The crystal structure of TlMgCl₃ 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 TlMgCl₃ to be hexa­gonal P6₃/mmc (No. 194) and isostructural with RbMgCl₃, contrary to previously reported data. Extending neutron diffraction measurements to high temperature, the data show that TlMgCl₃ maintains this crystal structure from 290 K up through 725 K, approaching the melting point of 770 K.

Abstract

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 TlMgCl₃ to be hexa­gonal P6₃/mmc (No. 194) and isostructural with RbMgCl₃, 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 TlMgCl₃ 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.

Chemical context  

In the ongoing search for inorganic scintillators with high gamma-stopping power, TlMgCl₃ has been identified. As a result of the presence of thallium, TlMgCl₃ has a high effective atomic number, Z _eff = 67 [calculation methodology (Derenzo & Choong, 2009 ▸) in the supporting information], and a moderate density, ρ = 4.47 g cm⁻³ (determined in this work). A pair of initial crystal growths of TlMgCl₃ have been conducted to assess the scintillation properties: Fujimoto et al. (2016 ▸) measured 46,000 ph MeV⁻¹ light yield with 5% energy resolution at 662 keV, and Hawrami et al. (2017 ▸) measured 30,600 ph MeV⁻¹ light yield with 3.7% energy resolution at 662 keV.

To develop this compound further, a precise determination of the crystal structure is necessary. This will enable first-principles calculations of the electronic configuration and may be useful in assessing challenges that arise during synthesis (e.g. from thermal stresses). This work reports the crystal structure of TlMgCl₃ between 290 K and 725 K, approaching the melting point of 770 K. Previous work on TlMgCl₃ by Beznosikov (1978 ▸) used powder diffraction to report the space group at room temperature as ortho­rhom­bic (a = 6.54, b = 9.22, c = 6.99 Å). However, despite using the same synthesis procedure, the structure reported by Beznosikov does not fit the diffraction data reported herein. Arai et al. (2020 ▸) published diffraction data but did not provide information on the crystal structure.

Structural commentary  

Single crystal X-ray diffraction (SC-XRD) determined TlMgCl₃ to have a hexa­gonal structure (space group P6₃/mmc, No. 194) with lattice parameters a = 7.0228 (4), c = 17.4934 (15) Å at 290 K. Fig. 1 ▸ visualizes the unit cell, which shows a three-dimensional corner- and face-sharing framework of six-coordinated Mg atoms encapsulating the 12-coordinated Tl atoms. There are six formula units in the unit cell. There are two thallium, two magnesium and two chlorine atoms in the asymmetric unit of TlMgCl₃, with site symmetries of m2 and 3m; 3m and m; mm2 and m, respectively; key bond distances and angles are listed in Table 1 ▸. Pairs of Mg2-centered octa­hedra share faces (via 3 × Cl1) and these octa­hedral pairs share corners (via Cl2) with the Mg1 octa­hedra to generate an ABACBC hexa­gonal stacking sequence of the chloride ions in the c-axis direction with the thallium cations occupying the vacant 12-coordinate sites. The coordination polyhedra of the chloride ions are distorted ClMg₂Tl₄ octa­hedra with the Mg²⁺ ions in a cis disposition for Cl1 and a trans disposition for Cl2. The title compound is isostructural with RbMgCl₃ as reported by Devaney et al. (1981 ▸) and RbMnCl₃ as reported by Goodyear et al. (1977 ▸), who describe the structure in more detail. This structure is more complex than that of CsMgCl₃ (McPherson et al., 1970 ▸), which also has space group P6₃/mmc but only requires two formula units per unit cell and has an AB hexa­gonal stacking sequence of the chloride ions in the c-axis direction.

Figure 1.

The unit cell of TlMgCl₃, with the MgCl₆ octa­hedra shown in polyhedral representation.

Table 1. Selected geometric parameters (Å, °).

