Measurement of jet-medium interactions via direct photon-hadron correlations in Au + Au and d + Au collisions at s N N = 200 GeV
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Here, the measurement of direct photons from Au + Au collisions at $\sqrt{s_{NN}}$ = 39 and 62.4 GeV in the transverse-momentum range 0.4 < $p_T$ < 3 Gev/c is presented by the PHENIX collaboration at the BNLRelativistic Heavy Ion Collider. A significant direct-photon yield is observed in both collision systems. A universal scaling is observed when the direct-photon $p_T$ spectra for different center-of-mass energies and for different centrality selections at $\sqrt{s_{NN}}$ = 62.4 GeV is scaled with $(dN_{\text{ch}}/dη)^α$ for α = 1.21 ± 0.04. This scaling also holds true for direct-photon spectra from Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV measured earlier by PHENIX, as well as the spectra from Pb + Pb at $\sqrt{s_{NN}}$ = 2760 GeV published by ALICE. The scaling power α seems to be independent of $p_T$, center of mass energy, and collision centrality. The spectra from different collision energies have a similar shape up to $p_T$ of 2 Gev/c. The spectra have a local inverse slope $T_{\text{eff}}$ increasing with $p_T$ of 0.174 ± 0.018 Gev/c in the range 0.4 < $p_T$ < 1.3 Gev/c and increasing to 0.289 ± 0.024 Gev/c for 0.9 < $p_T$ < 2.1 Gev/c. The observed similarity of low-$p_T$ direct-photon production from $\sqrt{s_{NN}}$ = 39 to 2760 GeV suggests a common source of direct photons for the different collision energies and event centrality selections, and suggests a comparable space-time evolution of direct-photon emission.
We previously published in 2018 a detailed measurement recorded in 2010 for Au+Au collisions at $\sqrt{^SNN}$ = 200 GeV of charged two-pion correlation functions in 0%-30% centrality. We found the data to be well described by Bose-Einstein correlation functions stemming from L$\acute{e}$vy-stable source distributions. Using a fine transverse momentum binning, we extracted the correlation strength parameter λ, the L$\acute{e}$vy index of stability α and the L$\acute{e}$vy length scale parameter R as a function of average transverse mass of the pair m T .
The PHENIX experiment measured the centrality dependence of two-pion Bose-Einstein correlation functions in $\sqrt{𝑠{𝑁𝑁}}$ = 200 GeV Au + Au collisions at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. The data are well represented by Lévy-stable source distributions. The extracted source parameters are the correlation-strength parameter 𝜆, the Lévy index of stability 𝛼, and the Lévy-scale parameter 𝑅 as a function of transverse mass 𝑚 𝑇 and centrality. The 𝜆(𝑚 𝑇 ) parameter is constant at larger values of 𝑚 𝑇 , but decreases as 𝑚 𝑇 decreases. The Lévy-scale parameter 𝑅(𝑚 𝑇 ) decreases with 𝑚 𝑇 and exhibits proportionality to the length scale of the nuclear overlap region. The Lévy exponent 𝛼(𝑚 𝑇 ) is independent of 𝑚 𝑇 within uncertainties in each investigated centrality bin, but shows a clear centrality dependence. At all centralities, the Lévy exponent 𝛼 is significantly different from that of Gaussian (𝛼 = 2) or Cauchy (𝛼 = 1) source distributions. Comparisons to the predictions of Monte-Carlo simulations of resonance-decay chains show that, in all but the most peripheral centrality class (50%–60%), the obtained results are inconsistent with the measurements, unless a significant reduction of the in-medium mass of the 𝜂′ meson is included. Finally, in each centrality class, the best value of the in-medium 𝜂′ mass is compared to the mass of the 𝜂 meson, as well as to several theoretical predictions that consider restoration of U 𝐴 (1) symmetry in hot hadronic matter.
