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Pressure-Stabilized Ir in a Superconducting Potassium Iridide Jakoah Brgoch, and Martin Hermus J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06732 • Publication Date (Web): 18 Aug 2016 Downloaded from http://pubs.acs.org on August 21, 2016

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The Journal of Physical Chemistry

Pressure-Stabilized Ir3– in a Superconducting Potassium Iridide Jakoah Brgoch* and Martin Hermus Department of Chemistry, University of Houston, Houston, TX 77204 Texas Center for Superconductivity at the University of Houston (TcSUH), Houston, TX 77204

Abstract The first charge-separated iridide (Ir3–) in an extended solid is identified at elevated pressure when combined with potassium. Using an unbiased structure searching method that combines first principles calculations with particle swarm optimization algorithms, K3Ir in the Cu3Ti-type structure shows a favorable formation enthalpy (ΔH) compared to the elements and is dynamically stable above 10 GPa. This novel semiconductor (Eg ≈ 1.6 eV) has sufficient orbital separation to allow complete charge transfer from K to Ir while a Bader charge analysis supports the formation of a formally anionic Ir3–. Further, electron-doping K3Ir through Pt substitution makes the system metallic and electron-phonon coupling calculations indicate K3(Ir0.875Pt0.125) falls in the strongcoupling regime with a predicted superconducting transition temperature (TC) of ≈27 K at 20 GPa. These results suggest that systems containing elements isoelectronic to classic BCS superconductors like mercury may have an increased probability of showing a superconducting transition.

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Introduction The late 5d transition metals like Pt, Au, and Hg contain some of the most distinctive crystal chemistry on the periodic table due to their propensity to both oxidize and become cationic or reduce and become anionic.1,2 The ability to gain electrons stems from a combination of relativistic effects and the lanthanide contraction, which causes a massive effective nuclear charge on the valence electrons.3-5 Consequently, these metals have unusually high electron affinities; in fact, the electron affinity for Pt is 2.13 eV while Au is 2.30 eV, which are both greater than many main group elements including sulfur (2.08 eV).1,4 The most notable compound with an anionic transition metal is cesium auride, CsAu, which adopts the CsCl-type crystal structure.6 Although assigning formal charge in extended solids is often ambiguous; a combination of 197Au Mössbauer,7 electrochemical studies,8,9 and computational modeling provides definitive support for the presence of Au–. Anionic Pt2− is considerably rarer. As a binary phase, there is only one example of a platinide, Cs2Pt.10 This compound is structurally related to alkali metal monochalcogenides, e.g., Cs2S, Cs2Se, and Cs2Te, and yields dark-red, transparent crystals indicating charge separation and highly ionic bonding in support of Pt2−. Beyond unique crystal chemistry stemming from intrinsic relativistic effects, applying external high pressure can also enhance the formation of fascinating compounds.11,12 For example, the completely filled Cs 5p electrons can be activated at high pressure to form crystalline CsFn (n>1) compounds.13 The bonding in these phases resembles XeFn advocating for the massive changes in electronic structure that can arise due to pressure. Applying pressure to (CsCl-type) CsAu can also lead to a predicted structural transformation above 14 GPa due to changes in gold orbital hybridization.14 Numerous other novel compounds have been discovered by increasing pressure including chemical reactions with noble gas elements even though they are “inert”,15,16 the discovery of new lithium crystal structures,17 and allowed the synthesis of novel nitrides18,19 and hydrides.20-22 High pressure has even lead to exceptional physical properties most notably with the discovery of high temperature superconductivity in sulfur hydride with its critical temperature of 203 K at 90 GPa.23 In fact, this result verified the prediction of hydrides undergoing a superconducting transition at high pressure.24 Beyond hydrides, transition metal-based systems like AuTe2,25 polymorphs of IrTe2,26 and compositions within the Ca–Li systems27 have also shown pressureinduced superconductivity. The origin of conventional superconductivity in these phases is combination of light and heavy elements producing high frequency phonons, rigid covalent bonding, and potentially contracted d-wavefunctions,23,28 all of which contribute to strong electron-


