Structure and chemical bonding in high-pressure potassium silver alloys

Analysis of X-ray diffraction patternsX-ray diffraction patterns of crystalline KAg2, K2Ag, and K3Ag1,2 were observed from compression/decompression experiments starting from mixtures of elemental K and Ag. The X-ray diffraction patterns at 4.13 (KAg2), 4.41 (K2Ag), and 5.88 GPa (K3Ag) are shown in Fig. 1. The X-ray diffraction patterns indicate the presence of residual K mixed from the respective K-Ag alloy phases. The K contamination, however, does not impede the quality of the patterns for Rietveld refinements and MEM analysis. The different phases identified are discussed in detail below.Fig. 1: Representative X-ray diffraction patterns for K-Ag alloys.KAg2 (top) K2Ag (middle) and K3Ag (bottom).KAg2
KAg2 is the lowest pressure compound among the K-Ag alloys identified from the X-ray diffraction data. The phase is observed between 1.56 GPa and 4.2 GPa at room temperature. The results of our analysis confirmed the unit cell reported2. It has a hexagonal P63/mmc space group with lattice parameters a = 5.7237 Å, c = 9.7411 Å and Z = 4 at 2.26 GPa. In the unit cell, the Ag atoms occupy the 2a and 6 h sites and the K atoms are located at the 4 f sites. The X-ray diffraction pattern (Fig. 2) shows the presence of cubic phase I of K (Im\(\bar{3}m\), K-I). A Rietveld refinement on the combined patterns was successful with Rw = 0.91% with the KAg2 to K-I ratio of about 10:1 (see Fig. 2).Fig. 2: Comparison of the Rietveld refined and measured X-ray diffraction pattern of KAg2 at recorded 2.36 GPa.The pure potassium contribution to the pattern belongs to the low-pressure body-centered cubic phase (Im\(\bar{3}m\) K-I). The KAg2 was obtained by releasing the pressure from a higher-pressure phase. Inevitably, different phases in small quality are present in the sample, resulting, for instance, in a weak line at 2θ = 9.7o.An important feature of KAg2 (Fig. 3a) that was overlooked in an earlier study2 is that its crystalline structure can be described by (Ag)4 clusters constructed from two-dimensional (2-D) layers of corner-shared triangular (Ag)3 units in the ab plane (plane A, Fig. 3b) linked through coplanar apical Ag atoms (plane B, Fig. 3c) in the c-direction. The in-plane Ag-Ag distances are identical at 2.84 Å. The distance from the apical Ag to the Ag in the plane is slightly longer at 2.92 Å. The K-Ag distances range from 3.36–3.49 Å. The shortest K-K separation is 3.39 Å.Fig. 3: Structural motifs of crystalline KAg2.The crystal structure is constructed from the precursor face-centered cubic (FCC) Ag. a shows interconnected Ag-tetrahedra (open circles) and K atoms (solid, purple). The Ag atoms are arranged in (b) 2-D quadrilateral (plane B) and hexagonal (Kagome) Ag planes (plane A). c shows the Ag sites replaced by K.When viewed down the c-axis, the A, B planes of Ag stacking resemble that of the precursor FCC Ag with the Ag atoms in the center of the hexagons removed (Fig. 3c). In KAg2, these “voids” are replaced with pairs of K atoms above and below and alternate the positions between planes A and B.A Le Bail refinement20 of the X-ray diffraction pattern was performed to extract the Bragg reflection intensities. Using a set of 19 reflections, convergence in the MEM analysis21 was reached. The electron density (ED) distribution obtained is consistent with the crystalline structure and the Fourier map resulting from the Rietveld refinement (Fig. 4). The MEM-derived valence electron topology (Fig. 4b) shows that the electron densities of the Ag atoms in the planar triangular clusters are spread along the c-direction. The electron density at the K atoms is also slightly distorted from the spherical distribution. The former observation suggests that there may be a covalent interaction between the Ag atoms. The electron density distribution revealed from the 3D Fourier maps, assuming spherical atomic scattering factors, also shows slight distortions around the