We present the first measurements of the forward and midrapidity 𝜂-meson cross sections from 𝑝 + 𝑝 collisions at $\sqrt{𝑠}$ = 500 and 510 GeV, respectively. We also report the midrapidity 𝜂/𝜋 0 ratio at 510 GeV. The forward cross section is measured differentially in 𝜂-meson transverse momentum (𝑝 𝑇 ) from 1.0 to 6.5 GeV/𝑐 for pseudorapidity 3.0 < |𝜂| < 3.8. The midrapidity cross section is measured from 3.5 to 44 GeV/𝑐 for pseudorapidity |𝜂| < 0.35. Both cross sections serve as critical inputs to an updated global analysis of the 𝜂-meson fragmentation functions.
Ta2Al is beta Plutonium-derived structured and crystallizes in the tetragonal P4_2/mnm space group. The structure is three-dimensional. there are three inequivalent Ta sites. In the first Ta site, Ta is bonded in a 11-coordinate geometry to nine Ta and five Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.69–3.30 Å. There are a spread of Ta–Al bond distances ranging from 2.97–3.13 Å. In the second Ta site, Ta is bonded in a 12-coordinate geometry to seven Ta and five Al atoms. There are one shorter (2.82 Å) and two longer (3.19 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.68–2.90 Å. In the third Ta site, Ta is bonded in a 2-coordinate geometry to eleven Ta and four Al atoms. The Ta–Ta bond length is 2.72 Å. There are two shorter (2.72 Å) and two longer (3.03 Å) Ta–Al bond lengths. There are two inequivalent Al sites. In the first Al site, Al is bonded in a 10-coordinate geometry to nine Ta and one Al atom. The Al–Al bond length is 2.79 Å. In the second Al site, Al is bonded to twelve Ta atoms to form edge-sharing AlTa12 cuboctahedra.
Al3Ta is beta Cu3Ti-like structured and crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Ta is bonded to twelve Al atoms to form TaAl12 cuboctahedra that share corners with four equivalent TaAl12 cuboctahedra, corners with eight equivalent AlTa4Al8 cuboctahedra, edges with eight equivalent TaAl12 cuboctahedra, edges with sixteen equivalent AlTa4Al8 cuboctahedra, faces with four equivalent TaAl12 cuboctahedra, and faces with fourteen AlTa4Al8 cuboctahedra. There are four shorter (2.73 Å) and eight longer (2.88 Å) Ta–Al bond lengths. There are two inequivalent Al sites. In the first Al site, Al is bonded to four equivalent Ta and eight equivalent Al atoms to form distorted AlTa4Al8 cuboctahedra that share corners with four equivalent AlTa4Al8 cuboctahedra, corners with eight equivalent TaAl12 cuboctahedra, edges with twenty-four AlTa4Al8 cuboctahedra, faces with six equivalent TaAl12 cuboctahedra, and faces with twelve AlTa4Al8 cuboctahedra. All Al–Al bond lengths are 2.88 Å. In the second Al site, Al is bonded to four equivalent Ta and eight Al atoms to form AlTa4Al8 cuboctahedra that share corners with twelve equivalent AlTa4Al8 cuboctahedra, edges with eight equivalent TaAl12 cuboctahedra, edges with sixteen AlTa4Al8 cuboctahedra, faces with four equivalent TaAl12 cuboctahedra, and faces with fourteen AlTa4Al8 cuboctahedra. All Al–Al bond lengths are 2.73 Å.
