⇦Chinese Physics Letters, 2020, Vol. 37, No. 2, Article code 026201 Stable Compositions, Structures and Electronic Properties in K–Ga Systems Under Pressure * Chao Wang (王超), Yun-Xian Liu (刘云仙)**, Xin Chen (陈欣), Pin Lv (吕品), Hai-Rui Sun (孙海瑞), Xiao-Bing Liu (刘晓兵)** Affiliations Laboratory of High Pressure Physics and Material Science, School of Physics and Physical Engineering, Qufu Normal University, Qufu 273165 Received 21 October 2019, online 18 January 2020 *Supported by the Shandong-Provincial Science Foundation (ZR2018PA010, ZR2017BA020, ZR2017BA012, ZR2019MA054 and 2019KJJ020), and the National Natural Science Foundation of China (11704220, 11674122, 11804184, 1180418 and 11974208).
**Corresponding author. Email: xiaobing.phy@qfnu.edu.cn; yunxianliu1988@163.com Citation Text: Wang C, Liu Y X, Chen X, Lv P and Sun H R et al 2020 Chin. Phys. Lett. 37 026201    Abstract New stable stoichiometries in K–Ga systems are firstly investigated up to 100 GPa by the unbiased structure searching techniques. Six novel compositions as K$_{4}$Ga, K$_{3}$Ga, K$_{2}$Ga, KGa, KGa$_{2}$ and KGa$_{4}$ are found to be thermodynamically stable under pressure. Most of the predicted stable phases exhibit metallic character, while the $Fd\bar{3}m$ KGa phase behaves as a semiconductor with a bandgap $\sim $1.62 eV. Notably, the gallium atoms exhibit different interesting morphologies; e.g., Ga$_{2}$ units, zigzag chains, six rings and cage. We further investigate the bonding nature of K–Ga systems with help of electron localization function and Bader charge analyses. Strong covalent bonding characteristics are found between the Ga and Ga atoms, and ionic bonding patterns are observed between the K and Ga atoms. Meanwhile, we notice charge transferring from the K atom to the Ga atom in the K–Ga systems. The present results can be helpful for understanding the diverse structures and properties of K–Ga binary compounds at high pressures. DOI:10.1088/0256-307X/37/2/026201 PACS:62.50.-p, 61.50.Ks, 71.20.-b © 2020 Chinese Physics Society Article Text Nowadays, high-pressure science is an attractive and significant scientific research area, especially for material science. Under high pressure conditions, the crystal structure and physical properties of elements and materials can be changed effectively.[1–4] Consequently, novel compounds with unusual stoichiometries can be formed and stabilized, which may be quite different from the traditional chemical valence rules.[5–8] Recently, the pressure-induced potassium-$X$ compounds ($X$ denotes other elements) have attracted considerable attention because of their outstanding properties and growing applications in industry, such as unconventional stoichiometries, novel structures, superconductivity, high hardness or potential application as high performance battery materials and high-energy-density materials.[1–11] In the K–Br and K–Cl systems, two (KBr$_{3}$ and KBr$_{5}$) and eight (K$_{3}$Cl, K$_{2}$Cl, K$_{3}$Cl$_{2}$, K$_{4}$Cl$_{3}$, K$_{5}$Cl$_{4}$, K$_{3}$Cl$_{5}$, KCl$_{3}$, and KCl$_{7}$) unconventional stoichiometric compounds have been experimentally synthesized and theoretically predicted at high pressures.[12,13] Using the Mao–Bell diamond anvil cell technology, three stoichiometric mixtures of KCu, KCu$_{2}$ and K$_{2}$Cu were discovered in potassium-copper mixtures.[14] A high pressure structure (anisotropic $\omega$ phase) as K$_{2}$Ag was found with graphite-like potassium layers.[15] The KC$_{8}$ and KP$_{2}$ compounds were predicted to be potential superconductors with $T_{\rm c}=0.14$ K and 22.01 K under pressure, respectively.[16,17] Furthermore, the KN$_{3}$ containing polymerized nitrogen under high pressure has also been extensively studied in experiment and theory because of its high potential application as a high energy density material.[18–20] Motivated by successful research on the diversity of phases and properties in the K–$X$ systems under pressure, in this work, we carry systematic studies on inbinary K–Ga systems to explore the stable stoichiometries, structures, electronic properties and bonding patterns. We report that six novel compositions K$_{4}$Ga, K$_{3}$Ga, K$_{2}$Ga, KGa, KGa$_{2}$, and KGa$_{4}$ are found to be thermodynamically stable at pressures up to 100 GPa. The stoichiometries and crystal structure prediction were performed using the evolutionary algorithm method as implemented in the USPEX code,[21–23] which has been successfully used in many systems.[24–29] Structures were produced randomly in the first generation with its population size of 20–60 structures. Every subsequent generation is produced from 60% of the lowest-enthalpy structures of the previous generation. New structures were produced by variation operator heredity (65% structures), atomic permutation (15%), and lattice mutation (20%). The calculation would keep working until the best structure contains more than 20 generations. The underlying ab initio structural relaxations, total energy, mechanical and electronic properties were calculated in the framework of density functional theory within the generalized gradient approximation Perdew–Burke–Ernzerhof (GGA-PBE)[30] exchange-correlation functional in the Vienna ab initio Simulation Package (VASP) code.[31] The all-electron projector augmented wave (PAW) method[32] with K $4s^{1}$ and Ga $4s^{2}4p^{1}$ treated as the valence electrons. The plane-wave basis sets with the 400 eV cutoff, and dense Monkhorst–Pack meshes with 2$\pi \times 0.03$ Å$^{-1}$ were chosen to ensure that all of the enthalpy calculations are well converged to better than 1 meV/atom. To evaluate the electron localization and the electronic charge, we used the electron localization function (ELF)[33] and Bader charge analysis.[34–36] The phonon calculations were carried out by supercell approach through the PHONOPY program.[37,38]
cpl-37-2-026201-fig1.png
Fig. 1. Convex hull diagrams of the K–Ga systems at selected pressures of 5, 40, 80 and 100 GPa.