K and Ag atoms (Fig. 4a). Indeed, an examination of the (004) plane of the Ag3 clusters in both the MEM electron density distribution and the Fourier map indicates the accumulation of electrons between the Ag atoms (Fig. 4c, d, respectively).Fig. 4: Charge Density Distribution in KAg2.Charge density distribution obtained (a) from Fourier analysis of the Rietveld refined results using spherical atomic scattering factors using an iso-surface value of 13.0 e/\({{{\rm{a}}}}_{0}^{3}\) and (b) from the MEM analysis using an iso-surface value of 6.5 e/\({{{\rm{a}}}}_{0}^{3}\). Electron density distribution of KAg2 in the (004) plane from (c) Fourier map and (d) MEM-derived. Note the contour scales for the two plots are different. The units of the scales are e/Å3.K2AgThe synthesis of K2Ag and its crystalline structure was first reported in ref.1. At 4 GPa, the unit cell was reported to be the hexagonal P6/mmm space group with Z = 1 and lattice parameters a = 5.5434 Å and c = 3.770 Å. In the hexagonal unit cell, Ag atoms are at the 1a (0,0,0) position, whereas the K atoms are at the 2d (1/3,2/3,1/2) site. Both atomic species form layers stacked along the c-axis. In the original study, Atou et al.1. noted the absence of (00 l) reflections in the X-ray diffraction pattern, which, with the assumption of preferred orientation, led to the conclusion of the P6/mmm space group.In the present study, high-resolution X-ray diffraction patterns recorded at 2.24 and 3.22 GPa (upon pressure decrease) show the existence of the K2Ag phase. Apart from a minor contribution of the K-I phase, the patterns would be seen in agreement with the proposed P6/mmm unit cell1 if the (001) reflection could be ignored. However, other absent reflections, particularly at higher scattering angles, indicate this is not the case. Table 1 lists the predicted but unobserved reflections below 15o (2θ) with the P6/mmm space group1.Table 1 Predicted but unobserved reflection for P6/mmm space groupA unit cell indexing performed using GSAS-II and JANA2000 predicted a P63/mmc space group, which matches better the X-ray diffraction pattern with the same lattice parameters. The new space group assignment eliminates the discrepancies related to the unobserved reflections as given in Table 1 (except for (301) line observed at 13.52°) and other high-angle reflections. However, by assuming the P63/mmc space group, Ag atoms would need to occupy the 2a sites and K atoms the 4 f sites. In this case, the resulting crystalline structure gives unrealistically short interatomic distances. There are two possible solutions to circumvent this issue to explain the observed X-ray diffraction patterns: (1) partial occupancy of the atomic sites or (2) to invoke the existence of a superlattice by doubling the cell along the c-axis.Before further addressing the pattern refinement problem, we analyzed the electron density distribution derived from MEM analysis in both P6/mmm and P63/mmc space groups. No convergence was achieved using either space group. Nevertheless, upon examination of the crude EDs, we found hints of atomic disordering along the c-axis in both space groups, indicated by a continuous electron density distribution in the [001] direction. The results lead us to advance the possibility of a superlattice. We then constructed a superlattice unit cell by doubling the c-axis for both space groups. In both models, a very good Le Bail fit with Rp less than 1% was obtained. However, the P6/mmm supercell predicts an additional peak at a low scattering angle that was not observed in the experiment.As shown in Fig. 5, ED maps obtained in both space groups clearly show a continuous electron density between the Ag atoms along the c-axis. The “extended” charge distribution is too large for Ag-Ag bonding. We speculate that there may be a “disordered” structure with Ag partial occupancy halfway along the c-axis and between the two equivalent Ag atoms in Wyckoff position 2b. In addition, the electron