Mechanochemical synthesis and structural evaluation of a metastable polymorph of Ti₃Sn

1 Introduction

In the course of preparing new catalyst materials, we intended to synthesize an intermetallic phase of the type A₃B with composition Ti₃Sn which may be used as a precursor for further transformations. h-Ti₃Sn as an intermetallic compound has been known since the 1950s and exhibits an “unusually high damping capacity” [1] which makes it interesting for application in various composite materials. It is also of interest as an anode material for Li-ion batteries [2, 3] as Sn-based materials appear to have high storage capacities [4], [5], [6], [7], [8].

h-Ti₃Sn is known to adopt the Ni₃Sn-type structure (space group P6₃/mmc) [9]. This crystal structure type is derived from a hexagonal closest packing (hcp) of the atoms and represents an ordered variant with layers exhibiting a 3:1 occupation of Ti and Sn. An investigation of the solidification process of undercooled Ti₃Sn melts revealed two metastable martensitic Ti₃Sn phases (an orthorhombic and a monoclinic phase) [10]. A reversible phase transition (starting at around 260 K) to an orthorhombic phase (o-Ti₃Sn) with space group Cmcm was observed by Du et al. upon cooling [11]. Also, for non-stoichiometric Ti₃Sn, a phase transition to an orthorhombic phase with space group Cmcm has been mentioned [12]. A high-pressure phase of Ti₃Sn is also known, crystallizing in the Cu₃Au type [13].

In this contribution, we report on the preparation of c-Ti₃Sn by ball milling, an economical and environmentally friendly synthesis method that is now used in inorganic as well as organic synthesis, including catalysts [14], [15], [16]. In this process, the mechanical energy applied induces a chemical reaction of the starting materials used. Various parameters such as milling time and atmosphere, rotational speed, material and size of the grinding balls and beakers, and also the ball-to-powder weight or volume/surface ratio can be varied in order to optimize the milling process and thus ensure a successful outcome of an experiment [17, 18]. It should be mentioned that this procedure may be also of interest for the preparation of metastable compounds [17, 19]. Here we present the synthesis of a new metastable polymorph of Ti₃Sn and its structural evaluation (on an experimental but also theoretical level).

2 Results and discussion

As described in the experimental section, the sample we report here was prepared by ball milling (steel beaker) with a subsequent annealing step. The powder exhibits a dark grey color and appears to be stable in air. According to energy dispersive X-ray spectroscopy (EDX), the chemical composition is in good agreement with its theoretical one showing a Ti/Sn ratio of 3:1. In addition, an average of ∼ 0.5 at% iron was detected which is most likely due to abrasion of the used steel beaker (mean values for Ti: 74.7(7) at%, Sn: 24.9(6) at%, Fe: 0.5(2) at%).

Due to the low annealing temperature (450 °C) maintained for the preparation of our sample, its crystallinity is rather poor. However, reflections are clearly visible in the diffraction pattern and, consequently, a structural evaluation is still possible. It should be stated that the observed reflections in the diffraction pattern do not match h-Ti₃Sn with Ni₃Sn-type structure or any other previously described polymorph of Ti₃Sn. Applying a slightly higher crystallization temperature (550 °C) led to the formation of h-Ti₃Sn. With longer holding times at 450 °C, the hexagonal phase also began to form and a two-phase-mixture was obtained. The crystal structure of our sample has been determined using X-ray powder diffraction. The diffraction pattern was first examined using the software X’pert HighScore Plus (PANalytical, Almelo, The Netherlands) referring to the Inorganic Crystal Structure Database ICSD (FIZ Karlsruhe). The results suggested the Cr₃Si-type structure with space group Pm 3 ‾ n of cubic symmetry. Interestingly, c-Ti₃Sn with Cr₃Si-type structure has already been mentioned in the literature [20, 21]. However, a detailed description of the synthesis or a structural evaluation cannot be found. Unfortunately, access to presumably available, more detailed information was not possible [22].

