Crystal Structures of Î±- and Î²-Nitrogen Trifluoride - Inorganic

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Crystal Structures of α- and β‑Nitrogen Trifluoride Sergei I. Ivlev,† Matthias Conrad,† Markus Hoelzel,‡ Antti J. Karttunen,§ and Florian Kraus*,† †

Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße, 35032 Marburg, Germany Heinz Maier-Leibnitz Zentrum (MLZ), Technische Universität München, Lichtenbergstraße 1, 85747 Garching, Germany § Department of Chemistry and Materials Science, Aalto University, 00076 Aalto, Finland ‡

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S Supporting Information *

ABSTRACT: The crystal structures of α-NF3 and β-NF3 are reported for the first time. As shown by powder neutron diffraction, the low-temperature α-NF3 crystallizes in the orthorhombic space group Pnma (oP16) with lattice parameters a = 6.71457(13) Å, b = 7.30913(14) Å, c = 4.55189(8) Å, V = 223.396(7) Å3, and Z = 4 at T = 6 K. The intramolecular atom distances in α-NF3 are 1.3639(16) and 1.3677(11) Å for N−F, and 2.1216(16) and 2.120(2) Å for F···F. The F−N−F bond angles are 101.92(7)° and 101.63(10)°. All data are in excellent agreement with quantum-chemical predictions and previously reported experimentally obtained gas-phase data. The high-temperature β-NF3 is a plastic crystal, space group P42/mnm (tP120), with the lattice parameters a = 15.334(6) Å, c = 7.820(3) Å, V = 1838.6(12) Å3, and Z = 30 at T = 60 K. Its crystal structure is closely related to that of the Frank−Kasper sigma phase.

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INTRODUCTION

RESULTS AND DISCUSSION At least two modifications of NF3 should exist at ambient pressure, which was deduced by investigation of cooling and heating curves,30,32 heat capacity measurements,29 and solid state 19F NMR spectroscopy.15,16 A transition temperature of 56.62 K has been reported.29 Therefore, we carried out powder neutron diffraction experiments at two different temperatures, one corresponding to the low-temperature phase α-NF3 and one to its high-temperature modification β-NF3. Crystal Structure of α-NF3. The powder diffraction pattern of α-NF3 was recorded at 6 K using the SPODI neutron diffractometer.33 All observed reflections could be directly indexed in the orthorhombic crystal system with lattice parameters a = 6.71457(13) Å, b = 7.30913(14) Å, c = 4.55189(8) Å, and V = 223.396(7) Å3. The observed and calculated powder diffraction patterns are shown in Figure 1. Some crystallographic data and details of the structure determination are given in Table 1. The obtained structure model is in agreement with the calculated (at the DFT-PAW/PBE level of theory) crystal structure of NF3 reported previously, which claimed it to be a stable modification between ambient pressure and 40 GPa.34 However, these authors erroneously assigned their NF3 crystal structure to the NCl3 structure type but provided the correct Z. α-NF3 crystallizes in the PCl3 structure type. It contains one nitrogen atom N(1) at the special Wyckoff position 4c (.m.) and two symmetry inequivalent fluorine atoms, F(1) and F(2), at the special 4c (.m.) and general 8d (1) Wyckoff positions, respectively. Table 2 contains atomic coordinates and equivalent isotropic displacement parameters for α-NF3.

