Crystal Structures and Electronic Properties of Cesium Xenides at

Oct 19, 2015 - at high pressure using the effective CALYPSO algorithm in combination with first-principles calculations. Strikingly, our results show ...
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Crystal Structures and Electronic Properties of Cesium Xenides at High Pressures Shoutao Zhang,† Haixin Bi,† Shubo Wei,† Jianyun Wang,† Quan Li,*,‡,† and Yanming Ma† †

State Key Laboratory of Superhard Materials and ‡College of Materials Science and Engineering, Jilin University, Changchun 130012, China ABSTRACT: The discovery of chemical reactivity of the noble-gas Xe at high pressure has reignited great interest in Xe-containing compounds. Here, we have extensively explored the Cs−Xe system at high pressure using the effective CALYPSO algorithm in combination with first-principles calculations. Strikingly, our results show that the stoichiometries of CsXe4, CsXe3, CsXe2, CsXe, Cs2Xe, Cs3Xe, and Cs4Xe have stability regimes on the phase diagram. A sequence of stable Cs−Xe compounds identified all exhibit metallic behaviors with several bands crossing the Fermi level. Our findings put forward further understanding of the crystal structures and electronic properties of Cs−Xe compounds at high pressures.

I. INTRODUCTION Since the first Xe compound Xe+(PtF6)− was synthesized by Bartlett in 1962,1 the compounds containing Xe were extensively investigated. Subsequently, a variety of xenon fluorides 2−6 and xenon oxides 7−10 were experimentally synthesized at atmospheric pressure. Recent theoretical investigations identified that Xe becomes more reactive under compression,11 e.g., (i) Xe oxides12,13 become stable at high pressures; (ii) Xe nitrides14 whose formation is long thought as impossible are stable at high pressures, which opens up the possibility of achieving Xe nitrides; (iii) Xe and Mg can form stable compounds under high pressure, in which Xe is negatively charged;15 and (iv) Xe and Fe/Ni can form stable compounds at the conditions of the Earth’s inner core, which provides a solution to the missing Xe problem in the Earth’s atmosphere.16 Theoretical studies indicate that Cs is capable of losing or even gaining electrons under high pressure, e.g., (i) in the presence of fluorine and under pressure, Cs atom can be oxidized beyond +1 state due to the reactivity of inner-shell 5p electrons;17 subsequently, another work performs a comprehensive investigation of the CsFn system up to 100 GPa and explains that interplay between two mechanisms (polyfluoride anions and increase of Cs oxidation state) results in an unexpected variety of stable CsFn compounds under moderate pressure18 and (ii) pressure causes electron transfer from Li to Cs, leading to Cs anions beyond the −1 state.19 As to the chemical reaction of alkali metal Cs and noble gas Xe, the van der Waals molecule CsXe has been observed spectroscopically in 1949.20 It was reported that the xenides were probably van der Waals crystals because of the small or negative ionic binding in 1967.21 Cs−Xe thin-film alloys were used to investigate the metal−insulator transition with Xe concentration increasing at low temperature.22 As pressure can increase the reactivity of noble gases, another relevant work © XXXX American Chemical Society

discovers that helium can form a compound with sodium at high pressure.23 By comparison with Xe, Cs has one more electron and lower electronegativity. At elevated pressures, when mixing with Xe, Cs (Xe) can lose (obtain) a partial electron and possess a nearly identical electron state with Xe (Cs). An interesting task is to predict the high-pressure phase diagram of the Cs−Xe system and to understand the competing relationship between Cs and Xe over an electron at high pressure. In the present study, using the developed CALYPSO (crystal structure analysis by particle swarm optimization) method,24−29 which has been successfully applied to a series of systems,16,30−34 we have systematically investigated the pressure−composition phase diagram of the Cs−Xe system up to 200 GPa. Our work uncovered that, when mixing with Xe under high pressure, Cs forms a variety of thermodynamically stable compounds with a sequence of stoichiometries (CsXe4, CsXe3, CsXe2, CsXe, Cs2Xe, Cs3Xe, and Cs4Xe). All of the stable structures can be seen as the structures with close-packed arrangements of Cs and Xe atoms. The calculations of electronic properties reveal the nature of metallicity of Cs− Xe compounds.

