Introduction

Heusler-phases have lately received much attention in the literature, both in fundamental research and in application-focused research areas like thermoelectrics and spin-tronics.[1] Heusler compounds are divided into full-Heusler (fH) and half-Heusler (hH). Both structures are cubic where fH is described with space group Fm-3m (no. 225, MnCu2Al-prototype), often referred to as XY 2 Z, and hH is described with space group F-43m (no. 216, MgAgAs-prototype), often referred to as XYZ, where X and Y are typically transition metals and Z is a main group element.

Early works on the Ti-Co-Sn system indicated the existence of both the fH TiCo2Sn and the hH TiCoSn.[2,3] These works reported a solid solution TiCo2−x Sn that follows Vegard’s law only for x > 0.4, while below 0.4 the lattice constant of the Heusler-phase stays very close to 6.00 Å. Later studies using extended X-ray absorption fine structure and neutron diffraction show that samples with composition TiCoSn after annealing at 1073 K (800 °C) are multi-phase, where the Heusler-phase has the composition TiCo1.5Sn and a unit cell close to 6.00 Å.[4,5] However, the most recent studies on the Ti-Co-Sn system again report the existence of hH TiCoSn with full solid solubility between hH and fH[6] or a partial solubility.[7]

This experimental work deals with annealed powder samples of ternary alloys containing Heusler-phases with elements Ti, Co and Sn. Samples were analyzed mainly by X-ray (XRD) and neutron powder diffraction (ND). The Rietveld method was used to analyze the diffraction data with respect to the compositions and unit cell parameters for the phases as well as the relative phase fractions. Based on these techniques, a revised isothermal section at 973 K (700 °C) with the focus on the Heusler-region of the phase diagram Ti-Co-Sn is proposed.

Experimental Methods

The investigated samples were made by arc melting of elements with purity 99.9 wt pct or better. Arc melting was done in Ti-gettered argon atmosphere in a water-cooled copper hearth and a tungsten electrode. The samples were turned and re-melted 3 times to improve homogeneity. Resulting buttons of about 5 g were ball-milled in argon atmosphere for 6 minutes in a SPEX SamplePrep 8000D Mixer/Mill in chromium steel vials (SPEX 8001) with 10 chromium steel balls (14 pct Cr) of 4 g each. Sample loss in this whole synthesis process was below 1 pct of the initial weight. No contamination of the samples with iron or chromium was detected with EDS in SEM.

The powder samples were annealed in evacuated silica ampoules at the temperatures 973 K and 1273 K (700 °C and 1000 °C) followed by quenching in water. Samples #16–19 (Table I) were annealed for 21 days at 973 K (700 °C) while the rest of the samples were annealed for 7 days. Annealing at 1273 K (1000 °C) was done for 48 hours, and if no severe sample loss (described in the next paragraph) was observed, they were annealed for another 48 hours.

Table I Equilibrium Phase Assembly in the Investigated Samples After Annealing at 973 K (700 °C)
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We chose to focus on the annealing temperature of 973 K (700 °C) since annealing at both lower and higher temperatures for some of these compositions is problematic. At temperatures 873 K (600 °C) and lower, most of the powder samples are not homogenized after annealing for 1 month. When annealed at temperatures above 1073 K (800 °C), samples that contain the phase Ti6Sn5 are found to form an oxide layer on the walls of the silica glass ampoule. The area of the ampoule wall that is in direct contact with the sample becomes coated with a Ti-Sn-oxide, while the rest of the ampoule becomes fully coated with an amorphous Ti-oxide of about 1 µm in thickness. Carbon coating of the ampoule wall does not hinder this process, but it can be suppressed by reducing the inner area of the ampoule, i.e., by soldering a silica rod just above the sample inside the ampoule. The amount of these oxides is relatively low compared to the amount of sample (<1 wt pct), but it involves only two of the components in the sample.

