An Atomistic Understanding of the Unusual Thermal Behavior of the

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

An Atomistic Understanding of the Unusual Thermal Behavior of the Molecular Oxide Tc2O7 Daniel S. Mast,†,‡ Keith V. Lawler,*,†,‡ Bradley C. Childs,† Kenneth R. Czerwinski,† Alfred P. Sattelberger,†,§ Frederic Poineau,† and Paul M. Forster*,†,‡ †

Department of Chemistry and Biochemistry, University of Nevada Las Vegas, Las Vegas, Nevada 89154, United States High Pressure Science and Engineering Center, University of Nevada Las Vegas, Las Vegas, Nevada 89154, United States § Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, United States Downloaded via UNIV OF MELBOURNE on April 22, 2019 at 15:01:31 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

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S Supporting Information *

ABSTRACT: The thermal behavior of Tc2O7 has been investigated by singlecrystal X-ray diffraction of the solid state over a range of 80−280 K and by ab initio molecular dynamics (MD) simulations. The thermal expansion coefficient of the solid was experimentally determined to be 189 × 10−6 Å3 K−1 at 280 K. The simulations accurately reproduce the experimentally determined crystal structures and thermal expansion within a few percent. The experimental melting point and vapor pressure for Tc2O7 are unusually high and low, respectively, in comparison to similar molecular solids. Through investigating the structure and the motion of the solid across a range of temperatures, we provide insights into the thermal behavior of Tc2O7.

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INTRODUCTION Technetium is the lightest radioelement. Spontaneous fission of 238U generates the only natural terrestrial occurrences of the element. Pitchblende, for example, contains approximately 10−10 g of 99Tc kg−1. However, the advent of nuclear fission has produced large quantities of 99Tc, as the isotope accounts for approximately ∼6% of the fission yield products from 235U. Technetium produced in the US nuclear fuel cycle is present in large quantities as pertechenate (TcO4−) in tanks at the Hanford site (WA), and one of their leading solutions to remediate the technetium is vitrification into borosilicate glass.1,2 One of the main challenges to safe and efficient vitrification processes is the volatility of several technetium species under typical vitrification conditions (>1000 °C).3,4 For instance, TcO2 begins to sublime at 900 °C and decomposes into solid Tc metal and gaseous Tc2O7 above 1100 °C.1 Tc2O7 is not the sole volatile species; a red phase with the probable composition Tc2O5 is also known to evaporate.5,6 The unwanted formation of these volatile species results in only 30−70% of the 99Tc being encapsulated during the glass melting process.1,3 Advances in technetium immobilization will require a deeper understanding of the structure and properties of all important oxide phases, especially those which exhibit volatility. It was first noted in 1953 that, while Tc2O7 is volatile under ambient conditions, the solid has an unexpectedly low vapor pressure on the basis of its molecular mass.7 It was also observed that the liquid stability range of Re2O7 spans only a 60 K range while that of Tc2O7 spans a 190 K range. Thus, although rhenium chemistry is often sufficiently close to © XXXX American Chemical Society

technetium chemistry in that it can be used as a nonradioactive surrogate, Re2O7 is a poor analogue to Tc2O7 in this respect. The lack of correspondence here presents challenges for experimentally validating industrial processes where the preferable course of action is working with nonradioactive homologues and assuming analogous behavior. Binary transition-metal oxides that exist in a solid molecular structure under ambient conditions are rare and include Mn2O7,8 Tc2O7,9 RuO4,10 and OsO4.11 Limited temperaturedependent studies of the behavior of these particular oxides exist, presumably due to the toxicity of OsO4 and RuO4, the explosive nature of Mn2O7, and the radioactive nature of technetium. A number of transition-metal fluorides and oxyhalides of groups 6−9 exist as molecular solids. The molecular structures of those species predominately have just a single metal atom in the molecule, although some form cluster structures with two to four metal atoms. A comparison of Tc2O7 with metal-containing molecules shows that the melting point and vapor pressure (Figure 1) are anomalously high and low, respectively. Developing a set of molecular species for comparison required eliminating examples which contained appreciable interactions in addition to dispersive; a thorough rationale for our choice of molecular solids is provided in the Supporting Information. Multiple structural determinations by X-ray diffraction show that Tc2O7 has no significant intramolecular interactions except for dispersive. Inspection of the crystal structure of Tc2O7 reveals a herringbone-type packing Received: August 21, 2018

