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CoS2 is trigonal omega-like structured and crystallizes in the trigonal R-3m space group. The structure is two-dimensional and consists of three CoS2 sheets oriented in the (0, 0, 1) direction. Co4+ is bonded to six equivalent S2- atoms to form edge-sharing CoS6 octahedra. All Co–S bond lengths are 2.25 Å. S2- is bonded in a distorted T-shaped geometry to three equivalent Co4+ atoms.
CoS2 is Pyrite structured and crystallizes in the cubic Pa-3 space group. The structure is three-dimensional. Co4+ is bonded to six equivalent S2- atoms to form CoS6 octahedra that share corners with twelve equivalent CoS6 octahedra and corners with six equivalent SCo3S tetrahedra. The corner-sharing octahedral tilt angles are 65°. All Co–S bond lengths are 2.31 Å. S2- is bonded to three equivalent Co4+ and one S2- atom to form distorted SCo3S tetrahedra that share corners with three equivalent CoS6 octahedra and corners with fifteen equivalent SCo3S tetrahedra. The corner-sharing octahedral tilt angles are 77°. The S–S bond length is 2.14 Å.
CoS2 is Pyrite-like structured and crystallizes in the orthorhombic Pbca space group. The structure is three-dimensional. Co4+ is bonded to six equivalent S2- atoms to form corner-sharing CoS6 octahedra. The corner-sharing octahedral tilt angles are 65°. There are a spread of Co–S bond distances ranging from 2.28–2.33 Å. S2- is bonded in a 4-coordinate geometry to three equivalent Co4+ and one S2- atom. The S–S bond length is 2.14 Å.
Zn(CoS2)4 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are two inequivalent Co+3.50+ sites. In the first Co+3.50+ site, Co+3.50+ is bonded to six equivalent S2- atoms to form CoS6 octahedra that share corners with six equivalent ZnS6 octahedra and edges with six equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 10°. All Co–S bond lengths are 2.28 Å. In the second Co+3.50+ site, Co+3.50+ is bonded to six S2- atoms to form CoS6 octahedra that share edges with two equivalent ZnS6 octahedra and edges with six CoS6 octahedra. There are four shorter (2.24 Å) and two longer (2.27 Å) Co–S bond lengths. Zn2+ is bonded to six equivalent S2- atoms to form ZnS6 octahedra that share corners with six equivalent CoS6 octahedra and edges with six equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 10°. All Zn–S bond lengths are 2.50 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a rectangular see-saw-like geometry to three Co+3.50+ and one Zn2+ atom. In the second S2- site, S2- is bonded in a 3-coordinate geometry to three equivalent Co+3.50+ atoms.
Ca(CoS2)2 is Spinel structured and crystallizes in the tetragonal I4_1/amd space group. The structure is three-dimensional. Ca2+ is bonded to four equivalent S2- atoms to form CaS4 tetrahedra that share corners with twelve equivalent CoS6 octahedra. The corner-sharing octahedra tilt angles range from 60–65°. All Ca–S bond lengths are 2.61 Å. Co3+ is bonded to six equivalent S2- atoms to form distorted CoS6 octahedra that share corners with six equivalent CaS4 tetrahedra and edges with six equivalent CoS6 octahedra. There are four shorter (2.31 Å) and two longer (2.32 Å) Co–S bond lengths. S2- is bonded to one Ca2+ and three equivalent Co3+ atoms to form a mixture of edge and corner-sharing SCaCo3 tetrahedra.
CoS2 is trigonal omega-like structured and crystallizes in the orthorhombic Imma space group. The structure is three-dimensional. there are two inequivalent Co4+ sites. In the first Co4+ site, Co4+ is bonded to six S2- atoms to form edge-sharing CoS6 octahedra. All Co–S bond lengths are 2.24 Å. In the second Co4+ site, Co4+ is bonded to six S2- atoms to form edge-sharing CoS6 octahedra. All Co–S bond lengths are 2.24 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted T-shaped geometry to three Co4+ atoms. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three Co4+ atoms.
Zn(CoS2)4 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are two inequivalent Co+3.50+ sites. In the first Co+3.50+ site, Co+3.50+ is bonded to six S2- atoms to form CoS6 octahedra that share edges with two equivalent ZnS6 octahedra and edges with six CoS6 octahedra. There are four shorter (2.24 Å) and two longer (2.26 Å) Co–S bond lengths. In the second Co+3.50+ site, Co+3.50+ is bonded to six equivalent S2- atoms to form CoS6 octahedra that share corners with six equivalent ZnS6 octahedra and edges with six equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 11°. All Co–S bond lengths are 2.29 Å. Zn2+ is bonded to six equivalent S2- atoms to form distorted ZnS6 octahedra that share corners with six equivalent CoS6 octahedra and edges with six equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 11°. All Zn–S bond lengths are 2.56 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a rectangular see-saw-like geometry to three Co+3.50+ and one Zn2+ atom. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Co+3.50+ atoms.