Nitrogen trifluoride was first synthesized by Otto Ruff in 1928.1 It is nowadays widely applied in the semiconductor industry as a cleaning agent for plasma-enhanced vapor deposition chambers.2−5 NF3 is also promising in some other scientific and industrial areas, including the following: as a cathode reactant in metal−gas batteries;6 in the nuclear industry for purification of molten salt reactor coolants,7 as well as for recycling of used nuclear fuels;8 as a fluorinating agent in organic chemistry;9 and as a working gas in remote plasma sources.10 Another emerging field, where NF3 is being extensively studied, is connected with its global warming potential of 17200 (GWP100, Climate Change 2007, the Fourth Assessment Report (AR4) of the UN Intergovernmental Panel on Climate Change) in comparison to that of CO2, which motivates the search for replacements in industrial processes.11−14 With this taken into account, the importance of in-depth knowledge of physical and chemical properties of NF3 cannot be overestimated. Nitrogen trifluoride has been characterized by many techniques so far: NMR,15−18 UV,19,20 IR,21−26 Raman,25 micro-22,24,27 and millimeter-wave spectroscopy,22 gas-phase electron diffraction,28 and thermodynamic investigations.29,30 To the best of our knowledge, no crystal structures have been reported for pure NF3. The crystal structure of its hydrate has been reported recently.31 Surprisingly, NF3 is so far the only binary fluoride (except for binary fluorides of some radioactive elements, e.g., RnF2, etc.), which has never been characterized by diffraction techniques in the solid state. Here, we present our crystallographic studies on NF3 using powder neutron diffraction data. © XXXX American Chemical Society

Received: March 5, 2019

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DOI: 10.1021/acs.inorgchem.9b00628 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 1. Observed (black circles) and calculated (red line) powder neutron diffraction patterns of α-NF3 at 6 K after Rietveld refinement. The calculated reflection positions are indicated by the vertical bars below the patterns. The curve at the bottom represents the difference between the observed and the calculated intensities. Rp = 0.0425, Rwp = 0.0513, and GOF = 9.90.

As shown in Figure 2, the nitrogen trifluoride molecule adapts a pyramidal molecular structure in the solid state, which

Table 1. Selected Crystallographic Data and Details of the Structure Determination of α-NF3 parameters

value

formula molar mass, g/mol cryst syst space group, Pearson symbol a/Å b/Å c/Å V/Å3 Z ρcalcd/g cm−3 λ/Å T/K profile function Rp, Rwp Rp′, Rwp′a RBragg (I) GOF no. of data points no. of params. no. of constraints 2θ range measured (min, max, step) 2θ range refined (min, max)

NF3 71.0 orthorhombic Pnma (No. 62), oP16 6.71457(13) 7.30913(14) 4.55189(8) 223.396(7) 4 2.11108(7) 1.5484 (neutrons) 6 Pearson VII 0.0425, 0.0513 0.0831, 0.0856 0.0324 9.90 2838 48 2 0.95, 153.90, 0.05 12.00, 153.90

Figure 2. Structure of the NF3 molecule of α-NF3. Displacement ellipsoids at 70% probability level at 6 K.

is in accord with gas-phase studies27,28 as well as theoretical predictions for the solid state (at 40 GPa).34 However, the point group of the molecule imposed by the space group is only Cs, but it is quite close to C3v symmetry. The N−F bond lengths are 1.3639(16) Å for N(1)−F(1) and 1.3677(11) Å for N(1)−F(2), with both being identical within 3 times the standard uncertainty. These bond lengths are in very good agreement with those determined by gas-phase electron diffraction (1.37 ± 0.02 Å)28 and microwave spectroscopy (1.371 Å, no standard uncertainty given),27 and also with the predicted N−F bond length for the solid state compound at 40 GPa (1.374 and 1.376 Å).34

a

R′-factors are the background-corrected R-factors.

Table 2. Atomic Coordinates and Equivalent Isotropic Displacement Parameters Uequiv of α-NF3 atom

position

x

y

z

Uequiv/Å2

N(1) F(1) F(2)

4c 4c 8d

0.95097(12) 0.79734(19) 0.90321(15)

1/4 1/4 0.10496(14)

0.58044(18) 0.3844(3) 0.7567(2)

0.007588(2) 0.004873(4) 0.009593(3)