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DOI: 10.1021/acs.inorgchem.8b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. (a) Melting points of transition-metal compounds with molecular structures and mass.7,45−49 Molecular oxides are represented by red squares, fluorides by blue circles, and oxyhalides by green diamonds. This table is limited to molecular solids where the nearest intermolecular distance is at least 40% greater than the average bond lengths found within the molecular species and where only weak additional van der Waals interactions such as quadrupole−quadrupole interactions should exist. (b) Vapor pressure of transition-metal compounds with molecular structures.8,11,47−62 The extended structure of Re2O7 creates a lower limit for the expected vapor pressure of Tc2O7. that the period of the fastest mode (a −TcO3 breathing mode) is ∼35 fs;27 therefore, a time step of 2 fs was used to adequately sample all the motions of the molecules. For each temperature, the structures were equilibrated with a 10 ps simulation in the isothermal−isobaric (NpT) ensemble. The final snapshots of the NpT trajectories were then propagated for another 10 ps in the isoenthalpic−isobaric (NpH) ensemble to obtain average properties. The NpH ensemble does not use a thermostat, which better represents elastic momentum transfer from collisions and thus atomic displacements. The Langevin damping parameters were selected following literature guidelines for classical simulations: 1 ≤ γ ≤ 10 ps−1 refined to one significant feature with short time test trajectories.20 The atoms had a friction coefficient of 3 ps−1 in the NpT ensemble and 0 ps−1 in the NpH ensemble. The lattice degrees of freedom had a friction coefficient of 1 ps−1 and a fictitious mass of 100 amu in every simulation. The initial structure was a 2 × 2 × 1 supercell (144 atoms) of the optimized crystal structure,27 which was chosen as it was the smallest cell where thermal fluctuations were ≤10% of the target temperature in the short-time test calculations of the damping parameters. The initial velocities came from a randomly generated Maxwell−Boltzmann distribution around the input temperature.

of molecules with D3d symmetry (linear Tc−OBri−Tc axis) that stabilizes the linear geometry without any strong intermolecular interactions (no pseudoextended structures/clusters/ bonding).9,12 Raman spectroscopy indicates that the same molecular structure found in the solid persists into the liquid and gas phases, although the molecular symmetry drops to C2v.13 In addition to the low volatility and high melting point, another temperature-dependent feature stood out. When we redetermined the crystal structure of Tc2O7 at 100 K, the bond lengths reported at room temperature were shorter than those we had measured at cryogenic temperatures.9,12 Given the unusual properties of Tc2O7 as well as the importance of understanding the behavior of this molecule during nuclear waste form production, we have performed a detailed examination through variable-temperature SC-XRD and complementary ab initio molecular dynamics (MD) simulations. Our investigation provides a detailed atomistic picture of the structure as a function of temperature, providing insight into the unique thermal behavior of Tc2O7.

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RESULTS AND DISCUSSION The thermal behavior of crystalline Tc2O7 presents several characteristics warranting further investigation. Counterintuitively, the intramolecular Tc−O bond distances, as measured by SC-XRD, appear to shorten with increasing temperature. Second, as shown in the Introduction, the melting point is anomalously high for a molecular solid bound only by dispersion interactions in comparison with other solids with similar molecular masses. The temperature-dependent properties were examined by measuring SC-XRD data over a range of steadily increasing temperatures from liquid nitrogen (80 K) to near ambient (280 K). The previously reported Pbca structure consistently provided the best structural model over the entire temperature range.9,12 The quality of data and structure refinement did not degrade markedly, as shown by the R values, which ranged from 1.74% to 2.37% with no systematic trend with respect to increasing temperature. The unit cell edge lengths and volume (plot in the Supporting Information) all exhibited positive thermal expansion throughout the temperature range studied. Smooth thermal expansion, observed over the entire temperature range and coupled with very similar structure refinements at each temperature, is consistent with the absence of any phase transitions over this temperature range. The coefficients of

