New Tetragonal ReGa₅(M) (M = Sn, Pb, Bi) Single Crystals Grown from Delicate Electrons Changing

Abstract

Single crystals of the new Ga-rich phases ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) were successfully obtained from the flux method. The new tetragonal phases crystallize in the space group P4/mnc (No. 128) with vertex-sharing capped Re₂@Ga₁₄ oblong chains. Vacancies were discovered on the Ga4 and Ga5 sites, which can be understood as the direct inclusion of elemental Sn, Pb and Bi into the structure. Heat capacity measurements were performed on all three compounds resulting in a small anomaly which resembles the superconductivity transition temperature from the impurity ReGa₅ phase. The three compounds were not superconducting above 1.85 K. Subsequently, electronic structure calculations revealed a high density of states around the Fermi level, as well as non-bonding interactions that likely indicate the stability of these new phases.

1. Introduction

Endohedral gallium cluster phases are a chemical family that has been sought after for their various electronic properties arising from the interesting cluster chemistry associated with gallium’s moderate electronegativity [1,2]. However, because of overly large anionicity, isolated Ga clusters will very rarely form. This leads to a significant interplay between Ga cluster-cluster interactions, i.e., exo-bond formations and the stability of the electronic structures. While moving across the periodic table, a spectrum of diverse Ga cluster phases can be observed. Beginning with electropositive alkali metals (A), A_mGa_n compounds most readily form electron precise Zintl phases as a result of the large electronegativity difference, making a promising candidate for thermoelectric materials [3,4,5]. In this sense, electrons will be transferred from the alkali metals to Ga_n clusters to satisfy its valence electron requirement. Many of these compounds will form deltahedral clusters, as in borane chemistry, and have skeletal electron counts which will typically follow Wade’s rules [6].

Decreasing the electronegativity difference and transitioning towards actinides and lanthanides (R), a significant reduction in the band gap is observed and, in some cases is completely diminished, resulting in metallic behavior. In search of stability, R_mGa_n clusters often distort from ideal deltahedral symmetries and form exo-bonds [7]. The addition of transition metals into R_mGa_n clusters can reduce the cluster charge and has led to various intriguing materials such as the unconventional superconductor PuCoGa₅ [8]. Finally, coming to the transition metal (T) gallide clusters, the ionic behavior becomes more obscure as a result of the similar electronegativities between Ga and transition metals. In this region, the relationship between electron counts and cluster formation with regards to the superconductivity transition temperature, unfolds. Currently, the only known T_mGa_n superconductors are low-temperature superconductors, making them potential materials for producing high magnetic fields at low temperatures. This can be observed in the superconductors Mo₈Ga₄₁ and Mo₆Ga₃₁—as the electron counts decrease, the T_c increases and the clusters form vertex-sharing interactions rather than edge-sharing [9]. MnGa_4.96 is another Ga-rich cluster which crystallizes into a tetragonal unit cell with capped face sharing Mn@Ga₈ clusters and correspondingly exhibits no superconductivity [10]. Therefore, the stoichiometry and valence electrons from the transition metal of endohedral gallide clusters play a critical role in the exo-bond formations, i.e., electron-rich clusters prefer edge-sharing while electron-poor ones prefer vertex-sharing clusters, which as a result, directly affects the T_c. Considering the significant decrease in T_c from Rh₂Ga₉ to Ir₂Ga₉, and contradictorily the increase in T_c from Cr-Ga to Mo-Ga clusters, the transition of T_c across T_mGa_n clusters can be further analyzed [11,12,13].

Narrowing the spectrum down to the 5d transition metal gallide clusters below Mn in group 7, we sought to further investigate the recently discovered ReGa₅ superconductor with a T_c of ~2.3 K and vertex sharing Re@Ga₉ clusters [14]. Proceeding to understand the structural characteristics and electron counts of endohedral Ga clusters on superconductivity and further exploring new Re-Ga phases, we successfully discovered three new compounds ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi). Reported here are the heat capacity measurements along with the crystal and electronic structure characterizations. No superconductivity was found for ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) down to 1.85 K.