cpl-37-2-026201-fig2.png
Fig. 2. Pressure–composition phase diagram of the K–Ga systems.
To study the thermodynamic stability of K–Ga compounds, we explore the crystal structures of various K$_{x}$Ga$_{y}$ ($x=y = 1$, 2, 3, 4) under high pressure up to 100 GPa. The calculated formation enthalpy values ($\Delta H_{\rm f}$) for the most stable candidate structures in the K–Ga systems are given in Fig. 1 and Fig. S1. The $\Delta H_{\rm f}$ values are calculated for each stoichiometry with respect to the decomposition to elemental K and Ga, which can be expressed as $$ \Delta H_{\rm f}({\rm K}_{x}{\rm Ga}_{y})\! = \![H({\rm K}_{x}{\rm Ga}_{y})\! -\! xH({\rm K}) \!-\! yH({\rm Ga})]/(x\! +\! y). $$ In general, new phases with their enthalpy values on the convex hull are stable against decomposition at a given pressure, while the structures above the convex hull are either metastable or unstable. We notice that the KGa$_{4}$ compound is the most thermodynamically stable composition throughout the entire studied pressure range. At 5 GPa, two stoichiometric KGa$_{2}$ and KGa$_{4}$ lie on the convex hull, demonstrating that they are energetically stable. Then, three more new stoichiometric K$_{4}$Ga, K$_{2}$Ga and KGa become stable at 20 GPa. At the pressure ranging from 40 and 60 GPa, a new stoichiometry appears on the hull as K$_{3}$Ga. With the exception of K$_{4}$Ga, K$_{3}$Ga and KGa$_{3}$ compounds, four stoichiometries (K$_{2}$Ga, KGa, KGa$_{2}$ and KGa$_{4}$) remain thermodynamically stable at 80 GPa. As pressures up to 100 GPa, only K$_{2}$Ga, KGa and KGa$_{2}$ are stable in our study. The stable pressure ranges for the corresponding phases of K–Ga compounds are shown in Fig. 2. Moreover, Fig. S2 in the Supplementary Material gives the enthalpy curves for K$_{4}$Ga, K$_{3}$Ga, K$_{2}$Ga, KGa$_{2}$ and KGa$_{4}$. The morphologies of the predicted structures are presented in Figs. 3 and 4. It can be seen that K atoms exist in isolated form. For K$_{4}$Ga, a tetragonal phase $I4/m$ is preferred to be stable from 12 GPa to 40 GPa, then a monoclinic structure $C2/m$ becomes more favored till 70.7 GPa. In the $I4/m$ phase, Ga exists in atomic form, occupying the crystallographic $2a$ position, and K atoms lie the $8h$ position (Fig. 3(a)). For the $C2/m$ structure, Ga atoms form Ga$_{2}$ units with the distances of 2.68 Å (Fig. 3(b)). The stoichiometry of K$_{3}$Ga is predicted to be stable at 23.5 GPa, which has two monoclinic structures $P2_{1}/c$ and $P2_{1}/m$ with a phase transition pressure of 42.3 GPa. Ga atoms appear in the $P2_{1}/c$ structure as pairs and the Ga–Ga distance is 2.45 Å (Fig. 3(c)). In the $P2_{1}/m$ structure, Ga atoms form zigzag chains with the distance of 2.47 Å (Fig. 3(d)). For K$_{2}$Ga stoichiometry, a monoclinic structure $P2_{1}/m$ transforms into a trigonal phase $P\bar{3}m1$ at 51.5 GPa. In the $P2_{1}/m$, the Ga atoms are in the form of zigzag chains, the nearest Ga–Ga length is 2.58 Å (Fig. 3(e)). In the $P\bar{3}m1$ structure, the Ga atoms form six rings with the distance of 2.40 Å, in which the Ga atoms are not on the same plane (Fig. 3(f)).
