Intermediate Range Order in Metal–Ammonia Solutions: Pure and Na-Doped Ca-NH3

The local and intermediate range ordering in Ca–NH3 solutions in their metallic phase is determined through H/D isotopically differenced neutron diffraction in combination with empirical potential structure refinements. For both low and high relative Ca concentrations, the Ca ions are found to be octahedrally coordinated by the NH3 solvent, and these hexammine units are spatially correlated out to lengthscales of ∼7.4–10.3 Å depending on the concentration, leading to pronounced ordering in the bulk liquid. We further demonstrate that this liquid order can be progressively disrupted by the substitution of Ca for Na, whereby a distortion of the average ion primary solvation occurs and the intermediate range ion–ion correlations are disrupted.


■ INTRODUCTION
The dissolution of electropositive group I and group II metals in liquid NH 3 yields a rich series of electronic liquids, whose properties are chemically tunable through both the concentration and nature of the parent metal. 1,2 Ca, as a divalent metal, shares many of the fascinating properties commonly associated with the group I metals when dissolved in NH 3 , forming an electrolytic system of solvated electrons at low concentrations and itinerant, metallic liquids as the concentration of Ca is increased. 1,3 As with other metal−ammonia systems, these different electronic states are not miscible and are separated by a forbidden region around a metal−insulator transition whereby a bulk liquid−liquid phase separation occurs, commonly referred to as the immiscibility region in the literature. Unusually, this immiscibility region is extremely pronounced in the Ca−NH 3 phase diagram, with the electrolytic state only surviving to a maximum Ca concentration of 1.68 mole percent metal (MPM) at the consolute point or a critical temperature of 290 K with the onset of phase separation at <0.1 MPM at 200 K. 1,4 For comparison, the Na− NH 3 consolute point is 4.12 MPM and 231 K with phase separation beginning at 1 MPM at 220 K, and in Li−NH 3 , the consolute point is 4.35 MPM at 210 K with phase separation beginning at 2 MPM at 220 K. 5 Such early onset and pronounced liquid−liquid phase separation clearly indicate the stability of, or energetic drive toward, the metallic liquid in Ca−NH 3 solutions.
Previous studies have sought to understand the link between the different electronic states of metal−ammonia systems and their liquid structure, whereby the charge of the metal cation, the extent of screening by the itinerant electron, and the secondary solvation effects from the NH 3 solvent can all be varied. Some metal−ammonia systems, including Li−NH 3 and Ca−NH 3 , have been shown to possess strong intermediate range ordering between ∼6 and 10.5 Å in their metallic phases, whereas other systems such as Na−NH 3 and K−NH 3 do not. 6−9 Interestingly, only those systems which exhibit such strong ordering in their liquid state are known to crystallize as solid phases at their concentration limit. All other metal− ammonia or metal−amine systems precipitate out the metal upon cooling and do not form solid metal−amine phases. Taking only the examples of the Ca−NH 3 and Na−NH 3 systems, it is notable that, despite their similar ionic-radii, 10 Ca−NH 3 possesses distinct intermediate range ordering in the liquid and crystallizes as the expanded metal Ca(NH 3 ) 6 , 9,11 whereas no such liquid order nor any crystalline phases have been witnessed in Na−NH 3 . 8 Herein, we use neutron scattering with combined H/D isotopic substitutions and empirical-potential structure refinements 12 to provide a more detailed study of the Ca−NH 3 system in the metallic phase than has been performed previously. Both the local and intermediate solvation environments of the Ca ions are determined alongside Ca−Ca correlations in the liquid phase. We also demonstrate that the intermediate range order of the Ca−NH 3 solution can be successively disrupted by the introduction of Na.

■ EXPERIMENTAL METHODS
Stoichiometric amounts of mechanically cleaned metal were loaded under argon into a sealed flat-plate null-coherent scattering Ti/Zr container of size 15 mm × 30 mm × 1 mm. The container and sample were attached to a stainless steel gas rig and evacuated to <10 −5 mbar. Appropriate ratios of isotopically unique ammonia (NH 3 /ND 3 ) were premixed to the exact volume required and cryogenically pumped onto the metal samples. The samples were isolated, warmed, and monitored for homogeneity. No notable sample decomposition occurred as monitored by lack of H 2 evolution.