Tl1—Cl1	3.5126 (2)	Tl2—Cl2iv	3.622 (5)
Tl1—Cl2i	3.576 (5)	Mg1—Cl2	2.448 (6)
Tl2—Cl1ii	3.510 (3)	Mg1—Cl1	2.499 (6)
Tl2—Cl2iii	3.5146 (3)	Mg2—Cl2	2.476 (4)
Mg1v—Cl1—Mg1	78.5 (3)	Mg1—Cl2—Mg2	178.8 (3)

Symmetry codes: (i) ; (ii) ; (iii) ; (iv) ; (v) .

Neutron diffraction (ND) conducted on powder samples produced diffraction patterns that were in agreement with the crystal structure determined by SC-XRD. Neutron diffraction was conducted at temperatures ranging from 300 K to 725 K. TlMgCl₃ maintains the same P6₃/mmc crystal structure over this measured temperature range (see supporting information for more details on the powder ND data and fits). Fig. 2 ▸ shows the lattice parameters as a function of temperature. From these data, the thermal expansion along each axis is calculated (Fig. 3 ▸). The thermal expansion is greater along the a axis than the c axis. Besides the anisotropy in the lattice parameters, the atomic positions did not vary significantly with temperature, and therefore the bond lengths change with temperature as dictated by the lattice parameters alone.

Figure 2.

The hexa­gonal lattice parameters of TlMgCl₃ as a function of temperature, from neutron diffraction data. Vertical error bars from Rietveld fitting are within the size of the symbols and are omitted. The dashed lines are second-order polynomial fits to the data.

Figure 3.

Thermal expansion coefficients as a function of temperature, calculated from the second-order polynomial fit of the lattice parameters in Fig. 2 ▸.

Synthesis and crystallization  

Crystals of TlMgCl₃ were grown from the melt using the vertical Bridgman method. High purity beads of TlCl and MgCl₂ were combined in a stoichiometric ratio and sealed in a quartz ampoule under vacuum (10⁻⁶ Torr). The crystal was grown with a translation speed of 0.5 mm h⁻¹ and was cooled over 72 h. To protect the moisture-sensitive reactants and products, all preparations before and after synthesis were conducted inside an argon-filled glove box.

Refinement  

SC-XRD was conducted on a Bruker Kappa APEXII CCD diffractometer. The crystal was protected from moisture by oil during mounting and by an Oxford dry nitro­gen gas cryostream system during data collection at 290 K. Crystal data, data collection and structure refinement details are summarized in Table 2 ▸.

Table 2. Experimental details.

Crystal data
Chemical formula	TlMgCl3
M r	335.03
Crystal system, space group	Hexagonal, P63/m m c
Temperature (K)	290
a, c (Å)	7.0228 (4), 17.4934 (15)
V (Å3)	747.18 (11)
Z	6
Radiation type	Mo Kα
μ (mm−1)	33.97
Crystal size (mm)	0.10 × 0.10 × 0.10
Data collection
Diffractometer	Bruker Kappa APEXII CCD
Absorption correction	Multi-scan (SADABS; Bruker, 2004 ▸)
T min, T max	0.578, 0.746
No. of measured, independent and observed [I > 2σ(I)] reflections	4109, 489, 387
R int	0.047
(sin θ/λ)max (Å−1)	0.718
Refinement
R[F 2 > 2σ(F 2)], wR(F 2), S	0.047, 0.113, 1.42
No. of reflections	489
No. of parameters	21
Δρmax, Δρmin (e Å−3)	1.88, −2.11

Computer programs: APEX2 and SAINT (Bruker, 2004 ▸), SHELXT2014/4 (Sheldrick, 2015a ▸), SHELXL2018/3 (Sheldrick, 2015b ▸) and VESTA (Momma & Izumi, 2011 ▸).

