenomena in ZrMnzH3 [14] which does not contain any Zr,Mn interstitial sites [2X]. In the QNS study cited above a third motional state was discovered which comprises a rapid hopping backwards and forwards with a jump length of 1.37 8. This jump length corresponds well to the distance between adjacent 241 sites.

317

4.3. Short-range order In the neutron diffractogram of Ti 1.2Mn,.sDs the pattern of Bragg peaks is superimposed on two broad liquid-like diffuse peaks. In the simplest approach these diffuse peaks can be related to preferred interatomic spacings of 2.1 and 1.4 A. The first peak corresponds exactly to Westlake’s minimum H-H distance [32] and can also be explained in terms of the exclusion principle proposed by Shoemaker and Shoemaker [26]. The similar average occupancy of all the available interstitial sites in Ti,.,Mn,.sDs indicates a large degree of disorder for the deuterium atoms. However, despite this overall disorder the deuterium atoms maintain a specific mutual minimum distance and do not occupy two adjacent sites. At high deuterium concentrations this results in a specific short-range order and therefore in the appearance of a diffuse diffraction peak similar to that reported by Fruchart et al. [30] for ZrCr,D,., which corresponded to a D-D spacing of 2.0 A. The second diffuse peak in Ti,.2Mnl.sD3 is not due to second-order scattering from the first diffuse peak because it does not appear at twice the Q value, but it may be the second-order scattering peak characteristic of a D-D separation of about 2.8 A (second coordination shell). As can be seen in Table 4, there is a distribution of D( 241)-D( 241) and D(241)-D( 12k) atomic distances with values near 2.0 A (1.928, 2.013, 2.025 and 2.094 A) which corresponds to the first diffuse peak, and there is a second distribution of atomic distances with values near 2.8 A (2.744, 2.790, 2.807, 2.815 and 2.821 A) which corresponds to the second diffuse peak. This schematic explanation has been proposed by a number of workers [30, 331. The simple model proposed by Irodova and coworkers [34,35] is often used to give a quantitative description of this short-range ordering. 4.4. Magnetic structure A detailed understanding of the magnetic properties of Ti,.,Mn,.,H, has been obtained from previous studies [ll, 121. Ti,.,Mni.,H, is ferromagnetic at temperatures below 213 K, and its spontaneous magnetization is 16.18 A m2 kg-‘. Since titanium does not exhibit magnetic moments in metallic alloys, the spontaneous magnetization is entirely due to the manganese. If all the manganese atoms were ferromagnetically aligned and carried the same magnetic moment, the spontaneous magnetization would be 0.257 pg (Mn atom)-‘. However, the manganese atoms occupy crystallographically different sites. Mijssbauer experiments on Til.2Mn,.sHs doped with 57Fe [ 121 provided the first evidence that crystallographically different manganese atoms also show different magnetic behaviour. The broad magnetic hyperfine pattern observed at 4.2 K (ref. 12, Fig. 9) cannot be described by a sum of sextuplets alone, although various assumptions concerning the environment of the manganese atoms have been adopted. In all cases a quadrupole split doublet had to be added indicating that between 10% and 20% of the 57Fe nuclei exhibited no hyperfine field 1361. This leads us to suggest that the manganese atoms on the 2a sites in the Til.zMnl., hydride remain non-magnetic. Hence the spontaneous magnetization is due

318

only to the 6h manganese atoms, and hence the effective magnetic moment is 0.308 &. The magnetic scattering is expected to be comp~atively small and a complete group theoretical determination of the magnetic structure under our experimental conditions is not possible. Complete neglect of the magnetic scattering, however, results in an increase in the R value of the fit by a factor of 2.5, i,e. it becomes 7.6% (Table 3, sixth column). Therefore we proceeded as described in Section 3 and were able to confirm that only the 6h mangane~ atoms carry a magnetic moment. The point symmetry of this’site is mm [23] with (001) and (110) mirror planes. This point symmetry allows the magnetic moment to be aligned either along the c axis or in the (001) planes. Our structure refinement allows a distinction between these two possibilities because we obtained a significantly better R value when the magnetic moments were located in the (OOl) planes than when they were directed parallel to e. Thus the 6h manganese atoms in Tii+zMni_sHs at low temperatures form ferromagnetically ordered layers with the easy axis in the basal plane. In a previous publication [ 123 the onset of ferromagnetism in Tii,,Mn,_s on hydrogenation was ascribed to both a large increase in the density of states at the Fermi level and a large volume expansion. The latter explanation can now be confirmed as we found in this work that the distances between the magnetic manganese atoms in Til,2 Mni.sDs at 240 K in the same plane are 3.4% and 12.9% larger than the corresponding distances in the pure alloy (see Table 4). These distances increased further at the magnetic transition, despite a slight lattice contraction. The increase in the Mn-Mn distances appears to be an important factor relative to the onset of ferrom~netism as is shown by the well-known Bethe-Slater-Neel curves.

Acknowledgments We should like to thank the staff of the Institut Laue-Langevin, particularly Dr. J. Pannetier, for their kind technical assistance during the experiment and Dr. G. Hilscher and Dr. G. Wiesinger for helpful discussions. D. P. Shoemaker provided sagacious comments; we wish to express our gratitude.

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