Phase relations in K${}_x$Fe${}_{2-y}$Se${}_2$ and the structure of superconducting K${}_x$Fe${}_2$Se${}_2$ via high-resolution synchrotron diffraction

Superconductivity in iron selenides has experienced a rapid growth, but not without major inconsistencies in the reported properties. For alkali-intercalated iron selenides, even the structure of the superconducting phase is a subject of debate, in part because the onset of superconductivity is affected much more delicately by stoichiometry and preparation than in cuprate or pnictide superconductors. If high-quality, pure, superconducting intercalated iron selenides are ever to be made, the intertwined physics and chemistry must be explained by systematic studies of how these materials form and by and identifying the many coexisting phases. To that end, we prepared pure K${}_2$Fe${}_4$Se${}_5$ powder and superconductors in the K${}_x$Fe${}_{2-y}$Se${}_2$ system, and examined differences in their structures by high-resolution synchrotron and single-crystal x-ray diffraction. We found four distinct phases: semiconducting K${}_2$Fe${}_4$Se${}_5$, a metallic superconducting phase K${}_x$Fe${}_2$Se${}_2$ with $x$ ranging from 0.38 to 0.58, the phase KFe${}_{1.6}$Se${}_2$ with full K occupancy and no Fe vacancy ordering, and a oxidized phase K${}_{0.51\left(5\right)}$Fe${}_{0.70\left(2\right)}$Se that forms the PbClF structure upon exposure to moisture. We find that the vacancy-ordered phase K${}_2$Fe${}_4$Se${}_5$ does not become superconducting by doping, but the distinct iron-rich minority phase K${}_x$Fe${}_2$Se${}_2$ precipitates from single crystals upon cooling from above the vacancy ordering temperature. This coexistence of separate metallic and semiconducting phases explains a broad maximum in resistivity around 100 K. Further studies to understand the solubility of excess Fe in the K${}_x$Fe${}_{2-y}$Se${}_2$ structure will shed light on the maximum fraction of superconducting K${}_x$Fe${}_2$Se${}_2$ that can be obtained by solid state synthesis.

Figure 1

Unit cells for (a) hypothetical $I4/mmm$ fully occupied KFe${}_2$Se${}_2$ and (b) Fe vacancy ordered K${}_2$Fe${}_4$Se${}_5$, which is equivalent to K${}_{0.8}$Fe${}_{1.6}$Se${}_2$. Fe/Se nets are viewed down the $c$ direction in (c) and (d).

Figure 2

Rietveld refinement to high-resolution synchrotron diffraction data for powder K${}_2$Fe${}_4$Se${}_5$ shows a pure compound with nearly complete vacancy ordering: Only 7% of the Fe $4d$ sites are occupied. Low-angle peaks corresponding to the $I4/m$ cell due to Fe ordering are arrowed. High-$Q$ data are enlarged in the inset to show fit quality. Structural details are given in Supplemental Material.[32]

Figure 3

Reciprocal space reconstruction of single crystal x-ray diffraction data from a nominal K${}_2$Fe${}_4$Se${}_5$ crystal. Reflections are labeled with Miller indices of the $I4/mmm$ ThCr${}_2$Si${}_2$ substructure. The fractional superstructure peaks, including the labeled peak at ($\frac{1}{5}\frac{3}{5}0$), arise from vacancy ordering and lowering of symmetry to $I4/m$ The (010) reflection is forbidden by both $I$-centered cells and represents a new, coherent phase. Subsequent analysis in this paper confirms it to be an oxidized phase with $c=9$ Å.

Figure 4

Rietveld refinement to high-resolution synchrotron diffraction data for a nonsuperconducting, ground single-crystal sample of nominal K${}_2$Fe${}_4$Se${}_5$ composition. This sample displays $I4/m$ vacancy ordering.

Figure 5

The reciprocal space reconstruction along the (100) direction of the parent $I4/mmm$ K${}_{0.8}$Fe${}_{1.6}$Se${}_2$ lattice shows that the extra reflections, including (010) from Fig. 3, lie along an $l$ index that is distinct from K${}_{0.8}$Fe${}_{1.6}$Se${}_2$. This distinct spacing is shown with $d=9$Å. An intensity linescan along $00l$ in (b) shows that these spots arise from a phase where the FeSe interlayer spacing is 9 Å, as opposed to $c/2=7$Å for K${}_2$Fe${}_4$Se${}_5$.