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phonon coupling and can be augmented by pressure. Yet, it remains unclear how far applying extreme pressure can push the quest for new superconducting phases. The research presented here highlights this dual effect that applying pressure can have on chemical systems. We demonstrate that pressure can lead to enhanced chemical reactivity in transition metals leading to rare oxidation states, most notably the formation of an iridide (Ir3−) anion. One of the most likely systems to achieve Ir3– under pressure, based on ionic size and electron affinities, is by combining monovalent potassium with iridium in the binary composition K3Ir. Because the crystal structure of this compound is unknown, density functional theory (DFT) in conjunction with a non-biased automatic structure search method based on the particle swarm optimization (PSO) algorithm is employed to find favorable crystal structures at ambient and nonambient conditions.29 These calculations lead to the first report of a charge-separated Ir3– anion. Additionally, the presence of Ir3– in this system makes the system isoelectronic with classic BCS superconductors like mercury. This research, therefore, explores the possibility of superconducting transition via electron-phonon coupling calculations in an electron-doped, metallic system. In combination, these results not only expand the number of known transition metals that can accept electrons and act as anions but it also provide new evidence for targeting anomalous superconductivity under pressure.

Computational Details Structure search A search for novel K3Ir crystal structures was conducted using particle swarm optimization (PSO) algorithms as implemented in the CALYPSO code,30,31 which efficiently searches the entire free energy surface calculated using DFT. These calculations target the general composition K3Ir with the number of formula units ranging between 2 to 4 yielding system sizes of 8, 12, and 16 atoms. The structure search was conducted at pressures of 1×10−4 GPa (i.e., 0 GPa) to 100 GPa in steps of 25 GPa. In the PSO, subsequent generations were developed based on the calculated enthalpies, where the best (lowest enthalpy) 60% from the preceding generation were carried over and the remaining 40% were randomly generated. This search produced 600 crystal structures over 30 generations. Final structural optimizations on the PSO identified structures were conducted for all crystals structures that had a negative formation enthalpy and were dynamically stable; this yielded two possible K3Ir candidate structures.

Electronic structure, chemical bonding, and phonon calculations



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All structural relaxations, total energies, and chemical bonding analysis were carried out using the Vienna ab initio Simulation Package (VASP),32,33 which employs a plane-wave basis sets and projector-augmented-wave (PAW) potentials.34 Exchange and correlation were treated with the generalized gradient approximation parameterized by Perdew, Burke, and Ernzerhof (GGA-PBE).35 The atomic positions and unit cell volumes were allowed to relax with the electronic structure calculation convergence criterion set to 1x10–8 eV and the ionic relaxation set to 1x10–2 eV/Å. A cutoff energy of 400 eV was chosen and a dense Gamma-centered Monkhorst-Pack k-point grid36 of at least 1000 k-points/atoms–1 was used for integrations within the first Brillouin zone. The bandgap of this phase was also estimated using the screed hybrid exchange and correlation functional of Heyd-Scuseria-Ernzerhof (HSE06).37 The mixture between PBE and Hartree-Fock was set to

75% PBE and 25% HF with a screening length of 0.2 Å–1. The vibrational properties were calculated based on the ab initio force constant method using PHONOPY.38,39 To construct the force constant matrix, forces were calculated by VASP on 2×2×2 supercells with symmetry independent atoms displaced from equilibrium 0.01 Å in the plus and minus direction. Chemical bonding analyses were based on the density of states (DOS) and the projected crystal orbital Hamilton populations (COHP) as implemented in the LOCAL-ORBITAL BASIS SUITE TOWARD ELECTRONIC-STRUCTURE RECONSTRUCTION (LOBSTER) code.40-42 The electron localization function (ELF)43 was also used to examine charge redistribution and bonding features in addition to the – COHP curves.

