Barium Sulfide under Pressure: Discovery of Metastable Polymorphs

Article pubs.acs.org/IC

Barium Sulfide under Pressure: Discovery of Metastable Polymorphs and Investigation of Electronic Properties on ab Initio Level Dejan Zagorac,*,† Klaus Doll,‡ Jelena Zagorac,† Dragana Jordanov,† and Branko Matović† †

Institute of Nuclear Sciences Vinca, Materials Science Laboratory, Belgrade University, 11001 Belgrade, Serbia Institute of Theoretical Chemistry, University of Stuttgart, 70569 Stuttgart, Germany

‡

S Supporting Information *

ABSTRACT: Barium sulfide (BaS) is an important precursor to other barium compounds with applications from ceramics and flame retardants to luminous paints and additives, and recent research shows potential technological applications in electrical and optical devices. Under normal conditions, BaS crystallizes in the NaCl type of structure, and with the increase in pressure BaS undergoes a structural phase transition to a CsCl type modification. This study presents modeling of barium sulfide under pressure with special focus on structural aspects and electronic properties. We predict metastable BaS polymorphs which have not yet been observed in the experiment or in previous calculations, and we investigated their vibrational and thermodynamical properties. Furthermore, we investigate the electronic properties of experimentally known structures as well as novel predicted modifications of BaS on ab initio level using Hartree−Fock, GGA-PBE, and the hybrid B3LYP functional. In this way, we address new possibilities of synthesizing BaS and possible band gap tuning which can have great applications in optoelectrical technologies.

1. INTRODUCTION One of the main goals of inorganic and theoretical chemistry is to find new compounds, possibly with advanced properties, or find advanced properties in already existing materials. In the past century, the only possible solution was experimental synthesis. However, in the last few decades, developments in theoretical chemistry and huge improvements in computational power have brought an alternative: theoretical prediction of new compounds and new (meta)stable crystalline modifications of already existing solids followed by their synthesis.1−8 Recently, many different groups have successfully performed crystal structure prediction using empirical potentials or/and ab initio approach.9−17 In the past few years, we performed such structure predictions, combining global and local optimization routines using empirical, semiempirical, and ab initio potentials, exploring energy landscapes of various binary and ternary systems.18−22 In the present study, as an example system, we chose barium sulfide (BaS), which is, like other barium chalcogenides, a wide band gap semiconductor.23,24 Barium chalcogenides BaX (X = S, Se, and Te) are currently under extensive research due to their potential technological applications in microelectronics, light-emitting diodes (LEDs), laser diodes (LDs), and magneto-optical devices.25 It is known that they have one of the highest ionic characters among all the alkaline-earth chalcogenide compounds and that they show metallization behavior under high pressures.26,27 Therefore, it is expected that these compounds may provide new II−VI candidates for the fabrication of various electrical and optical devices in the future.28,29 Among other BaX compounds, barium sulfide (BaS) has the greatest cation/anion radius ratio,30 and besides possible © 2017 American Chemical Society

electrical and optical applications, it is an important precursor to other barium compounds with applications from ceramics and flame retardants to luminous paints and additives.29 The first experimental studies have shown that under normal conditions BaS crystallizes in the NaCl (B1) type of structure (see Figure 1a).30−34 With the increase in pressure, BaS

Figure 1. Visualization of the experimentally observed and calculated structure types in BaS: (a) NaCl (B1) type and (b) CsCl (B2) type. Small (green) and large (red) spheres correspond to S and Ba atoms, respectively.

undergoes a reversible structural phase transition to a CsCl (B2) type modification at pressures above 6 GPa (see Figure 1b),30 like other chalcogenides.27,35 During the B1 → B2 (Strukturbericht designation) phase transition, no intermediate phase has been experimentally observed, and with the further increase in pressure, the CsCl type of structure continues to be Received: June 24, 2017 Published: August 24, 2017 10644

DOI: 10.1021/acs.inorgchem.7b01617 Inorg. Chem. 2017, 56, 10644−10654

Article

Inorganic Chemistry

coupled perturbed Kohn−Sham method.72 Structure analysis and visualization was performed using the KPLOT73 and VESTA74 programs.

stable. There are several experimental observations indicating that with the further increase in pressure above 80 GPa, the CsCl modification starts to show a metallic character.26,36 There have been many recent experimental investigations of barium chalcogenides directed to the development of these materials and investigation of their properties.37−40 On the other hand, theoretical investigations of the pressure-induced phase transitions of barium chalcogenides and barium sulfide have been performed.41−48 Due to potential optical and electrical applications, most of this work was focused on obtaining the transition pressure, band structure, density of states, and thermodynamic and elastic properties of already existing BaS phases. This leaves yet an unexplored field to investigate, although a great amount of theoretical work has already been done for the BaS system.

