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Multi-channel front-end ASIC for a 3D position-sensitive detector

Arrays of 3D position-sensitive detectors (3DPSD), operating at room temperature and using cadmium zinc telluride (CZT) and thallium bromide (TIBr) sensors, are suitable for gamma-ray spectrometry in many applications. One detector configuration, the 3D position-sensitive Virtual Frisch-Grid detector (VFG), is particularly advantageous for integrating into large area arrays. The signals generated inside each detector of the array are captured with the anode, cathode and four pads that enable the reconstruction of the position and energy of the ionizing interaction by measurements of amplitude and timing of the signals. For these applications, a low-noise front-end ASIC has been developed, capable of processing bipolar signals (needed because of AC-coupling of certain electrodes). The ASIC can be coupled to an ADC in order to form a compound “waveform digitizer” capable of post-processing the analog signals and determining amplitude and timing information. This paper describes a 32-channel front-end ASIC that is suitable for reading out a 3 × 3 or 4 × 4 element matrix in the VFG configuration. Each channel is composed of a low-noise charge amplifier with an adaptive continuous reset feedback circuit suitable for both positive and negative charge, a first order shaper and a single-to-differential converter output stage. Voltage and current references are all internally generated by 10-bit DACs and the chip is fully controllable with the I 2 C communication protocol. The readout channel response has been verified using the implemented injection circuit. Linear behavior up to ~75 ke ± with the gain of ~80 mV/fC, and up to ~200 ke ± with the gain of ~30 mV/fC was demonstrated. In conclusion, the first test result waveforms using a 137 Cs radioactive source on a 5 × 5 × 12 mm 3 TIBr crystal are reported.

47 OTHER INSTRUMENTATION↗

CeNTREX: a new search for time-reversal symmetry violation in the 205 Tl nucleus

The Cold molecule Nuclear Time-Reversal EXperiment (CeNTREX) is a new effort aiming for a significant increase in sensitivity over the best present upper bounds on the strength of hadronic time reversal (T) violating fundamental interactions. The experimental signature will be shifts in nuclear magnetic resonance frequencies of 205 Tl in electrically-polarized thallium fluoride (TlF) molecules. Here we describe the motivation for studying these T-violating interactions and for using TlF to do so. To achieve higher sensitivity than earlier searches for T-violation in TlF, CeNTREX uses a cryogenic molecular beam source, optical state preparation and detection, and modern methods of coherent quantum state manipulation. Details of the measurement scheme and the current state of the apparatus are presented, with quantitative measurements of the TlF beam. Lastly, the estimated sensitivity and methods to control systematic errors are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

γ-ray measurements in fast-neutron-induced reactions on 203 Tl

Fast-neutron-induced reactions can be used to characterize reaction mechanisms, investigate nuclear structure, and impose constraints on nuclear models. Because of the difficulty in predicting such effects, experimental data are important to constrain models. Thallium isotopes located close to the doubly magic Pb 208 nucleus are important for comparison with shell-model calculations. Study the population of excited states in Tl 203 and lighter isotopes in such reactions. Our methods are as follows. γ -ray cross sections were measured. The data were taken by using the Germanium Array for Neutron-Induced Excitations spectrometer. The pulsed neutron source of the Los Alamos Neutron Science Center's Weapons Neutron Research facility provided neutrons in the energy range from 1 to 300 MeV. The time-of-flight technique was used to determine the incident neutron energies. Cross sections for emission of several γ rays in 20 reaction channels were determined. Candidates for the intruder 9 / 2 - state in Tl 203 , from the odd proton in the h 9 / 2 orbital, and the first 5 + states in Tl 202 , 204 , from admixture of configurations, were identified. The excitation energy of the candidate 9 / 2 - , π h 9 / 2 state is in good agreement with the theoretical prediction from a semi-empirical weak-coupling model and its half-life is in the range of tens of nanoseconds. The feeding of a previously known isomer in Tl 202 exhibits similarities with the feeding of other isomers in this mass region.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of the sodium and iodine scintillation quenching factors across multiple NaI(Tl) detectors to identify systematics