Ta13Al23 is Bergman Structure: Mg32(Al,Zn)49 Bergman-derived structured and crystallizes in the trigonal R3m space group. The structure is three-dimensional. there are fifteen inequivalent Ta sites. In the first Ta site, Ta is bonded in a 12-coordinate geometry to three Ta and nine Al atoms. There are one shorter (2.86 Å) and two longer (3.16 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.77–3.03 Å. In the second Ta site, Ta is bonded in a 12-coordinate geometry to three Ta and nine Al atoms. There are one shorter (2.82 Å) and two longer (3.05 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.67–3.06 Å. In the third Ta site, Ta is bonded in a 11-coordinate geometry to one Ta and ten Al atoms. The Ta–Ta bond length is 2.88 Å. There are a spread of Ta–Al bond distances ranging from 2.76–3.07 Å. In the fourth Ta site, Ta is bonded in a 1-coordinate geometry to four Ta and ten Al atoms. There are one shorter (2.92 Å) and three longer (3.19 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.63–2.91 Å. In the fifth Ta site, Ta is bonded in a 11-coordinate geometry to four Ta and ten Al atoms. There are one shorter (2.96 Å) and three longer (3.25 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.76–2.92 Å. In the sixth Ta site, Ta is bonded in a 6-coordinate geometry to three equivalent Ta and twelve Al atoms. There are a spread of Ta–Al bond distances ranging from 2.78–3.06 Å. In the seventh Ta site, Ta is bonded in a 6-coordinate geometry to three Ta and twelve Al atoms. There are a spread of Ta–Al bond distances ranging from 2.78–3.06 Å. In the eighth Ta site, Ta is bonded in a 12-coordinate geometry to four Ta and twelve Al atoms. There are three shorter (2.99 Å) and nine longer (3.00 Å) Ta–Al bond lengths. In the ninth Ta site, Ta is bonded in a 9-coordinate geometry to two Ta and nine Al atoms. The Ta–Ta bond length is 2.95 Å. There are a spread of Ta–Al bond distances ranging from 2.69–2.89 Å. In the tenth Ta site, Ta is bonded in a 9-coordinate geometry to two Ta and nine Al atoms. The Ta–Ta bond length is 2.98 Å. There are a spread of Ta–Al bond distances ranging from 2.74–2.92 Å. In the eleventh Ta site, Ta is bonded in a 2-coordinate geometry to five Ta and nine Al atoms. There are one shorter (3.07 Å) and one longer (3.29 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.80–3.32 Å. In the twelfth Ta site, Ta is bonded in a 12-coordinate geometry to four Ta and twelve Al atoms. The Ta–Ta bond length is 3.09 Å. There are a spread of Ta–Al bond distances ranging from 2.97–3.05 Å. In the thirteenth Ta site, Ta is bonded in a 12-coordinate geometry to four Ta and twelve Al atoms. The Ta–Ta bond length is 3.11 Å. There are a spread of Ta–Al bond distances ranging from 2.98–3.00 Å. In the fourteenth Ta site, Ta is bonded in a 11-coordinate geometry to eleven Al atoms. There are a spread of Ta–Al bond distances ranging from 2.63–2.82 Å. In the fifteenth Ta site, Ta is bonded in a 12-coordinate geometry to four Ta and twelve Al atoms. There are nine shorter (3.02 Å) and three longer (3.03 Å) Ta–Al bond lengths. There are twenty-one inequivalent Al sites. In the first Al site, Al is bonded to six Ta and six Al atoms to form distorted AlTa6Al6 cuboctahedra that share corners with two AlTa7Al5 cuboctahedra, edges with two equivalent AlTa6Al6 cuboctahedra, and faces with eight AlTa6Al6 cuboctahedra. There are a spread of Al–Al bond distances ranging from 2.53–2.95 Å. In the second Al site, Al is bonded in a 7-coordinate geometry to four Ta and three equivalent Al