3. RESULTS AND DISCUSSION 3.1. Phase Transitions and Structural Aspects of BaS under Pressure. Under normal conditions, BaS crystallizes in the NaCl (B1) type of structure with the space group Fm3m ̅ (no. 225)30−34 and 6-fold coordination (CN = 6) of Ba by the S atom (see Figure 1a). With the increase in pressure above 6 GPa, the NaCl structure transforms into a CsCl (B2) type modification, where the two phases coexist above or below the transition pressure during the pressure increase or release, respectively.30,36 The CsCl type modification has space group Pm3̅m (no. 221) and 8-fold coordination (CN = 8, see Figure 1b). So far, no intermediate phase has been experimentally observed during the B1 → B2 pressure induced phase transition. Our previous ab initio studies on related systems, e.g., metal sulfides MS (M = Pb, Zn, Sn, or Ge),59,61,75 and metal oxides MO (M = Pb, Zn, Sn, or Ge),18−20,75 have provided a large number of possible structure candidates for the ab initio optimization of BaS. Furthermore, we performed data mining searches within studies involving alkaline earth metal oxides76,77 and alkali metal halides78 to get additional structure candidates. As a result, dozens of structure candidates were chosen for optimization (for a full list, see Supporting Information). Here, we show only the energetically most favorable modifications of barium sulfide found after ab initio optimization on the GGAPBE, B3LYP, and Hartree−Fock levels (see Table 2). Our calculations show good agreement with previous experimental30−36 and theoretical results26,27,41−46,67,68 involving the equilibrium NaCl (B1) and high pressure CsCl (B2) phase. When comparing the methods, the calculated cell parameters and atomic positions using the GGA-PBE functional are closest to the experimental values. Furthermore, our calculations show that the experimentally observed modification of barium sulfide is the energetically lowest and thermodynamically most stable one (see Table 3 and Figure 2) at ambient conditions regardless of the computational approach applied. Figure 2a shows E(V) curves of barium sulfide computed for the most relevant structure types. The pressure-driven phase transitions can be derived from the calculated enthalpy vs pressure (H(p)) diagrams, given in Figure 2b and c. Because the electronic structure of BaS calculated via the GGA-PBE functional showed the best agreement with the experimental results (compared to B3LYP and HF), in the following we present the results obtained using GGA-PBE, while HF and B3LYP diagrams are presented in the Supporting Information. Because no intermediate BaS phase has yet been experimentally observed during the B1 → B2 pressure induced phase transition, one of the most interesting results is the TlI (B33) modification calculated at high pressures (see Figure 2a). Furthermore, the TlI structure type is a promising candidate in the high pressure region when using B3LYP or Hartree−Fock (see Supporting Information). However, when analyzing H(p) curves, especially calculated with GGA, we observe that the B1 → B2 pressure induced phase transition is at around 5.9 GPa, and that the TlI modification is metastable, but only very close to the transition region. Below the transition region (∼5.5 GPa), we observe that the TlI structure is more stable than the CsCl modification of BaS.