2. Experimental Section

Synthesis. The new compounds ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) were synthesized via flux method using Ga as the self-flux. Elements used include tin granules (99.9%, BTC), lead shots (99.999%, BTC), bismuth chunks (99.999%, lump, Alfa Aesar), gallium ingot (99.99% (metals basis), Alfa Aesar) and rhenium powder (−325 mesh, 99.99% (metals basis), Alfa Aesar). The three reactions were prepared with sample sizes of ~1.5–2.0 g and loading compositions of ReSnGa₄₈, RePb₅Ga₂₅ and ReBi₅Ga₂₅. Each sample was placed in an alumina crucible then inside a silica tube. Quartz glass pieces and quartz wool were packed on top of the crucible as the filter. The silica tube was subsequently evacuated (<10⁻⁵ Torr) and sealed. Samples were heated to 950 °C at a rate of 200 °C/hr and annealed there for 24hr then slow cooled at a rate of 10 °C/hr for ReGa_~5(Sn) and 4 °C/hr for ReGa_~5(Pb) and ReGa_~5(Bi) to 600 °C at which the samples were centrifuged. Excess Ga flux was removed using ~2 M HCl. All products are found to be stable in air and moisture.

Phase Analysis. For each ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) sample the phase was identified and purity verified through a Rigaku MiniFlex 600 powder X-ray diffractometer using Cu Kα radiation (λ_Kα = 1.5406 Å, Ge monochromator) [15]. A scan speed of 1.25°/min and step of 0.005° were used over a Bragg angle (2θ) ranging from 5 to 90° for ReGa_~5(Pb) and ReGa_~5(Bi). For ReGa_~5(Sn) a scan speed of 0.6°/min and step of 0.005° were used over a Bragg angle (2θ) ranging from 10 to 90°. Full Proof software was used to analyze the phase identification and lattice parameters of the experimental and theoretical powder patterns for ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) and the experimental powder patterns for the impurity phases obtained from ICSD [16].

Structure Determination. Single crystals from ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) were picked to perform a structural analysis using a Bruker Apex II diffractometer equipped with Mo radiation (λ_Kα = 0.71073 Å). Scattering intensity data were collected at room temperature with 0.5° per scan in ω and an exposure time of 10s per frame. The crystal structure was solved using a SHELXTL package with direct methods and full-matrix least-squares on F² model [17,18].

Scanning Electron Microscopy. A FEI Quanta 3D Field Emission Gun (FEG) Focused Ion Beam (FIB)/Scanning Electron Microscope (SEM) and Energy Dispersive X-ray Spectroscopy (EDX) were utilized with the analysis of chemical stoichiometry. For each sample, multiple areas were selected for spectrum collection with a 20kV accelerating voltage and 100 seconds of scanning time.

Physical Property Measurements. Heat capacity measurements were carried out using the two-$\tau$ time- relaxation method in a Physical Property Measurement System (PPMS). The data was collected between 1.85 and 300 K. The sample was mounted to the measuring stage using Apiezon N grease to ensure good thermal contact.

Tight-Binding, Linear Muffin-Tin Orbital-Atomic Sphere Approximation (TB-LMTO-ASA) [19]. The TB-LMTO-ASA program with Stuttgart code was utilized to calculate the density of states (DOS) and Orbital Hamiltonian Population (COHP) curves of a hypothetically ordered “ReGa_4.5” [20,21]. The convergence criterion was set to 0.05 meV. The Muffin-Tin radius (RMT) for each element includes: 0.995 Å for Re1; 1.40 Å for Ga2; 1.88 Å for Ga3; 0.83 Å for Ga4. The band structure and DOS were both calculated with a 4 × 4 × 2 k-point in the Brillouin zone [22,23].

3. Results and Discussions

Phase Analysis. As a result of increasing the valence electron count from the orthorhombic ReGa₅, three new tetragonal phases ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) were revealed. Unreacted Re was present in all of the three compounds ranging from 5–15% as well as ReGa₅ from 0.1–39%, based on the HighScore Plus software. Unreacted Pb and Bi were also found in both ReGa_~5(Pb) and ReGa_~5 (Bi) by approximately 3 and 7%, respectively. A comparison of the three powder patterns, as well as images of the single crystals, are shown in Figure 1. Individual refined powder patterns of the three phases can be found in Figure S1 (Supplementary Materials) of the Supporting Information. To confirm the chemical composition and stoichiometry SEM-EDS was utilized. The determined chemical formulas are Re_1.0(3)Ga_5.0(2)Sn_0.1(8), Re_1.0(2)Ga_5.0(2)Pb_0.1(5) and Re_1.0(2)Ga_5.0(2)Bi_0.2(4). A complete table of the SEM-EDS data is shown in Table S2 in the Supporting Information.