atoms. All Al–Al bond lengths are 2.75 Å. In the third Al site, Al is bonded in a 10-coordinate geometry to four Ta and six Al atoms. There are a spread of Al–Al bond distances ranging from 2.69–3.04 Å. In the fourth Al site, Al is bonded to seven Ta and five Al atoms to form distorted AlTa7Al5 cuboctahedra that share corners with five AlTa6Al6 cuboctahedra, edges with two equivalent AlTa7Al5 cuboctahedra, and faces with eleven AlTa6Al6 cuboctahedra. There are a spread of Al–Al bond distances ranging from 2.46–2.65 Å. In the fifth Al site, Al is bonded to seven Ta and five Al atoms to form distorted AlTa7Al5 cuboctahedra that share corners with five AlTa6Al6 cuboctahedra, edges with two equivalent AlTa7Al5 cuboctahedra, and faces with eleven AlTa7Al5 cuboctahedra. There are two shorter (2.56 Å) and two longer (2.70 Å) Al–Al bond lengths. In the sixth Al site, Al is bonded to seven Ta and five Al atoms to form distorted AlTa7Al5 cuboctahedra that share corners with three AlTa7Al5 cuboctahedra, edges with two AlTa7Al5 cuboctahedra, and faces with twelve AlTa6Al6 cuboctahedra. There are a spread of Al–Al bond distances ranging from 2.45–2.68 Å. In the seventh Al site, Al is bonded in a 12-coordinate geometry to six Ta and six Al atoms. There are a spread of Al–Al bond distances ranging from 2.53–3.05 Å. In the eighth Al site, Al is bonded in a 12-coordinate geometry to six Ta and four Al atoms. There are one shorter (2.49 Å) and two longer (2.55 Å) Al–Al bond lengths. In the ninth Al site, Al is bonded in a 12-coordinate geometry to six Ta and six Al atoms. There are a spread of Al–Al bond distances ranging from 2.52–3.07 Å. In the tenth Al site, Al is bonded in a 5-coordinate geometry to five Ta and six Al atoms. There are a spread of Al–Al bond distances ranging from 2.74–3.03 Å. In the eleventh Al site, Al is bonded in a 6-coordinate geometry to five Ta and six Al atoms. There are a spread of Al–Al bond distances ranging from 2.69–3.01 Å. In the twelfth Al site, Al is bonded in a 5-coordinate geometry to five Ta and four Al atoms. The Al–Al bond length is 2.88 Å. In the thirteenth Al site, Al is bonded in a 9-coordinate geometry to five Ta and four Al atoms. There are one shorter (2.66 Å) and one longer (2.77 Å) Al–Al bond lengths. In the fourteenth Al site, Al is bonded in a 10-coordinate geometry to six Ta and four Al atoms. In the fifteenth Al site, Al is bonded in a 12-coordinate geometry to six Ta and four Al atoms. In the sixteenth Al site, Al is bonded to six Ta and six Al atoms to form distorted AlTa6Al6 cuboctahedra that share corners with two AlTa7Al5 cuboctahedra, edges with three AlTa6Al6 cuboctahedra, and faces with eight AlTa7Al5 cuboctahedra. The Al–Al bond length is 2.54 Å. In the seventeenth Al site, Al is bonded in a 8-coordinate geometry to two Ta and six Al atoms. In the eighteenth Al site, Al is bonded in a 11-coordinate geometry to four Ta and seven Al atoms. In the nineteenth Al site, Al is bonded in a 12-coordinate geometry to six Ta and six Al atoms. There are three shorter (2.55 Å) and three longer (2.86 Å) Al–Al bond lengths. In the twentieth Al site, Al is bonded in a 12-coordinate geometry to six Ta and six Al atoms. There are one shorter (2.54 Å) and two longer (2.85 Å) Al–Al bond lengths. In the twenty-first Al site, Al is bonded to six Ta and six Al atoms to form distorted AlTa6Al6 cuboctahedra that share corners with two equivalent AlTa7Al5 cuboctahedra, edges with two equivalent AlTa6Al6 cuboctahedra, and faces with ten AlTa6Al6 cuboctahedra.