METHODS

The sample for single-crystal X-ray diffraction (SC-XRD) was prepared in a sealed tube by the oxidation of TcO2 with O2 at 450 °C as previously reported.12 SC-XRD data were collected on a Bruker Apex II system equipped with an Oxford nitrogen cryostream. Diffraction data were collected from 80 K through 280 K at 20 K intervals. In order to minimize error, all data sets were collected on the same crystal that was initially cooled to 80 K and warmed as data were taken. In the APEX II suite,14 data reduction was performed using SAINT, the structure was solved with SHELXT,15 and an absorption correction was performed with SADABS.16 Structure solutions were conducted independently at each temperature. Structure refinements against F2 were carried out using the SHELXL refinement package in OLEX2-1.2.17 Plane-wave density functional theory (PW-DFT)18,19 Langevin ab initio molecular dynamics (MD)20−22 simulations were performed with the Vienna ab initio simulation package (VASP) version 5.4.1 using the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof (PBE)23 with Grimme’s D324 semiempirical dispersion correction. The projector augmented wave (PAW)25 pseudopotentials formulated for PBE GW calculations were used to represent the ionic cores with valence configurations 4s24p65s24d5 for Tc and 2s22p4 for O.26 The Γ point alone represented the first Brillouin zone with a plane wave cutoff of 600 eV. The energy convergence criterion for an SCF cycle was 10−5 eV. No electronic or molecular symmetry was imposed on any degree of freedom. Vibrational analysis of a single molecule of Tc2O7 indicated B

DOI: 10.1021/acs.inorgchem.8b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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this discussion, we will refer to the average position of atoms inferred by locating the maximum of the electronic density as the “apparent” positions and bond lengths. We will refer to the actual internuclear separation as the “real” or “instantaneous” bond length. Next, we must consider how increasing vibrational motion from higher temperatures affects the average electron density and thus the apparent bond length. Vibrations in the direction of the metal−oxygen bond will increase the real bond length as well as the apparent bond length. However, vibrations transverse to the metal−oxygen bond vector will result in the lighter oxygen atom following an arc around the metal atom. This type of vibrational motion is referred to as a libration (see Figure 3).31 The magnitude of

volumetric thermal expansion and linear thermal expansion for each cell edge length was fit with R2 values exceeding 0.95 for all fits. The coefficients of thermal expansion are αV = 189 × 10−6 Å3 K−1, αa = 103 × 10−6 Å K−1, αb = 67 × 10−6 Å K−1, and αc = 23 × 10−6 Å K−1. The thermal expansion of solid-state Pbca Tc2O7 is significantly anisotropic with the a crystallographic axis expanding more than the b and c crystallographic axes by factors of 1.5 and 4.5, respectively. This may be rationalized by considering that the linear Tc−OBri−Tc axes of the molecules lie in the [200] plane. The effect of thermal expansion along the a crystallographic axis is largely increasing the empty space between the packed molecules, whereas expansion along the b and c crystallographic axes requires disrupting the herringbone packing configuration that restricts rotation of the tetrahedra. The central linear axis of the molecules has a greater projection onto the c crystallographic axis, explaining why it is the direction most resistant to expansion. While a volumetric thermal expansion coefficient of 189 × 10−6 Å3 K−1 is larger than typical values across all solids, it is consistent with other molecular solids held together through weak van der Waals interactions. For example, the volumetric thermal expansion coefficients for ice (0 °C), aspirin (20 °C), and naphthalene (35 °C) are 151, 92.6, and 422 × 10 −6 Å 3 K −1 , respectively.28−30 The Tc−O bond distances experimentally measured by SCXRD are plotted in Figure 2. The Tc−O bond lengths clearly