Electron-phonon coupling calculations All-electron full-potential linearized augmented-plane wave calculations were conducted using the ELK code44 on the VASP-relaxed crystal structures to determine the electron-phonon coupling constants. A supercell approach and a k-mesh of 24×24×24 (2×2×2 q-mesh) was used for calculating the phonons while the superconducting critical temperature (Tc) can be estimated in the strong-coupling regime following McMillan-Allen-Dynes28 shown in equation 1. =

−1.04(1 + ) 1.2 − ∗ (1 + 0.62)

(1)

where, ωlog is the logarithmic average phonon frequency, is the RMS average phonon frequency, μ* is the effective Coulomb potential, λ is the electron-phonon coupling constant, and kB is Boltzmann’s

constant. (' /'

,)-(

( )*+ = 1 + -( .[./(.0.%1 ∗ )('

The

( ( /')*+ )]

= [1 + (/(2.46(1 + 3.8∗ )))%/ ]/%

value

. 4

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Results and Discussion Particle Swarm Optimization structure search Pursing novel crystal structures using density functional theory (DFT) requires an unbiased automatic structure search method based on the particle swarm optimization (PSO) algorithm to efficiently survey the potential energy surface.30,31,45 This method does not rely on previous knowledge of reported structure-types and has successfully predicted numerous new materials and crystal structures at ambient and high-pressure.29,46 To determine if the PSO crystal structures predicted here are energetically favorable, the formation enthalpy of the reaction (ΔH) can be calculated per atom following equation 2. ∆3 = [3(K % Ir) − 33(K) − 3(Ir)]

(2)

where, H(K3Ir) is the enthalpy of K3Ir for a given crystal structure, H(Ir) is the enthalpy of fcc Ir, and H(K) is the enthalpy of potassium. Because K is known to undergo a phase transition at 11.4 GPa the crystal structure of potassium is treated as bcc for the calculations with a pressure of 10 GPa and lower and as fcc for calculations at 15 GPa and higher.47 It is important to realize that the zero-point energy in these calculations is neglected; this is a safe assumption given the heavy elements calculated here. For the composition K3Ir, two plausible crystal structures were identified (Pmnm and Immm) by the PSO search at all elevated pressures searched (up to 100 GPa).

Figure 1. The formation enthalpy (ΔH) of K3Ir under pressure for a number of possible crystal structures. ΔH is calculated per atom following 3K + Ir K3Ir using crystal structures for K3Ir identified by particle swarm optimization (PSO) and from structural 5 ACS Paragon Plus Environment


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databases (ICSD). The negative preference to form the product.

ΔH

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indicates

Plotting ΔH as a function of pressure (Figure 1) indicates that applying pressure >10 GPa yields a negative ΔH for the PSO crystal structures indicating they should not decompose into elemental K + Ir. The positive ΔH for pressures lower 10 GPa is consistent with the absence of any known binary compounds between K and Ir at ambient pressure. The overall lowest enthalpy structure was identified using the unbiased PSO search and found to crystallize in space group Pmnm (No. 59) with the Cu3Ti-type structure.48 The structure is dynamically stable above 10 GPa according to the calculated phonon spectra (Figure 2a and Figure S1 in Supporting Information) indicating it is not prone to structural distortion. The origin of the thermodynamic stability dictating the formation of K3Ir in space group Pmnm can be investigated by decomposing ΔH into the partial energies including the internal energy (ΔE) and pressure-volume (pΔV). As shown in Figure 2b, the massive decrease of pΔV with increasing pressure is the initial driving force in the formation of K3Ir before ΔE takes over at higher pressure (>22 GPa). The second PSO structure predicted adopts space group Immm (No. 71) and is also dynamically stable. Information regarding K3Ir in space group Immm is available in Table S1 and Figure S2 of Supporting Information. This crystal structure is slightly lower in energy compared to Pmnm but in a very narrow pressure window, between 10 GPa and ≈12 GPa; at 20 GPa Immm is +25 meV/atom higher compared to Pmnm. Additional structure-types with A3X stoichiometry compiled in the Inorganic Crystal Structure Database (ICSD) were also considered to complement the PSO identified structures ensuring the complete potential energy surface is examined. As is evident in Figure 1, ΔH for these compounds become favorable at slightly higher pressures than the PSO structures (≈15 GPa). Nevertheless, all ICSD based structures are all substantially higher in total energy compared to the PSO structures across the entire pressure range probed (>100 meV/atom at 20 GPa) supporting their absence from the PSO search. From these results, it is clear that K3Ir with the Pmnm crystal structure has the most favorable ΔH across the widest pressure range; thus, it is the only compound explored in further detail. The origin of K3Ir phase formation is primarily dictated by the compressibility of the alkali metal under pressure. Applying high pressure to these elements causes a ns-orbital to nd-orbital charge transfer, which destabilizes the potassium.49 Further increasing the pressure eventually allows the internal energy to take over above 22 GPa, which continues to dominate phase formation at higher pressures. Thus, applying pressure is a feasible to drive the formation of K-Ir phases by destabilizing the starting materials until the internal energy of the products is sufficient to allow 6 ACS Paragon Plus Environment