Mg(CoS2)4 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Mg2+ is bonded to six equivalent S2- atoms to form distorted MgS6 octahedra that share corners with six equivalent CoS6 octahedra and edges with six equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 12°. All Mg–S bond lengths are 2.60 Å. There are two inequivalent Co+3.50+ sites. In the first Co+3.50+ site, Co+3.50+ is bonded to six S2- atoms to form CoS6 octahedra that share edges with two equivalent MgS6 octahedra and edges with six CoS6 octahedra. There are four shorter (2.25 Å) and two longer (2.26 Å) Co–S bond lengths. In the second Co+3.50+ site, Co+3.50+ is bonded to six equivalent S2- atoms to form CoS6 octahedra that share corners with six equivalent MgS6 octahedra and edges with six equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 12°. All Co–S bond lengths are 2.28 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Mg2+ and three Co+3.50+ atoms. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three equivalent Co+3.50+ atoms.
Ca(CoS2)4 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Ca2+ is bonded to six equivalent S2- atoms to form CaS6 octahedra that share corners with six equivalent CoS6 octahedra and edges with six equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 11°. All Ca–S bond lengths are 2.66 Å. There are two inequivalent Co+3.50+ sites. In the first Co+3.50+ site, Co+3.50+ is bonded to six equivalent S2- atoms to form CoS6 octahedra that share corners with six equivalent CaS6 octahedra and edges with six equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 11°. All Co–S bond lengths are 2.23 Å. In the second Co+3.50+ site, Co+3.50+ is bonded to six S2- atoms to form CoS6 octahedra that share edges with two equivalent CaS6 octahedra and edges with six CoS6 octahedra. All Co–S bond lengths are 2.29 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Ca2+ and three Co+3.50+ atoms. In the second S2- site, S2- is bonded in a distorted trigonal non-coplanar geometry to three equivalent Co+3.50+ atoms.
Mg(CoS2)2 is Spinel structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Mg2+ is bonded to four equivalent S2- atoms to form MgS4 tetrahedra that share corners with twelve equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 61°. All Mg–S bond lengths are 2.44 Å. Co3+ is bonded to six equivalent S2- atoms to form CoS6 octahedra that share corners with six equivalent MgS4 tetrahedra and edges with six equivalent CoS6 octahedra. All Co–S bond lengths are 2.28 Å. S2- is bonded to one Mg2+ and three equivalent Co3+ atoms to form a mixture of distorted corner and edge-sharing SMgCo3 tetrahedra.
Zn(CoS2)2 is Spinel structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Co3+ is bonded to six equivalent S2- atoms to form CoS6 octahedra that share corners with six equivalent ZnS4 tetrahedra and edges with six equivalent CoS6 octahedra. All Co–S bond lengths are 2.26 Å. Zn2+ is bonded to four equivalent S2- atoms to form ZnS4 tetrahedra that share corners with twelve equivalent CoS6 octahedra. The corner-sharing octahedral tilt angles are 60°. All Zn–S bond lengths are 2.35 Å. S2- is bonded to three equivalent Co3+ and one Zn2+ atom to form a mixture of distorted edge and corner-sharing SZnCo3 tetrahedra.
Li(CoS2)2 is Spinel structured and crystallizes in the tetragonal I4_1/amd space group. The structure is three-dimensional. Li1+ is bonded to four equivalent S2- atoms to form LiS4 tetrahedra that share corners with twelve equivalent CoS6 octahedra. The corner-sharing octahedra tilt angles range from 59–61°. All Li–S bond lengths are 2.35 Å. Co+3.50+ is bonded to six equivalent S2- atoms to form CoS6 octahedra that share corners with six equivalent LiS4 tetrahedra and edges with six equivalent CoS6 octahedra. All Co–S bond lengths are 2.26 Å. S2- is bonded to one Li1+ and three equivalent Co+3.50+ atoms to form a mixture of distorted edge and corner-sharing SLiCo3 tetrahedra.
Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations
Abstract Pre-edge X-ray absorption features are commonly used to derive redox states for transition metal oxides in crystals and glasses. Several calibrations for Fe2+ and Fe3+ in silicate glasses have utilized the general relationships among pre-edge peak intensity, energy, and redox state. However, absorption variations complicate those relationships in anisotropic crystals. Although absorption anisotropy at and above the energy of the rising edge adheres to the typical cos2 relationship observed in absorption spectroscopies at other energies, the anisotropy of the pre-edge is far more complicated. Prior studies focusing on pre-edge absorption anisotropy demonstrate a 1-cos4φ dependence of absorption magnitudes with rotation. Experiments presented here show that absorption magnitudes of the pre-edge vary as a function of both electric field vector orientation and wave vector direction. However, rotations around the field vector axis or wave vector axis individually result in cos2 dependence of absorption magnitudes. Rotations where both wave vector and field vector orientation are varied are not well fit by either model in the pre-edge. The resulting anisotropy complicates the process of measuring characteristic absorption in the pre-edge, making valence state determinations challenging for strongly anisotropic crystal structures such as pyroxene.
Dilepton production in pp collisions through the Drell-Yan process provides a crucial tool for studying the internal quark-gluon structure of the nucleon. By precisely measuring the $\cos2\phi$ asymmetry, where $\phi$ represents the azimuthal angle of the $l^{+}l^{-}$ pair in the Collins-Soper frame, we can gain valuable insights into the proton’s structure and the transverse momentum ($q_{T}$) dependence of the $\cos2\phi$ asymmetry. SeaQuest, a fixed-target Drell-Yan experiment at Fermilab, involved an unpolarized proton beam colliding with unpolarized LH$_{2}$ and LD$_{2}$ targets. Measurements obtained from experiments typically require corrections for detector inefficiencies, smearing, and acceptance. Traditionally, these corrections involve “unfolding” the detector-level measurements through matrix operations. However, in higher-dimensional phase space, these conventional methods fail to scale effectively. To overcome these limitations, we employ an unbinned unfolding method that utilizes deep neural networks for unfolding higher-dimensional phase space. In this presentation, we will explain the design of the neural network architecture, our training strategies, and outline our plans to achieve conclusive results.
In the E906/SeaQuest Fermilab experiment, we report a measurement of the angular distributions by measuring the angular parameters $\lambda$, $\mu$, and $\nu$ of Drell-Yan dimuons produced using a 120 GeV proton beam incident on an iron target. The angular distribution in the naive Drell-Yan model does not show any $\cos2\phi$ dependency, where $\phi$ denotes the azimuthal angle of dimuons in the Collins-Soper frame. However, pion-induced Drell-Yan experiments, such as NA10 and E615, have observed a significant dependence on $\cos2\phi$. The Boer–Mulders function, a transverse momentum-dependent distribution function, represents the correlation between the transverse spin and the transverse momentum of the quark. A non-zero Boer-Mulders function or an improved higher-order Drell-Yan model considering QCD effects can produce a $\cos 2\phi$ modulation in the Drell-Yan angular distribution. To measure the angular distributions, we have used an event mixing method to construct the combin atorial background, which was then subtracted from the data to isolate the Drell-Yan signal. Following this, we corrected the detector, trigger, and reconstruction efficiencies using a doubly-iterative Bayesian Unfolding method. This iterative unfolding technique improves the response matrix based on the results of the previous unfolding step, ensuring robust convergence without exaggeration of uncertainties. The angular distributions of the dimuons were measured over the invariant mass range $5.0 < M_{\mu^+ \mu^-} < 8.0$ $GeV/c^2$, with dimuon transverse momentum $P_T < 2$ GeV/c and Feynman-x $-0.18 < x_F < 0.9$. The measured angular distributions are then compared with the QCD calculations for $p + \text{Fe}$ interactions, and proton-induced angular distribution measurements from other experiments. We have observed weak $\cos 2\phi$ modulations as a function of $P_T$. For $P_T > 1.0 \, \text{GeV}/c$, the predicted NNLO perturbative QCD value of $\nu$ is larger than what we have me asured at E906/SeaQuest. Moreover, we have not observed a strong dependence of $\nu$ on the kinematic variables, such as dimuon mass $M_{\mu^+ \mu^-}$ and Bjorken-$x$. The spin alignment of the virtual photon, $\lambda$, measured from the SeaQuest Drell-Yan $p+\text{Fe}$ data, is found to be strongly dependent on $P_T$, decreasing as $P_T$ increases. $\lambda$ also holds to the upper bound condition $\lambda < 1.0$ within the statistical uncertainty, showing a trend similar to that predicted by NNLO perturbative QCD. However, for $1.0 < P_T < 2.0 \, \text{GeV}/c$, the extracted $\lambda$ value from SeaQuest is smaller than that predicted by perturbative QCD at NNLO.