Powder X-ray diffraction (XRD) was done with a Bruker AXS D8 Discover in Bragg-Brentano geometry with Ge(111)-monochromated Cu Kα1-radiation and LynxEye™ 1D strip detector with energy filtering to suppress the Co-fluorescence. Data were collected on glass plate holders in the 2θ range of 20 to 120 deg with step-size 0.015 deg. Silicon standard NIST 640d with the lattice constant a = 5.43123 Å was used as internal standard for the XRD measurements. Some samples were also analyzed with ND for a different scattering contrast between the elements as compared to X-rays (neutron scattering lengths: b Ti = −3.4, b Co = 2.5, b Sn = 6.2 fm). ND experiments were done at the JEEP II research reactor facility at Kjeller in Norway, on the diffractometer PUS equipped with a focusing composite Ge monochromator and two detector banks with 7 3He-filled position-sensitive detector tubes in each. The sample was contained in a vanadium sample holder with 6 mm inner diameter. Data were collected in the 2θ range 10 to 130 deg with a wavelength of 1.5548 Å for samples Ti33.3Co33.3Sn33.3 and Ti28.6Co42.8Sn28.6 and 1.5539 Å for the sample Ti25.0Co50.0Sn25.0. Rietveld analysis was carried out with the software Bruker’s Topas[8] for XRD and GSAS EXPGUI+[9,10] for ND. Standard deviations derived from the Rietveld refinements are given in parentheses after the refined values.

Experimental Results and Discussion

Twenty-nine different compositions within the Ti-Co-Sn system have been investigated in this work and the samples annealed at 973 K (700 °C) are summarized in Table I. Space groups of the phases used in Rietveld refinements are listed in Table II.

Table II The Space Group of the Observed Phases
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We propose a revised isothermal section at 973 K (700 °C) (Figure 1) based on the observed phase relations that are listed in Table I.

Fig. 1
figure 1

The proposed isothermal section at 973 K (700 °C) of the ternary phase diagram Ti-Co-Sn. The single phase regions are colored in blue and three-phase regions in yellow to facilitate reading. (At 1273 K (1000 °C) the solubility gap between two solubility regions around Ti25Co50Sn25 disappears)

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A solid solubility range (SSR) TiCo2−x Sn (x ≤ 0.48) was observed in the investigated temperature interval 973 K to 1273 K (700 °C to 1000 °C); however, no hH with composition TiCoSn was found.

The SSR TiCo2−x Sn has space group F-43m with Wyckoff-positions 4a (0, 0, 0), 4b (½, ½, ½) and 4c (¼, ¼, ¼), fully occupied with Ti, Sn and Co; respectively, while the excess Co is located in the Wyckoff-position 4d (¾, ¾, ¾) with site occupancy between 0.52 and 1.0 (Figure 2). A Co 4d occupancy of 0.52 gives composition TiCo1.52Sn while occupancy 1.0 gives composition TiCo2Sn. Rietveld refinement of the diffraction data clearly show that at larger values of x (lower amount of Co) the hH structure describes the observed SSR better than the fH-structure, but at values of x around 0.3 (higher Co-content) these two models become indistinguishable. After all, the composition TiCo2Sn is a fH where the Wyckoff-position 8c in the space group Fm-3m is fully occupied by Co, which is equivalent to having fully occupied Wyckoff-positions 4c and 4d in the space group F-43m. For convenience, we chose to call this SSR intermediate Heusler (iH) (Figure 2).

Fig. 2
figure 2

The unit cell of (a) half-Heusler (hH) (F-43m), (b) full-Heusler (fH) (Fm-3m), (c) proposed intermediate-Heusler (iH) (F-43m) and (d) TiCo (Pm-3m). For all of the Heusler structures Ti is in 4a (0, 0, 0); for hH, fH and iH Sn is in 4b (½, ½, ½); for hH Co is in 4c (¼, ¼, ¼) while 4d (¾, ¾, ¾) is unoccupied, while for iH 4d (¾, ¾, ¾) is partially occupied; for fH Co is in 8c (¼, ¼, ¼). For TiCo Ti is in 1a (0,0,0) and Co is in 1b (½, ½, ½)

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Samples with composition Ti33.3Co33.3Sn33.3 contain three phases after annealing at 973 K (700 °C). XRD and ND show that the iH-phase is the main phase in these samples and has composition TiCo1.52(2)Sn and a = 5.9994(2) Å (Table I). After annealing at 1273 K (1000 °C), the sample consists of iH-phase with phase composition TiCo1.60(2)Sn and a = 6.0139(2) Å (70.7 wt pct), Ti6Sn5 (rt) (4.8 wt pct) and Sn-rich liquid that is solidified dominantly into the phase β-Sn (24.5 wt pct) during quenching. (On the diffraction pattern of 1273 K (1000 °C) some additional weak reflections are present that cannot be indexed to known intermetallic phases of Ti, Co and Sn.) These iH-phase compositions make one of the end points of the SSR TiCo2−x Sn, and from these observations we can see that the temperature dependence of x goes as follows: x ≤ 0.48 for 973 K (700 °C) and x ≤ 0.40 for 1273 K (1000 °C).