Figure 3. Representation of correlated thermal motion which causes the apparent reduction in bond length. Recreated on the basis of the work of Evans et al.32

librations increase as the temperature rises. When the electron density of the atom oscillating on an arced path is modeled with an ellipsoid, the center of the ellipsoid (i.e., the atom position) is determined to be closer than its true position. The magnitude of this phenomenon is amplified at elevated temperatures when the motion is larger. It should be recalled that this shortening is in the apparent bond length;32 the real (instantaneous) bond distance does not decrease at any time. This basic effect may lead to overall negative thermal expansion of the whole system, depending on the extent of the bonding network; in truly molecular solids the negative thermal expansion should be limited to just the bonds. The discovery by Sleight and co-workers of substantial isotropic negative thermal expansion over a very wide temperature in ZrW2O8 prompted significant interest in negative thermal expansion solids.32−35 Since then, a number of families of negative thermal expansion materials have been identified.36,37 The origin of the negative thermal expansion in these solids is somewhat more complex, as phonons must be considered, but a clear theoretical picture is well-established.38 The effect of librations on molecular bond distances has been recognized previously for diffraction experiments,31 and this effect can be corrected for in the software package Platon using Schomaker and Trueblood’s Rigid Body Motion analysis, the TLS model.39,40 When the TLS model is applied at each temperature, it significantly reduces the apparent rate of contraction but does not yield a positive thermal bond expansion for any of the Tc−O bonds (plot in the Supporting Information). To further test if the negative thermal bond expansion in Tc2O7 is due to symmetry constraints of the space group, the TLS model was applied to the structure as solved in

Figure 2. Bond length variation of the metal to the bridging oxygen (top) and terminal oxygen atoms (bottom). Error bars represent standard uncertainty in SC-XRD refinement.

contract across the temperature range of the measurements. In the Pbca space group, the individual molecules are exactly linear and are arranged as (OTer)3−Tc−OBri−Tc−(OTer)3, with the central bridging oxygen sitting on an inversion center. The Pbca asymmetric cell consists of one Tc atom and four unique oxygen atoms, resulting in four unique Tc−O bonds all exhibiting slightly different bond lengths contracting at roughly consistent rates: −3.8 to −5.7 × 10−5 Å K−1. As the potential energy curves which describe bonding are intrinsically anharmonic such that increased vibration always leads to longer average bond lengths, the observation of contracting Tc−O bonds appears counterintuitive. The apparent shortening of Tc−O bonds can be accounted for by initially recalling that diffraction techniques measure average electron density distributions for crystalline solids. In C

DOI: 10.1021/acs.inorgchem.8b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry the lower symmetry space group Pca21. As may be seen by examining the bond lengths and angles (Table S1), the refinement becomes less stable. Since lowering the symmetry does not yield improved R1 values or structural features not present in the centrosymmetric structure, we concluded that the inability to account for librations is not due to a misassigned space group. We examine this issue in detail in the Supporting Information. As conventional bond distance corrections could not adequately explain the temperature-dependent structures of Tc2O7, MD simulations of the solid (at 50, 100, 150, 200, 250, 300, 350, 400, 500, and 600 K and 1 bar) were employed to determine if the negative bond thermal expansion is real and gain insight into the thermal behavior of solid Tc2O7. The MD trajectories confirm the measured positive volumetric thermal expansion. The PW-DFT-optimized edge lengths for the a and b crystallographic axes are only 1−2% smaller than the 100 K experimentally measured values. MD predicts a nearly identical trend for the expansion of the a crystallographic axis as a function of temperature, while the b crystallographic axis expands at a slightly lower rate than for the experiment. On the other hand, the PW-DFT optimized edge length for the c crystallographic axis is ∼1% larger than that in the experiment at 100 K, and MD predicts it to expand at a much lower rate than is observed experimentally. This mismatch between simulated and experimental results stems from the periodicity of the cell and the intrinsic error of the density functional. Average structural information was extracted from a series of snapshots provided by the MD simulations using two different methods. First, the time average of each atomic position can be evaluated; distances between those average atomic positions provide bond lengths consistent with structural methods that provide average structures such as SC-XRD. Results from treating the MD predictions this way are plotted as an orange line labeled as “average” in Figure 4. These trends, as anticipated, follow the experimental data provided by SCXRD. It should be noted that all the atoms were independent and unique during the simulations. However, in the simulation

