Phase relations in the Ti3Sn–D system

Phase relations in the Ti3Sn–D system

Journal of Alloys and Compounds 364 (2004) 127–131 Phase relations in the Ti3Sn–D system M. Vennström a,∗ , A. Grechnev b , O. Eriksson b , Y. Anders...

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Journal of Alloys and Compounds 364 (2004) 127–131

Phase relations in the Ti3Sn–D system M. Vennström a,∗ , A. Grechnev b , O. Eriksson b , Y. Andersson a a

The Ångström Lab, Department of Materials Chemistry, Uppsala University, Box 538, SE-75212 Uppsala, Sweden b Department of Physics, Uppsala University, Box 530, SE-75121, Uppsala, Sweden Received 6 May 2003; accepted 14 May 2003

Abstract Ti3 Sn forms an orthorhombic metal hydride phase at 25-kPa deuterium pressure and 650 ◦ C. The unit cell parameters were determined to be a = 6.179(1) Å, b = 9.877(2) Å and c = 4.7898(6) Å and the space group to be C2221 . The crystal structure was determined from neutron powder diffraction data with the Rietveld method. Three phases are formed in the Ti3 Sn–D system upon hydrogenation, and appear in the following order at increasing deuterium pressures: an orthorhombic structure (Ti3 SnD0.80 ), a hexagonal phase and a cubic metal hydride phase (Ti3 SnD). The cubic phase, Ti3 SnD, crystallises in the CaTiO3 -type structure, space group Pm3m, with the unit cell parameter a = 4.1776(2) Å. The stability of the three Ti3 SnDx phases is in agreement with calculated total energies, based on first principles theory. © 2003 Elsevier B.V. All rights reserved. Keywords: Transition metal compounds; Metal hydrides; Crystal structure; Neutron diffraction

1. Introduction

2. Experimental

Ti3 Sn crystallises with the hexagonal Ni3 Sn-type structure with a narrow homogeneity range [1]. The hydrogen absorption has been studied by Rudman et al. [2] who reported a cubic hydride phase of the filled Cu3 Au-type structure, CaTiO3 , with the unit cell parameter a = 4.17 Å. A neutron powder diffraction investigation of Ti3 SnDx confirmed the formation of a cubic metal hydride phase and found that hexagonal Ti3 Sn forms a solid solution with deuterium [3]. The same type of phase transition, from hexagonal Ni3 Sn-type to cubic CaTiO3 -type, has also been reported for the Ti3 Al–H system [4]. The electronic structure and total energies of the cubic and hexagonal structures for three different deuterium contents, Ti3 SnHx (x = 0, 0.5, 1) have been calculated by first principles theory [5]. The H–H distances were found to be very important. H–H interactions always have an attractive component due to the bonding molecular H2 state, but large H–H overlaps reduce the stronger H–Ti interactions, and consequently the effective H–H interactions are repulsive. This mechanism is important for H–H distances larger than 2.1 Å, which is the crucial distance in the observed phase transition.

2.1. Sample preparation



Corresponding author. E-mail address: [email protected] (M. Vennström).

0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0925-8388(03)00494-8

Ti3 Sn was synthesised by arc melting titanium (99.99%) and tin (99.995%) in argon atmosphere. The sample was powdered after heat treatments in a deuterium atmosphere. The deuterium was then removed by heating in vacuum. The powder was homogenised at 800 ◦ C for 7 days in an evacuated quartz ampoule. The metal hydride phases were obtained by heating the samples to 650 ◦ C for 12 h in 0.25–80-kPa deuterium pressure followed by slow cooling to room temperature. 2.2. X-ray diffraction Phase analysis was performed and unit cell dimensions were determined using X-ray powder diffraction techniques. Powder patterns were recorded using a Guinier-Hägg-type focusing camera with CuK␣1 radiation and with silicon as internal standard, a = 5.43088(4) Å at 25 ◦ C. X-ray powder diffraction patterns were collected on a high resolution STOE and CIE STDI transmission X-ray powder diffractometer, equipped with a small linear position-sensitive-detector (PSD, 6◦ in 2Θ) using CuK␣1 radiation.