2. COMPUTATIONAL METHODS Our general approach to the determination of structure candidates is given in detail elsewhere.1,6,7 The ab initio calculations were performed with the CRYSTAL14 code,49,50 which is based on local Gaussian type orbitals. The local optimizations employed analytical gradients with respect to the atom positions,51,52 the cell parameters,53−55 and a local optimizing routine.56 These local optimizations were performed both on the Hartree−Fock and the DFT level, employing the B3LYP functional (Becke’s three parameter functional57 in combination with the correlation functional of Lee, Yang, and Parr) and the generalized gradient approximation (GGA) with the PBE (Perdew, Burke, and Ernzerhof) functional.58 This broad range of methods allows wider estimation of the error due to the choice of the functional used. Though Hartree−Fock theory usually agrees less with the experiment than DFT, it is a well-controlled approach and may serve as a reference. The deviations of the various methods from each other can be viewed as error bars concerning the method. In the discussion, we mainly focus on PBE results. This is because for the related PbS system, calculations using PBE functional turned out to agree better with the experimental data than the B3LYP calculations.59 For the ab initio calculations, a [5s4p1d] all-electron basis set was used for sulfur. The inner [3s2p] shells were chosen as in ref 60 together with three additional exponents (sp 0.2413, sp 0.106, d 0.383) used in refs 59 and 61. For barium, we used the pseudopotential by Hay and Wadt62 in combination with the tightest sp contraction from ref 63. In addition, we used three sp shells with exponent 0.95, 0.45, 0.17 and two d shells with exponents 0.4 and 0.15 (see Table 1).

Table 1. Gaussian Type [4s4p2d] Basis Set Used for Barium Ba: small core pseudopotential, 10 valence electrons64 type

exponent

sp

8.55243254 2.113983 1.87184187 0.95 0.45 0.17 0.4 0.15

sp sp sp d d

contraction coefficient 0.00444607339 (s) −0.760825674 (s) 1.0 (s) 1.0 (s) 1.0 (s) 1.0 (s)

0.0108828307 (p) −0.598137631 (p) 1.0 (p) 1.0 (p) 1.0 (p) 1.0 (p) 1.0 (d) 1.0 (d)

Therefore, in total a [4s4p2d] basis set was used for Ba as in ref 64, which is especially important to obtain the proper conduction band structure and band gap of BaS.65−70 Vibrational and thermodynamical properties were calculated using a supercell approach as implemented in CRYSTAL14 (see, e.g., ref 71). To achieve maximum computational efficiency and keep the calculations tractable, supercells of the size 2 × 2 × 2 were used for the various directions and modifications. The LO-TO splitting at the Γ point was calculated by using the dielectric function, which was computed within the framework of the 10645


Article

Inorganic Chemistry

Table 2. Cell Parameters and Atom Positions of the Energetically Most Favorable Modifications of BaS Found after Local Optimization on GGA-PBE, B3LYP, and Hartree−Fock Level cell parameters (Å) and fractional coordinates space group and modification Fm3̅m (225) NaCl type

previous work

GGA-PBE

exp. a = 6.39 Å30 exp. a = 6.38 Å34a GGA a = 6.41 Å24 GGA a = 6.47 Å42a

P63/mmc (194) 5−5 type

P63/mmc (194) NiAs type

Cmcm (63) TlI type

F4̅3m (216) Sphalerite type

Pm3̅m (221) CsCl type

a

exp. a = 3.69 Å30a GGA a = 3.85 Å42a

B3LYP

HF

a = 6.44 Ba (0 0 0) S (1/2, 1/2, 1/2)

a = 6.50 Ba (0 0 0) S (1/2, 1/2, 1/2)

a = 6.63 Ba (0 0 0) S (1/2, 1/2, 1/2)

a = 5.40, c = 6.41 Ba (1/3, 2/3, 3/4) S (2/3, 1/3, 3/4) a = 4.47, c = 7.84 Ba (0 0 0) S (1/3, 2/3, 1/4) a = 4.20, b = 12.37, c = 4.87 Ba (0, 0.1230, 1/4) S (0, 0.3758, 1/4) a = 7.05 Ba (0 0 0) S (1/4, 1/4, 1/4) a = 3.87 Ba (0 0 0) S (1/2, 1/2, 1/2)

a = 5.45, c = 6.47 Ba (1/3, 2/3, 3/4) S (2/3, 1/3, 3/4) a = 4.52, c = 7.92 Ba (0 0 0) S (1/3, 2/3, 1/4) a = 4,31, b = 13.11, c = 4.80 Ba (0, 0.1286, 1/4) S (0, 0.3697, 1/4) a = 7.12 Ba (0 0 0) S (1/4, 1/4, 1/4) a = 3.92 Ba (0 0 0) S (1/2, 1/2, 1/2)

a = 5.55, c = 6.58 Ba (1/3, 2/3, 3/4) S (2/3, 1/3, 3/4) a = 4.60, c = 8.04 Ba (0 0 0) S (1/3, 2/3, 1/4) a = 4.41, b = 13.87, c = 4.81 Ba (0, 0.1328, 1/4) S (0, 0.3658, 1/4) a = 7.27 Ba (0 0 0) S (1/4, 1/4, 1/4) a = 3.98 Ba (0 0 0) S (1/2, 1/2, 1/2)