Consequently, Rietveld refinements [23] using the Cr₃Si-type structure model were performed. A refinement using a single-phase model led to a mediocre residual value of R_wp = 0.0392. The reflection near 2 θ  = 40° appears to be slightly broader than the other ones and cannot be fitted into the single-phase model (see Figure 1a). This indicates the presence of an additional phase. Based on diffraction pattern analysis, possible side phases such as α -Ti or Ti₂Sn could be identified, both crystallizing in the hexagonal crystal system with space group P6₃/mmc [24, 25]. It should be noted that the strongest reflection of these phases appears at around 2 θ  = 40°. Due to the fact that the secondary phase could not be clearly assigned, only a Le-Bail refinement of the side phase was performed. Finally, an improved residual value of R_wp = 0.0233 could be reached. From the refined lattice parameters, the presence of titanium metal seemed to be a reasonable assumption. As a result, the broadened reflection could be refined thoroughly and the bump in the difference plot finally was smoothed out (see Figure 1b). Interestingly, the formation of α -Ti as a minor phase using arc melting for the preparation of Ti₃Sn samples was observed as well [26]. The X-ray powder diffraction pattern with the results of the Rietveld refinements are shown in Figure 1a and b. Refined structural and atomic parameters are summarized in Tables 1 and 2.

Figure 1:

(a) Powder X-ray diffraction pattern of the mechanochemically prepared c-Ti₃Sn phase with the results of the Rietveld refinement using the Cr₃Si-type model (space group Pm 3 ‾ n). Red: measured, black: calculated, blue: measured − calculated. (b) Results of the Rietveld refinement considering a secondary phase in space group P6₃/mmc.

The Cr₃Si type belongs to one of the most dense crystal structures [27]. The Sn atoms form a bcc-related substructure where the six faces of the unit cell are occupied by pairs of Ti atoms. These units are assembled into chains in three perpendicular directions through the crystal structure. The metal–metal distances are rather short which formally results in a coordination number of 14 for the Ti atoms, which are surrounded by ten Ti and four Sn atoms (Figure 2). The Ti–Ti distances in c-Ti₃Sn correlate well with those in other Cr₃Si-type phases (e.g. Ti₃Sb, Ti₃Au calculated from [28, 29]) and vary from 2.6207(11) Å (2×) to 3.2097(10) Å (8×). In comparison, elemental titanium (space group P6₃/mmc) exhibits Ti–Ti distances of 2.8953(1) Å (calculated from [30]). Comparable titanium chains have also been observed in the structures of Ti₂In₅ (300 pm Ti–Ti) [31] and Ti₃Rh₂In₃ (307 pm Ti–Ti) [32]. The Sn atom is surrounded by 12 Ti atoms forming an icosahedron (Figure 2). The Ti–Sn distances exhibit an average value of 2.9300(10) Å and are in good agreement with those observed for h-Ti₃Sn [33] and the cubic Ti₃Sn high-pressure phase [13].

Figure 2:

Coordination polyhedra around Sn (left) and Ti (right) in the Cr₃Si-type structure of c-Ti₃Sn. Orange: Sn, blue: Ti, unit cell in black.

In order to investigate if the incorporation of Fe leads to a stabilization of the Cr₃Si-type structure with respect to the Ni₃Sn structure, we performed quantum-chemical calculations at DFT level with the dispersion-corrected meta-GGA functional r2SCAN. We also considered other structure types such as the orthorhombic structure with space group Cmcm [11], the Cu₃Au structure type [13], and the Li₂AgSb structure type as observed for TiCuHg₂ [34]. Here the 4c Wyckoff site was occupied with Sn, the 4a, 4b and 4d sites with Ti. The primitive cells of the Cmcm structure of Ni₃Sn, and Cr₃Si contain 6 Ti atoms and 2 Sn atoms. For the other two polymorphs supercells of corresponding size were constructed. One of the six Ti atoms was replaced by an Fe atom. In cases where the Ti sites are not symmetry-equivalent, the most stable substitution position was considered. In Table 3 the relative stabilities per formula unit are given for the five polymorphs. For comparison, the corresponding Ti₃Sn energies are also given. The optimized lattice parameters are shown in Table 4. After Ti/Fe substitution, the symmetry was lowered. Therefore, some lattice parameters were averaged.