The amount of light produced by nuclear recoils in scintillating targets is strongly quenched compared to that produced by electrons. A precise understanding of the quenching factor is particularly interesting for weakly interacting massive particles (WIMP) searches and coherent elastic neutrino-nucleus scattering ( CE ν NS ) measurements since both rely on nuclear recoils, whereas energy calibrations are more readily accessible from electron recoils. There is a wide variation among the current measurements of the quenching factor in sodium iodide (NaI) crystals, especially below 10 keV, the energy region of interest for dark matter and CE ν NS studies. A better understanding of the quenching factor in NaI(Tl) is of particular interest for resolving the decades-old puzzle in the field of dark matter between the null results of most WIMP searches and the claim for dark matter detection by the DAMA/LIBRA collaboration. In this work, we measured sodium and iodine quenching factors for five small NaI(Tl) crystals grown with similar thallium concentrations and growth procedures. Unlike previous experiments, multiple crystals were tested, with measurements made in the same experimental setup to control systematic effects. The quenching factors agree in all crystals we investigated, and both sodium and iodine quenching factors are smaller than those reported by DAMA/LIBRA. The dominant systematic effect was due to the electron equivalent energy calibration originating from the nonproportional behavior of the NaI(Tl) light yield at lower energies, potentially the cause for the discrepancies among the previous measurements. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Proton emission in ultraperipheral Pb-Pb collisions at $\sqrt{𝑠_{𝑁⁢𝑁}}$ = 5.02 TeV

The first measurements of proton emission accompanied by neutron emission in the electromagnetic dissociation (EMD) of 208 Pb nuclei in the ALICE experiment at the Large Hadron Collider are presented. The EMD protons and neutrons emitted at very forward rapidities are detected by the proton and neutron zero degree calorimeters of the ALICE experiment. The emission cross sections of zero, one, two, and three protons accompanied by at least one neutron were measured in ultraperipheral 208 Pb − 208 Pb collisions at a center-of-mass energy per nucleon pair $\sqrt{𝑠_{𝑁⁢𝑁}}$ = 5.02TeV. The 0p and 3p cross sections are described by the RELDIS model within their measurement uncertainties, while the 1p and 2p cross sections are underestimated by the model by 17–25%. According to this model, these 0p, 1p, 2p, and 3p cross sections are associated, respectively, with the production of various isotopes of Pb, Tl, Hg, and Au in the EMD of 208 Pb . The cross sections of the emission of a single proton accompanied by the emission of one, two, or three neutrons in EMD were also measured. The data are significantly overestimated by the RELDIS model, which predicts that the (1p,1n), (1p,2n), and (1p,3n) cross sections are very similar to the cross sections for the production of the thallium isotopes 206,205,204 Tl.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The crystal structure of TlMgCl 3 from 290 K to 725 K

The title compound, thallium magnesium trichloride, has been identified as a scintillator with both moderate gamma-stopping power and moderate light yield. Knowledge of its crystal structure is needed for further development. This work determines the crystal structure of TlMgCl 3 to be hexa­gonal P6 3 /mmc (No. 194) and isostructural with RbMgCl 3 , contrary to previously reported data. This structure was obtained by single-crystal X-ray diffraction and was further confirmed by neutron diffraction measurements. Extending neutron diffraction measurements to high temperature, the data show that TlMgCl 3 maintains this crystal structure from 290 K up through 725 K, approaching the melting point of 770 K. Anisotropic thermal expansion coefficients increase over this temperature range, from 31 to 38 × 10 –6 K –1 along the a axis and from 19 to 34 × 10 –6 K –1 along the c axis.

36 MATERIALS SCIENCE↗

Materials Data on Tl(FeS)2 by Materials Project

Tl(FeS)2 crystallizes in the tetragonal I4/mmm space group. The structure is two-dimensional and consists of two thallium molecules and two FeS sheets oriented in the (0, 0, 1) direction. In each FeS sheet, Fe is bonded to four equivalent S atoms to form a mixture of distorted edge and corner-sharing FeS4 tetrahedra. All Fe–S bond lengths are 2.35 Å. S is bonded in a 4-coordinate geometry to four equivalent Fe atoms.