H/D substitution experiments on the Ca−NH 3 and mixed metal NaCa−NH 3 solutions were performed using the SANDALS and NIMROD diffractometers, respectively, at the ISIS Spallation Neutron and Muon Source, UK. 13,14 The sample data were corrected for sample containment, multiple scattering, and incoherent scattering according to standard procedures using the Gudrun package. 15,16 The resultant total structure factor can be expressed as where c i and b i are the atomic fraction and bound coherent neutron scattering length of species i, respectively. S αβ (Q) is the Faber−Ziman partial structure factor, and Q is the magnitude of the scattering vector. The real space function G(r) corresponding to F(Q) is obtained by replacing S αβ (Q) with the partial pair distribution functions g αβ (r) by the signed Fourier transform relationship to give In the current context, G(r) can be written as a sum of three partial pair distribution functions The label H refers to substituted atoms in the sample, and X refers to unsubstituted atomic species. It follows from eq 4 that c H = 1 − c X . Then, the g HH (r) term in eq 3 is calculated from where the subscripts H, D, and HD refer to experiments on the protonated, deuterated, and mixture samples, respectively, and x is the fraction of protonated ammonia in the mixture sample. Then The remaining partial pair distribution functions can be calculated in an analogous way to g HH (r) − 1 in eq 3 Structural models for the liquid systems at 4 and 10 MPM were refined to the respective neutron datasets using the empirical potential structure refinement (EPSR) software. 12 This technique refines a structural model based upon an equilibrated Monte Carlo simulation using seed pair-potentials. These potentials are iteratively modified through the introduction of an empirical potential based upon the difference between simulated and measured, isotopically unique neutron scattering structure factors. Simulation boxes consisted of 6000 molecules within the cubic cell of length 64.588 and 66.674 Å for the 4 and 10 MPM systems, respectively, constructed using the reported densities for the Ca−NH 3 system. The seed Lennard-Jones plus Coulomb potentials used in the refinement are reported in Table 1. The all-atom optimized potential for liquid simulation Lennard-Jones parameters of Jorgensen have been used for NH 3 with an adjustable Coulomb term to ensure net neutrality in the simulations of the itinerant electron systems. 17 The reduced charge of Ca ions was taken as those reported from ab initio simulations for single ions in NH 3 solutions 18 and was found to be necessary for subsequent structural refinement to the experimental neutron data.

■ RESULTS AND DISCUSSION
The experimental neutron total structure factors, F(Q), for metallic Ca−NH 3 solutions at 4 and 20 MPM are presented in Figure 1 for the deuterated, proteated, and mixed proteated−  It can also be seen that the principal diffraction peak in the 2.5−3.0 Å −1 region displays considerable broadening with increasing metal concentration, and the feature between 4.0 and 10.0 Å −1 is distinctly structured in the more concentrated Ca−NH 3 solution.
The origin of these features is clearer when looking at the real space transforms for the neutron data. Figures 2 and 3 show the real space correlation functions, G(r), for the 4 and 10 MPM Ca−NH 3 data, respectively, as well as the extracted partial pair distribution functions, G HH (r), G XH (r), and G XX (r) as defined in eqs 5, 7, and 8. It can be seen that the G XH (r) and G XX (r) partials are far more structured in the 10 MPM Ca− NH 3 solution than they are at 4 MPM in the 2.5−6.0 Å region, indicating a distinctly ordered solvation environment of the Ca ions. In particular, we can assign the feature at 2.52 Å in G XX (r) to the Ca−N distance, being far more pronounced in the 10 MPM solution. Likewise, the narrowing in the most intense feature to 3.2 Å and the appearance of a peak at 5.0 Å can be assigned to cis-and trans-N−N distances, which would be consistent with an octahedral arrangement of NH 3 around Ca. It is interesting to compare these liquid, metallic Ca−NH 3 solutions to solvated, aqueous calcium solutions, 19 whereby the Ca−O distances reported are only slightly shorter at 2.46 Å despite the aqueous ions being 8-coordinate as opposed to 6coordinate for the amines. Turning to the G XH (r) partials, we see again that the 10 MPM system is more structured with correlations presumably being successive Ca−H, N−H distances.