density distribution around the K sites in the middle of the unit cell also appears to show disorder. Based on this observation, we propose four possibilities for the structure of K2Ag: a supercell (i) with no partial occupancy (i.e., with all atoms in their respective Wyckoff symmetry positions) (ii) with the (0,0,1/4) site partially occupied with Ag (iii) with K atoms displaced from the ideal Wykoff sites, or (iv) with one K and all Ag sites allowed to be partially occupied. We performed a Rietveld refinement on the above-mentioned models without considering the preferred orientation. Table 2 reports the Rw-factor for the refined models in the P63/mmc space group.Fig. 5: ED maps derived from MEM analysis.Supercells in P63/mmc (left) and P6/mmm (right) space groups with non-distorted atomic positions were used. In both space groups, the Ag atoms are located at the corners and the edges of the unit cell, and the K atoms are inside the unit cells. The units of scale are e/Å3.Table 2 Rw agreement factor for the Rietveld refinement of the four proposed structural models in the P63/mmc space groupThe Rietveld refinements show gradual but significant improvements in Rw when a supercell with doubling of the c-axis is adopted and disordering K and Ag atoms when partial occupancy is considered. The results lend support to the “continuous” electron distribution between the Ag atoms due to the disordering as revealed by MEM analysis. The best fit achieved is when partial occupancy of disordered K and Ag sites is considered. It is noteworthy to indicate that low-angle, high-intensity reflections bias the goodness-of-fit parameter, Rw, of the Rietveld refinement. However, a qualitative comparison of the calculated and experimental patterns supports the results of the Rietveld analysis. With no partial occupancy, some unobserved reflections appeared at high angles and their intensities did not fit well. In contrast, when partial occupancy is considered, those reflections disappear, and concomitantly, fits to the intensity of the high-angle reflections improves. Even with the best structural model, not all high-angle features are adequately accounted for. As mentioned in the earlier study, the discrepancy could be due to a preferential orientation of the sample. Indeed, we obtain a significant improvement using a preferential orientation model that reduces Rw to 0.83%. Furthermore, the refined isotropic thermal parameters are also very reasonable. A comparison of the measured and fitted X-ray diffraction patterns is shown in Fig. 6. The final model gives a stoichiometry of K2Ag0.94, almost identical to the ideal composition. The structural parameters obtained from the Rietveld refinement of the final model are presented in Table 3.Fig. 6: Comparison of Rietveld refined and measured X-ray diffraction pattern of K2Ag.Refinement was performed in the P63/mmc supercell with disordered Ag and K atoms (for details see K2Ag section). For this refinement, a preferred orientation is considered leading to an Rw = 0.83%.Table 3 Parameters obtained from Rietveld refinement of the data presented in Fig. 6, considering the disordered K2Ag model in the P63/mmc space groupA similar analysis was performed considering the P6/mmm space group. In this case, the agreement is significantly inferior. Moreover, a diffraction peak at around 2.5o, predicted for the supercell, is not accounted for in the experimental X-ray diffraction pattern. In addition, many predicted high-angle reflections are also not present in the data, resulting in a poor fit. We rule out the possibility of a unit cell with the P6/mmm space group on this basis. Our analysis thus indicates that the best structural model consistent with the measured diffraction patterns of K2Ag has a P63/mmc supercell, with a = 5.604 Å, c = 7.757 Å and Z = 2. The 3D Fourier map (Fig. 7a) with ED obtained from the MEM analysis (Figs. 5 and 7b) shows a remarkable resemblance.Fig. 7: Comparison of 3D Fourier map