results, the Tc2O7 molecules are presented as having only two chemically unique oxygen atoms: viz., the terminal and bridging atoms. The result is that only a single bond length is calculated for the terminal oxygen atoms as opposed to the three unique bond lengths of the asymmetric Pbca cell used in the analysis of the SC-XRD data. A different way to extract average bond distances from the MD simulations is to calculate the “instantaneous” atom−atom separation in each snapshot and to average those values. For a completely static structure, this is equivalent to the first method. Extraction of bond distances with this approach yields the purple curve labeled “instantaneous” in Figure 4. In the 50 K trajectory, the overall motion is quite low and the “instantaneous” vs “average” approaches provide nearly identical bond distances, as expected when approaching the limit of a static structure with no thermal motion. The simulations show that all of the “instantaneous” Tc−O bond distances increase with increasing temperature, while the “average” bond distances decrease appreciably. The major difference between the two ways of assessing the bond distance is that transverse thermal motion does not cause an apparent bond length shortening in the “instantaneous” distances (from MD) while it does in the “average” distances (as measured crystallographically). Therefore, the terminal oxygen atoms are undergoing librational motion. We note that the simulated instantaneous bond lengths increase only slightly with increased temperature. The low intrinsic bond thermal expansion is likely why the TLS correction was unable to capture the effect, especially with the large apparent bond contraction from the librations. By inspection of the trajectories in the MD simulations, especially at higher temperatures, the bridging oxygen is undergoing transverse librational motion in a circular path about the line of centers between the Tc atoms (snapshots in the Supporting Information). Correspondingly, the average of the “instantaneous” Tc−OBri−Tc bend increases monotonically from 175° at 50 K to 164° at 600 K. The lower average Tc−OBri−Tc angle coupled with a low energy barrier to go linear27 is the source of the transverse librational motion. The lack of directional dependence to the Tc−OBri−Tc bending vibration is what causes the electron density to be fit with a linear Tc−OBri−Tc; similarly, the single structure “average” Tc−OBri−Tc angle remains ∼180° for all the temperatures simulated. These complexities of the electron density of the bridging oxygen are beyond what can accurately be described without high-resolution charge density studies.41 The MD simulations through 600 K show the same overall molecular motion described above, although it increases in magnitude with temperature. The distinctly herringbone arrangement of molecules persists with no appreciable change. The MD simulations were extended in temperature to further probe the temperature dependence of Tc2O7. While melting was observed at 1100 K (plot in the Supporting Information), additional NpT equilibrations of an expanded 2 × 2 × 2 supercell (with the standard PBE PAW pseudopotentials) were run to improve the description of the thermal behavior of Tc2O7, particularly at higher temperatures relevant to melting. The resultant volume versus temperature curve (Figure 5) takes on the expected sigmoidal shape of a melting curve with three distinct regions. The first region is linear thermal expansion extending up to 600 K that mirrors the experimental thermal expansion data. The volume abruptly increases by 9% at 700 K. The rapid growth of the volume persists until 1000

Figure 4. Bond length variation in Tc2O7 for a single structure with positions averaged over an MD simulation (average) and the average of the bond lengths oberserved in each snapshot (instantaneous). The temperature is the average temperature during the 10 ps NpH MD simulation. D

DOI: 10.1021/acs.inorgchem.8b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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At this time, this could only be feasible with a classical force field. Apart from the broad transition region and too high melting point, the effects of periodicity are also apparent from a lack of a good fit to a low-order polynomial through the second region700 and 800 K have volumes that are too similar. We interpret this as the molecules trying to nucleate but being confined by their motions still being too correlated over the medium range. If the experimental volumetric data could be extended to the melting point, we could determine if the solid does experience the disordered premelt expansion of the second region or if that is purely an artifact of the simulations. Significant insights into the unique thermal properties of Tc2O7 may be gained from the simulations. The molecules are strongly interlocked in their [200] planes, and this interlocking persists until a transition related to melting occurs. This confirms previous speculation that the herringbone interlocking is the origin of the high melting point for Tc2O7 in comparison to other molecular solids. The interlocking is twodimensional but is stronger in the [001] direction, as can be inferred by the experimental thermal expansion values. It is only once the interlocking in the [001] direction is broken that Tc2O7 melts (computationally), and the breaking of the interlocking in the [001] direction is prompted by the breaking of the interlocking in the [010] direction. As the herringbone structure breaks up due to large thermal motion, the unit cell expands considerably. In other words, once the thermal motion overcomes the packing, a crystalline-like phase persists, but with far larger volumes as the strengths of the intermolecular interactions are far weaker without the interlocking molecular arrangement. This strongly supports the previous hypothesis that the high lattice energy for a dispersion-bound molecular structure is due to the herringbone packing. The three distinct regions of the melting curve are also evident in the “instantaneous” Tc−OBri−Tc bond angles as a function of temperature (Figure 6). The bond angles