cpl-37-2-026201-fig3.png
Fig. 3. Stable crystal structures of the predicted K-rich compounds: (a) $I4/m$ K$_{4}$Ga, (b) $C2/m$ K$_{4}$Ga, (c) $P2_{1}/c$ K$_{3}$Ga, (d) $P2_{1}/m$ K$_{3}$Ga, (e) $P2_{1}/m$ K$_{2}$Ga, and (f) $P\bar{3}m1$ K$_{2}$Ga. Purple and green balls denote K and Ga atoms, respectively.
Turning to KGa, we predict a cubic phase $Fd\bar{3}m$ with stable pressure range of 9.2–100 GPa. In the $Fd\bar{3}m$ structure, K and Ga atoms occupy the crystallographic $8a$ and $8b$ positions. Ga atoms form zigzag chains and the nearest distance is 2.53 Å, as displayed in Fig. 4(a). For KGa$_{2}$, two monoclinic structures $P2/m$ and $C2/c$ are obtained at 20 and 60 GPa, and phase transition occurs at 34.5 GPa. For the $P2/m$ structure, there are two nonequivalent Ga atoms, in which one occupies the crystallographic $4o$ position and the other one sites at the crystallographic $2n$ position, forming eight rings with the nearest lengths of 2.50 Å (Fig. 4(b)). In the $C2/c$, Ga atoms constitute zigzag chains and the nearest lengths is 2.42 Å (Fig. 4(c)). For the KGa$_{4}$ composition, three structures of $I4/mmm$, $Pnma$ and $C2/m$ are predicted. The phase of $I4/mmm$ with the lowest enthalpy remains up to 27.3 GPa. For the Ga atoms, there are two nonequivalent positions, and they occupy the crystallographic $4e$ and $4d$ position, which form cages with the distance of 2.50 Å, as illustrated in Fig. 4(d). Then at higher pressure, $Pnma$ becomes more favored until 92.6 GPa, wherein Ga atoms occupy $4k$ and $2e$ positions, forming chains with the shortest Ga–Ga length of 2.33 Å (Fig. 4(e)). Table S1 in the Supplementary Material gives the detailed structural information for each phase of the K–Ga systems.
cpl-37-2-026201-fig4.png
Fig. 4. Stable crystal structures of the predicted Ga-rich compounds: (a) $Fd\bar{3}m$ KGa, (b) $P2/m$ KGa$_{2}$, (c) $C2/c$ KGa$_{2}$, (d) $I4/mmm$ KGa$_{4}$, and (e) $Pnma$ KGa$_{4}$. Purple and green balls denote K and Ga atoms, respectively.
To judge their stability, the phonon dispersion curves for all the considered structures of K–Ga compounds are calculated, as presented in Fig. S3. No imaginary vibrational modes are observed in the Brillouin zone, suggesting that all the above phases are dynamically stable in their accessible pressures. The electronic properties of various K–Ga compounds are also investigated by calculating band structures and the partial density of states (PDOS), as shown in Figs. 5 and 6 and Figs. S4–S7. Except the $Fd\bar{3}m$-KGa phase, all the other structures (K-rich: $I4/m$ K$_{4}$Ga, $C2/m$ K$_{4}$Ga, $P2_{1}/c$ K$_{3}$Ga, $P2_{1}/m$ K$_{3}$Ga, $P2_{1}/m$ K$_{2}$Ga, $P\bar{3}m1$ K$_{2}$Ga, Ga-rich: $P2/m$ KGa$_{2}$, $C2/c$ KGa$_{2}$, $I4/mmm$ KGa$_{4}$, $Pnma$ KGa$_{4}$) exhibit metallic feature by evidence of the finite electronic DOS at the Fermi level (Figs. 5 and 6). We notice different occupations of states near the Fermi level for K-rich and Ga-rich compounds. For K-rich compositions, the majority of occupied states near the Fermi level come from the K $s$, K $p$, K $d$ and Ga $p$ states (Fig. 5), whereas in Ga-rich phases, the Ga $p$ states mainly occupy the Fermi level (Fig. 6). The structure $Fd\bar{3}m$ KGa is semiconductor with energy band gaps less than 3 eV, as depicted in Fig. S4.
cpl-37-2-026201-fig5.png
Fig. 5. Calculated PDOS of K-rich compounds. The vertical dashed line at zero is the Fermi level.
cpl-37-2-026201-fig6.png
Fig. 6. Calculated PDOS of Ga-rich compounds. The vertical dashed line at zero is the Fermi level.