Powder high-temperature ND measurements were obtained using the high-pressure preferred orientation (HIPPO) neutron diffractometer at the short-pulsed spallation neutron source of the Lujan Neutron Scattering Center at Los Alamos National Laboratory (Wenk et al., 2003 ▸; Vogel et al., 2004 ▸). Powder samples were sealed under argon in vanadium tubes to protect from moisture during data collection. Time-of-flight data were collected with HIPPO detector panels of ³He detector tubes arranged on five rings with nominal diffraction angles of 2θ = 39, 60, 90, 120, and 144°. Count times were 90 minutes per dwell time. ND data were analyzed for all five rings simultaneously using the Rietveld method implemented in the GSAS code (Larson & Von Dreele, 2004 ▸) and automated by scripts through gsaslanguage (Vogel, 2011 ▸). To yield reliable absolute lattice parameters, the DIFC instrument calibration parameters were fitted for the room-temperature data using the lattice parameters from SC-XRD and were kept constant for the rest of the ND data at higher temperatures. For more details on the data collection and refinement of these neutron diffraction data, see Onken et al. (2018 ▸).

The thermal expansion tensor was generated using a quadratic fit to the lattice parameters (R ² = 0.999), using the Thermal Expansion Visualization (TEV) program (Langreiter & Kahlenberg, 2015 ▸).

Supplementary Material

CCDC reference: 2034695

Additional supporting information: crystallographic information; 3D view; checkCIF report

supplementary crystallographic information

Crystal data

TlMgCl3	Dx = 4.467 Mg m−3
Mr = 335.03	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P63/mmc	Cell parameters from 1053 reflections
a = 7.0228 (4) Å	θ = 3.6–28.2°
c = 17.4934 (15) Å	µ = 33.97 mm−1
V = 747.18 (11) Å3	T = 290 K
Z = 6	Block, colorless
F(000) = 864	0.10 × 0.10 × 0.10 mm

Data collection

Bruker Kappa APEXII CCD diffractometer	387 reflections with I > 2σ(I)
ω scans	Rint = 0.047
Absorption correction: multi-scan (SADABS; Bruker, 2004)	θmax = 30.7°, θmin = 2.3°
Tmin = 0.578, Tmax = 0.746	h = −8→9
4109 measured reflections	k = −8→8
489 independent reflections	l = −23→25

Refinement

Refinement on F2	0 restraints
Least-squares matrix: full	Primary atom site location: dual
R[F2 > 2σ(F2)] = 0.047	w = 1/[σ2(Fo2) + 23.1798P] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.113	(Δ/σ)max < 0.001
S = 1.42	Δρmax = 1.88 e Å−3
489 reflections	Δρmin = −2.11 e Å−3
21 parameters

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Tl1	0.000000	0.000000	0.250000	0.0375 (5)
Tl2	0.333333	0.666667	0.09002 (7)	0.0395 (4)
Mg1	0.666667	0.333333	0.3404 (4)	0.0115 (14)
Mg2	1.000000	1.000000	0.500000	0.017 (2)
Cl1	0.5075 (4)	0.0150 (8)	0.250000	0.0211 (9)
Cl2	0.8336 (4)	0.6671 (9)	0.4185 (2)	0.0379 (10)

Atomic displacement parameters (Ų)

	U11	U22	U33	U12	U13	U23
Tl1	0.0378 (7)	0.0378 (7)	0.0369 (8)	0.0189 (3)	0.000	0.000
Tl2	0.0353 (5)	0.0353 (5)	0.0479 (7)	0.0176 (2)	0.000	0.000
Mg1	0.011 (2)	0.011 (2)	0.013 (3)	0.0053 (11)	0.000	0.000
Mg2	0.019 (4)	0.019 (4)	0.014 (5)	0.0094 (19)	0.000	0.000
Cl1	0.0224 (18)	0.011 (2)	0.0261 (19)	0.0055 (10)	0.000	0.000
Cl2	0.0418 (18)	0.027 (2)	0.0399 (18)	0.0135 (10)	−0.0123 (9)	−0.0246 (18)

Geometric parameters (Å, º)