B


Article

Inorganic Chemistry The intramolecular F···F distances are 2.1216(16) Å for F(1)···F(2) and 2.1202(14) Å for F(2)···F(2)#1. The bond angles are 101.92(7)° for F(1)−N(1)−F(2) and 101.63(10)° for F(2)−N(1)−F(2)#1. Thus, these angles are also equivalent within three times the standard uncertainty, which is expected for the C3v symmetric NF3 molecule. A comparison with atom distances and bond angles determined by other techniques shows an excellent agreement despite the very different conditions: The gas-phase electron diffraction results are 2.14(2) Å for the F···F distance and 102.5(15)° for the F−N− F angles,28 whereas the corresponding values obtained using microwave spectroscopy are 2.133 Å and 102.15°.27 The theoretically predicted F···F distances and the F−N−F angles at 40 GPa are, as expected, slightly different due to molecular deformation: 2.123 and 2.147 Å; 101.06° and 102.54°.34 We therefore conclude that the molecular structure of the NF3 molecule is little influenced by the physical conditions. The crystal structure of α-NF3 is shown in Figure 3. From the

Figure 4. Coordination of the nitrogen atom of NF3 by fluorine atoms of adjacent NF3 molecules in α-NF3. The weak intermolecular interactions are shown in dashed lines with given atom distances. The NF3 molecules shown in gray belong to B layers, the colored to the A layer. The light blue plane indicates a mirror plane.

crystal structure of α-NF3. The geometric centers of the NF3 molecules are close to the N atoms. Each N atom is surrounded by 12 other N atoms which are located on the vertices of a distorted anticuboctahedron (Figure 5). Thus, the

Figure 3. Crystal structure of α-NF3. The “upper” NF3 (at y = 3/4) molecules point with their N atoms in average to the left, and those on the “bottom” (at y = 1/4) to the right.

Figure 5. Surrounding of a central N atom by N atoms of other NF3 molecules. The polyhedron is a distorted anticuboctahedron.

crystal structure it becomes obvious that the NF3 molecules are arranged due to the interaction of their dipole moments. In the case of the NF3 molecules located in the mirror plane at y = 1/ 4, the dipole moments point roughly in the direction [100] (Figure 3). Since the NF3 molecules located in the mirror plane in y = 3/4 are related by an inversion center to the former ones, their dipole moments point in the opposite direction. Overall, the dipole moments cancel out. Thus, αNF3 can be described as an AB layer structure, with a ferroelectric dipole−dipole interaction within each layer and an antiferroelectric interaction between different layers. To the best of our knowledge, no detailed information on the intermolecular atom distances between NF3 molecules in the solid state was reported. The nitrogen atom of the NF3 molecule in α-NF3 is coordinated by six F atoms, belonging to four different NF3 molecules. Of these four NF3 molecules, two belong to the A layer, and the other two to the adjacent B layers. These intermolecular N···F distances are the shortest with 3.1442(16), 3.1694(11), 3.3006(13), and 3.3679(16) Å. Therefore, we conclude that the only intermolecular interactions in α-NF3 are due to the van der Waals forces (dipole−dipole interactions and London dispersion forces), since there are no intermolecular N···F contacts shorter than the sum of the van der Waals radii of N and F atoms (1.40 Å + 1.46 Å = 2.86 Å).35,36 The overall coordination of the nitrogen atom by fluorine atoms is shown in Figure 4. By visual inspection and using the ToposPro software,37 we investigated the topology of the molecular packing in the

crystal structure of α-NF3 can be derived from the Mg structure type (hexagonal closest packing of spheres) with an AB stacking sequence of the hexagonal close-packed layers. The layers A and B are the same as those mentioned above in the context of dipole interaction. Two fluorine F(2) atoms of the NF3 molecule are located within the octahedral voids among the nitrogen atoms. The other fluorine atom F(1) is located approximately on the line connecting two neighboring nitrogen atoms within one hexagonal layer. No quantum-chemically calculated bond lengths and angles are available for α-NF3 at ambient pressure. Therefore, we carried out a full optimization of the unit cell and the atom positions in α-NF3 using the CRYSTAL17 software.38,39 The calculated lattice parameters, bond lengths and angles, their experimentally observed counterparts, and the values reported in the literature are given in Table 3. The calculated volume differs only by ca. 2.7% from the experimentally observed value. The largest discrepancy between theory and experiment is observed for the lattice parameter b. It is overestimated by ∼2.6% with 7.496 Å (experiment: 7.30913(14) Å). The molecular structure of NF3 was predicted very accurately (less than 0.3% differences in bond length, less than 0.5% differences in bond angles). We attempted to introduce dispersion corrections (Grimme D340) in our calculations, but an underestimation of the other two lattice parameters (see Table S1, Supporting Information) was the result, which is due C