36 MATERIALS SCIENCE↗

Materials Data on Tl(TeMo)3 by Materials Project

(MoTe)3Tl crystallizes in the hexagonal P6_3/m space group. The structure is one-dimensional and consists of two thallium molecules and one MoTe ribbon oriented in the (0, 0, 1) direction. In the MoTe ribbon, Mo is bonded in a 10-coordinate geometry to six equivalent Mo and four equivalent Te atoms. There are two shorter (2.67 Å) and four longer (2.78 Å) Mo–Mo bond lengths. There are two shorter (2.84 Å) and two longer (2.89 Å) Mo–Te bond lengths. Te is bonded in a 4-coordinate geometry to four equivalent Mo atoms.

36 MATERIALS SCIENCE↗

Materials Data on Tl3Ir(NO2)6 by Materials Project

IrTl(Tl(NO2)3)2 crystallizes in the cubic Fm-3m space group. The structure is three-dimensional and consists of four iridium molecules, four thallium molecules, and one Tl(NO2)3 framework. In the Tl(NO2)3 framework, Tl+1.67+ is bonded in a distorted q4 geometry to twelve equivalent O2- atoms. All Tl–O bond lengths are 2.77 Å. N+2.33+ is bonded in a distorted square co-planar geometry to four equivalent O2- atoms. All N–O bond lengths are 2.24 Å. O2- is bonded in a 5-coordinate geometry to two equivalent Tl+1.67+, two equivalent N+2.33+, and one O2- atom. The O–O bond length is 1.31 Å.

36 MATERIALS SCIENCE↗

Materials Data on TlHg(NO2)3 by Materials Project

HgTl(NO2)3 is Cyanogen Chloride-derived structured and crystallizes in the cubic Pm-3 space group. The structure is zero-dimensional and consists of three hydroxylamine, n-hydroxy- molecules; one mercury molecule; and one thallium molecule.

36 MATERIALS SCIENCE↗

Materials Data on TlCd(NO2)3 by Materials Project

CdTl(NO2)3 is Cyanogen Chloride-derived structured and crystallizes in the cubic Pm-3 space group. The structure is zero-dimensional and consists of one cadmium molecule; three hydroxylamine, n-hydroxy- molecules; and one thallium molecule.

36 MATERIALS SCIENCE↗

Materials Data on TlBrO4 by Materials Project

TlBrO4 is Iron carbide-derived structured and crystallizes in the orthorhombic Pnma space group. The structure is zero-dimensional and consists of four hypobromous acid;trihydrate molecules and four thallium molecules.

36 MATERIALS SCIENCE↗

Materials Data on Tl(BH)6 by Materials Project

Tl(BH)6 crystallizes in the cubic Fm-3 space group. The structure is zero-dimensional and consists of forty-eight boranediylradical molecules and eight thallium molecules.

36 MATERIALS SCIENCE↗

Materials Data on TlCl2 by Materials Project

TlTlCl4 is Iron carbide-like structured and crystallizes in the tetragonal I4_1/a space group. The structure is zero-dimensional and consists of four thallium molecules and four TlCl4 clusters. In each TlCl4 cluster, Tl is bonded in a tetrahedral geometry to four equivalent Cl atoms. All Tl–Cl bond lengths are 2.49 Å. Cl is bonded in a single-bond geometry to one Tl atom.

36 MATERIALS SCIENCE↗

Materials Data on TlBr2 by Materials Project

TlTlBr4 is Iron carbide-like structured and crystallizes in the orthorhombic Pnna space group. The structure is zero-dimensional and consists of four thallium molecules and four TlBr4 clusters. In each TlBr4 cluster, Tl is bonded in a tetrahedral geometry to four Br atoms. There are two shorter (2.63 Å) and two longer (2.64 Å) Tl–Br bond lengths. There are two inequivalent Br sites. In the first Br site, Br is bonded in a single-bond geometry to one Tl atom. In the second Br site, Br is bonded in a single-bond geometry to one Tl atom.