For a full scope of previous experimental and theoretical work, please check the references.26,27,30−36,41−46,67,68

Table 3. Calculated Total Energies of the BaS Polymorphsa total energy (total energy difference per formula unit, ΔEmethod = E(NaCl) − E(type)) structure type NaCl NiAs 5−5 TlI CsCl ZnS

GGA-PBE −423.48285 −423.47998 −423.47923 −423.47701 −423.47133 −423.46854

B3LYP −423.57269 −423.56843 −423.56899 −423.56355 −423.55528 −423.55874

(0.0) (+0.0780) (+0.0985) (+0.1589) (+0.3135) (+0.3894)

(0.0) (+0.1159) (+0.1007) (+0.2487) (+0.4738) (+0.3796)

HF −422.66258 −422.65366 −422.65450 −422.64775 −422.63855 −422.64340

(0.0) (+0.2427) (+0.2199) (+0.4035) (+0.6539) (+0.5219)

Note that total energies per formula unit are given in hartrees (Eh), while total energy differences per formula unit, ΔEmethod = E(NaCl) − E(type) presented in brackets are given in electronvolts (eV). Local optimizations were performed employing the Hartree−Fock method (HF), DFT (with GGA-PBE), and a hybrid (B3LYP) functional. a

ΔEGGA = 0.00287 Eh ∼ 900 K, ΔEB3LYP ∼ 1350 K, ΔEHF ∼ 2800 K, see Table 3). Because this modification is only metastable even with an increase in temperature and/or pressure, it would be very hard to synthesize, although its coordination number 6 (CN = 6, see Figure 3b) suggests that it might be a metastable phase at high temperatures in the BaS system. The NiAs structure is frequently encountered in many related systems within our calculations18−20,59,61 and by others,76−78,86 where it was found to be an interesting candidate for 2D materials.86 Furthermore, for a long time, a NiAs phase is known to exist in the BaO system at high pressures.36 Therefore, we suggest that it might be possible to observe this hypothetical NiAs modification in the experiment if one could use, e.g., the NiAs modification of BaO as a template for BaS deposition. At effective negative pressures, we observe two energetically favorable structure candidates (see Tables 2 and 3 and Figure 2): the 5−5 type and the ZnS structure type (see Figure 4). These structures are stable regardless of the computational approach (see Supporting Information). For calculations performed on the GGA-PBE level, we observe from the H(p) curves that the 5−5 modification is stable below −1 GPa (see

We note that this NaCl (B1) → TlI (B33) → CsCl (B2) phase transition is known to exist in TlI79,80 and PbS59,61,81−85 systems. The orthorhombic TlI type (Cmcm) can be considered to be a rather distorted NaCl structure type.79 It can be described as a chain of monocapped trigonal prisms sharing common rectangular faces with a Ba atom in the center of this S7 polyhedron (see Figure 3a). The stacking order is ABAB. In the thallium iodide system, this orthorhombic modification of thallium iodide transforms to the CsCl type modification with increasing temperature,80 while in PbS, the same process occurs upon further increase in pressure.59,61,81−85 In barium sulfide, we find a metastable TlI structure which might be observed at elevated pressures and temperatures (see Figure 2 and Table 3). Quenching or slow decompression of the high-pressure CsCl modification of BaS could be possible synthesis routes where TlI modification might be observed in the experiment. The calculated E(V) curves have shown one promising structure candidate at elevated temperatures regardless of the computational approach: the NiAs (B81) structure type (see Figure 2, Table 2, and Supporting Information). For calculations performed on the GGA-PBE level, the total energy difference per formula unit can be estimated to be ∼900 K (ΔEGGA = E(NaCl) − E(NiAs) = (−423.48285 + 423.47998), 10646


Article

Inorganic Chemistry

Figure 2. Energy and enthalpy versus volume of BaS using GGA-PBE: (a) E(V) curves calculated for the most relevant structure types, (b) H(p) curves calculated at high pressures, and (c) H(p) curves calculated at effective negative pressures. Note that the energies per formula unit are given in hartrees (Eh), and volumes are given in Angstroms cubed (Å3).

