Stability and Superconductivity of K–P Compounds under Pressure

Article pubs.acs.org/IC

Stability and Superconductivity of K−P Compounds under Pressure Yunxian Liu,*,† Chao Wang,† Xiangmu Kong,† and Defang Duan*,‡ †

College of Physics and Engineering, Qufu Normal University, Qufu, 273165, People’s Republic of China State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun, 130012, People’s Republic of China

‡

S Supporting Information *

ABSTRACT: We explore the phase diagram, structures, electron properties, and potential superconductivity of the K−P system at pressures of up to 200 GPa through unbiased structure searching techniques and first-principles calculations. Five stable chemical stoichiometries (K4P, K3P, K2P, KP, and KP2) have been theoretically predicted. In particular, P2 units or P-chains are uncovered in K2P, KP, and KP2 compounds with the existence of covalent bonds by analyzing the electron localization functions. And the Bader analysis demonstrates that charges transfer from K atoms to P atoms. Electron−phonon calculations show that the Tc of metallic I4/mmm-KP2 is 22.01 K at 5 GPa. The investigating of the K−P system is in favor of understanding the crystal structures and corresponding properties of potassium phosphides, which also give a strong motivation to search and design new superconductor materials in other phosphides.

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INTRODUCTION Phosphides have attracted a considerable number of investigations because they exhibit a great variety of structural features and extensive applications.1−7 For example, GaP and InP are important materials in the design of light-emitting diodes and transferred-electron devices.1 Boron phosphide can be used as a refractory material.2 Some phosphides can be applied in the field of lithium and sodium ion batteries.3,4 Cadmium phosphide can be applied in infrared detectors, lasers, solar cells, ultrasonic multipliers, etc.5−7 Moreover, in these compounds, phosphorus atoms can form different onedimensional (1D), two-dimensional (2D), or three-dimensional (3D) frameworks, especially in the compounds with a high ratio of phosphorus. In NaP7 and CsP7, the phosphorus forms a 1D extended chain.8,9 While in AgP15, phosphorus atoms consist of tubular units.10 As we known, high pressure can provide a good way to search new materials with new crystal phases, nonconventional stoichiometry, and outstanding properties. In recent years, some phosphides have been explored in theory and experiment under pressure. For instance, the superconductivity of molybdenum phosphide was found at high pressure.11 Some stoichiometries of phosporous-hygrogen (PH2 and PH3) were studied both in theory and in experiment, and it is found that they all exhibit superconductivity.12−16 A novel high-pressure phase (C2/m) of BP is found to be a superconducting material with zigzag phosphorus chains.17 Three novel phosphides (SrP3, BaP8, and LaP5) were synthesized at high pressure, and they all display expected diamagetic behaviors.18 At high pressure and high temperature, a hard material, Ir2P, was synthesized with a hardness of 11.8(4) GPa in an experiment.19 This research advanced the understanding of phosphides and resulted in extensive interest in the search for new phosphides © XXXX American Chemical Society

under high pressure. Up to now, the potassium−phosphorus (K−P) system is rarely explored under high pressure. Owing to the novel structures, stoichiometries, and intriguing properties of other studied phosphides, we embark on an investigation of the structure and corresponding properties of potassium phosphides under high pressure. We focus on the stable stoichiometries at moderate pressures, the new phase, and the structural character, as well as the existent form of phosphorus, the bonding nature, and superconductivity. In the present work, we theoretically investigated the phase diagram, structures, and properties of the potassium− phosphorus system under high pressure. We used the evolutionary algorithm Universal Structure Predictor: Evolutionary Xtallography (USPEX)20−22 in combination with firstprinciples density functional theory (DFT) to search the energetically stable stoichiometries and structures of K−P compounds in the range of 5−200 GPa and zero temperature. Then, dynamical stability, electronic properties, electronic band structures, and bonding patterns of the optimum static structures were systematically investigated in detail. The calculated electronic band structure and partial densities of states (PDOS) show that some phases of K−P compounds (I4/m-K4P and I4/mmm-KP2) are metallic, while others (Pmmn-K3P, Immm-K2P, Cmcm-K2P, and P6/mmm-K2P) exhibit semiconducting characters. And it is worth noting that with phosphorus content increasing, the P bonding pattern evolves from an ionic bond to a covalent bond. The calculated Tc of metallic I4/mmm-KP2 is 22.01 K at 5 GPa. Received: August 8, 2017

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DOI: 10.1021/acs.inorgchem.7b02006 Inorg. Chem. XXXX, XXX, XXX−XXX