Anti-site disorder between Co and Ti in the Ti25.0Co50.0Sn25.0 (fH composition) has previously been studied by 119Sn Mössbauer spectroscopy and 59Co nuclear magnetic resonance spectroscopy.[12] The reported distortion of a local probe of a sample annealed at 800 K (527 °C) for 14 days is (Ti0.91Co0.09)(Co1.91Ti0.09)Sn with a = 6.0718(3) Å (from XRD). Our observations from XRD show a similar lattice constant a = 6.0707(1) Å in a sample with nominal composition Ti25.0Co50.0Sn25.0 annealed at 773 K (500 °C), but no anti-site disorder between Co and Ti is observed. Instead, the Rietveld refinement shows that the site of Sn (4b) is missing 5 pct scattering intensity in XRD, which might indicate vacancies or a small substitution of the lighter elements Co or Ti on the Sn site. Samples annealed at 973 K (700 °C) have a larger lattice constant a = 6.0797(1) Å and show no indication of disorder. These values are supported by ND experiments. However, samples annealed at 1273 K (1000 °C) have a lower lattice constant a = 6.0721(2) Å for the iH-phase and show no indication of any large disorder in the structure (Table III).

Table III Refinement Results from XRD of the iH-Phase in Samples with Composition Ti25.0Co50.0Sn25.0 After Different Annealing Temperatures
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It should be emphasized that the samples in the compositional range between Ti33.3Co33.3Sn33.3 and Ti25.0Co50.0Sn25.0 are not single phase. They consist of the iH-phase together with secondary phases (Table I). From the relative amounts of phases obtained by Rietveld refinements, without taking any substitutions mechanisms into account, the composition of the iH can be calculated. This shows that the composition of the iH is enriched in Ti and Co. This effect is largest for Ti and gives 0.7 at. pct excess Ti in the iH for sample Ti25.0Co50.0Sn25.0 and 3 at. pct for Ti33.3Co33.3Sn33.3. One explanation for this could be that the excess of the Ti atoms is allocated on the semi-filled 4d site (¾, ¾, ¾), something that will be hard to establish by Rietveld refinement of XRD data since the scattering difference of Co and Ti is so small that XRD is unreliable. For the compositions close to fH, the 4d site fills up and in sample Ti25.0Co50.0Sn25.0 there is no room for allowing Ti in 4d (¾, ¾, ¾). From the refinement, we see that sites 4a, 4c and 4d are fully occupied with, respectively, Ti and Co at 973 K (700 °C) (Table III). However, 4b, the Sn position, has a scattering deficiency of 3 pct. Vacancies on the Sn site would be in accordance with the observation, but so also would be substitution of Ti/Co for Sn. Later, we will show that for TiCo2Sn substitution of Ti for Sn indeed takes place.

Similar off-stoichiometry has been reported in the closely related system, Ti-Ni-Sn. Samples of TiCo2Sn show similar off-stoichiometry where the reported fH has the composition Ti23.3Ni52.2Sn24.4 after annealing at 1223 K (950 °C). The authors explained this as Ti/Ni substitution on the Sn site 4b.[13] Off-stoichiometry is also reported for the annealed samples TiNiSn containing mostly hH, but phases Ti6Sn5 and β-Sn are also present.[14]

Samples with compositions Ti33.3Co33.3Sn33.3, Ti28.6Co42.8Sn28.6 and Ti25.0Co50.0Sn25.0, all annealed at 973 K (700 °C) (Table I; Figure 3), were analyzed with ND. All of these samples give small diffraction peaks at d = 2.44(1) and 1.27(1) Å that fit to a cubic cell with a = 4.23(1) Å, possibly related to a divalent oxide of Ti or/and Co. These peaks were not observed in the XRD patterns. This can possibly be attributed to the specimen size where the amount of analyzed sample for the XRD is in the order of milligrams while the amount of the sample for ND is in the order of grams. In the refinement, the peaks were modeled as TiO (Fm-3m) and were found to make up about 0.5(2) wt pct.

Fig. 3
figure 3

ND data from samples Ti33.3Co33.3Sn33.3, Ti28.6Co42.8Sn28.6 and Ti25.0Co50.0Sn25.0 after annealing at 973 K (700 °C). Peaks marked with (*) were modeled as TiO with a = 4.23 (1) Å (see text)

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In this work, we have also discovered a previously unreported SSR between the compositions Ti25.0Co50.0Sn25.0 and Ti50.0Co50.0 (Table IV). At 1273 K (1000 °C), there is full solubility of Ti on the Sn-site (0.0 ≤ y ≤ 1.0), but at 973 K (700 °C) there is a solubility gap that reduces the solubility range to 0.2 ≤ y ≤ 1.0. Together with the SSR TiCo2−x Sn, they form a larger solid solution Ti1+y Co2−x Sn1−y (Figures 1 and 4).