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phase formation. These conclusions are valuable for guiding future synthetic efforts towards novel compounds containing anionic transition metals.

Figure 2. (a) The total and partial phonon DOS (PhDOS) for K3Ir shows the Pmnm crystal structure is dynamically stable. (b) The enthalpy (ΔH) into its component energies, the internal energy (ΔE) and pΔV. The dashed line shows the pressure at which K3Ir becomes stable against decomposition into the elements. Crystal chemistry, electronic structure, and chemical bonding K3Ir adopts space group Pmnm, as illustrated in Figure 3, and has two formula units per unit cell (Z = 2) with calculated lattice parameters: a = 4.903 AW , b = 4.943 AW , c = 6.681 AW , and a unit cell volume of 161.86 AW 3. The structure is isotypic to an ordered Cu3Ti-type crystal structure and contains two nonequivalent K atoms and one independent Ir (see Table 1). Here, K1 creates a skewed square net that stacks along the c-direction producing distorted square prisms, which are centered by Ir and K2. The result is a dense packed, three-dimensional network of face sharing [IrK8] and [KK8] polyhedra. The average K−Ir bond length at 20 GPa is 2.982 AW is similar to the polar intermetallic MgIr, which has bond lengths between 2.806 AW and 3.081 AW . The K−K (2.984 AW ) contacts are nearly identical to the K−Ir bonds but are substantially shorter than fcc-potassium (3.640 AW ) or bcc-potassium (4.614 AW ). Interestingly, the coordination environment of this novel compound is similar to the binary Bi4Ir,50 which also contains a mixture of distorted square prims and square antiprisms. Bi4Ir compound is also believed to contain an anionic Ir-based on electronic 7 ACS Paragon Plus Environment


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structure calculations, yet, the metallic nature of this compound makes assigning formal charge challenging. Nevertheless, the similarity between these two compounds suggests that Ir-centered square prisms may be a common structural motif for anionic Ir.

Figure 3. K3Ir adopts space group Pmnm above 10 GPa, K3Ir contains distorted [IrK8] (orange) and [KK8] (blue) square prisms that form a dense packed structure. Table 1. The VASP optimized atomic positions for Pmnm-K3Ir at 20 GPa. Atom Wyck. x/a y/b

z/c

K1

4e

¼

0.2213 0.5000

K2

2a

¼

0.7139 ¼

Ir1

2b

¼

0.7240 ¾

The electronic structure calculated at 20 GPa shows a number of unique features for a composition that closely resembles a polar intermetallic. Most notably, the DOS (Figure 4a) indicates the presence of a surprisingly wide indirect band gap of approximately 1 eV. The corresponding electronic band structure is presented in Figure S3 in the Supporting Information. Because the PBE functional is known to underestimate band gaps, the hybrid functional HSE0637 was used to determine a ≈1.6 eV band gap. Decomposing the total DOS into their component atomic orbitals indicates the Ir 5d bands are fully filled with a narrow dispersion between –1 eV and the Fermi level (EF) while the K 4p bands have a wider dispersion. The electronic structure shows a lack of interaction between the occupied Ir 5d bands, Ir 6s bands, and K 4p bands implying minimal hybridization between these orbitals. In conjunction with the presence of the band gap, these results support mainly ionic bonding, which is essential for the formation of a formally anionic Ir3–.