36 MATERIALS SCIENCE↗

Materials Data on TlClO4 by Materials Project

TlClO4 is Silicon tetrafluoride-derived structured and crystallizes in the cubic F-43m space group. The structure is zero-dimensional and consists of four thallium molecules and four ClO4 clusters. In each ClO4 cluster, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.47 Å. Cl is bonded in a tetrahedral geometry to four equivalent O atoms.

36 MATERIALS SCIENCE↗

Materials Data on Tl3SiTe3 by Materials Project

(Tl)3SiTe3 crystallizes in the triclinic P-1 space group. The structure is zero-dimensional and consists of twelve thallium molecules and two SiTe3 clusters. In one of the SiTe3 clusters, Si4- is bonded in a tetrahedral geometry to one Si4- and three Te+0.33+ atoms. The Si–Si bond length is 2.36 Å. There are a spread of Si–Te bond distances ranging from 2.53–2.55 Å. There are three inequivalent Te+0.33+ sites. In the first Te+0.33+ site, Te+0.33+ is bonded in a single-bond geometry to one Si4- atom. In the second Te+0.33+ site, Te+0.33+ is bonded in a single-bond geometry to one Si4- atom. In the third Te+0.33+ site, Te+0.33+ is bonded in a single-bond geometry to one Si4- atom. In one of the SiTe3 clusters, Si4- is bonded in a tetrahedral geometry to one Si4- and three Te+0.33+ atoms. The Si–Si bond length is 2.36 Å. There are one shorter (2.53 Å) and two longer (2.55 Å) Si–Te bond lengths. There are three inequivalent Te+0.33+ sites. In the first Te+0.33+ site, Te+0.33+ is bonded in a single-bond geometry to one Si4- atom. In the second Te+0.33+ site, Te+0.33+ is bonded in a single-bond geometry to one Si4- atom. In the third Te+0.33+ site, Te+0.33+ is bonded in a single-bond geometry to one Si4- atom.