Crystal Structure. Single crystal X-ray diffraction was utilized to further understand the effect of atomic size and electron counts on the stability of Ga-rich phases. As a result of the increase in valence electron counts induced from the elements Sn, Pb and Bi, a tetragonal structure with space group P4/mnc (No. 128) was formed. A table of the single crystal refinement data as well as atomic coordinates and equivalent isotropic displacement parameters are given in

Table 1. Single crystal refinement data for ReGa_4.96(Sn), ReGa_5.08(Pb) and ReGa_5.13(Bi).

Refined Formula	ReGa4.96(9)(Sn)	ReGa5.08(5)(Pb)	ReGa5.13(5)(Bi)
FW (g/mol)	532.19	540.55	543.86
Space group; Z	P 4/m n c; 4	P 4/m n c; 4	P 4/m n c; 4
a (Å)	6.4680(9)	6.4830(13)	6.474(2)
c (Å)	10.166(2)	10.229(2)	10.213(4)
V (Å3)	425.29(15)	429.9(2)	428.0(3)
Extinction Coefficient	0.0017(4)	0.0037(3)	0.0044(3)
θ range (°)	3.734–33.135	3.721–33.166	3.726–33.240
No. reflections; Rint	5007; 0.0646	5731; 0.0700	5798; 0.1039
No. independent reflections	429	436	438
No. parameters	30	29	30
R1; ωR2 (I > 2δ(I))	0.0397; 0.0932	0.0284; 0.0552	0.0263; 0.0464
Goodness of fit	1.311	1.197	0.999
Diffraction peak and hole (e−/Å3)	2.713; −2.981	1.572; −2.359	1.822; −1.863

and

Table 2. Atomic coordinates and equivalent isotropic displacement parameters for ReGa_4.96(Sn), ReGa_5.08(Pb) and ReGa_5.13(Bi) (U_eq is defined as one-third of the trace of the orthogonalized U_ij tensor (Ų)).

Atom	Wyck.	x	y	z	Occ.	Ueq
ReGa4.96(9)(Sn)
Re	4e	0	0	0.3451(1)	1	0.008(1)
Ga2	8h	0.4535(3)	0.1808(3)	0	1	0.016(1)
Ga3	8g	0.7431(3)	0.2431(3)	¼	1	0.045(1)
Ga4	4e	0	0	0.051(3)	0.18(3)	0.021(8)
Ga5	16i	0.0426(18)	0.096(2)	0.0947(8)	0.20(1)	0.028(4)
ReGa5.08(5)(Pb)
Re	4e	0	0	0.3453(1)	1	0.007(1)
Ga2	8h	0.4622(2)	0.1816(2)	0	1	0.016(1)
Ga3	8g	0.7462(2)	0.2462(2)	¼	1	0.040(1)
Ga4	2a	0	0	0	0.75(1)	0.022(1)
Ga5	16i	0.0389(11)	0.0883(19)	0.0970(5)	0.18(1)	0.024(2)
ReGa5.13(5)(Bi)
Re	4e	0	0	0.3451(1)	1	0.006(1)
Ga2	8h	0.4692(1)	0.1821(1)	0	1	0.018(1)
Ga3	8g	0.7467(1)	0.2467(1)	¼	1	0.033(1)
Ga4	4e	0	0	0.0318(3)	0.62(1)	0.012(1)
Ga5	16i	0.039(2)	0.079(5)	0.1001(6)	0.13(1)	0.027(3)