For Ti₃Sn, the Cmcm structure is slightly more stable than the experimentally observed Ni₃Sn-type structure. This is in agreement with previous DFT calculations [11]. Also, the Cr₃Si structure is only 0.08 eV less stable, followed by Cu₃Au (0.17 eV) and Li₂AgSb (0.59 eV). The Ti/Fe substituted structures are energetically much closer (within 0.11 eV) than the Ti₃Sn structures. In particular the Cu₃Au and Li₂AgSb structures are strongly stabilized, so that the Cr₃Si-type structure of Ti_2.5Fe_0.5Sn is now the least stable among the considered structure types, although its relative stability with respect to the Ni₃Sn-type structure is not significantly different.

The optimized lattice parameter of the Cr₃Si-type structure (a = 5.22 Å) is in good agreement with the measured value (a = 5.24 Å, Table 1). It decreases to 5.16 Å when 16.6% Ti atoms are substituted with Fe. It can be expected that the structural effect is much smaller if only 0.5% Ti is replaced by Fe. For the other structures (except Li₂AgSb) the reduction of the lattice parameters is much smaller.

From the experimental and theoretical results presented above, the mechanochemically prepared cubic phase has to be considered as metastable. At about 450 °C, the transformation to the well-known hexagonal phase (Ni₃Sn type) was observed. All this is in accordance with Ostwald’s step rule, which predicts the crystallization of a metastable polymorph out of a mainly amorphous material. Our calculations point to the fact that the incorporation of iron due to the use of a steel beaker does not stabilize this particular cubic structure type. Interestingly, it should be mentioned that other milling materials such as silicon nitride or zirconia directly led to the formation of the hexagonal Ti₃Sn phase using identical crystallizing conditions. Apparently, the local structure of the as-milled materials seems to be an important determinant for the formed polymorph.

2.1 ¹¹⁹Sn Mössbauer spectroscopy

Two different Ti₃Sn:Fe samples were analyzed through their ¹¹⁹Sn Mössbauer spectra at 78 K. The spectrum of sample A is shown as an example in Figure 3. It was well reproduced with a single signal at an isomer shift of δ = 1.70(1) mm s⁻¹. Due to the cubic site symmetry of the tin atoms (2a, m 3 ‾ .) no quadrupole splitting parameter was introduced. The experimentally determined line width parameter of Γ = 1.19(1) mm s⁻¹ is in the usual range observed for intermetallic tin compounds. The ¹¹⁹Sn Mössbauer spectrum thus confirms the single crystallographic tin site. Sample B is essentially identical to sample A; however, a very weak shoulder (<5% of the intensity) was observed in the spectrum at a slightly higher δ value. This signal could not be attributed to any known phase.

Figure 3:

Experimental (data points) and simulated (colored line) ¹¹⁹Sn Mössbauer spectrum of the Ti₃Sn sample measured at 78 K.

The isomer shift value of the present sample is slightly lower than the one reported for an arc-melted h-Ti₃Sn sample which was additionally annealed at 600 °C and cooled to room temperature at a rate of 4 K h⁻¹ [35]: δ = 1.80(1) mm s⁻¹, ΔE_Q = 0.98(1) mm s⁻¹ and Γ = 0.50(1) mm s⁻¹. The lower isomer shift indicated slightly lower s electron density in the present sample [36]. The quadrupole splitting parameter reflects the non-cubic site symmetry ( 6 ‾ m2) in the hexagonal modification.

3 Experimental section