36 MATERIALS SCIENCE↗

Materials Data on Tl8Sb21As19(PbS17)4 by Materials Project

(Tl)7TlSb21As19(PbS17)4 crystallizes in the triclinic P1 space group. The structure is three-dimensional and consists of seven thallium molecules and one TlSb21As19(PbS17)4 framework. In the TlSb21As19(PbS17)4 framework, Tl is bonded in a 1-coordinate geometry to one S atom. The Tl–S bond length is 3.26 Å. There are four inequivalent Pb sites. In the first Pb site, Pb is bonded in a 6-coordinate geometry to six S atoms. There are a spread of Pb–S bond distances ranging from 2.94–3.16 Å. In the second Pb site, Pb is bonded in a 6-coordinate geometry to six S atoms. There are a spread of Pb–S bond distances ranging from 2.83–3.30 Å. In the third Pb site, Pb is bonded in a 5-coordinate geometry to five S atoms. There are a spread of Pb–S bond distances ranging from 2.84–3.20 Å. In the fourth Pb site, Pb is bonded in a 6-coordinate geometry to six S atoms. There are a spread of Pb–S bond distances ranging from 2.90–3.23 Å. There are twenty-one inequivalent Sb sites. In the first Sb site, Sb is bonded in a rectangular see-saw-like geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.44–2.87 Å. In the second Sb site, Sb is bonded in a square pyramidal geometry to five S atoms. There are a spread of Sb–S bond distances ranging from 2.52–2.98 Å. In the third Sb site, Sb is bonded in a 4-coordinate geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.52–3.11 Å. In the fourth Sb site, Sb is bonded in a distorted rectangular see-saw-like geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.49–2.94 Å. In the fifth Sb site, Sb is bonded in a 4-coordinate geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.51–2.95 Å. In the sixth Sb site, Sb is bonded in a 4-coordinate geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.52–3.10 Å. In the seventh Sb site, Sb is bonded in a distorted square pyramidal geometry to five S atoms. There are a spread of Sb–S bond distances ranging from 2.52–2.99 Å. In the eighth Sb site, Sb is bonded in a 6-coordinate geometry to six S atoms. There are a spread of Sb–S bond distances ranging from 2.52–3.19 Å. In the ninth Sb site, Sb is bonded in a 3-coordinate geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.54–3.14 Å. In the tenth Sb site, Sb is bonded in a 5-coordinate geometry to three S atoms. There are a spread of Sb–S bond distances ranging from 2.47–2.61 Å. In the eleventh Sb site, Sb is bonded in a distorted rectangular see-saw-like geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.42–2.95 Å. In the twelfth Sb site, Sb is bonded in a distorted square pyramidal geometry to five S atoms. There are a spread of Sb–S bond distances ranging from 2.47–3.03 Å. In the thirteenth Sb site, Sb is bonded in a 5-coordinate geometry to five S atoms. There are a spread of Sb–S bond distances ranging from 2.49–3.11 Å. In the fourteenth Sb site, Sb is bonded in a 3-coordinate geometry to three S atoms. There are a spread of Sb–S bond distances ranging from 2.54–2.60 Å. In the fifteenth Sb site, Sb is bonded in a distorted octahedral geometry to six S atoms. There are a spread of Sb–S bond distances ranging from 2.55–3.10 Å. In the sixteenth Sb site, Sb is bonded in a 4-coordinate geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.52–3.01 Å. In the seventeenth Sb site, Sb is bonded in a distorted octahedral geometry to six S atoms. There are a spread of Sb–S bond distances ranging from 2.57–3.06 Å. In the eighteenth Sb site, Sb is bonded in a 5-coordinate geometry to five S atoms. There are a spread of Sb–S bond distances ranging from 2.50–3.13 Å. In the nineteenth Sb site, Sb is bonded in a distorted square pyramidal geometry to five S atoms. There are a spread of Sb–S bond distances ranging from 2.46–3.04 Å. In the twentieth Sb site, Sb is bonded in a 4-coordinate geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.51–3.05 Å. In the twenty-first Sb site, Sb is bonded in a 4-coordinate geometry to four S atoms. There are a spread of Sb–S bond distances ranging from 2.51–3.07 Å. There are nineteen inequivalent As sites. In the first As site, As is bonded in a distorted T-shaped geometry to three S atoms. There are one shorter (2.30 Å) and two longer (2.31 Å) As–S bond lengths. In the second As site, As is bonded in a distorted trigonal non-coplanar geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.24–2.37 Å. In the third As site, As is bonded in a distorted trigonal non-coplanar geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.29–2.34 Å. In the fourth As site, As is bonded in a distorted trigonal non-coplanar geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.26–2.37 Å. In the fifth As site, As is bonded in a distorted T-shaped geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.26–2.35 Å. In the sixth As site, As is bonded in a 3-coordinate geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.28–2.35 Å. In the seventh As site, As is bonded in a 3-coordinate geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.30–2.36 Å. In the eighth As site, As is bonded in a distorted T-shaped geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.26–2.37 Å. In the ninth As site, As is bonded in a 4-coordinate geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.25–2.42 Å. In the tenth As site, As is bonded in a trigonal non-coplanar geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.25–2.37 Å. In the eleventh As site, As is bonded in a 3-coordinate geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.24–2.39 Å. In the twelfth As site, As is bonded in a rectangular see-saw-like