Tl1—Cl1i	3.5126 (2)	Tl2—Cl2x	3.5146 (3)
Tl1—Cl1ii	3.5126 (2)	Tl2—Cl2xvi	3.5146 (3)
Tl1—Cl1iii	3.5126 (2)	Tl2—Cl2xvii	3.622 (5)
Tl1—Cl1	3.5126 (2)	Tl2—Cl2xviii	3.622 (5)
Tl1—Cl1iv	3.5126 (2)	Tl2—Cl2xix	3.622 (5)
Tl1—Cl1v	3.5126 (2)	Mg1—Cl2	2.448 (6)
Tl1—Cl2vi	3.576 (5)	Mg1—Cl2ii	2.448 (6)
Tl1—Cl2vii	3.576 (5)	Mg1—Cl2vii	2.448 (6)
Tl1—Cl2viii	3.576 (5)	Mg1—Cl1vii	2.499 (6)
Tl1—Cl2ix	3.576 (5)	Mg1—Cl1	2.499 (6)
Tl1—Cl2x	3.576 (5)	Mg1—Cl1ii	2.499 (6)
Tl1—Cl2xi	3.576 (5)	Mg1—Mg1xvi	3.162 (13)
Tl2—Cl1ii	3.510 (3)	Mg2—Cl2xx	2.476 (4)
Tl2—Cl1xii	3.510 (3)	Mg2—Cl2xxi	2.476 (4)
Tl2—Cl1iv	3.510 (3)	Mg2—Cl2xxii	2.476 (4)
Tl2—Cl2xiii	3.5146 (3)	Mg2—Cl2xxiii	2.476 (4)
Tl2—Cl2xiv	3.5146 (3)	Mg2—Cl2xxiv	2.476 (4)
Tl2—Cl2viii	3.5146 (3)	Mg2—Cl2	2.476 (4)
Tl2—Cl2xv	3.5146 (3)
Cl1i—Tl1—Cl1ii	120.0	Cl1iv—Tl2—Cl2xvi	123.81 (8)
Cl1i—Tl1—Cl1iii	57.02 (16)	Cl2xiii—Tl2—Cl2xvi	175.12 (14)
Cl1ii—Tl1—Cl1iii	177.02 (16)	Cl2xiv—Tl2—Cl2xvi	119.820 (11)
Cl1i—Tl1—Cl1	62.98 (16)	Cl2viii—Tl2—Cl2xvi	119.820 (10)
Cl1ii—Tl1—Cl1	57.02 (16)	Cl2xv—Tl2—Cl2xvi	59.85 (17)
Cl1iii—Tl1—Cl1	120.0	Cl2x—Tl2—Cl2xvi	60.03 (17)
Cl1i—Tl1—Cl1iv	177.02 (16)	Cl1ii—Tl2—Cl2xvii	176.96 (10)
Cl1ii—Tl1—Cl1iv	62.98 (16)	Cl1xii—Tl2—Cl2xvii	119.42 (7)
Cl1iii—Tl1—Cl1iv	120.0	Cl1iv—Tl2—Cl2xvii	119.42 (7)
Cl1—Tl1—Cl1iv	120.000 (1)	Cl2xiii—Tl2—Cl2xvii	58.64 (11)
Cl1i—Tl1—Cl1v	120.000 (1)	Cl2xiv—Tl2—Cl2xvii	58.64 (11)
Cl1ii—Tl1—Cl1v	119.999 (1)	Cl2viii—Tl2—Cl2xvii	88.00 (9)
Cl1iii—Tl1—Cl1v	62.98 (16)	Cl2xv—Tl2—Cl2xvii	88.00 (9)
Cl1—Tl1—Cl1v	177.02 (16)	Cl2x—Tl2—Cl2xvii	116.71 (6)
Cl1iv—Tl1—Cl1v	57.02 (16)	Cl2xvi—Tl2—Cl2xvii	116.71 (6)
Cl1i—Tl1—Cl2vi	60.17 (6)	Cl1ii—Tl2—Cl2xviii	119.42 (7)
Cl1ii—Tl1—Cl2vi	118.86 (6)	Cl1xii—Tl2—Cl2xviii	176.96 (10)
Cl1iii—Tl1—Cl2vi	60.17 (6)	Cl1iv—Tl2—Cl2xviii	119.42 (7)
Cl1—Tl1—Cl2vi	90.84 (4)	Cl2xiii—Tl2—Cl2xviii	88.00 (9)
Cl1iv—Tl1—Cl2vi	118.86 (6)	Cl2xiv—Tl2—Cl2xviii	116.71 (6)
Cl1v—Tl1—Cl2vi	90.84 (5)	Cl2viii—Tl2—Cl2xviii	58.64 (11)
Cl1i—Tl1—Cl2vii	90.84 (4)	Cl2xv—Tl2—Cl2xviii	116.71 (6)
Cl1ii—Tl1—Cl2vii	60.17 (6)	Cl2x—Tl2—Cl2xviii	58.64 (11)
