The pristine material, black P, is a layered structure that contains six-membered P rings. The known phosphorus-rich polyphosphide of NaP (40) was considered and found to lie on the convex hull. In NaP, one Na coordinates to each [P] subunit–phosphorus motifs that form infinite tubes arranged in helices about theaxis. (40) In previous work, Morris and co-workers found a series of structures containing P cages (Naand Naexhibit Pand Pcages, respectively) (where 0 << 0.43 in NaP) that fall on the convex hull. (38) As the sodium content increases, the next on-hull phases are NaP and Na, which exhibit P helices and four-member P zig-zags, respectively. At the end of sodiation, isolated P ions are found in NaP.

The GA was initiated from low-lying AIRSS-derived phases to avoid the need to extrapolate to entirely new regions of composition space. Evaluating the fitness of child structures as a function of distance from the convex hull, the GA uncovered several motifs from less ordered phases that could not be sampled with any individual technique alone. These new motifs provided a vast library of possible P binding environments to evaluate as potential local environments and motifs that may arise in the amorphous NaP structures formed on cycling. These GA-derived phases were added to the previously constructed (38) convex hull of thermodynamically stable NaP structures in Figure 1 a.

The theoretical structure models (with energies depicted in Figure 1 a) were compared to NaP phases that arise during cycling of black P in NIBs. Black P electrodes were assembled into Na half-cells for electrochemical measurements. Near-theoretical capacity was reached on the first discharge (2510 mA h g, based on the mass of P alone) and one of the highest reversible capacities observed to date of 2074 ± 80 mA h gwithout the use of additives is achieved in the first cycle. The improved capacity may be due to the use of 1.0 M NaFSI in 2-MeTHF as the electrolyte, which differs from the electrolytes used previously (1.0 M NaClOin EC/DMC or 1.0 M NaPFin PC). When compared to PC, methyl acetate, or THF, 2-MeTHF shows improved stability against Li, (41) and similar stability is likely present toward Na, thus improving the electrochemical performance of the NIBs. The experimental P reduction profile was compared to the average voltages for on-hull NaP structures predicted by Morris and co-workers (38) 1 Figure b). When a constant current is applied (C/100), the voltage drops from the open circuit voltage to 1.10 V ( Figure 1 b). This initial voltage drop suggests that Pand Psubunits, such as those found in NaPand the computed structures of Naand Na, may not form electrochemically during sodiation in a NIB. Their absence may be due to the unfavorable energetics involved with breaking the six-membered P rings in black P and re-forming P–P bonds to form the Pand/or Pcages in these structures. Instead a sloping region is seen between 1.10 and 0.63 V, corresponding to 31–420 mA h gand approximate compositions of NaP–NaP. A steep, but short-lived sloping region is observed from 1.10–0.48 V (420–562 mA h g, approximate compositions of NaP–NaP); which is followed by a more shallow, sloping region from 0.48–0.22 V (562–1358 mA h g, approximate compositions of NaP–NaP), implying gradual sodiation of NaP (whereranges from 0.04 to 1.57) from 0.63 to 0.22 V. Following this, a plateau at 0.21 V (ranging from 1358–2340 mA h g, wherecorresponds to 1.57–2.70) is observed with a distinct peak in the d/dplot ( Figure S2 ), which is attributed to the formation of-NaP. (21)

Following the formation of-NaP, a sharpP resonance (fwhm = 10 ppm) emerges at −207 ppm ( Figure 2 b) that is coincident with the plateau at 0.21 V in the electrochemical profile and is assigned to-NaP on the basis of previous (21) (and current; see Supporting Information (SI) XRD characterization at the corresponding state of charge. The set of broadP resonances decrease in intensity near the end of this plateau (1666 mA h g, approximate composition of NaP) consistent with a two-phase reaction of-NaP to-NaP (whereis about 0.6; approximately composition-NaP), and vanish by the end of sodiation at 0.01 V (2510 mA h g, approximate composition of NaP). Herewas quantified based on the capacity and integrating the area corresponding to the shifts of black P (14 ppm),-NaP (−207 ppm), and assuming the integral of the remaining broad resonances corresponds to-NaP).