geometry to four S atoms. There are a spread of As–S bond distances ranging from 2.27–2.84 Å. In the thirteenth As site, As is bonded in a distorted trigonal non-coplanar geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.27–2.36 Å. In the fourteenth As site, As is bonded in a distorted trigonal non-coplanar geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.29–2.35 Å. In the fifteenth As site, As is bonded in a distorted T-shaped geometry to three S atoms. All As–S bond lengths are 2.31 Å. In the sixteenth As site, As is bonded in a distorted T-shaped geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.25–2.35 Å. In the seventeenth As site, As is bonded in a distorted T-shaped geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.30–2.32 Å. In the eighteenth As site, As is bonded in a distorted T-shaped geometry to three S atoms. There are two shorter (2.31 Å) and one longer (2.32 Å) As–S bond lengths. In the nineteenth As site, As is bonded in a distorted trigonal non-coplanar geometry to three S atoms. There are a spread of As–S bond distances ranging from 2.26–2.37 Å. There are sixty-eight inequivalent S sites. In the first S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the second S site, S is bonded in a 3-coordinate geometry to one Pb, one Sb, and one As atom. In the third S site, S is bonded in an L-shaped geometry to two Sb atoms. In the fourth S site, S is bonded in a distorted single-bond geometry to one Pb and one As atom. In the fifth S site, S is bonded in a distorted L-shaped geometry to one Sb and one As atom. In the sixth S site, S is bonded in an L-shaped geometry to two Sb atoms. In the seventh S site, S is bonded in a distorted trigonal non-coplanar geometry to two Sb and one As atom. In the eighth S site, S is bonded in a distorted water-like geometry to one Sb and two As atoms. In the ninth S site, S is bonded in a distorted L-shaped geometry to one Sb and one As atom. In the tenth S site, S is bonded in a distorted see-saw-like geometry to one Pb, two Sb, and one As atom. In the eleventh S site, S is bonded in a 3-coordinate geometry to two Sb and one As atom. In the twelfth S site, S is bonded in a water-like geometry to one Sb and one As atom. In the thirteenth S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the fourteenth S site, S is bonded in a distorted trigonal non-coplanar geometry to one Pb and two Sb atoms. In the fifteenth S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the sixteenth S site, S is bonded in a 3-coordinate geometry to three Sb atoms. In the seventeenth S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the eighteenth S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the nineteenth S site, S is bonded in a water-like geometry to one Sb and one As atom. In the twentieth S site, S is bonded in a distorted L-shaped geometry to one Pb and two As atoms. In the twenty-first S site, S is bonded in a water-like geometry to two As atoms. In the twenty-second S site, S is bonded in a distorted L-shaped geometry to one Sb and one As atom. In the twenty-third S site, S is bonded in a distorted water-like geometry to two As atoms. In the twenty-fourth S site, S is bonded in a distorted L-shaped geometry to two Sb atoms. In the twenty-fifth S site, S is bonded in a water-like geometry to one Sb and one As atom. In the twenty-sixth S site, S is bonded in a distorted trigonal non-coplanar geometry to one Sb and two As atoms. In the twenty-seventh S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the twenty-eighth S site, S is bonded in an L-shaped geometry to two Sb atoms. In the twenty-ninth S site, S is bonded in a 4-coordinate geometry to three Sb and one As atom. In the thirtieth S site, S is bonded in a distorted water-like geometry to one Pb and two Sb atoms. In the thirty-first S site, S is bonded in a distorted water-like geometry to one Pb, one Sb, and one As atom. In the thirty-second S site, S is bonded in a water-like geometry to one Sb and one As atom. In the thirty-third S site, S is bonded in a 2-coordinate geometry to two Sb and one As atom. In the thirty-fourth S site, S is bonded in a distorted trigonal non-coplanar geometry to one Pb and two Sb atoms. In the thirty-fifth S site, S is bonded in a distorted trigonal non-coplanar geometry to two Sb and one As atom. In the thirty-sixth S site, S is bonded in a 4-coordinate geometry to one Tl, one Pb, and two Sb atoms. In the thirty-seventh S site, S is bonded in a distorted single-bond geometry to one Pb and one As atom. In the thirty-eighth S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the thirty-ninth S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the fortieth S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the forty-first S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the forty-second S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the forty-third S site, S is bonded in a distorted trigonal non-coplanar geometry to two Sb and one As atom. In the forty-fourth S site, S is bonded in a distorted trigonal non-coplanar geometry to two Sb and one As atom. In the forty-fifth S site, S is bonded in an L-shaped geometry to one Sb and one As atom. In the forty-sixth S site, S is bonded in a distorted see-saw-like geometry to one Pb, two Sb, and one As atom. In the forty-seventh S site, S is bonded in a distorted water-like geometry to one Pb and one As atom. In the forty-eighth S site, S is bonded in a 2-coordinate geometry to two Sb atoms. In the forty-ninth S site, S is bonded in a distorted trigonal non-coplanar geometry t

36 MATERIALS SCIENCE↗