II. COMPUTATIONAL DETAILS We implemented the structure prediction via a global minimization of free energy surfaces based on the CALYPSO methodology combining with first-principles calculations. The ab initio structural relaxations and electronic properties calculations were performed within the framework of density functional theory as implemented in the Vienna ab initio Received: September 2, 2015 Revised: October 16, 2015

A

DOI: 10.1021/acs.jpcc.5b08567 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C simulation package (VASP) code.35 The Perdew−Burke− Ernzerhof (PBE) generalized gradient approximation (GGA)36 was adopted for exchange-correlation functional. The electron−ion interaction was described by use of allelectron projector augmented-wave method (PAW)37 with 5s25p66s1 and 4d105s25p6 treated as valence for Cs and Xe atoms, respectively. The plane-wave kinetic energy cutoff of 1500 eV and appropriate Monkhost-Pack k-meshes with grid spacing of 0.03 Å−1 were chosen to ensure that total energy calculations are well converged. The validity of used PAW pseudopotentials at high pressures was carefully verified with the full-potential linearized augmented plane-wave (LAPW) method using the WIEN2k code.38 By using the two different methods, we calculated total energies of CsXe in the Pm-3m structure at various pressures and then fitted the obtained energy-volume data into the Birch−Murnaghan equation of states.39 Figure 6 shows that the results derived from the two methods are almost identical, which clearly indicates the suitability of the PAW pseudopotentials for describing the energetics of cesium xenides at megabar pressures. The phonon calculations were performed to determine the dynamical stability of predicted structures by using the finite displacement approach40 with the supercell method as implemented in the Phonopy code.41 The Bader’s quantum theory of atoms in molecules (QTAIM) analysis42 was adopted for the charge transfer calculation.

Figure 2. Stable structures of Cs−Xe compounds. (a) P4/mmm structure of CsXe. (b) I41/amd structure of CsXe. (c) Pm-3m structure of CsXe. (d) Immm structure of CsXe2. (e) I4/mmm structure of CsXe2. (f) I4/mmm structure of CsXe3. (g) Fm-3m structure of CsXe3. (h) P21/m structure of CsXe4. (i) Immm structure of Cs2Xe. (j) I4/ mmm structure of Cs3Xe. (k) P-1 structure of Cs4Xe. Detailed structural parameters of stable Cs−Xe compounds are shown in Table 1.

III. RESULTS AND DISCUSSION In order to obtain stable structures for Cs−Xe compounds, the stoichiometries of CsxXey (x = 1−4; y = 1−4) with cells size of 1−4 formula units (f.u.) were systematically searched up to 200

GPa. To explore the thermodynamic stability of CsxXey compounds, we computed the formation enthalpies of CsxXey compounds relative to the decomposition into the constituents of Cs and Xe. The formation enthalpy per atom ΔH of CsxXey compounds was calculated by means of the following formula: ΔH = [H(CsxXey) − xH(Cs) − yH(Xe)]/(x+ y ), in which H represents the enthalpy per formula unit of the most stable structure for each composition at a given pressure. Based on the definition of formation enthalpies of Cs−Xe compounds, the pressure−composition phase diagram of the Cs−Xe system is shown in Figure 1, in which the convex hull (Figure 1a) was constructed by the calculated enthalpies of the most stable structures for each composition. All of the structures whose formation enthalpies lie on the convex hull (the global stability line) are deemed stable with respect to decomposition into elements or other compounds. Moreover, it is interesting to note that the effect of pressure stabilizes more stoichiometries of cesium xenides at high pressures; however, it is impossible to determine how many Cs per Xe are the absolute minimum and how this might change with pressure due to the limited computing resource. At 20 GPa, all the investigated stoichiometries are energetically unstable with respect to decomposition into the pure Cs and Xe. With increasing pressure to 50 GPa, all of the stoichiometries show a negative enthalpy of formation, although CsXe4, Cs3Xe, and Cs4Xe stoichiometries still lie above the convex hull. At 100 GPa, CsXe4 stoichiometry becomes energetically stable over other compositions while Cs3Xe and Cs4Xe stoichiometries remain