Cl1iii—Tl1—Cl2vii	118.86 (6)	Cl2xvi—Tl2—Cl2xviii	88.00 (9)
Cl1—Tl1—Cl2vii	60.17 (6)	Cl2xvii—Tl2—Cl2xviii	58.07 (11)
Cl1iv—Tl1—Cl2vii	90.84 (4)	Cl1ii—Tl2—Cl2xix	119.42 (7)
Cl1v—Tl1—Cl2vii	118.86 (6)	Cl1xii—Tl2—Cl2xix	119.42 (8)
Cl2vi—Tl1—Cl2vii	147.12 (6)	Cl1iv—Tl2—Cl2xix	176.96 (10)
Cl1i—Tl1—Cl2viii	118.86 (6)	Cl2xiii—Tl2—Cl2xix	116.71 (6)
Cl1ii—Tl1—Cl2viii	90.84 (5)	Cl2xiv—Tl2—Cl2xix	88.00 (9)
Cl1iii—Tl1—Cl2viii	90.84 (5)	Cl2viii—Tl2—Cl2xix	116.71 (6)
Cl1—Tl1—Cl2viii	118.86 (6)	Cl2xv—Tl2—Cl2xix	58.64 (11)
Cl1iv—Tl1—Cl2viii	60.17 (6)	Cl2x—Tl2—Cl2xix	88.00 (9)
Cl1v—Tl1—Cl2viii	60.17 (6)	Cl2xvi—Tl2—Cl2xix	58.64 (11)
Cl2vi—Tl1—Cl2viii	58.71 (11)	Cl2xvii—Tl2—Cl2xix	58.07 (11)
Cl2vii—Tl1—Cl2viii	147.12 (6)	Cl2xviii—Tl2—Cl2xix	58.07 (11)
Cl1i—Tl1—Cl2ix	118.86 (6)	Cl2—Mg1—Cl2ii	91.8 (2)
Cl1ii—Tl1—Cl2ix	90.84 (5)	Cl2—Mg1—Cl2vii	91.8 (2)
Cl1iii—Tl1—Cl2ix	90.84 (5)	Cl2ii—Mg1—Cl2vii	91.8 (2)
Cl1—Tl1—Cl2ix	118.86 (6)	Cl2—Mg1—Cl1vii	91.84 (10)
Cl1iv—Tl1—Cl2ix	60.17 (6)	Cl2ii—Mg1—Cl1vii	91.84 (10)
Cl1v—Tl1—Cl2ix	60.17 (6)	Cl2vii—Mg1—Cl1vii	174.7 (3)
Cl2vi—Tl1—Cl2ix	147.12 (6)	Cl2—Mg1—Cl1	174.7 (3)
Cl2vii—Tl1—Cl2ix	58.71 (11)	Cl2ii—Mg1—Cl1	91.84 (10)
Cl2viii—Tl1—Cl2ix	111.04 (14)	Cl2vii—Mg1—Cl1	91.84 (10)
Cl1i—Tl1—Cl2x	90.84 (4)	Cl1vii—Mg1—Cl1	84.3 (2)
Cl1ii—Tl1—Cl2x	60.17 (6)	Cl2—Mg1—Cl1ii	91.84 (10)
Cl1iii—Tl1—Cl2x	118.86 (6)	Cl2ii—Mg1—Cl1ii	174.7 (3)
Cl1—Tl1—Cl2x	60.17 (6)	Cl2vii—Mg1—Cl1ii	91.84 (10)
Cl1iv—Tl1—Cl2x	90.84 (5)	Cl1vii—Mg1—Cl1ii	84.3 (2)
Cl1v—Tl1—Cl2x	118.86 (6)	Cl1—Mg1—Cl1ii	84.3 (2)
Cl2vi—Tl1—Cl2x	58.71 (11)	Cl2xx—Mg2—Cl2xxi	90.17 (16)
Cl2vii—Tl1—Cl2x	111.04 (14)	Cl2xx—Mg2—Cl2xxii	89.83 (16)
Cl2viii—Tl1—Cl2x	58.71 (11)	Cl2xxi—Mg2—Cl2xxii	180.0
Cl2ix—Tl1—Cl2x	147.12 (6)	Cl2xx—Mg2—Cl2xxiii	90.17 (16)
Cl1i—Tl1—Cl2xi	60.17 (6)	Cl2xxi—Mg2—Cl2xxiii	90.17 (17)
Cl1ii—Tl1—Cl2xi	118.86 (6)	Cl2xxii—Mg2—Cl2xxiii	89.83 (17)
Cl1iii—Tl1—Cl2xi	60.17 (6)	Cl2xx—Mg2—Cl2xxiv	89.83 (16)
Cl1—Tl1—Cl2xi	90.84 (4)	Cl2xxi—Mg2—Cl2xxiv	89.83 (17)
Cl1iv—Tl1—Cl2xi	118.86 (6)	Cl2xxii—Mg2—Cl2xxiv	90.17 (17)