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2.3. Neutron powder diffraction Neutron powder diffraction intensities were recorded at 25 ◦ C at the R2 reactor (Studsvik, Sweden). The samples were contained in vanadium cylinders and the measurements were performed using a multi-detector system with 35 independent detectors mounted 4◦ apart measuring intensities in 2Θ steps of 0.08◦ . The neutron flux at the sample was ∼106 cm−2 s−1 from a parallel double Cu (220) monochromator system, with a wavelength of 1.47 Å. The 2Θ ranges covered were 4.00–139.39◦ for both measurements. 2.4. Crystal structure analysis and refinements Crystal structure refinements of the X-ray and neutron powder diffraction profiles were performed according to the Rietveld method using the program FULLPROF [6]. The 2Θ ranges used in the refinements were 12.00–139.39◦ . The pseudo-Voigt function was used to describe the peak shape and a polynomial expression was used to describe the background of the diffractogram. 2.4.1. Refinements of orthorhombic Ti3 SnD0.8 A total of 23 parameters were refined in total; profile parameters: 2Θ zero point (one), scale factor (one), background coefficients (six), half-width parameters (three), profile shape parameter (one), asymmetry parameter (one); structural parameters: atomic coordinates (six), temperature factors (two), occupancy (one), lattice parameter (one). Occupancy and temperature factors were not varied simultaneously due to the large correlation between these parameters. 2.4.2. Refinement of cubic Ti3 SnD A total of 14 parameters were refined in the last refinement cycle; profile parameters: 2Θ zero point (one), scale factor (one), background coefficients (four), half-width parameters (three), profile shape parameter (one); structural parameters: temperature factors (three), lattice parameter (one).

Fig. 1. X-ray powder diffraction profile of (a) Ti3 Sn hexagonal, (b) orthorhombic Ti3 SnD0.8 and (c) Ti3 Sn–D orthorhombic and hexagonal.

terium pressures, and X-ray powder diffraction patterns were recorded after each deuteration. First the orthorhombic structure appears as a single phase on hydrogenation. At 1 kPa a two-phase region with a hexagonal phase is reached (Fig. 1). At higher deuterium pressures the orthorhombic phase disappears, and the cubic hydride phase appears (Fig. 2). The phase transitions from orthorhombic and hexagonal to hexagonal and cubic are sluggish, according to diffuse diffraction lines. 3.2. Calculations using first principles theory The total energies of orthorhombic Ti3 SnHx , with x = 0, 1, were calculated by first principles theory using LDA and VASP [7] methods. A comparison with the previously reported total energies of the hexagonal and cubic Ti3 SnHx phases (Table 1) reveals that the stability of the orthorhombic phase is intermediate, and very close to the hexagonal

2.4.3. Theoretical calculations The total energies of orthorhombic Ti3 SnHx (x = 0, 1) were calculated from first principles theory (LDA and VASP [7]) using the volume of 68 Å3 per formula unit. The calculations were converged to self-consistency and care was taken of truncation of basis function, expansion of density and k-space sampling.

3. Results 3.1. The Ti3 Sn–D system Three phases are formed in the Ti3 Sn–D system upon hydrogenation: an orthorhombic structure, a hexagonal phase and a cubic metal hydride phase. A sample of Ti3 Sn was treated at the same temperatures using different deu-

Fig. 2. X-ray powder diffraction profile of (a) Ti3 Sn hexagonal, (b) Ti3 Sn–D hexagonal and cubic and (c) Ti3 SnD cubic.

M. Vennström et al. / Journal of Alloys and Compounds 364 (2004) 127–131 Table 1 Calculated total energies

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Table 2 Final structural parameters of orthorhombic Ti3 SnD0.80(1)

Phase

Ea Hostcompound (eV)

Ea Metalhydridephase (eV)

Atom

Position

x

y

z

Biso (Å2 )

Cubic Hexagonal Orthorhombicb

−31.37 −31.51 −31.47

−36.00 −35.82 −35.88

Ti 1 Ti 2

8c 4b

0.2656(9) 0

0.0950(6) 0.8554(8)

0.252(4)

0.8(1) 0.7(1)

Sn 1 D1

4b 4aa

0 0.052(1)

0.3326(5) 0

a b

Å3

Energies are given for volume of 68 per formula unit. Experimental unit cell parameters and atomic coordinates were used.

1 4 1 4

0

0.25(9) 2.0b

a

The occupancy of this position is 0.402(5). Temperature factor has been fixed to 2.0. Results of the refinement using the Rietveld method and the program FULLPROF: Rp : 4.31%; Rwp : 5.70%; Rexp : 3.64%; χ2 = 2.59; RBragg : 6.97%; RF -factor: 4.01%. b

structure, for both Ti3 Sn and Ti3 SnH, which is in agreement with experimental results. Note that for x = 0 the hexagonal is lowest in energy and that for x = 1 the cubic is lowest. Both these results are in agreement with experimental results. 3.3. The orthorhombic Ti3 SnD0.80(1) structure An orthorhombic metal hydride phase, space group C2221 , was found in the Ti3 Sn–D system at 0.25-kPa deuterium pressure and 650 ◦ C (Fig. 3). The deuterium content was determined to be Ti3 SnD0.80(1) from refinements of neutron powder diffraction data (Table 2, Fig. 4). The unit cell parameters were determined from X-ray powder diffraction patterns to be a = 6.179(1) Å, b = 9.877(2) Å, c = 4.7898(6) Å. The orthorhombic unit cell is related

Fig. 4. Observed (full line) and calculated (cross) neutron powder diffraction profile of orthorhombic Ti3 SnD0.80(1) . Lower full line shows the difference between observed and the calculated profiles and the ticks mark the position of the Bragg reflections.