Figure 1. Chemical stabilities of Cs−Xe compounds. (a) Calculated enthalpy of formation per atom of the Cs−Xe system with respect to decomposition into the elemental Cs and Xe. The dashed lines connect the data points, and the solid lines represent the convex hull. (b) Pressure−composition phase diagram of the Cs−Xe system. B

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Figure 3. Calculated phonon spectra for various Cs−Xe compounds at the respective stable pressure range. (a) CsXe(P4/mmm) at 50 GPa. (b) CsXe(I41/amd) at 100 GPa. (c) CsXe(Pm-3m) at 200 GPa. (d) CsXe2(Immm) at 50 GPa. (e) CsXe2(I4/mmm) at 200 GPa. (f) CsXe3(I4/mmm) at 50 GPa. (g) CsXe3(Fm-3m) at 200 GPa. (h) CsXe4(P21/m) at 200 GPa. (i) Cs2Xe(Immm) at 200 GPa. (j) Cs3Xe(I4/mmm) at 200 GPa. (k) Cs4Xe(P-1) at 200 GPa.

b = 3.255 Å and c = 4.354 Å at 50 GPa. The P4/mmm structure can also be viewed as a distorted CsCl-type structure. In this structure, each Cs atom has the eight nearest neighboring Xe atoms which form a hexahedron. Each Xe has also the eight nearest neighboring Cs atoms. Upon compression, at pressures higher than 58.0 GPa obtained from the pressure−composition phase diagram (Figure 1b), the tetragonal P4/mmm phase undergoes a phase transition to the tetragonal I41/amd phase (4 f.u. per cell, Figure 2b). In view of this structure, each Cs atom is in 12-fold coordination with 4 Cs atoms and 8 Xe atoms which form a tetrakaidecahedron. Each Xe atom is in 12-fold coordination with 8 Cs atoms and 4 Xe atoms. In the I41/amd structure, the arrangement of Cs atoms is identical to that of Cs−IV phase.44 With further increasing pressure, the tetragonal I41/amd phase undergoes further phase transition and transforms into the cubic Pm-3m phase (Figure 2c) at pressures higher than 158.5 GPa. The Pm-3m structure is thermodynamically stable at pressures ranging from 158.5 GPa to at least 200 GPa (Figure 1b). The lattice parameter for the Pm-3m structure is a = 3.140 Å at 200 GPa. It is the simplest CsCl-type structure for a binary compound, in which Cs and Xe atoms are both in 8-fold coordination.

unstable. At 200 GPa, all the investigated stoichiometries are stable. Strikingly, the Xe-rich CsXe2 stoichiometry is the most stable phase at pressures of 50, 100, and 200 GPa. Our calculations indicate that CsXe4, CsXe3, CsXe2, CsXe, Cs2Xe, Cs3Xe, and Cs4Xe have thermodynamic stability regimes on the phase diagram: CsXe4, stable above 93.5 GPa; CsXe3, stable above 24.0 GPa; CsXe2, stable above 26.5 GPa; CsXe, stable above 36.0 GPa; Cs2Xe, stable 49.5 GPa; Cs3Xe, stable above 158.6 GPa; Cs4Xe, stable above 158.4 GPa (Figure 1b). At elevated pressures, a variety of stable Cs−Xe compounds are synthesizable and most of them mainly exist in the form of close packing, which are depicted in Figure 2. For all of the predicted structures, calculated phonon dispersion curves confirm their dynamical stability with no imaginary frequencies observed in the whole Brillouin zone (Figure 3). With the aim of further analyzing these predicted structures, we mainly investigate their structural and electronic properties. According to our calculations, three thermodynamically stable phases with P4/mmm, I41/amd, and Pm-3m symmetry are established at the studied pressure region (Figure 2a−c). As shown in Figure 2a, CsXe stabilizes into a tetragonal AuCu-type structure43 (space group P4/mmm) at pressures higher than 36 GPa. The lattice parameters for the P4/mmm structure are a = C