Ta11Al4 is beta Uranium-derived structured and crystallizes in the monoclinic P2/m space group. The structure is three-dimensional. there are nine inequivalent Ta sites. In the first Ta site, Ta is bonded in a 6-coordinate geometry to ten Ta and four Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.61–3.30 Å. There are a spread of Ta–Al bond distances ranging from 2.89–2.93 Å. In the second Ta site, Ta is bonded in a 6-coordinate geometry to ten Ta and four Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.57–3.37 Å. There are a spread of Ta–Al bond distances ranging from 2.89–2.94 Å. In the third Ta site, Ta is bonded in a 9-coordinate geometry to nine Ta and six Al atoms. There are two shorter (2.78 Å) and one longer (2.92 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.99–3.09 Å. In the fourth Ta site, Ta is bonded in a 7-coordinate geometry to eleven Ta and four Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.77–3.06 Å. There are two shorter (2.99 Å) and two longer (3.10 Å) Ta–Al bond lengths. In the fifth Ta site, Ta is bonded in a 6-coordinate geometry to twelve Ta and two equivalent Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.73–3.24 Å. Both Ta–Al bond lengths are 2.85 Å. In the sixth Ta site, Ta is bonded in a 6-coordinate geometry to six Ta and four Al atoms. The Ta–Ta bond length is 2.64 Å. There are a spread of Ta–Al bond distances ranging from 2.80–2.85 Å. In the seventh Ta site, Ta is bonded in a 6-coordinate geometry to six Ta and four Al atoms. The Ta–Ta bond length is 2.68 Å. There are a spread of Ta–Al bond distances ranging from 2.80–2.84 Å. In the eighth Ta site, Ta is bonded in a 6-coordinate geometry to twelve Ta and two equivalent Al atoms. There are one shorter (2.69 Å) and two longer (2.86 Å) Ta–Ta bond lengths. There are one shorter (2.84 Å) and one longer (2.86 Å) Ta–Al bond lengths. In the ninth Ta site, Ta is bonded to ten Ta and two Al atoms to form distorted TaTa10Al2 cuboctahedra that share a cornercorner with one TaTa10Al2 cuboctahedra, corners with ten AlTa10Al2 cuboctahedra, edges with three equivalent TaTa10Al2 cuboctahedra, and faces with seven AlTa11Al cuboctahedra. There are one shorter (2.67 Å) and one longer (2.76 Å) Ta–Al bond lengths. There are five inequivalent Al sites. In the first Al site, Al is bonded to ten Ta and two Al atoms to form AlTa10Al2 cuboctahedra that share corners with four equivalent TaTa10Al2 cuboctahedra, corners with seven AlTa10Al2 cuboctahedra, edges with three equivalent AlTa10Al2 cuboctahedra, and faces with seven AlTa11Al cuboctahedra. There are one shorter (2.71 Å) and one longer (2.79 Å) Al–Al bond lengths. In the second Al site, Al is bonded to eleven Ta and one Al atom to form AlTa11Al cuboctahedra that share corners with two equivalent TaTa10Al2 cuboctahedra, corners with nine AlTa11Al cuboctahedra, edges with three equivalent AlTa11Al cuboctahedra, faces with two equivalent TaTa10Al2 cuboctahedra, and faces with five AlTa10Al2 cuboctahedra. The Al–Al bond length is 2.75 Å. In the third Al site, Al is bonded to ten Ta and two Al atoms to form AlTa10Al2 cuboctahedra that share corners with eleven AlTa10Al2 cuboctahedra, edges with three equivalent AlTa10Al2 cuboctahedra, faces with three AlTa10Al2 cuboctahedra, and faces with four equivalent TaTa10Al2 cuboctahedra. The Al–Al bond length is 2.71 Å. In the fourth Al site, Al is bonded to ten Ta and two equivalent Al atoms to form AlTa10Al2 cuboctahedra that share corners with four equivalent TaTa10Al2 cuboctahedra, corners with twelve AlTa10Al2 cuboctahedra, edges with two equivalent AlTa10Al2 cuboctahedra, faces with two equivalent TaTa10Al2 cuboctahedra, and faces with two equivalent AlTa11Al cuboctahedra. In the fifth Al site, Al is bonded to eight Ta and four Al atoms to form AlTa8Al4 cuboctahedra that share corners with four equivalent TaTa10Al2 cuboctahedra, corners with twelve AlTa10Al2 cuboctahedra, edges with two equivalent AlTa8Al4 cuboctahedra, and faces with four AlTa10Al2 cuboctahedra.