√ to the hexagonal Ti3 Sn, as aortho ≈ ahex , bortho ≈ ahex · 3, cortho ≈ chex . The unit cell parameters of hexagonal Ti3 Sn were determined to be a = 5.9162(6) Å, c = 4.7627(8) Å, which corresponds to an ortho-hexagonal b-axis of 10.247(1) Å. The unit cell volume increase 3.6(2) Å3 on hydrogen absorption. The a-axis expands, 4.44(3)%, while the b-axis contracts, 3.61(3)%, and the c-axis remains almost unchanged, 0.57(4)% (Table 3). The deuterium atoms are located off the centre in the Ti6 -octahedra, which causes a distortion of the hexagonal symmetry. The deuterium atom has four close titanium atoms at 1.89–2.03-Å distance and two at 2.46 Å. The four closest titanium neighbours form a somewhat distorted tetrahedral coordination around the deuterium atom, which Table 3 Unit cell parameters of Ti3 Sn and Ti3 SnD0.80(1)

Fig. 3. The crystal structure of orthorhombic Ti3 SnD0.8 .

Phase

a (Å)

b (Å)

c (Å)

Ti3 SnD0.80(1) Ti3 Sn (calc.)

6.179(1) 5.9162(6)

9.877(2) 10.247(1)a

4.7898(6) 4.7627(8)

a/a·100

b/b·100

c/c·100

4.44(3)

−3.61(3)

0.57(4)

a



bortho = 5.9162· 3 = 10.2471.

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Fig. 6. Observed (full line) and calculated (cross) neutron powder diffraction profile of cubic Ti3 SnD1.0 . Lower full line shows the difference between observed and the calculated profiles and the ticks mark the position of the Bragg reflections.

Fig. 5. The crystal structure of cubic Ti3 SnD.

Table 5 Inter atomic distances in Ti3 SnD

is a common coordination for hydrogen in titanium containing metal hydrides such as TiD1.97 and Ti3 PD2.4 [8,9]. Possible space groups were Cmcm, Cmc21 and C2221 . The main expansion of the unit cell is accounted for by an increase of the a-axis, and the C2221 space group provides a good description of the structure since this symmetry allows the x-coordinate of the deuterium atom to be varied.

Distances

Orthorhombic (Å)

Hexagonal (Å)

Cubic (Å)

Ti–Da

1.89 2.03 2.46 2.47

2.09

2.09

2.40

4.17

D–Da a

Standard deviations are less than 0.02.

Atom

Position

x

y

z

Biso (Å2 )

be described as a distorted tetrahedron with four close Ti neighbours at the vertices and two more distant neighbours, compared to the ideal octahedral coordination for the hexagonal and cubic phases. The shortest D–D distance is 2.40 Å in the hexagonal structure and 2.47 Å in the orthorhombic, but considerably longer, 4.17 Å, in the cubic structure [3] (Table 5). Deuterium atoms in metallic compounds are normally not found closer than 2 Å to each other [10]. In the Ti3 Sn–D system all D–D distances are greater than 2.4 Å. The deuterium tin distances were found to be larger than 3.45 Å in all three phases. The deuterium atoms have 4 + 2 tin atoms in the second coordination sphere in the orthorhombic, six in the hexagonal and eight in the cubic structure. The distance between tin and deuterium increases from 3.45 Å in orthorhombic Ti3 SnD0.8 to ∼3.6 Å in the hexagonal and cubic structures. Generally p-elements influence absorption of deuterium; they are seldom found close to each other in metal rich phases [11].