and electron density distribution obtained from MEM of KAg2.a 3D Fourier map for the disordered structure of K2Ag and (b) superposition of the rescaled Fourier map with the electron density distribution (grey colour) obtained from the MEM analysis.It is worth noting that although the Ag-Ag distance is longer than in the elemental phase, K2Ag maintains the morphology of 2D honeycomb layers, which stack in a (disordered) …A-A-A… manner with layers intertwined with K atoms.K3AgK3Ag is the highest-pressure K-Ag phase observed in this study, up to 13.2 GPa. It typically appears at pressures above 5.5 GPa. It has a cubic Fm\(\bar{3}\)m structure and the unit cell parameter decrease from a = 7.89 Å at 5.5 GPa to a = 7.41 Å at 13.2 GPa1. The X-ray diffraction patterns show the presence of a small amount of the K-I phase, which is taken into account during the full-pattern refinement without complications. Le Bail and Rietveld refinements were conducted on five diffraction patterns measured at different pressures. A comparison of the refined and measured pattern at 5.5 GPa is shown in Fig. 8. In this case, the goodness-of-fit factor, Rw equals 0.84%. In the unit cell, the Ag atoms occupy the 4a site and the K atoms the 4b and 8c sites. The crystalline structure can simply be described with K atoms inserted into the octahedral (4b) and tetrahedral (8c) sites of the FCC Ag lattice and expanding the unit cell parameter from 4.042 Å of pure Ag at 5.5 GPa to 7.89 Å for the K3Ag unit cell at the same pressure.Fig. 8: Rietveld refined and measured X-ray diffraction pattern of K3Ag.The pattern (Fm\(\bar{3}\)m) was recorded at 5.5 GPa.The MEM analysis converged readily on all X-ray diffraction patterns. The 3D ED maps derived from the Rietveld refined patterns at five pressure points are presented in Fig. 9. The 3D electron density distribution around the K and Ag atom locations shows no apparent deviation from a spherical distribution. A detailed examination of the charge density on the (100) and (110) planes, encompassing the Ag-Ag and Ag-K atoms in the unit cell, shows hints of K-K and K-Ag interactions as observed in Figs S1–S10. However, no discernible interactions between Ag atoms are found. This observation is at odds with a previous suggestion4 based on theoretical band structures whereas Ag accepts electrons from K to populate its 5p orbitals leading to the formation of Ag-Ag bonds.Fig. 9: MEM-derived ED of K3Ag at the indicated pressures.The ED at 5.50 GPa has an iso-surface value of 0.77 e/\({{{\rm{a}}}}_{0}^{3}\). All other pressures have an isosurface value of 2.0 e/\({{{\rm{a}}}}_{0}^{3}\).Theoretical analysisElectronic structureAlthough there are ambiguities in the structure of K2Ag, nonetheless, the models proposed above are all based on the same basic structural motif, i.e., the stacking of hexagonal 2D-Ag layers with K atoms situated between the layers, as derived from the P6/mmm space group. As it is not possible to compute the electronic structure of the P63/mmc disordered solid, we employed the ordered P6/mmm structure in the calculation for comparison. The GW disentangled band structures together with the dominant Wannier orbitals in the indicated electronic band regions for KAg2, K2Ag, and K3Ag are depicted in Fig. 10. Examination of the electron band dispersions indicates substantially different chemical interactions for the three K-Ag alloys considered.Fig. 10: GW electronic band structures and dominant Wannier orbitals.