Ta2Al is beta Uranium-derived structured and crystallizes in the tetragonal P4_2/mnm space group. The structure is three-dimensional. there are three inequivalent Ta sites. In the first Ta site, Ta is bonded in a 9-coordinate geometry to nine Ta and six Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.75–3.30 Å. There are two shorter (2.98 Å) and four longer (3.08 Å) Ta–Al bond lengths. In the second Ta site, Ta is bonded in a 6-coordinate geometry to two Ta and four equivalent Al atoms. The Ta–Ta bond length is 2.67 Å. There are a spread of Ta–Al bond distances ranging from 2.78–2.84 Å. In the third Ta site, Ta is bonded in a 7-coordinate geometry to five Ta and five Al atoms. There are one shorter (2.59 Å) and one longer (2.63 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.87–2.90 Å. There are two inequivalent Al sites. In the first Al site, Al is bonded to eight Ta and four equivalent Al atoms to form AlTa8Al4 cuboctahedra that share corners with sixteen equivalent AlTa10Al2 cuboctahedra, edges with two equivalent AlTa8Al4 cuboctahedra, and faces with four equivalent AlTa10Al2 cuboctahedra. All Al–Al bond lengths are 2.69 Å. In the second Al site, Al is bonded to ten Ta and two Al atoms to form AlTa10Al2 cuboctahedra that share corners with eleven AlTa8Al4 cuboctahedra, edges with three equivalent AlTa10Al2 cuboctahedra, and faces with seven AlTa8Al4 cuboctahedra. The Al–Al bond length is 2.77 Å.
Ta17Al12 is alpha-derived structured and crystallizes in the cubic I-43m space group. The structure is three-dimensional. there are three inequivalent Ta sites. In the first Ta site, Ta is bonded in a 12-coordinate geometry to four equivalent Ta and twelve equivalent Al atoms. All Ta–Ta bond lengths are 3.07 Å. All Ta–Al bond lengths are 3.05 Å. In the second Ta site, Ta is bonded in a 9-coordinate geometry to four Ta and nine equivalent Al atoms. All Ta–Ta bond lengths are 2.86 Å. There are six shorter (2.98 Å) and three longer (3.30 Å) Ta–Al bond lengths. In the third Ta site, Ta is bonded in a 12-coordinate geometry to seven Ta and five equivalent Al atoms. There are two shorter (2.83 Å) and four longer (3.04 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.72–2.92 Å. Al is bonded in a 12-coordinate geometry to nine Ta and three equivalent Al atoms. There are one shorter (2.56 Å) and two longer (2.63 Å) Al–Al bond lengths.
Ta24Al19 is Frank-Kasper $\mu$ Phase-like structured and crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. there are twelve inequivalent Ta sites. In the first Ta site, Ta is bonded in a 6-coordinate geometry to nine Ta and five Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.64–3.43 Å. There are a spread of Ta–Al bond distances ranging from 2.80–2.93 Å. In the second Ta site, Ta is bonded in a 10-coordinate geometry to seven Ta and seven Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.79–3.30 Å. There are a spread of Ta–Al bond distances ranging from 2.79–3.07 Å. In the third Ta site, Ta is bonded in a 7-coordinate geometry to nine Ta and five Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.65–3.21 Å. There are a spread of Ta–Al bond distances ranging from 2.80–2.92 Å. In the fourth Ta site, Ta is bonded in a 6-coordinate geometry to nine Ta and five Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.87–3.27 Å. There are a spread of Ta–Al bond distances ranging from 2.84–2.89 Å. In the fifth Ta site, Ta is bonded in a 1-coordinate geometry to three Ta and nine Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.82–3.11 Å. There are a spread of Ta–Al bond distances ranging from 2.70–3.20 Å. In the sixth Ta site, Ta is bonded in a 1-coordinate geometry to five Ta and seven Al