Article

Inorganic Chemistry Table 3. Experimentally Observed and Theoretically Predicted Structural Data for α-NF3 param a/Å b/Å c/Å V/Å N−F/Å F···Fa/Å F···Fb/Å N···Fb/Å N···N/Å F−N−F/deg a

powder neutron diffraction at 6 K (this work) 6.71457(13) 7.30913(14) 4.55189(8) 223.396(7) 1.3639(16), 1.3677(11) 2.1216(16), 2.120(2) 2.9803(12) 3.1442(16) 3.6952(6), 3.7849(4), 4.5078(11), 4.55189(8) 101.63(10), 101.92(7)

DFT/PBE0-TZVP calculation at 0 K (this work)

gas-phase electron diffraction28

6.734 7.496 4.547 229.5 1.362 1.364 2.120 2.123 3.050 3.183 3.684 3.892 4.544 4.547 102.08 102.18

microwave spectroscopy27

1.37(2) 2.14(2)

1.371 2.133

102.5(15)

102.15

DFT-PAW/PBE at 0 K and 40 GPa34 5.093 6.212 3.928 124.3 1.374, 1.376 2.123, 2.147 2.275 2.268 2.870, 3.177, 3.642, 3.928 101.06, 102.54

b

Intramolecular distance. Shortest intermolecular distance.

Figure 6. Powder neutron diffraction patterns of solid NF3 recorded at different temperatures. The sample was warmed from 16 K (bottom, blue) to 64 K (top, blue).

determined from Le Bail fits and given in Table 4 and Figures S1−S4. For measurement conditions, see Figure S5. As seen in

to an underestimation of the intermolecular distances. The intramolecular atom distances are virtually unchanged in comparison. In the Supporting Information we report IR and Raman spectra of α-NF3 that were calculated on the basis of the computationally optimized structure, which was a true local minimum. The spectra may be of help for future experimental spectroscopic studies on solid NF3. The calculated spectra, which are in good agreement with the previously reported spectra of liquid and gaseous NF3, are shown in Figure S7, and the assignment of the vibration modes is given in Table S2. The lattice vibration modes are reported there for the first time. Usually, harmonic frequencies calculated by DFT methods are overestimated;41 however, due to the lack of experimentally obtained vibrational spectra of solid α-NF3, we provide our data without the application of any harmonic frequency scaling factor. Phase Transition α → β. The transition temperature α → β was estimated by temperature-dependent in situ powder neutron diffraction. α-NF3 was first warmed to 16 K, and then short diffraction measurements were carried out with stepwise warming to a temperature above the reported phase transition point at 56.62 K.29 At each temperature step a powder diffraction pattern was recorded (Figure 6). The temperature dependence of the lattice parameters of α-NF3 were

Table 4. Temperature Dependence of the Lattice Parameters of α-NF3 temp/K

a/Å

b/Å

c/Å

V/Å3

6 16 26 36 46 52 54 56 58

6.71457(13) 6.7189(2) 6.7344(2) 6.7611(2) 6.7990(3) 6.8214(3) 6.8340(2) 6.8450(3) 6.8565(3)

7.30913(14) 7.3093(3) 7.3155(3) 7.3247(3) 7.3382(3) 7.3451(3) 7.3498(3) 7.3531(3) 7.3558(3)

4.55189(8) 4.55214(16) 4.55427(15) 4.55795(14) 4.56234(18) 4.56459(19) 4.56584(18) 4.56686(18) 4.56676(18)

223.396(7) 223.557(18) 224.367(18) 225.724(18) 227.63(2) 228.70(2) 229.34(2) 229.86(2) 230.32(2)