Figure 5. Volume of a unit cell of Tc2O7 as a function of temperature from the NpT MD equilibrations. The three regions of the heating curve are indicated with the following: linear solid expansion, yellow squares; premelt rapid expansion, orange diamonds; the melt, red triangles. The linear fits to the solid and melt regions are shown with dashed lines in their respective colors. The cooling curve of the melt is shown with blue circles.

K, when the system resumes linear expansion. These three regions can be simply divided into solid expansion, the system attempting to melt, and the liquid. The Tc2O7 molecular units remain intact throughout each of the three regions. Using linear fits of the solid and melt regions, the density of liquid Tc2O7 is estimated to be 15.2−15.9% (15.4% at the melting point, 393 K) less than the density of the solid from 0 to 600 K. Analysis of the molecular motions within the second region helps to better understand the behavior of Tc2O7 as it melts, where experimental data is scarce (select movies are given in the Supporting Information). Tc2O7 remains a crystalline solid in the 600 K simulationthe molecules remain tightly aligned in the [200] planes, and the atomic motion is largely limited to the librations of the oxygen atoms. The rigid molecular alignment relaxes some at 700 K with the Tc−OBri−Tc axes of the molecules beginning to rotate independently of the other molecules, but the Tc−OBri−Tc molecular axes remain confined to the [200] planes. The motion at 800 K is similar to that of 700 K but with limited rotation of the −TcO3 pertechnetate groups. At 900 K, the Tc−OBri−Tc molecular axes are no longer confined to a [200] plane. However, the molecules remain within the same molecular volumes they occupy in the solid with the planes separating the molecules still visually apparent at their crystallographic positions of c = 1/4 and c = 3/4. Tc2O7 has melted at 1000 K, as the molecules are displaying liquidlike motion and can move out of the distinct volumes that they occupy in the solid. There are a number of challenges to accurately simulating melting computationally. Periodic boundary conditions are a practical necessity to accurately model both solids and liquids, but they impose periodicity even when the most favorable state does not possess periodicity. Computational complexity typically limits DFT simulations to a modest total number of unit cells and relatively short total times. Nucleation is highly improbable to occur on the size and time scales possible in ab initio simulations, effectively locking a material into a solid form and preventing phase transitions such as melting from occurring. While the expanded 2 × 2 × 2 simulations had the desired effect of improving the description of melting, much larger scales are required to more closely replicate experiment.

Figure 6. “Instantaneous” Tc−OBri−Tc bond angle as a function of temperature from the heating and cooling NpT MD equilibrations. The markers are the same as in Figure 5.

monotonically decrease from 177.4° at 1 K to 162.5° at 600 K. After that, the bond angles take on large decreases as a function of temperature, resulting in a much steeper descent until melting. After computational melting, the angle remains nearly constant around 144°. This helps to explain one counterintuitive feature of solid Tc2O7. Previous liquid- and gas-phase studies13 as well as our recent computational27 work show that the lowest energy configuration of Tc2O7 is bent E

DOI: 10.1021/acs.inorgchem.8b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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and corresponding low vapor pressure results from molecules packing with a herringbone-like motif.