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COMPUTATIONAL METHOD

compounds of K3P, K2P, and KP2 lay on the convex hull, and K2P has the most negative enthalpy of formation. When pressure is up to 100 GPa, the stoichiometry of KP2 is no longer stable and decomposes into K2P and P, whereas K4P, K3P, and K2P are thermodynamically stable. In the pressure range of 150−200 GPa, both K4P and K2P still emerge on the convex hull, and K2P is still the global minimum one. We also give the convex hull diagram of the K−P system at pressures of 5 GPa, as graphed in FigureS1. The pressure−composition phase diagram of the K−P system was constructed in 5−200 GPa, as presented in Figure 2. The phase I4/m of K4P is stable from 79.3 to 200 GPa. And

Searches for candidate stoichiometries and structures of KxPy (x, y = 1−4) were performed under a pressure of 5−200 GPa and at 0 K, with system sizes of 1−4 formula units per cell via the evolutionary algorithm USPEX, implemented in the USPEX code (Universal Structure Predictor: Evolutionary Xtallography),20−22 which has successfully predicted some systems.23−26 In the evolutionary structural searching, the first generation of structures was always created randomly with a population size of 20−60 structures. The succeeding generations are produced by variation operator heredity (60%), lattice mutation (30%), and permutation (10%). The obtained global structures were fully optimized within the framework of density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP).27 The generalized gradient approximation of the Perdew−Burke−Ernzerh functional (PBE-GGA)28 for the exchange-correlation interaction was employed. The projector augmented wave (PAW)29 potentials were adopted from the VASP potential library. The 3d64s1 and 3s23p3 are treated as valence electrons for K and P, respectively. The plane-wave cutoff energy was 500 eV, and Monkhorst−Pack k-point meshes chose 2π × 0.03 Å−1, in order to ensure that the enthalpy calculations were converged to better than 1 meV/atom. Iterative relaxation of atomic positions was stopped when all forces were smaller than 0.005 V/Å−1. A finite displacement approach,30 as implemented in the PHONOPY code31 was adopted to calculate the phonon. The electron localization function (ELF)32 was used to analyze the chemical bonds as done in VASP. The calculations of the electronic charge transfer are based on Bader charge analysis.33−35 The superconducting properties and the electron− phonon calculations (EPC) were performed using the Quantum ESPRESSO package.36 Norm-conserving pseudopotentials for K and P were considered with a kinetic energy cutoff of 90 Ry. A q-mesh of 3 × 3 × 3 and a k-mesh of 18 × 18 × 18 were used in the first Brillouin zone for KP2-I4/mmm phase.

Figure 2. Pressure−composition phase diagram for K−P crystal phases.

the K3P (space group Pmmn) keeps stable up to 123 GPa. For K2P stoichiometry, the phase Immm remains stable up to 50 GPa, then the Cmcm becomes energetically favorable and remains up to 150 GPa. At higher pressure, P6/mmm becomes more favored, as shown in Figure S2. For KP (space group Imma) and KP2 (space group I4/mmm) compounds, they are stable in the pressure ranges of 5−28 GPa and 5−69 GPa, respectively. The high pressure structures of stable stoichiometries for the K−P system are plotted in Figure 3. For K4P and K3P, the predicted energetically favored structures are I4/m and Pmmn at 100 GPa. In both above structures, P atoms can be viewed as being composed of a body-centered tetragonal (bct) lattice, and K atoms form a one-dimensional (1D) chain (Figure 3a and b). Moreover, the nearest P−P distances are 4.5270 and 3.83935 Å, respectively. In the I4/m phase, the K atoms are equivalent, while in the Pmmn structure, the K atoms occupy the crystallographic 2a and 4f sites. Figure 3c−e give the crystal structure motifs of K2P. The predicted crystalline phase of K2P has three structures in the Immm, Cmcm, and P6/mmm space groups at 50, 100, and 200 GPa, respectively. Note that P atoms are found in pairs in both Immm and P6/mmm structures (Figure 3c and d), and the P−P distances are 2.23703 and 2.22611 Å. While in the Cmcm phase, P atoms consist of a chain and are bonded; the distance of P−P is 2.22930 Å, illustrated in Figure 3e. Turning to KP and KP2 stoichiometries, we predicted an orthorhombic Imma structure (Figure 3f) and a tetragonal I4/mmm phase (Figure 3g) at 50 GPa, respectively. In these two phases, P atoms are in the form of a zigzag; the nearest P−P lengths are 2.16324 and 2.20661 Å, respectively. Detailed parameters of the above structures at different pressures are given in Table S1. Then, we performed the phonon dispersion calculations for the K−P system. It is seen that no imaginary vibrational modes exist in the Brillouin zone for I4/m-K4P, Pmmn-K3P, I4/mmm-KP2, Immm-K2P, CmcmK2P, P6/mmm-K2P, and Imma-KP at selected pressure, as