atoms. There are one shorter (2.73 Å) and one longer (3.33 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.65–3.05 Å. In the seventh Ta site, Ta is bonded in a 1-coordinate geometry to four Ta and seven Al atoms. There are a spread of Ta–Ta bond distances ranging from 2.83–3.04 Å. There are a spread of Ta–Al bond distances ranging from 2.68–3.09 Å. In the eighth Ta site, Ta is bonded in a 7-coordinate geometry to six Ta and five Al atoms. There are one shorter (2.67 Å) and one longer (3.12 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.70–2.86 Å. In the ninth Ta site, Ta is bonded in a 7-coordinate geometry to six Ta and five Al atoms. The Ta–Ta bond length is 3.23 Å. There are a spread of Ta–Al bond distances ranging from 2.72–2.93 Å. In the tenth Ta site, Ta is bonded in a 2-coordinate geometry to nine Ta and five Al atoms. There are one shorter (3.25 Å) and one longer (3.37 Å) Ta–Ta bond lengths. There are a spread of Ta–Al bond distances ranging from 2.73–2.93 Å. In the eleventh Ta site, Ta is bonded in a 1-coordinate geometry to six Ta and nine Al atoms. There are a spread of Ta–Al bond distances ranging from 2.78–3.20 Å. In the twelfth Ta site, Ta is bonded in a 1-coordinate geometry to six Ta and eight Al atoms. There are a spread of Ta–Al bond distances ranging from 2.77–3.14 Å. There are ten inequivalent Al sites. In the first Al site, Al is bonded in a 11-coordinate geometry to eight Ta and three Al atoms. There are a spread of Al–Al bond distances ranging from 2.50–3.00 Å. In the second Al site, Al is bonded to seven Ta and five Al atoms to form AlTa7Al5 cuboctahedra that share corners with eight AlTa12 cuboctahedra, an edgeedge with one AlTa7Al5 cuboctahedra, and faces with eight AlTa7Al5 cuboctahedra. There are a spread of Al–Al bond distances ranging from 2.65–2.75 Å. In the third Al site, Al is bonded to eight Ta and four Al atoms to form AlTa8Al4 cuboctahedra that share corners with ten AlTa12 cuboctahedra, edges with two equivalent AlTa7Al5 cuboctahedra, and faces with seven AlTa7Al5 cuboctahedra. There are one shorter (2.64 Å) and two longer (2.66 Å) Al–Al bond lengths. In the fourth Al site, Al is bonded in a 12-coordinate geometry to eight Ta and four Al atoms. There are one shorter (2.75 Å) and one longer (2.85 Å) Al–Al bond lengths. In the fifth Al site, Al is bonded to twelve Ta atoms to form AlTa12 cuboctahedra that share corners with sixteen AlTa9Al3 cuboctahedra and faces with six AlTa7Al5 cuboctahedra. In the sixth Al site, Al is bonded to seven Ta and five Al atoms to form distorted AlTa7Al5 cuboctahedra that share corners with eight AlTa7Al5 cuboctahedra, edges with two AlTa9Al3 cuboctahedra, and faces with seven AlTa12 cuboctahedra. There are one shorter (2.61 Å) and one longer (2.79 Å) Al–Al bond lengths. In the seventh Al site, Al is bonded to nine Ta and three Al atoms to form AlTa9Al3 cuboctahedra that share corners with seven AlTa7Al5 cuboctahedra, edges with three AlTa7Al5 cuboctahedra, and faces with six AlTa12 cuboctahedra. There are one shorter (2.56 Å) and one longer (2.61 Å) Al–Al bond lengths. In the eighth Al site, Al is bonded to seven Ta and five Al atoms to form AlTa7Al5 cuboctahedra that share corners with nine AlTa12 cuboctahedra, edges with two equivalent AlTa8Al4 cuboctahedra, and faces with six AlTa7Al5 cuboctahedra. The Al–Al bond length is 2.60 Å. In the ninth Al site, Al is bonded in a 11-coordinate geometry to eight Ta and three Al atoms. In the tenth Al site, Al is bonded to nine Ta and three Al atoms to form distorted AlTa9Al3 cuboctahedra that share corners with eight AlTa12 cuboctahedra, edges with three AlTa7Al5 cuboctahedra, and faces with seven AlTa12 cuboctahedra.