Figure 6

Powder XRD of the K${}_2$Fe${}_4$Se${}_5$ after exposure to moist air shows conversion to the oxidized phase K${}_{0.51\left(5\right)}$Fe${}_{0.70\left(2\right)}$Se with the PbClF structure, containing buckled K${}^{+}$ layers and Fe vacancies. Results from single-crystal structure solution are given in the Supplemental Material.[32]

Figure 7

Reciprocal-space reconstruction of a superconducting crystal of nominal K${}_{0.85}$Fe${}_{1.9}$Se${}_2$ composition, with the octagon of twinned peaks corresponding to K${}_2$Fe${}_4$Se${}_5$. Reflections are labeled with Miller indices of the $I4/mmm$ substructure. Again, the (110) peak is present due to formation of the oxidized phase after minor air exposure.

Figure 8

Comparison of diffraction peaks for powder K${}_2$Fe${}_4$Se${}_5$ versus nonsuperconducting crystals (nominal K${}_2$Fe${}_4$Se${}_5$) and superconducting crystals (nominal K${}_{0.85}$Fe${}_{1.9}$Se${}_2$). All data were collected at 300 K. In (a), the synchrotron diffraction peak (002) shows a split of the c-axis in the SC sample. In (b), the magnified (110) peak shows significant disorder in the $ab$ plane in both crystals. In (c), the magnetic (011) reflection viewed by neutron diffraction from HIPD shows strong magnetic ordering in the powder, weak magnetic ordering in nominal K${}_2$Fe${}_4$Se${}_5$ crystals, and no magnetic ordering in superconducting nominal K${}_{0.85}$Fe${}_{1.9}$Se${}_2$.

Figure 9

Rietveld refinement to high-resolution synchrotron x-ray diffraction data of a superconducting sample of nominal K${}_{0.85}$Fe${}_{1.9}$Se${}_2$ composition displays peak splitting corresponding to a distinct $I4/mmm$ phase at room temperature. Selected regions are expanded in (a), (b), and (c) to show detail on equivalent pairs of reflections. The labeled peaks would be coincident for both phases in the absence of lattice distortions.

Figure 10

Lattice parameters for the bulk K${}_x$Fe${}_{2-y}$Se${}_2$ phase with $I4/m$ structure obtained from Rietveld refinement of high-resolution synchrotron diffraction data display a narrow range of $c$ axis for superconducting samples, but only in crystals grown from the melt. Temperatures of pre-reaction and subsequent crystal growth are shown for each sample. Refined parameters and detailed synthesis conditions are given in the Supplemental Material.[32]

Figure 11

K and Fe content from Rietveld refinements of the majority $I4/m$ phases in superconducting (SC) and nonsuperconducting samples show no clear distinction between the two groups. Fe tends to be slightly deficient in superconducting samples. Fe valence derived from Rietveld-refined stoichiometry shows a strong tendency for majority Fe${}^{2+}$ in the $I4/m$ phase.

Figure 12

Synchrotron x-ray diffraction Rietveld refinement of a vacancy-disordered, nonsuperconducting K${}_{0.959\left(4\right)}$Fe${}_{1.606\left(6\right)}$Se${}_2$ powder sample with fully occupied K sites. Refinement results are given in the Supplemental Material.[32]

Figure 13

Trends of $a$ and $c$ lattice parameters at 300 K across the K${}_x$Fe${}_{2-y}$Se${}_2$ phase space, as determined by Rietveld refinement to high-resolution synchrotron diffraction data. The trend implies that the minority phase in superconducting samples is very K-deficient and distinct from the stability regions of pure $\beta$-FeSe or $I4/m$ K${}_2$Fe${}_4$Se${}_5$.

Figure 14

Magnetization of a superconducting sample of nominal K${}_{0.85}$Fe${}_{1.9}$Se${}_2$ composition.

Figure 15

Heat capacity of a superconducting crystal shows a very small anomaly at $T_c$. This feature is magnified in (b) by subtracting the $H=1$ T measurement from the zero-field measurement.

Figure 16

Resistivity of nonsuperconducting K${}_2$Fe${}_4$Se${}_5$ crystal and a nominal K${}_{0.85}$Fe${}_{1.9}$Se${}_2$ superconducting crystal. The K${}_2$Fe${}_4$Se${}_5$ is an insulator, but the superconductor behavior can be fit as a metallic and insulating composite over the full temperature range.