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RESULTS AND DISCUSSION In this work, we investigated the stable stoichiometries and structures for KxPy (x, y = 1−4) in the pressure range of 5−200 GPa. The enthalpies of formation (ΔHf) of the most stable candidate structures for KxPy (x, y = 1−4) with respect to elemental potassium and phosphorus are presented in Figure 1. And the ΔHf is given by the expression ΔHf(KxPy) = [H(KxPy) − xH(K) − yH(P)]/(x + y). Structures located on the hull are thermodynamically stable relative to dissociation into other stoichiometries and/or pure elements, while those above the convex hull are metastable. Note that, at 50 GPa, the three

Figure 1. Convex hull diagram for the K−P system at pressures of 50, 100, 150, and 200 GPa. Solid shapes fall on solid lines, which represent thermodynamically stable phases, while open shapes locate on dashed lines, which denote unstable/metastable phases. B

DOI: 10.1021/acs.inorgchem.7b02006 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 3. Crystal structures of (a) I4/m-K4P at 100 GPa, (b) Pmmn-K3P at 100 GPa, (c) Immm-K2P at 50 GPa, (d) Cmcm-K2P at 100 GPa, (e) P6/ mmm-K2P at 200 GPa, (f) Imma-KP at 50 GPa, and (g) I4/mmm-KP2 at 50 GPa. Green and orange spheres denote the K and P atoms, respectively.

Figure 4. Phonon dispersion curves for I4/m-K4P, Pmmn-K3P, I4/mmm-KP2, Immm-K2P, Cmcm-K2P, and P6/mmm-K2P at selected pressures.

Immm-K2P, Cmcm-K2P, and P6/mmm-K2P structures, we see that in the former two phases, the ELF value located between P2 units is close to 0.8, indicating that covalent bonds are formed in P2 units (Figure S4d and e). For the latter phase (P6/mmm-K2P), high electron localization can be seen between P atoms in the region of the chain, suggesting strong covalent P−P bonding. And, no electrons localize between P−K atoms, reflecting the ionic interactions. It is worth noting that with the phosphorus content increasing, the P bonding pattern evolves from an ionic bond to a covalent bond. To obtain more insight into the bond features, the Bader charge analysis was performed to calculate the transferred electrons for the K−P system at different pressures, as shown in Table S2. It demonstrates that there may exist ionic bonding between the K and P atoms due to the charges transferring from K to P atoms. On the basis of the stable pressure range of metallic I4/ mmm-KP2 being accessible to current experiments (5−69 GPa), we further explored its superconductivity and calculated the EPC parameter λ, the logarithmic average phonon frequency, ωlog, and the electronic DOS at the Fermi level N(Ef). The Tc was estimated by using the Allen−Dynes modified McMillan equation:37

shown in Figure 4 and Figure S3, suggesting that they are all dynamically stable. To investigate the pressure induced electronic properties and chemical bonding of the K−P system, we calculate the electronic band structures and density of states (DOS) of I4/ m-K4P, Pmmn-K3P, I4/mmm-KP2, Immm-K2P, Cmcm-K2P, P6/ mmm-K2P, and Imma-KP at selected pressures, as presented in Figure 5a-c, Figure S4a−c, and Figure S5. Note that I4/m-K4P, I4/mmm-KP2, and Imma-KP exhibit a clear metallic type by the evidence of the finite DOS at the Fermi level and overlap between the conduction and valence bands (Figure 5a,c and Figure S5), while for Pmmn-K3P, Immm-K2P, Cmcm-K2P, and P6/mmm-K2P phases, they are semiconductors with energy band gaps less than 3 eV, as seen in Figure 5b and Figure S3a− c. In order to understand the bonding nature between the atoms for K−P system, electronic localization function (ELF) calculations are performed for I4/m-K4P, Pmmn-K3P, I4/mmmKP2, Immm-K2P, Cmcm-K2P, and P6/mmm-K2P, shown in Figure 5d−f and Figure S4d−f. As we know, we can get the bond type of materials (such as metallic, covalent, or ionic bond) by the ELF calculation. It is found that in I4/m-K4P and Pmmn-K3P structures (Figure 5d and e), the ELF values located between P and P, P and K, and K and K atoms are less than 0.5, which indicates no electrons localized. However, the ELF value of P atoms in the zigzag for I4/mmm-KP2 is above 0.7, illustrating the formation of a covalent bond (Figure 5f). For