while the experimental crystal structure shows a 180° Tc− OBri−Tc angle. The favorable herringbone packing requires this linear conformation of the molecule, despite an isolated C2v Tc2O7 molecule being ∼5 meV lower in energy than a D3d molecule.27 As the crystal packing forces gradually decrease from thermal expansion, the angle gradually decreases. As the herringbone packing itself breaks apart, the angle lowers toward lower energy values. When liquid conditions are achieved, it is remarkable that the computed equilibrium angle so closely resembles the experimental gas-phase angle of 143.6° for Re 2 O 7 from electron diffraction.42 We previously rationalized that the appearance of a bent Re2O7 despite its ground-state structure being linear was because of strong thermal motions, and these data on similar Tc2O7 molecules corroborate that rationalization. A one-phase approach to simulating melting should result in a hysteresis curve (whose width depends on the simulation size),43 and the actual melting point can be extracted from the heating and cooling transition temperatures.44 To that extent, NpT MD equilibrations cooling the melt at several temperatures were run. The starting structure was a snapshot taken from the end of the 1000 K heating MD simulation. The cooling curve in Figure 5 does not reconvene with the heating curve to produce a hysteresis loop. The snapshots of the cooled structures (final snapshot of 1 K simulation in the Supporting Information) show disordered molecules with no obvious adherence to the molecular planes of the solid, which confirms the system remained in the melt at all temperatures examined. Unfortunately, this system size and time scale examined are too small for the more difficult process of nucleation from a liquid to occur. The “instantaneous” Tc− OBri−Tc bond angles in the melt exhibit a curious trend, starting at 144° at 900 K and becoming monotonically more linear until 600 K, after which they fluctuate between 150 and 155°. It should be noted that the 900 K cooling simulation produced a larger volume in comparison to the molten heating simulations. This is because the PW-DFT G vectors of the cooling simulations were reset to the larger molten initial volume, which reduces the Pulay stress and affords a more accurate predicted volume for the melt. Fitting the cooling curve with its better melt volume to a quadratic function refines the prediction for the density of liquid Tc2O7 to 7.2− 11.8% (8.5% at the melting point, 393 K) less than the density of the solid from 0 to 600 K.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b02368. Metric for molecular solids, experimental thermal expansion plot, bonding parameters as a function of temperature for fits in Pca21, small cell volume versus temperature MD plot, electron localization function and charge density plots to demonstrate molecular nature, MD snapshots, and plots of MD volume versus time (PDF) Movie of a portion of the 600 K NpT MD trajectory (MPG) Movie of a portion of the 700 K NpT MD trajectory (MPG) Movie of a portion of the 800 K NpT MD trajectory (MPG) Movie of a portion of the 900 K NpT MD trajectory (MPG) Movie of a portion of the 1000 K NpT MD trajectory (MPG) Accession Codes

CCDC 1900429−1900439 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 Authors

*E-mail for K.V.L.: [email protected]. *E-mail for P.M.F.: [email protected]. ORCID

Daniel S. Mast: 0000-0002-6020-9100 Keith V. Lawler: 0000-0003-1087-5815 Paul M. Forster: 0000-0003-3319-4238 Notes

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The authors declare no competing financial interest.

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CONCLUSION In conclusion, Tc2O7 is a molecular oxide with an unusually low vapor pressure and high melting point. A combined SCXRD and DFT-MD study provides a consistent picture of the temperature-dependent changes. Thermal expansion is anisotropic, with the relative stiffness of the axes corresponding to the degree of alignment of the central bonding and compression axis. X-ray diffraction measurements indicate apparent negative thermal bond expansion for all Tc−O bonds in the molecule. Simulations show that the bonds do exhibit normal positive thermal expansion when they are viewed instantaneously and that the apparent negative thermal expansion is due to librational motion. While the limits of size and length scales which are tractable to simulate prevent directly simulating melting, they do provide information related to how the herringbone structure is disrupted prior to the onset of melting. These simulations offer significant evidence to support the hypothesis that the high melting point

ACKNOWLEDGMENTS The authors gratefully acknowledge computational resources and support provided by the UNLV National Supercomputing Institute. D.S.M. acknowledges support under an Integrated University Program Graduate Fellowship. This research was sponsored by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Cooperative Agreement #DE-NA0001982. This material is based on work supported in part by the Department of Energy, National Nuclear Security Administration, through the Nuclear Science and Security Consortium under award number #DE-NA-0003180.

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REFERENCES

(1) Darab, J. G.; Smith, P. A. Chemistry of Technetium and Rhenium Species during Low-Level Radioactive Waste Vitrification. Chem. Mater. 1996, 8, 1004−1021.

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DOI: 10.1021/acs.inorgchem.8b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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DOI: 10.1021/acs.inorgchem.8b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b02368 Inorg. Chem. XXXX, XXX, XXX−XXX