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The Journal of Physical Chemistry C Table 1. Crystal Structure Information of Stable Cs−Xe Compounds P (GPa)

lattice parameters (Å, °)

CsXe4-P21/m

200

CsXe3-Fm-3m

200

a = 7.415 b = 4.572 c = 4.856 a = γ = 90.0 β = 71.097 a = b = c = 6.284 α = β = γ = 90.0

CsXe2-I4/mmm

200

CsXe-Pm-3m

200

Cs2Xe-Immm

200

Cs3Xe-I4/mmm

200

Cs4Xe-P-1

200

CsXe-I41/amd

100

CsXe3-I4/mmm

50

CsXe2-Immm

50

CsXe-P4/mmm

50

phases

atomic coordinates (fractional)

a = b = 3.168 c = 9.312 α = β = γ = 90.0 a = b = c = 3.14 α = β = γ = 90.0 a = 2.821 b = 3.943 c = 8.419 α = β = γ = 90.0 a = b = 3.976 c = 7.896 α = β = γ = 90.0 a = 4.851 b = 4.866 c = 7.404 α = 109.033 β = 102.602 γ = 99.381 a = b = 4.235 c = 8.514 α = β = γ = 90.0 a = b = 4.506 c = 9.172 α = β = γ = 90.0 a = 9.715 b = 3.289 c = 4.366 α = β = γ = 90.0 a = b = 3.255 c = 4.354 α = β = γ = 90.0

Cs(2e) Xe1(2e) Xe2(2e) Xe3(2e) Xe4(2e) Cs(4a) Xe1(4b) Xe2(8c) Cs(2b) Xe(4e)

0.2 0.599 0.0 0.401 0.199 0.0 0.0 0.25 0.5 0.0

0.25 0.25 0.25 0.25 0.75 0.0 0.5 0.25 0.5 0.0

0.233 0.033 0.833 0.633 0.568 0.0 0.0 0.25 0.0 0.166

Cs(1b) Xe(1a) Cs(4j) Xe(2b)

0.5 0.0 0.0 0.5

0.5 0.0 0.5 0.0

0.5 0.0 0.166 0.0

Cs1(2b) Cs2(4d) Xe(2a) Cs1(2i) Cs2(2i) Cs3(2i) Cs4(1b) Cs5(1d) Xe(2i) Cs(4a) Xe(4b)

0.5 0.0 0.0 0.499 0.501 0.999 0.0 0.5 0.999 0.0 0.5

0.5 0.5 0.0 0.598 0.2 0.199 0.0 0.0 0.6 0.5 0.0

0.0 0.25 0.0 0.199 0.4 0.899 0.5 0.0 0.7 0.25 0.25

Cs(2b) Xe1(2a) Xe2(4d) Cs(2b) Xe(4e)

0.5 0.0 0.5 0.0 0.165

0.5 0.0 0.0 0.5 0.0

0.0 0.0 0.25 0.5 0.0

Cs(1c) Xe(1b)