Cl1v—Tl1—Cl2xi	90.84 (5)	Cl2xxiii—Mg2—Cl2xxiv	180.0
Cl2vi—Tl1—Cl2xi	111.04 (14)	Cl2xx—Mg2—Cl2	180.0
Cl2vii—Tl1—Cl2xi	58.71 (11)	Cl2xxi—Mg2—Cl2	89.83 (17)
Cl2viii—Tl1—Cl2xi	147.12 (6)	Cl2xxii—Mg2—Cl2	90.17 (17)
Cl2ix—Tl1—Cl2xi	58.71 (11)	Cl2xxiii—Mg2—Cl2	89.83 (16)
Cl2x—Tl1—Cl2xi	147.12 (6)	Cl2xxiv—Mg2—Cl2	90.17 (16)
Cl1ii—Tl2—Cl1xii	63.03 (10)	Mg1xvi—Cl1—Mg1	78.5 (3)
Cl1ii—Tl2—Cl1iv	63.03 (10)	Mg1xvi—Cl1—Tl2xxv	87.89 (12)
Cl1xii—Tl2—Cl1iv	63.03 (10)	Mg1—Cl1—Tl2xxv	166.36 (18)
Cl1ii—Tl2—Cl2xiii	123.81 (8)	Mg1xvi—Cl1—Tl2xxvi	166.36 (18)
Cl1xii—Tl2—Cl2xiii	91.92 (9)	Mg1—Cl1—Tl2xxvi	87.89 (12)
Cl1iv—Tl2—Cl2xiii	60.79 (8)	Tl2xxv—Cl1—Tl2xxvi	105.74 (13)
Cl1ii—Tl2—Cl2xiv	123.81 (8)	Mg1xvi—Cl1—Tl1xxvii	91.16 (6)
Cl1xii—Tl2—Cl2xiv	60.79 (8)	Mg1—Cl1—Tl1xxvii	91.15 (6)
Cl1iv—Tl2—Cl2xiv	91.92 (9)	Tl2xxv—Cl1—Tl1xxvii	89.10 (5)
Cl2xiii—Tl2—Cl2xiv	59.85 (17)	Tl2xxvi—Cl1—Tl1xxvii	89.10 (5)
Cl1ii—Tl2—Cl2viii	91.92 (9)	Mg1xvi—Cl1—Tl1	91.15 (6)
Cl1xii—Tl2—Cl2viii	123.81 (8)	Mg1—Cl1—Tl1	91.15 (6)
Cl1iv—Tl2—Cl2viii	60.79 (8)	Tl2xxv—Cl1—Tl1	89.10 (5)
Cl2xiii—Tl2—Cl2viii	60.03 (17)	Tl2xxvi—Cl1—Tl1	89.10 (5)
Cl2xiv—Tl2—Cl2viii	119.820 (10)	Tl1xxvii—Cl1—Tl1	177.02 (16)
Cl1ii—Tl2—Cl2xv	91.92 (9)	Mg1—Cl2—Mg2	178.8 (3)
Cl1xii—Tl2—Cl2xv	60.79 (8)	Mg1—Cl2—Tl2xvi	88.60 (7)
Cl1iv—Tl2—Cl2xv	123.81 (8)	Mg2—Cl2—Tl2xvi	91.44 (7)
Cl2xiii—Tl2—Cl2xv	119.820 (10)	Mg1—Cl2—Tl2xxviii	88.60 (7)
Cl2xiv—Tl2—Cl2xv	60.03 (17)	Mg2—Cl2—Tl2xxviii	91.44 (7)
Cl2viii—Tl2—Cl2xv	175.12 (14)	Tl2xvi—Cl2—Tl2xxviii	175.12 (14)
Cl1ii—Tl2—Cl2x	60.79 (8)	Mg1—Cl2—Tl1xxix	90.52 (17)
Cl1xii—Tl2—Cl2x	123.81 (8)	Mg2—Cl2—Tl1xxix	90.67 (16)
Cl1iv—Tl2—Cl2x	91.92 (9)	Tl2xvi—Cl2—Tl1xxix	88.02 (8)
Cl2xiii—Tl2—Cl2x	119.820 (11)	Tl2xxviii—Cl2—Tl1xxix	88.02 (8)
Cl2xiv—Tl2—Cl2x	175.12 (14)	Mg1—Cl2—Tl2xxx	89.9 (2)
Cl2viii—Tl2—Cl2x	59.85 (17)	Mg2—Cl2—Tl2xxx	88.94 (11)
Cl2xv—Tl2—Cl2x	119.820 (11)	Tl2xvi—Cl2—Tl2xxx	91.99 (9)
Cl1ii—Tl2—Cl2xvi	60.79 (8)	Tl2xxviii—Cl2—Tl2xxx	91.99 (9)
Cl1xii—Tl2—Cl2xvi	91.92 (9)	Tl1xxix—Cl2—Tl2xxx	179.61 (13)