To further understand the bonding character of the K–Ga compounds, the electron localization function (ELF), a measure of relative electron localization in extended structures is calculated, as depicted in Fig. 7 and Figs. S8 and S9. Generally speaking, large ELF values ($> $0.5) occur in regions where there is a high tendency of electron pairing (such as cores, and lone pairs), indicating the formation of covalent bonds, while small values ($ < $0.5) suggests non/less electron-localization, implying the existence of ionic/metallic bonds between atoms. It is seen that the ELF values between Ga and Ga atoms are pretty high ($\sim $0.7), which indicates a covalent bonding pattern, whereas there is no electron localization between K and Ga atoms, implying an ionic/metallic bonding character. Moreover, we also study the Charge transfer on the basis of the electron density using Bader analysis, as graphed in Table S2, which shows charge transfer from the K atom to Ga.
cpl-37-2-026201-fig7.png
Fig. 7. ELFs of (a) $C2/m$ K$_{4}$Ga, (b) $P2_{1}/m$ K$_{2}$Ga, and (c) $P2/m$ KGa$_{2}$.
In summary, six unusual stoichiometries (K$_{4}$Ga, K$_{3}$Ga, K$_{2}$Ga, KGa, KGa$_{2}$ and KGa$_{4}$) of K–Ga compounds are discovered under high pressure using unbiased structure searching combined with density functional theory calculations. The predicted structures contain a rich variety of polygallium forms, such as Ga$_{2}$ units, zigzag chains, six rings (Ga$_{6}$ units) and cage. Electronic structure calculations suggest that the $Fd\bar{3}m$-KGa phase is semiconductor, while all the other predicted K–Ga systems exhibit metallic character. Further analysis of the bonding nature shows that charges transfer from potassium atoms to gallium atoms. Our results are important for understanding the structures and properties of potassium-gallium under high pressure. The calculations were performed at the High Performance Computing Center (HPCC) of Qufu Normal University. References Transparent dense sodiumStructural stability and vibrational characteristics of CaB 6 under high pressurePressure-induced metallization of dense (H2S)2H2 with high-Tc superconductivitySuperconductivity in Topological Semimetal θ -TaN at High Pressure *Gold with +4 and +6 Oxidation States in AuF 4 and AuF 6LaB${}_{6}$ Work Function and Structural Stability under High PressureRoute to high-energy density polymeric nitrogen t-N via He−N compoundsThe Stable or Metastable Phases in Compressed Zn-O SystemsGlobal Structural Optimization of Tungsten BoridesExtraordinary Indentation Strain Stiffening Produces Superhard Tungsten NitridesPotassium-Ion Oxygen Battery Based on a High Capacity Antimony AnodeThe synthesis of unconventional stoichiometric compounds in the K–Br system at high pressuresStability of numerous novel potassium chlorides at high pressureThe high-pressure chemistry of potassium–copper mixturesUnusual Chemical Behavior for Potassium under Pressure: Potassium−Silver CompoundsSuperconductivity in Potassium-Doped Few-Layer GrapheneStability and Superconductivity of K–P Compounds under PressureHigh pressure X-ray diffraction study of potassium azidePressure-induced polymerization of nitrogen in potassium azidesA new high-pressure polymeric nitrogen phase in potassium azideCrystal structure prediction using ab initio evolutionary techniques: Principles and applicationsHow Evolutionary Crystal Structure Prediction Works—and WhyNew developments in evolutionary structure prediction algorithm USPEXStructural evolutions and electronic properties of Au n Gd ( n = 6–15) small clusters: A first principles studyStructures and properties of binary Mg Bi compounds under pressureStructural and electrical properties of Ga–Te systems under high pressurePressure‐Induced Stable Binary Compounds of Magnesium and GermaniumGround State Structures of Boron-Rich Rhodium Boride: An Ab Initio StudyFirst-principles study of structural, electronic, elastic, and thermal properties of Imm 2-BCGeneralized Gradient Approximation Made SimpleEfficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis setFrom ultrasoft pseudopotentials to the projector augmented-wave methodA simple measure of electron localization in atomic and molecular systemsAtoms in moleculesA fast and robust algorithm for Bader decomposition of charge densityA grid-based Bader analysis algorithm without lattice biasFirst-Principles Determination of the Soft Mode in Cubic ZrO 2 First-principles calculations of the ferroelastic transition between rutile-type and CaCl 2 -type SiO 2 at high pressures
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