TheP MAS NMR spectrum for the sample extracted at 0.60 V (approximate composition NaP) spans a broad chemical shift range from the resonance of the pristine material (14 ppm) to the small, sharp peak at −224 ppm ( Figure 2 b). Two pronounced broad peaks with centers-of-mass at −104 and −143 ppm are clearly resolved, these peaks becoming more pronounced as sodiation proceeds ( Figure S8 ). The correspondingXRD pattern of this material does not show any Bragg reflections that are distinct from the pristine material ( Figure S13 ) indicating that an amorphous or highly disordered phase is present in addition to residual black P. At 0.38 V (780 mA h g; approximately NaP;= 1), a broad set of resonances spanning aP chemical shift region from ca. –260 to 40 ppm is again observed, along with the lack of Bragg reflections ( Figure S13 ), suggesting that this phase is also amorphous (-NaP).

Figure 2. Ex situ 31 P MAS NMR spectra (MAS = 60 kHz) of black P recorded at various stages of sodiation/desodiation (right) and the corresponding electrochemistry (left). The circles on the electrochemical profile indicate where cycling was arrested and samples were extracted for the NMR experiments. The 31 P chemical shift of the pristine material, black P (dark gray, 14 ppm), and the final discharge product, crystalline Na 3 P (light gray, –207 ppm) are shown in dashed lines. 31 P chemical shift regions corresponding to P helical motifs and P near the end of chains are shaded in blue and green, respectively.

P MAS NMR spectra were acquired at different stages of (de)sodiation to probe the structural features of various NaP phases ( Figure 2 ) directly. TheP MAS NMR spectrum collected in the first sloping region at 0.90 V (124 mA h g, approximate composition, NaP) is nearly identical to that of the pristine material, with the exception that a weak peak at −227 ppm emerges (see Figure S8 for a magnified version of Figure 2 b). Assignment of this low frequency resonance is not obvious based on its isotropicP shift alone. However, we note that peaks in this region (ca. – 220 to −250 ppm) persist throughout all stages of (de)sodiation, suggesting this region arises from NaP species formed in side reactions, minor NaP intermediates or perhaps Na near P defects (such as the end of a P chain).

Both structural models (and) feature only one independent P position, with isolated P ions. DFT calculations of the correspondingP NMR shifts appear in a similar spectral region (−180 vs −217 ppm forvs, respectively) and fall on either side of the experimentally observed value (−207 ppm). Furthermore, both crystal structures show very little anisotropy based on computed CS tensor values (anisotropy, Δ = 38 ppm and asymmetry parameter, η = 0.41 for; Δ = −39 ppm, η = 0 for), makingP NMR an inconclusive diagnostic for structural determination of this species in the NIBs. However, the reduction of symmetry fromtoresults in four instead of two crystallographically independent Na environments—all of which exhibit characteristicNa quadrupolar coupling constants and asymmetry parameters ( Table 1 and η, respectively). Comparison of theNa MAS NMR of the active materials at the end of sodiation (0.01 V, 2510 mA h g) to simulations of theNa spectra for both structures reveal significantly better agreement with the NaP-structure ( Figure 3 b), supporting the assignment of the formation of NaP-in NIBs.

Figure 3. (a) Crystal structures of Na 3 P- P 6 3 cm (left, calculated) and Na 3 P- P 6 3 / mmc (right). (b) 23 Na NMR (MAS = 60 kHz) of a sample extracted at the end of sodiation (0.01 V, 2510 mA h g –1 , black, bottom) compared to calculated spectra of Na 3 P- P 6 3 cm (purple, middle) and Na 3 P- P 6 3 / mmc (teal, top) at 7.05 (left) and 16.4 T (right). The shaded 23 Na peaks in the experimental spectra correspond to Na in the CMC binder, carbon mixture, and/or SEI ( Figure S7 ). (c) PXRD patterns of NIBs (black, top) compared to calculated patterns for Na 3 P- P 6 3 cm (purple, middle, refined model) and Na 3 P- P 6 3 / mmc (teal, bottom). The asterisk at approximately 27, 2θ denotes the major reflection from KBr, which was used as an internal standard. Inset shows the region containing characteristic reflections for Na 3 P- P 6 3 cm .