. The three new phases ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) consist of two face-sharing square antiprismatic Re@Ga₈ polyhedra capped by four Ga atoms, or five Ga atoms when considering ReGa_~5(Sn), on the remaining free square faces. Consequently, these clusters form networks of vertex sharing capped Re₂@Ga₁₄ oblong chains, similar to MnGa_4.96. The Re@Ga₈ clusters in ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) resemble the geometry of the Re@Ga₉ endohedral clusters found in the ReGa₅ orthorhombic structure, however, in this case, the polyhedra are more than singly capped. Conversely, the Re@Ga₉ clusters in ReGa₅ are vertex sharing, while ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi) not only have vertex sharing but also face sharing polyhedra, which resultantly produces the capped Re₂@Ga₁₄ oblong chains. As seen in the decrease in T_c from the superconductor Mo₈Ga₄₁ to Mo₆Ga₃₁ the exo-bond formation, as well as the additional electron counts, may be a key factor causing the loss of superconductivity in ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi). Initially, atomic vacancies were tested and revealed vacancies on the Ga4 and Ga5 sites. The Ga4 site vacancies were found to vary significantly depending on the electron count. After further inspection of the change in atomic distances with varying electron count, it was found that the Re-Ga4 distance experiences the most significant change. A table of atomic distances for each new phase is given in

Table 3. List of atomic distances for ReGa_4.96(Sn), ReGa_5.08(Pb) and ReGa_5.13(Bi).

ReGa4.96(Sn)
Atom1	Atom2	Distances (Å)
Re	Ga2	2.614(2)
Re	Ga3	2.484(2)
Re	Ga4	2.99(4)
Re	Ga5	2.635(9)
Ga5	Ga5	1.36(3) (diagonally along the b axis)
ReGa5.08(Pb)
Atom1	Atom2	Distances (Å)
Re	Ga2	2.612(1)
Re	Ga3	2.491(1)
Re	Ga4	3.5322(6)
Re	Ga5	2.616(6)
Ga5	Ga5	1.25(1) (diagonally along the b axis)
ReGa5.13(Bi)
Atom1	Atom2	Distances (Å)
Re	Ga2	2.604(1)
Re	Ga3	2.487(1)
Re	Ga4	3.200(4)
Re	Ga5	2.566(8)
Ga5	Ga5	1.14(4) (diagonally along the b axis)

. This occurrence may have been understood by the Re@Ga₈ polyhedra undergoing stretching and compression due to the various applied chemical pressures. However, the atomic distances in the Re@Ga₈ polyhedra appear to remain relatively consistent. The changes in distance experienced by Re-Ga4 resulted from the vacancies on the Ga4 site. As the vacancies decrease, the Ga4 site merges two atoms into one and the Re-Ga4 distance increases. This occurs as the structure changes from Sn to Bi to Pb, where ReGa_~5(Sn) and ReGa_~5(Bi) have Ga4 on the 4e site while ReGa_~5(Pb) has Ga4 on the 2a site. As a result, the Ga4 and Ga5 vacancies can be realized as Sn, Pb and Bi giving a mixture of Ga and Sn, Pb or Bi on the Ga4 and Ga5 sites, as shown in Figure 2d. Therefore, considering both the atomic size and electron count of Sn, Pb and Bi the changing Ga4 vacancies and Re-Ga4 distance can be well understood. Taking into account that the most significant changes are resulting from the Re-Ga4 and the Ga5-Ga5 distances (diagonally along the b axis) then both can be recognized as contributing factors to the change in structure between the three compounds. The four Ga5 atoms that sit on either side of the Ga4 site seem to open and compress, in sync with the Ga5 occupancies as the Ga4 atomic vacancy and site location changes, subsequently pushing Ga4 from the 4e to the 2a site. This then increases the Re-Ga4 distance as the structures transition from ReGa_~5(Sn) to ReGa_~5(Bi) to ReGa_~5(Pb).