Ti Sn D

3c 1b 1a

1 2

1 2

0

0 0

0

1 2

1 2

1 2

0.44(5) 0.40(3) 1.31(5)

4. Discussion

3.4. The cubic Ti3 SnD structure At 80-kPa deuterium pressure the cubic metal hydride phase was obtained with the unit cell parameter a = 4.1776(2) Å, space group Pm3m (Fig. 5). The crystal structure was determined from neutron powder diffraction intensities and the results of the refinements are shown in Table 4 and Fig. 6. The deuterium atoms were found to occupy all available Ti6 -octahedra. 3.5. Interatomic distances in the Ti3 Sn–D system Deuterium atoms occupy Ti6 -octahedral positions in all Ti3 SnDx phases, but off the centre in the orthorhombic modification. The coordination polyhedron around D can Table 4 Final structural parameters of cubic Ti3 SnD

Unit cell parameter a = 4.1776(2) Å and space group Pm3m. Result of the refinement using the Rietveld method and the program FULLPROF: Rp : 3.70%, Rwp : 4.68%, Rexp : 3.74%, χ2 = 1.56, RBragg : 5.00%, RF -factor: 5.31%.

Three phases, an orthorhombic, a hexagonal and a cubic structure, have been determined in the Ti3 Sn–D system, after heat-treatments of Ti3 Sn in deuterium pressures between

M. Vennström et al. / Journal of Alloys and Compounds 364 (2004) 127–131

C2221 , could be considered as a ‘filled’ somewhat distorted ErCd3 -type structure.

Table 6 Calculated cubic unit cell parameters Phase

c (Å)

Ti3 Sn hex. 4.7627(8) Ti3 SnD0.80(1) ortho. 4.7898(6) Ti3 SnD0.7 hex.b 4.8219(6) Ti3 SnD cubicc √ a a t-cubic = ( 3·chex/ortho. )/2. b Previously published results [3]. c Experimental unit cell parameter.

131

Calculated at-cubic a (Å) 4.1246(7) 4.1480(6) 4.1759(6) 4.1776(2)c

0.25 and 80 kPa. In a previous investigation the hexagonal phase was described as a solid solution of deuterium in Ti3 Sn with the approximate composition Ti3 SnD0.7 . This conclusion has to be reconsidered, since an orthorhombic distortion of the hexagonal structure occurs from very low deuterium contents up to at least Ti3 SnD0.8 . The crystal structure determination of the hexagonal phase is inaccurate with respect to the deuterium occupancy, because this phase could not be obtained as a majority phase. The deuterium atoms are not located in the centre of the octahedron in orthorhombic Ti3 SnD0.8 , but prefer a tetrahedral-like titanium coordination. The octahedral voids may be too large and a tetrahedral coordination is energetically favourable. The orthorhombic distortion causes a contraction of the b- and an increase of the a-axis. The hexagonal phase with deuterium shows an expansion of the unit cell along the c-axis, since the deuterium atoms are located in the centre of the Ti6 -octahedron, which share faces along this direction [3]. The stacking direction of the closed-packed metal planes are parallel to the c-axis in the hexagonal structure and the body diagonal of the cube. A theoretical cubic unit cell parameter, at-cubic , can thus be calculated from the hexagonal and√orthorhombic c-parameter, chex. and cortho. , by the formula 3/3·at-cubic = chex./ortho. /2; the results obtained are shown in Table 6. The theoretical cubic unit cell parameter obtained for hexagonal Ti3 SnD0.7 , at-cubic = 4.176 Å, is very close to the cubic unit cell parameter, acubic = 4.178 Å, found experimentally. This indicates that the phase transition from orthorhombic to cubic goes via the hexagonal structure. A similar phase transition from the Ni3 Sn- to the Cu3 Au-type structures has been reported in the metal hydride system, Ti3 Al–H [4]. The transition from hexagonal Ni3 Sn-type to an orthorhombic structure has been found for RECd3 compounds. For RE = Gd, Tb the hexagonal structure is stable but for heavier 4f-elements the orthorhombic ErCd3 -type structure, space group Cmcm, is stabilised [12,13]. The orthorhombic Ti3 SnD0.8 structure, space group

5. Conclusions Three metal hydride phases have been found in the Ti3 Sn–D system. The deuterium atoms occupy Ti6 octahedral interstitial voids in all structures, but for lower deuterium concentrations the Ti6 -octahedra are distorted and the crystal structure becomes orthorhombic. The metal hydride phases in the Ti3 Sn–D system appear in the following order upon hydrogenation: orthorhombic, hexagonal and cubic structure. The phase transitions cannot empirically be explained in terms of D–D distances, however, the first principles theory calculations show that the H–H distances are very important.

Acknowledgements Håkan Rundlöf at the Neutron Research Laboratory, Studsvik, Sweden is gratefully acknowledged for his assistance with neutron powder diffraction measurements. The Swedish Science Research Council and the Swedish Energy Agency (Statens Energimyndighet) are acknowledged for financial support.

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