In order to extract more information from the experimental datasets, individual pair distribution functions were determined from EPSR models for both 4 and 10 MPM systems, with refinements reported alongside the experimental data in Figures 1−3. These structural models, refined as they are to the isotopically unique neutron datasets, are a notable improvement on previous Monte Carlo simulations for the Ca−NH 3 solutions. 9 The refinements for both 4 and 10 MPM solutions are well described even down to the low-Q region where the relative intensities of the prepeak in F(Q) are matched across datasets, albeit slightly over-fit in the 10 MPM system. Likewise, the full extent of the structuring of the feature between 4.0 and 10.0 Å −1 in the more concentrated Ca−NH 3 solution is not fully captured by the EPSR model. We can see clearly where this discrepancy arises by examining the simulated G XX (r). The Ca−N distance is correct in the   The Journal of Physical Chemistry B pubs.acs.org/JPCB Article EPSR refinement, but the feature is sharper than in the measured neutron data, where the intensity is moved into the peak wings. This is most likely due to the insufficiencies of the seed and empirical potentials being too "hard" for a good description of the Ca ions in a metallic solution. Nevertheless, the high level of agreement between our structural models and the neutron data lends credence to our extracted pair distributions functions presented in Figure 4.
The pair distribution functions extracted from the EPSR model allow us to confirm our assignment of the Ca−N and N−N distances from the measured neutron data and the origin of the prepeak as being due to Ca−Ca correlations. The structuring of the measured G XH (r) partials in the 10 MPM solution can now be interpreted further as the increasing contribution from the Ca−H correlations at 3.0 Å as the Ca concentration is increased. Only a minor low-r shoulder is seen in the N−H partials, in agreement with the large disruption of any hydrogen bonding in these metallic systems, a commonality of all measured metal−amine systems in their metallic phases. The EPSR models also allow us to determine correlations which are only a minor contribution to the experimental data, such as the secondary solvation of Ca(NH 3 ) 6 in the 4 MPM solution. Clear secondary and tertiary solvation distances are found at 4.8 and 8.2 Å.
In order to build up a three-dimensional picture of the Ca− NH 3 system, Figure 5 details the angular distributions and spatial probability density maps extracted from the refined structural models for Ca−NH 3 solutions. As expected from our assignments of the experimental data, the inner coordination sphere (corresponding to the sharp first peak in g CaN (r) in Figure 4) shows an octahedral arrangement of ammonia nitrogen atoms about the central Ca. This solvation is more regular for the 10 MPM system, with the 4 MPM system having a slightly less well-defined octahedral geometry as demonstrated with the broadening of angular distributions for NH 3 coordinated trans to each other. The second coordination shell (corresponding to the broader g CaN (r) peak in the range of 4.0−7.0 Å) contains those NH 3 molecules not directly bound to the Ca ions in solution and demonstrate a drastic change between those located up to ∼5 Å and those beyond. The second peak in g CaN (r) for the 4 MPM solutions occurs at 4.8 Å, where there is only a minor contribution in the 10 MPM system. This can be assigned to the hydrogen-bonded, secondary solvation of the Ca centers and can be seen in Figure 5 corresponding to a facial approach to the primary Ca(NH 3 ) 6 species. The 10 MPM system exhibits its secondary solvation maximum in g CaN (r) at 5.9 Å, at which distance there is very little angular dependence in the spatial density. This demonstrates that neighboring Ca(NH 3 ) 6 units are only weakly correlated in terms of their relative orientations despite the strong radial correlation between Ca ions in the metallic solutions. While in the 4 MPM solutions, there is no angular correlation in the distribution of Ca ions, in the 10 MPM solution, we do find a slight dominance for a facial approach of one Ca(NH 3 ) 6 unit to the next, consistent with the bcc arrangement of the solid calcium hexammine structure, Ca(NH 3 ) 6 , formed at the pseudo-eutectic point whereby cooling any metallic Ca−NH 3 solution to 185 K excess NH 3 crystallizes out leaving only the expanded metal. 20,21 This expanded-metal hexammine crystallizes in the Im3m space group with a lattice constant, a o = 9.12 Å, and an octahedral orientation of NH 3 molecules around each Ca atom. 11,20 Bond distances in the crystal have been determined as r(Ca−N) = 2.56 Å and r(Ca−D) = 3.12 Å, correlations which we have now . Extracted partial pair radial distribution functions for 4 MPM (red) and 10 MPM (black) Ca−NH 3 solutions. Column 1, from top to bottom: g CaN (r), g NH (r), and g HH (r). Column 2, from top to bottom: g CaN (r), g NH (r), and g HH (r). We have previously suggested that for a metal−amine system to crystallize into an expanded metal upon cooling, there must be a substantial order already present in the liquid both in terms of primary solvation and intermediate range order of the metal centers. This leads to the stability of the pseudo-eutectic and prevents the formation of crystalline NH 3 and metal. Our findings for the Ca−NH 3 system further strengthen this viewpoint and certainly provide a solutionphase limit in the future search for new, crystalline expanded metals.