0.5 0.0

0.5 0.0

0.0 0.5

As to CsXe3, two thermodynamically stable phases with I4/ mmm and Fm-3m symmetry are determined at the selected pressure region. The low-pressure tetragonal I4/mmm structure (2 f.u. per cell, Figure 2f) becomes stable above 24.0 GPa (Figure 1b). The lattice parameters for the I4/mmm structure are a = b = 4.506 Å and c = 9.172 Å at 50 GPa. It can be seen as the tetragonal TaNi3-type structure.47 In this structure, each Cs atom has the four nearest neighboring Xe atoms which form a square plane. The Xe atoms have two sites, of which each Xe atom is in 4-fold coordination with 4 Xe atoms making up a square plane, another Xe atom is in 4-fold coordination with 4 Cs atoms. At pressures higher than 83.5 GPa (Figure 1b), the I4/mmm phase undergoes a phase transition and transforms into the cubic FeAl3-type structure48 (space group Fm-3m, 4 f.u. per cell, Figure 2g). The lattice parameter for the Fm-3m structure is a = 6.284 Å at 200 GPa. Each Cs atom has the eight nearest neighboring Xe atoms. The Xe atoms have also two sites, of which each Xe atom is in 8-fold coordination with 4 Cs atoms and 4 Xe atoms, another Xe atom is in 8-fold coordination with 8 Xe atoms.

For the Xe-rich CsXe2 stoichiometry, two thermodynamically stable phases with Immm and I4/mmm symmetry are identified over the entire pressure range. The orthorhombic Immm structure (2 f.u. per cell, Figure 2d) is thermodynamically stable above 26.5 GPa (Figure 1b). The lattice parameters for the Immm structure are a = 9.715 Å, b = 3.289 Å, and c = 4.366 Å at 50 GPa. It can be seen as a distorted CsCl-type structure. Therefore, each Cs atom has the eight nearest neighboring Xe atoms which form a hexahedron. Each Xe atom is in 8-fold coordination with 4 Cs atoms and 4 Xe atoms forming a hexahedron. The Immm structure is stable in the pressure region of 26.5−65.0 GPa. Above 65.0 GPa, it transforms into the tetragonal MoSi2-type structure45,46 (space group I4/mmm, 2 f.u. per cell, Figure 2e) which is stable up to at least 200 GPa. The lattice parameters for the I4/mmm structure are a = b = 3.168 Å and c = 9.312 Å at 200 GPa. It can also be seen as a distorted CsCl-type structure. Thus, each Cs atom has the eight nearest neighboring Xe atoms, and each Xe atom is surrounded by 4 Cs atoms and 4 Xe atoms. D

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Figure 4. Calculated electronic band structures and projected density of states (PDOS) for CsXe2. (a) Electronic band structure of CsXe2 (Immm) at 50 GPa. (b) Electronic band structure of CsXe2 (I4/mmm) at 200 GPa. (c) PDOS of CsXe2 (Immm) at 50 GPa. (d) PDOS of CsXe2 (I4/mmm) at 200 GPa. The dashed horizontal and vertical lines denote the Fermi level.