Previously, the crystallographic structure of NaP formed on discharge has been assigned as NaP-on the basis of both powder (42) and single crystal (43) XRD characterizations of solid state syntheses of NaP. However, our prior DFT calculations predicted asymmetry phase to be the most stable crystal structure of-NaP (i.e., located on the convex hull). (38) This phase was constructed via species swapping from the NaAs structure (44) and can be rationalized as a distorted variant of a previously reported crystal structure of NaP- (42,43) which resides 0.005 eV·f.u.above the DFT hull. (38) These two structural models ( Figure 3 a) are closely related by a group–subgroup transition of the order 6 ( Figure S17 ). In thestructure, the PNatrigonal bipyramids are distorted and tilted, which can be interpreted as frozen vibrational motion of the NaP-crystal structure, consistent with the anisotropic displacement parameters. The simulated XRD pattern of NaP-shows additional reflections at 31.3° and 33.3° (Cu Kα) that are absent in the otherwise essentially identical pattern of NaP-. Examination of the XRD of NaP samples derived by sodiation of black P in the NIBs revealed similar superstructure reflections and thus lower symmetry ( Figure 3 c). In addition, we find that NaP synthesized using standard solid-state synthesis techniques in our laboratory also exhibits these superstructure reflections ( Figure S16 ), consistent with the formation of NaP-. A Rietveld refinement starting from the calculated structure model was performed on both samples. The refined atomic parameters for the sample synthesized via solid state synthesis differ only marginally from those calculated with DFT ( Table S2 Figures S14 and S16 ). The slightly larger deviation observed for NaP formed electrochemically is attributed to the broadening of the Bragg reflections and thus lower signal-to-noise ratio of the data ( Figure S15 ).

Structural Assignment of P Motifs in Amorphous Na x P (x = 1) During Sodiation

31P NMR resonances to specific local structures. [N.B. 23Na MAS NMR spectra were acquired for all the samples studied (31P spectra (see 1 P 1 (NaP, Na 5 P 6 , Na 5 P 4 , Na 7 P 8 , Na 8 P 7 ) were first calculated (31P site variation that may be observed in the amorphous Na x P phases more fully. Unfortunately, the 31P isotropic shifts calculated for these structural models were associated with a narrow spectral range, or the materials themselves did not exhibit a bandgap (which did not allow us to calculate accurate values for δ iso because the Knight shift contribution that describes the influence of free carriers could not be computed), prohibiting assignment based on isotropic shift alone. However, we found that individual 31P sites within the structural models exhibited distinct differences in chemical shift anistropies (CSAs). Therefore, local 31P environments in the a-NaP phase were examined in greater detail with 2D 31P PASS experiments to separate isotropic and anisotropic chemical shifts and thus enable analysis of the full CS tensors of individual P sites. 2D PASS is particularly useful here, not only because of ambiguity in the isotropic 31P dimension, but these spectra are also broadened by strong intramolecular 31P–31P dipolar interactions With assignment of the crystallographic structure of the final discharge product in hand, the structures of the amorphous intermediates that form during (de)sodiation are now investigated in order to assign the observedP NMR resonances to specific local structures. [N.B.Na MAS NMR spectra were acquired for all the samples studied ( Figure S6 ) and compared with DFT calculations of on-hull structures, but they were less informative than theP spectra (see SI ).] NMR parameters for energetically low-lying compositions corresponding to stoichiometries at or near Na(NaP, Na, Na, Na, Na) were first calculated ( Figure S12 ). The structural diversity computationally accessed in this composition range from known, AIRSS, prototype, and GA-derived structures allows us to sample theP site variation that may be observed in the amorphous NaP phases more fully. Unfortunately, theP isotropic shifts calculated for these structural models were associated with a narrow spectral range, or the materials themselves did not exhibit a bandgap (which did not allow us to calculate accurate values for δbecause the Knight shift contribution that describes the influence of free carriers could not be computed), prohibiting assignment based on isotropic shift alone. However, we found that individualP sites within the structural models exhibited distinct differences in chemical shift anistropies (CSAs). Therefore, localP environments in the-NaP phase were examined in greater detail with 2DP PASS experiments to separate isotropic and anisotropic chemical shifts and thus enable analysis of the full CS tensors of individual P sites. 2D PASS is particularly useful here, not only because of ambiguity in the isotropicP dimension, but these spectra are also broadened by strong intramolecularP–P dipolar interactions (45) – potential interferences that are eliminated in the anisotropic dimension in PASS.

31P isotropic projection shows the presence of (at least) three environments with associated 31P shifts at −29, –78, and −143 ppm that correspond to a-Na x P species (31P sites in DFT models (vide supra). Deconvolution of theP isotropic projection shows the presence of (at least) three environments with associatedP shifts at −29, –78, and −143 ppm that correspond to-NaP species ( Figure 4 a), (with anisotropic projections shown in Figure 4 b–d), the width and asymmetry of the CSA patterns differing noticeably for the three resonances. Sideband patterns were simulated in dmfit (46) 4 Figure b–d, gray) and compared to those calculated forP sites in DFT models ( Figure 4 b–d, purple) with similar compositions ().