We can investigate the manner in which the structural order in the liquid Ca−NH 3 system can be disrupted by examining the effect of progressive substitution of Ca by Na. The ionic radii of Ca 2+ and Na + are similar, and both have been determined to be octahedrally coordinated in aqueous salt solutions, but in the case of Na + , there is some uncertainty in this, with the experimentally determined coordination numbers ranging from 4 to 8. 22,23 We should also note that when considering NaCa−NH 3 solutions in their metallic phase, despite maintaining the concentration of metal ions (MPM), the density of conduction electrons in the solution (sometimes referred to as mole-percent electrons) can vary up to a factor of 2 due to the difference in valence between Na and Ca. This conduction electron density is believed to lie predominantly between solvated ion units in metal−amine solutions, and we can thus determine the effect on the liquid structure of varying this electron density through control of the Na/Ca content. Figure 6 reports the experimental neutron structure factors for the 10 MPM, deuterated NaCa−NH 3 system at various Na/Ca ratios. We can clearly see that the pronounced prepeak in Ca−NH 3 rapidly decreases in intensity as the Na content increases, indicating that ion−ion correlations are decreasing, and both the width of the principal peak and structuring of the feature from 4.0 to 10.0 Å −1 decrease. This would indicate a disruption of the octahedral arrangement of the solvated metal ions, which can be confirmed by examining the equivalent data in real space. Interestingly, while the M−NH 3 correlations are still found at ∼2.5 Å, we see a slight shift to shorter bond lengths as the Na content increases, despite the lower charge of these ions, and there is a progressive disruption of the structure in the 3.0−5.0 Å range. This shorter bond is consistent with the Na−N distances previously reported for pure Na−NH 3 solutions in their metallic phase. 8 It is likely that the longer Ca−N distances in Ca−NH 3 is a reflection of the highly structured Ca(NH 3 ) 6 units being more "molecular" in nature than the Na−NH 3 analogue. It is clear that the incorporation of Na ions into the Ca−NH 3 solution disrupts the local solvation structure of the metal ions, with the distinctly octahedral coordination of Ca being lost upon substitution by Na. This in turn leads to a loss of intermediate range order in the mixed-ion solutions.

■ CONCLUSIONS
Despite its molecular nature and the large concentration range over which a metallic phase occurs, the liquid Ca−NH 3 system is structurally quite simple. There is a strong local ordering whereby the octahedral coordination of Ca by NH 3 comprise the solvated ion cores for both the most dilute and more concentrated itinerant electron liquids. The approach of additional NH 3 is toward the octahedral faces, being driven by the formation of hydrogen bonding interactions with the solvated ion cores. Beyond this, further NH 3 molecules still exist in distinct solvation shells but are spatially isotropic. It is striking to note that even at low metal concentrations of 4 MPM, a significant intermediate range order exists in these solutions, with the solvated ion cores being correlated out to >10 Å. This becomes more pronounced and with a shift to a shortened distance of 7.4 Å for the 10 MPM solution. As we have previously noted, this structuring in the liquid state seems to be a feature of metal−amine systems, which undergo crystallization at their concentration limit, and is significantly reduced or absent in those which do not. 24 Furthermore, we have showed that the miscibility of Na− and Ca−NH 3 enables the local and intermediate structure of the bulk liquid to be controlled as a function of the conduction electron density. Sequential disruption of the primary solvation environment upon incorporation of Na is evident from the neutron scattering data, which in turn is reflected in the intermediate range, ion−ion correlations being reduced. Whether this has an effect on the electronic properties of the liquids, or indeed one which can be carried across into any crystalline material, is yet to be determined. It is now clear that, at the very least, the liquid structure for metal−NH 3 and other metal−amine systems is amenable to chemical control.