(top) KAg2, (middle) K2Ag, and (bottom) K3Ag.In KAg2, the band structure shows mixing of the participating K and Ag atoms. The Ag 4d bands are not distinguishable and are heavily involved in the bonding. Disentanglement into K and Ag atoms is more complicated. The Ag 4d band is broad and extends from −5.5 eV to −4.0 eV. The shape of the dominant Ag 4d Wannier orbitals (Fig. 10, top) is distorted from the ideal atomic orbitals, indicating hybridization with other orbitals. K-Ag bonding is observed from −3 eV to the Fermi level. Above the Fermi level, K orbitals with “d” character start to appear. To accurately disentangle the bands in the lower valence state in K2Ag, we employed a projection-based method with the inner and outer disentanglement energy windows set to −6 eV and 0 eV, respectively. As depicted in Fig. 10 (middle), the disentangled Wannier orbital shows the band mixing is primarily due to the 4d and 5 s orbitals of the Ag atom. The localized bands between −4 eV and −5.2 eV correspond to 4d orbitals of the Ag atoms, which do not participate strongly to the bonding. Similarly, the bands around the Fermi level are disentangled by freezing the electron states up to the Fermi level, with the inner and outer energy windows set to −2 eV and 4 eV, respectively. The Wannier functions around the Fermi level are mostly for Ag 4p. The Wannier orbitals indicate that the Ag 4d and 5 s electrons are strongly mixed with the K orbitals, showing a significant chemical bonding. In K3Ag, the Ag atom dominates the lower energy valence states (Fig. 10 bottom). The 4d bands between −4.5 and 5.0 eV are very narrow and completely isolated from the 5 s with a gap of 1 eV. Using inner and outer energy windows of −1 eV and 2 eV, respectively, with the frozen state set to the Fermi level (i.e. only states up to the Fermi level are included in the wannierization), the Wannier orbitals extracted from the upper valence state and lower conduction bands reveal a significant contribution from K atoms to the bonding states. The Wannier orbital shows a K s, p, and d (\({d}_{{z}^{2}}\) and \({d}_{{x}^{2}-{y}^{2}}\)) hybrid orbital.The analysis of the calculated projected electron density of states (PDOS) corroborates the qualitative description of the chemical bonding in the K-Ag alloys. The Ag and K projected density of states for the three alloys are shown in Fig. 11. With 8 Ag atoms (each with 10 d-orbitals) and four K atoms in the unit cell of KAg2, the 4d density of states dominates the lower valence level from −7 to −3 eV. The 4d contribution relative to 5 s and 5p is relatively significant up to the Fermi level (Fig. 11). In comparison, the PDOS of Ag in K2Ag is more localized between −4.4 and 4.0 eV, albeit mixed with a small amount of 5 s, and did not extend into the upper valence region. The dominance of Ag 5 s between −4.0 to −0.8 eV is discernible. The PDOS of Ag is a mixture of 5 s and 5p orbitals close to the Fermi level (Fig. 11). Clear separation of the 4d and 5 s bands is displayed in K3Ag (Fig. 11). Contributions from the 5p orbitals are becoming more significant around −0.8 eV.Fig. 11: Plane-wave projected electron density of states (PDOS).Orbitally resolved Ag and K PDOS in the valence band of KAg2, K2Ag and K3Ag. Note that different scales were used for the PDOS plots.The K PDOS in KAg2 shown in Fig. 11 indicates strong participation of the 3p orbitals in the entire valence region. In particular, the high PDOS between −5.5 and −3.0 eV overlaps with the Ag 4d and 5 s bands (Fig. 11), showing, unambiguously, Ag-K bonding. The PDOS of K profiles from −3.0 eV to the Fermi level exhibit dissimilarities to the PDOS of Ag (Fig. 11), indicating the likelihood of predominantly K-K interactions. In K2Ag, the distribution of the PDOS of K (Fig. 11) of predominantly 3 s is quite broad between −4.4 eV and −2.0 eV and corresponds well with the 4d and 5 s bands of the Ag atom, indicating K (4 s) – Ag (4d, 5 s) bonding. The predominantly 4 s PDOS profile near the Fermi level from −1.60 eV is not similar to the Ag, so it likely indicates K-K interactions. The K “d” character becomes stronger above the Fermi level. The PDOS of K in K3Ag is less complicated (see Fig. 11). It overlaps with the Ag 5 s from −4.2 to 2.5 eV (cf. Fig. 11). The peak at −0.8 eV matches the Ag 5p in the PDOS of Ag suggesting Ag-K bonding. It is noteworthy to highlight that the PDOS of the Ag atom near or at the Fermi level decreases as the K content increases in the alloy.