Table IV Refinement Results from XRD of the Heusler-Phase in Selected Samples Within Composition Range Ti1+y Co2Sn1-y After Annealing at 973 K and 1273 K (700 °C and 1000 °C)
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Fig. 4
figure 4

Compositional dependence of the lattice parameters for solid solubility regions Ti1+y Co2Sn1−y and TiCo2−x Sn in the samples annealed at 973 K (700 °C) (from Table I). Blue triangles mark the nominal composition of the sample and red diamonds mark the refined iH-phase composition for that sample (sample with y = 0.1 contains two iH phases). Homogeneity regions are shaded. The deviation between sample and iH composition is due to the presence of other phases, see text. The value of a for y = 1 is taken from Ref. [15]

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A similarly large solubility region at 1123 K (850 °C) has recently been found in the system Ti-Ni-Sn that extends between TiNi-TiNi2Sn-TiNi1.654Sn.[13] In this system, there is a small solubility gap between Ti1.68Ni2Sn0.32 and Ti1.64Ni2Sn0.34.

There is full solid solubility (Ti1+y Co2Sn1−y for 0 ≤ y ≤ 1.0) in the samples within this compositional range after annealing at 1273 K (1000 °C). However, samples annealed at 973 K (700 °C) indicate a solubility gap in the composition range 0.0 ≤ x ≤ 0.2. This manifests itself as shoulders on the iH-peaks in the XRD data (Figure 5). The shape of this shoulder remains the same even after increased annealing time up to 1 month at 973 K (700 °C). After annealing at 1273 K (1000 °C), the diffraction data of these samples are easily fitted with one Heusler-like phase with sharp peaks. Re-annealing down from 1273 K (1000 °C) makes the peaks broader, which indicates phase separation, and shifts the a-axis back to larger values. Since the shoulder reappears after re-annealing, there are grounds to assume that compositions with 0.0 ≤ y ≤ 0.2 experience a transition from a single-phase to a two-phase area somewhere between 973 K and 1273 K (700 °C and 1000 °C). Surprisingly, the lattice constants a for the iH-phases within this SSR become noticeably lower with the increase in the annealing temperature; for instance, Ti35.0Co50.0Sn15.0 contains iH-phase with a = 6.04752(5) Å after annealing at 973 K (700 °C) and 6.04323(3) Å after annealing at 1273 K (1000 °C) (Table IV and Figure 5).

Fig. 5
figure 5

220-peaks of the iH phases in samples Ti27.5Co50.0Sn22.5 (red triangle), Ti30.0Co50.0Sn20.0 (blue square) and Ti32.5Co50.0Sn17.5 (green diamond) after annealing at 973 K and 1273 K (700 °C and 1000 °C). A distinctive shoulder is visible for the Ti27.5Co50.0Sn22.5 annealed at 973 K (700 °C)

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These two solid solubility ranges form together a continuous solid solution at 1273 K (1000 °C) that may be written schematically as Ti1+y Co2−x Sn1−y for (0 ≤ x ≤ 0.40 and y = 0; or 0 ≤ y ≤ 1 and x = 0), while at 973 K (700 °C) there is a gap in the composition and thus the solid solution can be written as (0 ≤ x ≤ 0.48 and y = 0; or 0.2 ≤ y ≤ 1 and x = 0) (Figure 4). This fact that none of the samples on the compositional line TiCo2Sn-TiCoSn are single phase at 973 K (700 °C) complicates the representation of the figure.

Conclusions

In this work, we have revised the isothermal section at 973 K (700 °C) of the ternary system Ti-Co-Sn. The main focus of the study was to explore the phase relationships around the Heusler-phases. The stoichiometric half-Heusler TiCoSn was not found to be present. Solid solution from TiCo2Sn to TiCo1.52Sn at 973 K (700 °C) has been established. In addition, a solid solution between TiCo2Sn and TiCo, with Ti substitution for Sn, has been shown to exist. This solid solution is full at 1273 K (1000 °C) but has a miscibility gap at 973 K (700 °C). The full solubility range of the Heusler-related phases may be written as 0 ≤ x ≤ 0.48 and y = 0; or 0.2 ≤ y ≤ 1 and x = 0 at 973 K (700 °C) and 0 ≤ x ≤ 0.40 and y = 0; or 0 ≤ y ≤ 1 and x = 0 at 1273 K (1000 °C).