TC = C

⎡ ⎤ 1.04(1 + λ) exp⎢ ⎥ ⎣ λ − μ*(1 + 0.62λ) ⎦ 1.2

ω log

DOI: 10.1021/acs.inorgchem.7b02006 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 5. (a−c) The electronic band structures, DOS, and (d−f) electron localization function (ELF) maps of I4/m-K4P, Pmmn-K3P, and I4/mmmKP2 at different pressures.

the fade of soft vibrational modes induced by increasing pressure. This phenomenon was also found in other stystems, e.g., magnesium dicarbide and so on.39

With a nominal Coulomb pseudopotential parameter (μ*) of 0.1, the calculated EPC parameter λ of I4/mmm-KP2 at 5 GPa is 0.99, and the estimated Tc is 22.01 K. Moreover, the pressure dependence of the superconducting critical temperature Tc of I4/mmm-KP2 was also calculated, and the values of λ, ωlog, and N(Ef) at different pressures are listed in Table 1. It is

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CONCLUSION In summary, we performed a systematic search for possible stoichiometries, structures, electron properties, and potential superconductivity of the K−P system in the pressure range of 5−200 GPa. Under pressure, five stoichiometries of K4P, K3P, K2P, KP, and KP2 are found to be thermodynamically stable. Especially, in K2P, KP, and KP2 compounds, all phosphorus atoms exist in the form of P2 units or P chains with covalent interactions. Furthermore, the charges transferred from K atoms to P atoms are calculated by the Bader charge analyses. By applying the Allen−Dynes modified McMillan equation, the estimate of superconducting transition temperature Tc of metallic I4/mmm-KP2 is carried out, and the resulting Tc reaches 22.01 K at 5 GPa. Our present findings provide a perspective toward the structures and properties of potassium phosphides under pressure, which have broad implications for further investigation other new phosphides.

Table 1. Calculated Electron-Phonon Coupling Parameters (λ), the Logarithmic Average Phonon Frequency ωlog, Electronic Density of States at the Fermi Level N(Ef) (states/spin/Ry/Unit cell), and Superconducting Critical Temperatures Tc for I4/mmm-KP2 at Different Pressures pressure (GPa)

λ

ωlog (K)

N(Ef)

Tc (K) μ* = 0.1

5 10 20 30 50

0.99 0.69 0.48 0.39 0.36

320.85 395.49 471.70 512.66 439.56

3.16 2.88 2.94 3.20 3.17

22.01 13.19 4.77 1.72 0.97

noteworthy that with pressure increasing, the calculated average frequency ωlog increases, but the parameter λ decrease. Therefore, we consider that the decrease of the Tc values with pressure may mainly be due to the diminishing λ. As we know, the decrease/increase in EPC (λ) with pressure is mainly attributed to the weakening/intensifying of the “soft” vibrational mode caused by pressure.38 So we calculated the phonon dispersion curves for the I4/mmm structure of KP2 at 5, 10, 20, 30, and 50 GPa by using a primitive cell as implemented in the Quantum ESPRESSO package, as plotted in Figure S6. For the I4/mmm structure, it can be clearly seen that there are two “softenings” in the mode along the X−P and P−N directions, and soft vibrational modes gradually fade away with pressure increasing. Therefore, we think that the decrease in EPC (λ) of the I4/mmm phase under pressure might mainly derive from

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02006. The convex hull diagram of the K−P system at 5 GPa, enthalpy curves, phonon dispersion curves, the electronic band structures, DOS, electron localization function (ELF) maps, structural parameters, and Bader analysis for different structures in the K−P system (PDF) D

DOI: 10.1021/acs.inorgchem.7b02006 Inorg. Chem. XXXX, XXX, XXX−XXX

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Yunxian Liu: 0000-0003-2435-5765 Chao Wang: 0000-0002-0344-4964 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China No. 11704220, No. 11504200, No. 11675090, No. 11674122, and No. 11647170 and by the Natural Science Foundation of Shandong Province of China (Grant No. ZR2017BA020 and ZR2017BA012).

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DOI: 10.1021/acs.inorgchem.7b02006 Inorg. Chem. XXXX, XXX, XXX−XXX