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Figure 4. (a) The partial DOS calculated using PBE for K3Ir in the Pmnm crystal structure. EF is set to 0 eV. (b) The –COHP curves for the average Ir−K interactions (left) and the average K−K interactions (right). Positive is bonding and negative is antibonding. EF is set to 0 eV. (c) The electron localization function is plotted for near the (010) plane. K is shown in blue and Ir is shown in orange.

A complete picture chemical bonding in this structure can be generated through a combination of computational methods. The projected crystal orbital Hamilton population (–COHP) is ideal for identifying and quantifying pairwise, energy-resolved covalent bonding. As shown in Figure 4b, a majority of the Hamilton populations indicating bonding interactions (positive in the plot) for the average K-Ir and K-K interactions are around −15 eV, well below EF. These interactions correspond to K(4s)-Ir(5p) σ-bonding as well as K(4s)-K(4s) σ-bonding. Nearer EF, the populations are all near zero revealing mostly non-bonding/non-covalent interactions. An ELF plot (Figure 4c) of the interactions in the (010) surface does not show any high ELF values between atoms indicating minimal covalent bonding, in support of the –COHP analysis. Larger ELF values usually correspond to inner shell or lone pair electrons and covalent interactions whereas the ionic and metallic interactions produce to smaller ELF values as is observed in K3Ir. The ELF section does show significant asymmetry around the atoms implying the bonding is between ionic and polar.51 The charge separation and lack of covalent interactions provides strong evidence for the formation of an iridide. A Bader's quantum mechanics atom-in-molecule (QM-AIM) charge analysis52 is also a valuable tool to approximate an atom's charge and substantiate the presence of electron transfer. At 20 GPA K3Ir has an average ionic charge of +0.55 electrons on each K and –1.64 electrons per Ir clearly demonstrating the formation of an iridide anion. Although the charge on Ir is lower than the anticipated –3 electrons, the Bader charge is usually smaller than the nominal charge



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even in ionic compounds.15 Moreover, the charge calculated here is considerably larger than in Bi4Ir (–1.0 electrons)50 further arguing for the presence of the first iridide anion in K3Ir.

High-pressure superconductivity Given that elemental iridium shows superconductivity (≈0.14 K at ambient pressure),53,54 potassium is predicted to develop superconductivity at high pressure,55 and Ir3– in K3Ir makes the compound isoelectronic with Hg, a classic BCS superconductor,56 it is plausible that phases containing Ir3– may also show superconductivity. However, K3Ir is a semiconductor meaning the system must be electron (or hole) doped to become metallic for the superconductivity. Substituting Pt for Ir in K3Ir is the best opportunity to increase the electron count based on atomic size and propensity to accept electrons while maintaining an anionic transition metal. The energetics of such an atomic substitution are described following equation 3. ∆3 = 3[(K % (Ir–8 Pt 8 )] − 33(K) − (1 − )3(Ir) − 3(Pt)

(3)

Supercell calculations varying the concentration of Pt reveal this reaction is energetically favorable; for example, when x = 0.0125 the ΔH is ≈35 meV more favorable relative to the x = 0 composition. Pt in this crystal structure has a Bader charge of –1.44 electrons indicating that anionic character is maintained while the DOS, plotted in Figure 5a and Figure S4 of the Supporting Information, shows that at least 12.5% Pt substitution (0.25 electrons per unit cell) is required to shift the Fermi level sufficiently into the conduction band and make the system metallic as desired. Calculating the electron-phonon coupling at 20 GPa on a model electron-doped, metallic system shows the Eliashberg spectral function (α2F(ω)) spans the entire frequency spectrum, as plotted in Figure 5b and Figure 5c. This is clearly illustrated by comparing the contribution to the electron phonon-coupling constant (λ) across the vibrational spectrum. At 20 GPa, the low frequency region (

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