Figure 6, the powder diffraction pattern changes between 60 and 62 K, which is slightly higher than the reported value of 56.62 K.29 The value obtained in our experiment should be regarded with care as the experimental conditions were not optimized for the determination of the transition temperature. As far as the variations of the lattice parameters with temperature from 6 to 58 K are concerned (Table 4), the a axis undergoes the largest change of ca. +2.1% upon heating. The b D


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Inorganic Chemistry

Figure 7. Observed (black circles) and calculated (red line) powder neutron diffraction patterns of β-NF3 at 60 K after the Rietveld refinement. The calculated reflection positions are indicated by the vertical bars below the patterns. The curve at the bottom represents the difference between the observed and the calculated intensities. The gray areas were excluded from the refinement. Rp = 0.0107, Rwp = 0.0137, and GOF = 2.13.

axis shows an elongation of ca. 0.6% upon heating. The c axis shows an increase of only ca. 0.3%. The relative change of the unit cell volume equals ca. +3.1%. As the lattice parameter c can be rather poorly approximated by the chosen polynomial at temperatures near the phase transition, we carried out a structure refinement using the powder pattern at 58 K to exclude the presence of another polymorph in this temperature region. The results did not show any significant deviations from the structure model obtained at 6 K. The only noticeable difference is an enlargement of displacement parameters (Figure S6), which is, however, expected due to the increased temperature. β-Nitrogen Trifluoride. The powder diffraction pattern of β-NF3 (Figure 7) used for structure solution and refinement was recorded at 60 K. Due to the rapid decrease of diffraction intensities with increasing diffraction angle, it is evident that the long-range order in β-NF3 decreases. This agrees with solid state NMR investigations, which showed β-NF3 to be a plastic crystal. The reflections were indexed using the TOPASAcademic program. Due to the small number of reflections suitable for indexing, several different unit cells had to be evaluated. On the basis of the best agreement of the Le Bail fit with the diffraction pattern, a tetragonal unit cell with a = 15.334(6) Å, c = 7.820(3) Å, and V = 1838.6(12) Å3 was chosen. Despite the shortage of data, we solved the crystal structure using the SUPERFLIP algorithm and carried out a Rietveld refinement using the Jana2006 software. We obtained a structure model in space group P42/mnm (No. 136), which describes only the averaged nuclear densities of the NF3 molecules as is expected for a plastic crystalline phase with complete rotational disorder. To refine the rotating NF3 molecules, we employed the anharmonic displacement parameter approach in Jana2006.42 The observed and calculated powder diffraction patterns are shown in Figure 7. Some crystallographic data and details of the structure determination of β-NF3 are given in Table 5. The obtained structure model for β-NF3 contains five crystallographically independent NF3 molecules with their diffraction centers at the special 2b (m.mm), 4f (m.2m), and 8j

Table 5. Selected Crystallographic Data and Details of the Structure Determination of β-NF3 parameters

value

formula molar mass, g/mol cryst system space group Pearson symbol a/Å c/Å V/Å3 Z ρcalc/g cm−3 sample diameter/mm λ/Å T/K Rp, Rwp RBragg(F) (all data), wR(F2) (all data) GOF no. of data points, parameters, constraints, restraints 2θ range measured (min, max, step) 2θ range refined (min, max)

NF3 71.0 tetragonal P42/mnm (No. 136) tP120 15.334(6) 7.820(3) 1838.6(12) 30 2.052 12 1.5484 (neutrons) 60 0.0107, 0.0137 0.0440, 0.0408 2.13 969, 67, 0, 0 0.95, 153.90, 0.05 9.35, 57.8

(..m) Wyckoff positions, and twice on the 8i (m..) Wyckoff positions. Figure 8 shows the observed nuclear density map for β-NF3 obtained by Fourier transformation. The Fourier map does not contain discrete nuclear density peaks of the individual atoms; instead, the probabilities of nuclear positions are shown as isosurfaces of constant nuclear density. We interpret this smearing of the nuclear density as a consequence of the dynamical rotation of the molecules. The asymmetric shapes of the isosurfaces indicate that the rotation is likely not isotropic. The shortest distance between the positions of the refined molecular centers is 3.62(3) Å, which is very close to the shortest N···N distances in α-NF3. The next shortest distances are observed in a range from 4.19(2) to 4.30(3) Å, which is also similar to that for the α-modification. E


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Inorganic Chemistry

composed of two types of triangles and two types of hexagons. The three different vertex configurations are 32.62, 3.6.3.6, and 63 . The second type of layer, the so-called secondary layer, can be described as the semiregular tiling with vertex configuration 32.4.3.4. It is located close to z = 1/4 and is shown in Figure 10. Note that the molecules within this layer are not in direct contact to each other. Both nets are repeated by the 4+2 symmetry operation.