Figure 4 Figure 4. (a) Deconvolution of the 31P isotropic projection from 2D 31P PASS experiments (black line) performed on a sample of approximate composition NaP, extracted from a NIB at 0.38 V (780 mA h g–1) during sodiation. Five regions with centers-of-mass at 14 (black P), −29, −78, −143, and −235 ppm are observed. The fit of the line shape from deconvolution is shown in gray. (b–d) Corresponding experimental anisotropic projections from 2D 31P PASS (black, bottom) showing sideband patterns for δ iso = −29 (b), −78 (c), and −143 ppm (d) with the respective fits (middle, gray) compared to sideband patterns calculated for individual P sites in DFT models (top, purple) at MAS = 10 kHz. The corresponding P sites (top) and extended P structures (bottom) are displayed to the right of each sideband pattern and are listed in Table 2.

31P site at δ iso = −29 ppm agrees well with the CS tensor found for one crystallographically independent P site (P2 of P1–P2) in a metastable phase of NaP + 96 meV above the hull ( iso = −78 ppm resonance. Similarly, the 31P environment at δ iso = −78 ppm agrees with the CS tensor found for the third independent P site (P3, of P1–P7) in NaP + 75 meV above the hull that also contains P helices (31P site at δ iso = −143 ppm closely resembles that of the fourth independent P site (P4, of P1–P8) in a second NaP structure + 96 meV above the hull, found via GA ( iso = −104 ppm is not observed in the isotropic projection from 2D PASS. The absence of this and other possible resonances may be due to short spin–spin (T 2 ) relaxation (all sites show T 2 values <1 ms) with respect to the rotor period (100 μs) that significantly lowers the signal over the course of the five consecutive π pulses that are applied during the PASS experiment. Thus, while we can identify individual 31P sites from different structural models that show similar CS tensors to the experimental PASS data, the remaining sites in these helical units may also not be observed due to fast T 2 relaxation and subsequent dephasing and/or overlap in the isotropic projection. TheP site at δ= −29 ppm agrees well with the CS tensor found for one crystallographically independent P site (P2 of P1–P2) in a metastable phase of NaP + 96 meV above the hull ( Figure 4 b, Table 2 ), which contains P arranged in a 3-fold helix that winds through the Na network. (In general, we find that all P atoms that comprise helical fragments are bound to two P atoms and surrounded by four to six Na atoms.) The P1 site of this phase is associated with a chemical shift of −57 ppm, and if present, would likely be obscured by the much more intense δ= −78 ppm resonance. Similarly, theP environment at δ= −78 ppm agrees with the CS tensor found for the third independent P site (P3, of P1–P7) in NaP + 75 meV above the hull that also contains P helices ( Figure 4 c, Table 2 ) but has very different CSA parameters. TheP site at δ= −143 ppm closely resembles that of the fourth independent P site (P4, of P1–P8) in a second NaP structure + 96 meV above the hull, found via GA ( Figure 4 d and Table 2 ), this site corresponding to a terminal unit of a four-member P zig-zag motif, suggesting that this site represents a terminal unit of a P chain (i.e., site of P–P bond cleavage). Although there are exceptions, Δ is generally larger for sites at the end of P chains or in small clusters, in all the calculated structures examined, again supporting this assignment. It is important to stress that we do not believe that the various crystalline structures are formed, simply that CSA parameters consistent with terminal and helical structures appear to be present in the amorphous phase. We note that (in contrast to the one pulse spectra ( Figure 2 b) a well-defined peak for δ= −104 ppm is not observed in the isotropic projection from 2D PASS. The absence of this and other possible resonances may be due to short spin–spin () relaxation (all sites showvalues <1 ms) with respect to the rotor period (100 μs) that significantly lowers the signal over the course of the five consecutive π pulses that are applied during the PASS experiment. Thus, while we can identify individualP sites from different structural models that show similar CS tensors to the experimental PASS data, the remaining sites in these helical units may also not be observed due to fastrelaxation and subsequent dephasing and/or overlap in the isotropic projection.

Table 2. Comparison of the Experimental 31P CS Tensors Obtained for the “NaP” Sample Extracted at 0.38 V during Sodiation and Calculated CS Tensor Parameters for Individual 31P Sites in Structural Models with Stoichiometries at or near NaP 31P site/compound δ iso (ppm) Δ (ppm) η experimental –29 179 0.72 P2 in NaP + 96 meV above hulla –21 171 0.55 experimental –78 –261 0.75 P3 in NaP + 75 meV above hullb –109 –291 0.71 experimental –143 –432 0.87 P4 in NaP + 96 meV above hullb 92c –438 0.85