Symmetry codes: (i) −y, x−y−1, z; (ii) −x+y+1, −x+1, z; (iii) −x+y, −x, z; (iv) −y, x−y, z; (v) x−1, y, z; (vi) x−1, y−1, −z+1/2; (vii) −y+1, x−y, z; (viii) −x+y, −x+1, −z+1/2; (ix) −x+y, −x+1, z; (x) −y+1, x−y, −z+1/2; (xi) x−1, y−1, z; (xii) x, y+1, z; (xiii) x−1, y, −z+1/2; (xiv) −y+1, x−y+1, −z+1/2; (xv) −x+y+1, −x+2, −z+1/2; (xvi) x, y, −z+1/2; (xvii) x−y, x, z−1/2; (xviii) −x+1, −y+1, z−1/2; (xix) y, −x+y+1, z−1/2; (xx) −x+2, −y+2, −z+1; (xxi) x−y+1, x, −z+1; (xxii) −x+y+1, −x+2, z; (xxiii) y, −x+y+1, −z+1; (xxiv) −y+2, x−y+1, z; (xxv) x, y−1, z; (xxvi) x, y−1, −z+1/2; (xxvii) x+1, y, z; (xxviii) x+1, y, −z+1/2; (xxix) x+1, y+1, z; (xxx) −x+1, −y+1, z+1/2.

Funding Statement

This work was funded by U.S. Defense Threat Reduction Agency (DTRA) grant HDTRA19-31194 to Lawrence Berkeley National Laboratory (LBNL) authors. U.S. Department of Energy, National Nuclear Security Administration (NNSA), Office of Defense Nulear Nonproliferation (DNN) grant AC02-05CH11231 to LBNL authors. U.S. Department of Energy, NNSA grant 89233218NCA000001 to Los Alamos National Laboratory (LANL).