Figure 8. Projection of one unit cell of β-NF3 as produced by the marching cube electron density MCE program.43 The green isosurfaces depict constant nuclear density. The small spheres indicate the refined centers of the NF3 molecules.

Figure 10. Secondary layer in β-NF3 projected along the c axis (around z = 1/4). The corner of the polygons shows the centers of the NF3 molecules.

For the analysis of the crystal structure of β-NF3, we investigated the packing of the NF3 molecules by visual inspection and the ToposPro software. This inspection revealed that the NF3 molecules in the β-modification are packed in the same way as the metal atoms in the CrFe structure type (P42/mnm, Pearson symbol tP30, Strukturbericht designation D8b).44 This so-called sigma phase structure belongs to Frank−Kasper structures in which only tetrahedral voids occur.45,46 The CrFe structure is composed of five crystallographically distinct atoms with coordination numbers 15, 14, and 12. Usually this structure is described in terms of two distinct atomic layers, both running parallel to (001). In Figure 9, the first layer of NF3 molecules, the so-called primary layer, located in a mirror plane at z = 0 is depicted. Within the layer, the intermolecular contacts span a tiling

To summarize, the crystal structure of β-NF3 is a further example of a packing of molecules which resembles the motif of an intermetallic structure. For example, β-F2,47 γ-O2,48 and δ-N249 crystallize in structures closely related to the Cr3Si structure type (Strukturbericht designation: A15). Moreover, some polymers and macromolecules crystallize in packings which occur in various Frank−Kasper phases.50−52

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CONCLUSIONS Using powder neutron diffraction, we characterized two polymorph modifications of nitrogen trifluoride. The lowtemperature modification, α-NF3, crystallizes in the PCl3 structure type, space group Pnma (No. 62). The intramolecular distances in α-NF3 are 1.3639(16) and 1.3677(11) Å for N−F, and 2.1216(16) and 2.120(2) Å for F···F. The bond angles F− N−F are 101.92(7)° and 101.63(10)°. The data from the neutron diffraction experiment are in very good correspondence with the results previously obtained from gas-phase electron diffraction and microwave spectroscopy in the gaseous state. Additionally, we carried out full structural optimization within the DFT method, which showed very good agreement with the experimentally obtained data. The calculated Raman and IR spectra of α-NF3 correspond well to the literature data on liquid and gaseous NF3. The high-temperature phase β-NF3 crystallizes in the tetragonal crystal system, space group P42/mnm. Only the centers of the molecules could be refined, which is a consequence of its plastic crystalline nature. Considering only the positions of the molecules, β-NF3 is isopointal to the σ-phase CrFe structure type. The shortest distance between the NF3 centers equals 3.62(3) Å.

Figure 9. Primary layer in β-NF3 projected along the c axis (z = 0). The corners of the polygons show the centers of gravity of the NF3 molecules. F


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Inorganic Chemistry

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assignment was carried out by visual inspection of the normal modes in the Jmol program package.66