fold coordinated by 6 Xe atoms, 11-fold coordinated by 3 Cs atoms and 8 Xe atoms, 6-fold coordinated by 6 Xe atoms, and 10-fold coordinated by 4 Cs atoms and 6 Xe atoms. In contrast to the Xe-rich compounds, a variety of Cs-rich compounds have also stability region on the phase diagram. Cs2Xe is found to be stable in a structure with Immm symmetry (2 f.u. per cell, Figure 2i) in a wide pressure region (49.5−200.0 GPa; Figure 1b). Interestingly, the Immm structure of Cs2Xe is isostructural to CsXe2 with Immm symmetry (Figure 2d). It is noted that all the Cs atoms are 10-fold coordinated with 5 Cs atoms and 5 Xe atoms. Each Xe atom is surrounded by 10 nearest neighboring Cs atoms which form a dodecahedron. With the Cs concentration increasing, Cs3Xe with I4/mmm symmetry (2 f.u. per cell, Figure 2j) is thermodynamically stable in the pressure region of 158.6−200.0 GPa (Figure 1b). Strikingly, in view of this structure, it is isostructural to the CsXe3 with I4/mmm symmetry (Figure 2f). The Cs atoms have two sites, of which each Cs atom is 8-fold coordinated by 8 Cs atoms, another Cs atom is 8-fold coordinated by 4 Cs atoms and 4 Xe atoms. Each Xe atom is 8-fold coordinated by 8 Cs atoms. In addition, Cs4Xe with P-1 symmetry (2 f.u. per cell, Figure 2k) is thermodynamically stable in the pressure region of 158.4−200.0 GPa (Figure 1b). In view of this structure, The Cs atoms have five sites. The Cs atoms have the following coordination: 9-fold coordinated by 7 Cs atoms and 2 Xe atoms, 5-fold coordinated by 4 Cs atoms and 1 Xe atoms, 6-fold coordinated by 4 Cs atoms and 2 Xe atoms, 4-fold coordinated by 4 Cs atoms, and 10-fold coordinated by 10 Cs atoms. Each Xe atom is 10-fold coordinated with 9 Cs atoms and 1 Xe atom. Under high pressure, Cs reacts with Xe to form the electronrich compounds, which should exhibit metallic features. Thus, all of the Cs−Xe compounds should be regarded as intermetallic compounds. To analyze the electronic properties of Cs−Xe compounds, we focus on the most stable CsXe2 stoichiometry in the studied pressure range. The calculated electronic band structure and the projected density of states (PDOS) are shown in Figure 4. Notably, the calculated

Figure 5. Calculated electron localization function (ELF) for CsXe2. (a) ELF in the (001) plane of CsXe2(Immm) at 50 GPa. (b) ELF in the (100) plane of CsXe2 (I4/mmm) at 200 GPa.

Figure 6. Comparison of the fitted Birch−Murnaghan equation of states for CsXe in the Pm-3m structure by using the calculated results from the PAW pseudopotentials and the full-potential LAPW methods.

As the Xe concentration increases, CsXe4 with P21/m symmetry (2 f.u. per cell, Figure 2h) is thermodynamically stable above 93.5 GPa and remains stable up to at least 200 GPa. No phase transitions were found in CsXe4. The lattice parameters for the P21/m structure are a = 7.415 Å, b = 4.572 Å, and c = 4.856 Å at 200 GPa. From a structural point of view, each Cs atom is surrounded by the 12 nearest neighboring Xe atoms which form a tetrakaidecahedron. The Xe atoms have four sites. The Xe atoms have the following coordination: 6E

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electronic band structure and PDOS of low-pressure Immm phase and high-pressure I4/mmm phase of CsXe2 reveal that the conducting states mainly derive from the Cs and Xe 5d states around the Fermi level. However, the Cs 6s states make a quite small contribution to the states near the Fermi level. This result demonstrates partial charge transfer from Cs 6s to the Cs and Xe 5d orbitals. To illustrate the charge transfer between Cs and Xe atoms, we calculated the Bader charge of the Immm phase at 50 GPa and the I4/mmm phase at 200 GPa. A small charge transfer for Immm and I4/mmm phases was found. The calculated Xe charges for Immm and I4/mmm phases are −0.18 and −0.14, respectively, whose difference derives from the reason that pressure leads to more electrons of Cs transiting to its 5d orbital. The results show that Cs and Xe form intermetallic compounds with weak ionicity, which may be a reason for stabilizing Cs−Xe compounds. In addition, to illustrate the bonding features of the Cs−Xe compounds, we adopted an intuitive approach through the calculation of the electron localization function (ELF).49 The ELF can be used to represent the relative electron localization in crystal structures, and large ELF values (>0.5) are usually corresponding to core or lone pair electrons and covalent bonds, while small ELF values signify the ionic bonds. The calculated ELFs of the Immm phase at 50 GPa and the I4/mmm phase at 200 GPa are shown in Figure 5, indicating a metallicity of CsXe2 with delocalized electrons. The areas with large ELF values (>0.5) near the Cs and Xe atoms indicate the core 5p electrons in Cs and Xe. The areas with small ELF values (