Physical Properties. To evaluate the impact of chemical pressure on superconductivity, specific heat measurements were carried out. Figure 3a,c,e show the specific heat data plotted as, C_P/T versus T², and Figure 3b,d,f display C_P versus T for ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi), respectively. The low-temperature experimental data (obtained under field of 0.3 T) were fitted using C_p/T = γ + βT², where the first and second terms are attributed to the electronic (C_el) and lattice contributions (C_ph) to the specific heat, respectively. The fit, represented by the red solid line (see Figure 3a,c,e), gives the Sommerfeld coefficient,γ,4.0(1), 3.4(1), and 3.5(2) mJ mol⁻¹ K⁻² and β equals to 0.39(2), 0.55(1) and 0.84(3) mJ mol⁻¹ K⁻⁴ for ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi), respectively. Furthermore, the Debye temperature Θ_D can be determined using the simple Debye model: ${\mathrm{\Theta }}_{\mathrm{D}}={\left(\frac{12{\pi }^4}{5\beta }nR\right)}^{1/3}$, where R = 8.31 J mol⁻¹K⁻¹. The calculated Debye temperature Θ_D is 309(4), 275(1) and 239(1) K for compounds with elemental Sn, Pb and Bi, respectively. The obtained values of the Sommerfeld coefficient and Debye temperature are significantly lower when compared with ReGa₅ (γ = 4.68(7) mJ mol⁻¹ K⁻² and Θ_D = 314(2)K). A small anomaly at around 2.2 K, is observed for each phase in the specific heat data measured under zero field, that resembles the critical superconducting temperature of ReGa₅ (not shown here). This is consistent with the high concentration of ReGa₅ present in each compound. Thus, we conclude that no phase transition was observed for ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi), indicating that the effect of the valence electron counts on the ReGa₅ system resulted not only in a change of the crystal structure but also a loss of superconductivity. The whole temperature range C_p(T), see Figure 3b,d,f, shows a typical behavior and at high temperature, C_p approaches the expected Dulong–Petit value (3nR ≈ 150 J mol⁻¹ K⁻¹), where n is the number of atoms per formula unit (n = 6) and R is the gas constant (R = 8.31 J mol⁻¹ K⁻¹).

Electronic Structure. To evaluate the influence of the electronic structure on ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi), TB-LMTO-ASA calculations were performed to analyze the density of states (DOS), Crystal Orbital Hamiltonian Population (-COHP) curves and band structures. Due to the Ga vacancies and close proximity with regards to other atoms, a hypothetical “ReGa_4.5” was utilized to calculate the electronic structure, these plots are shown in Figure 4a–c. Based on the stoichiometry of Sn, Pb and Bi determined from the SEM/EDS data, the electron counts of ReGa_4.96Sn_0.1, ReGa_5.08Pb_0.1 and ReGa_5.13Bi_0.2 were calculated to be 22.28, 22.64 and 23.39 valence electrons (VE) per Re, respectively. The Fermi energy level is indicated for each compound in Figure 4. As seen with ReGa₅ and other endohedral gallide cluster superconductors, the Fermi energy level is located in a pseudo gap in the DOS, which is thought to play a role in the structural stability [24]. However, no von Hove singularities are found in the electronic structure of ReGa_4.96(Sn), ReGa_5.08(Pb) and ReGa_5.13(Bi) around the Fermi level [25]. Consequently, this could be a key factor in the loss of superconductivity in these gallide clusters. This is consistent with the band structure calculation, Figure 4c, which indicates metallic behavior and shows no sign of flat bands near the Fermi energy. The DOS at the Fermi energy increases from ReGa_5.08(Pb) to ReGa_5.13(Bi) to ReGa_4.96(Sn) suggesting the stability of the structures may come from the degree of Ga4 vacancies. -COHP curves, shown in Figure 4b, were calculated to analyze the interactions between Re and Ga in ReGa_~5(Sn), ReGa_~5(Pb) and ReGa_~5(Bi). The -COHP shows the Fermi levels tend to move from strong antibonding interactions to the non-bonding interactions. This could be strongly related to the structural stability of these distorted phases and a major influence on the lack of superconductivity.

4. Conclusions

The understanding of Ga-rich T_mGa_n endohedral clusters was further assessed through three new phases: ReGa_~5(Sn); ReGa_~5(Pb) and ReGa_~5(Bi) presented here. The crystal structure characterization reveals that the new phases crystallize in a tetragonal unit cell resembling that of MnGa_4.96. The electron-rich new Re-Ga phases produced edge-sharing polyhedra, further confirming the exo-bond formations between electron-rich and poor gallide clusters. Heat capacity measurements were performed, and no superconductivity was found down to 1.85 K, only a small anomaly associated with the ReGa₅ superconductivity transition temperature. The Sommerfeld and Debye temperatures are significantly lower than ReGa₅. Electronic structure calculations offered additional insight into the structural stability. Conclusively, the non-bonding character and absence of a pseudo gap and at the Fermi energy level along with the capped face sharing square antiprismatic Re@Ga₈ polyhedra likely have a direct impact on the structural stability and loss of superconductivity in these Re-Ga clusters. These non-superconducting compounds may be useful for other potential applications.