EXPERIMENTAL SECTION

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General. All operations with nitrogen trifluoride were carried out in a stainless steel/perfluoropolymer (FEP) or Monel vacuum lines. As an inert atmosphere, either dry and purified argon (5.0, Westfalen AG, Germany) or helium (5.0, Westfalen AG, Germany) was used so that a possible contact of the inner surfaces of the apparatus and the NF3 with moisture or air was excluded. As vacuum pumps, either twostage rotary vane pumps (pmin = 10−3 mbar) or turbomolecular pumps (pmin = 10−7 mbar) were used. Approximately 4 g of NF3 (Linde, 4.0) was condensed from a nickel bottle into a vanadium sample holder at 69 K. Powder Neutron Diffraction. The powder patterns of NF3 were recorded at temperatures between 6 and 69 K on the SPODI neutron powder diffractometer (λ = 1.5484 Å) at the research reactor FRM II using a vanadium ampule of 12 mm inner diameter and of approximately 60 mm height.33 NF3 was condensed from the gas phase directly into the ampules. Measurements were carried out at 6 K (for α-NF3) and 60 K (for β-NF3), each for ca. 16 h. Refinement of α-NF3. The structure solution of the crystal structure of α-NF3 was carried out using the SUPERFLIP algorithm53 implemented in Jana2006.42,54 The Rietveld refinement of the structure was performed in the TOPAS-Academic software (Version 6).55 An 8-term Chebyshev polynomial was used to describe the background. The peak profiles were fitted with a Pearson VII shape function, and the zero shift was refined. The slight peak asymmetry was corrected with a simple asymmetry correction implemented in TOPAS. To account for a strong preferred orientation, an 8-term spherical harmonic function was used. The anisotropic displacement parameters of all atoms were refined. The U11 parameters for the N(1) and F(1) atoms were fixed at 0.003 and 0.005, respectively. Powder patterns for the studies of temperature dependence were recorded after annealing times of 1−2 min after each temperature change; measurement times were about 10 min each. CCDC 1891640 contains the supplementary data for this structure determination. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via http://www.ccdc.cam.ac.uk/ structures. Refinement of β-NF3. Indexing of the unit cell of β-NF3 was performed in the TOPAS-Academic software. The structure solution and refinement of the crystal structure were carried out using the SUPERFLIP algorithm and the Jana2006 software. A manual background was chosen. The pseudo-Voigt functions were used for fitting the pattern, and the zero shift was refined. The slight asymmetry was corrected by the divergence algorithm implemented in the Jana2006. The averaged nuclear densities of the NF3 molecules were refined using the anharmonic displacement parameter approach. CCDC 1891641 contains the supplementary data for this structure determination. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/ structures. Computational Details. The structural properties of α-NF3 were investigated using the CRYSTAL17 program package.38,39 Both the atomic positions as well as the lattice parameters were fully optimized using the PBE0 hybrid density functional method.56,57 Valence tripleζ + polarization (TZVP) level basis sets,58,59 derived from the molecular Karlsruhe basis sets,60 were applied (see Supporting Information for additional basis set details). Additionally, we checked the significance of weak van der Waals interactions by using Grimme’s D3 dispersion correction.40 The reciprocal space was sampled using a Monkhorst−Pack-type 6 × 6 × 8 k-point grid.61 For the evaluation of the Coulomb and exchange integrals (TOLINTEG), tight tolerance factors of 8, 8, 8, 8, and 16 were used. Default optimization convergence thresholds and DFT integration grids were applied in all calculations. The harmonic vibrational frequencies,62,63 Raman and IR intensities,64,65 were obtained by using the computational schemes implemented in CRYSTAL. A Lorentzian line shape with fwhm of 16 cm−1 was used for the calculation of the IR spectrum. The pseudoVoigt (Gaussian:Lorentzian = 50:50) line shape with fwhm of 8 cm−1 was used for the calculation of the Raman spectrum. The peak

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b00628. Results of quantum-chemical solid state calculations, temperature dependence of lattice parameters, pictures of crystal structures, calculated IR and Raman spectra, and additional basis set details (PDF) Accession Codes

CCDC 1891640−1891641 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Florian Kraus: 0000-0003-4368-8418 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Deutsche Forschungsgemeinschaft and the Deutscher Akademischer Austauschdienst for funding. We gratefully acknowledge the Forschungs-Neutronenquelle Heinz Maier-Leibnitz for granting beam time. A.J.K. thanks CSC, the Finnish IT Center for Science, for computational resources.

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REFERENCES

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Crystal Structures of Î±- and Î²-Nitrogen Trifluoride - Inorganic

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