by S in a hexagonal lattice (P63/mmc) with ABAB stacking. The S and Ba atoms form trigonal bipyramids around Ba and S, respectively (see Figure 4a).75 The 5−5 structure type has been found on the energy landscapes of many AB compounds,18−20,59,61,75−78,87,88 but in case of the PbS and BaS system, it appears only in the effective negative pressure region. Because GGA-PBE calculations for BaS show a smaller energy difference to the equilibrium NaCl structure as well as a smaller negative transition pressure compared to that of PbS, it would be more likely to experimentally observe the 5−5 modification in the BaS system. Furthermore, the existence of the 5−5 modification has been proposed in some recent thin film experiments in the ZnO89,90 and MgO91 system as well as related distorted structures away from the equilibrium NaCl synthesized as nanostructures or thin films in the MX system (M = Pb, Sn, or Ge; X = Se, S, or Te).92−96 Many of these examples could be an indication of a possible synthesis route to the 5−5 modification for barium sulfide. Recent pioneering work from Ihanus et al.,97,98 where BaS thin films were deposited by the atomic layer deposition (ALD) technique, are the first steps of a possible synthesis of the 5−5 modification in the BaS system. One could estimate the stress associated by using elastic properties of the 5−5 modification and, for example, other BaS modifications, and the strain due to a lattice mismatch between a potential substrate and the 5−5 modification in BaS. The stress can then be evaluated to further help guide a possible synthesis route using the expression:

Figure 3. Visualization of the predicted structure types in the BaS compound: (a) TlI (B33) type and (b) NiAs (B81) type. Small (green) and large (red) spheres correspond to S and Ba atoms, respectively.

Figure 4. Visualization of the predicted structure types for BaS: (a) 5− 5 type and (b) Sphalerite (ZnS) type. Small (green) and large (red) spheres correspond to S and Ba atoms, respectively.

σ=ϵ

Figure 2c), which is also observed with the B3LYP and HF calculations (see Supporting Information). On the other hand, the sphalerite (ZnS, B3) modification has much higher total energy and transition pressure regardless of the computational approach (see Supporting Information) and is therefore less likely to be observed in the experiment. We can describe the 5−5 structure type as a 5-fold coordination of Ba

E 1−ν

with an elastic modulus E of 53.1 GPa for the related PbTe-PbS system,99 a Poisson ratio v = 0.254 for BaS,100 and a strain due to the lattice mismatch ϵ = (asub − aBaS)/aBaS = 0.19, we obtain a value of the stress σ = 14 GPa for the corresponding 5−5 structure using NaCl as a substrate (with the lattice parameters 10647


Article

Inorganic Chemistry

Figure 5. (a) DOS and (b) band structure of the NaCl (B1) modification at equilibrium volume. Calculation performed using GGA-PBE.

Figure 6. (a) DOS and (b) band structure of the CsCl (B2) structure at equilibrium volume showing the indirect band gap. Calculation performed using GGA-PBE.

5, showing a calculated band gap size of 2.55 eV and an indirect band gap along Γ → X direction of the Brillouin zone using GGA-PBE method, which is in very good agreement with previous theoretical work. Furthermore, we observe from the DOS that the valence bands are dominated by sulfur and the conduction bands by barium, which is in agreement with previous calculations.64−70 Therefore, we note that our calculations are in very good agreement with theoretical and experimental results and that the use of our optimized basis set for barium (see Table 1) is especially important to obtain the proper conduction band structure and band gap of BaS. In the next step, we calculated the DOS and the band structure of the CsCl (B2) modification (see Figure 6). While the orbital contributions observed from the DOS look similar as for the equilibrium NaCl structure, our results for CsCl modification show a band gap size of 1.64 eV and an indirect band gap along Γ → M direction of the Brillouin zone using the GGA-PBE method. This large shrinking of the CsCl (B2) band gap compared to the NaCl (B1) modification is connected to the B1 → B2 phase transition at high pressures. There are few experiments performed at high pressures, where it has been shown that with the further increase in pressure (>80 GPa), the CsCl modification becomes metallic.26,27,36 We are aware of an early calculation with the LDA gave a metallization pressure of

from the present GGA calculations). Thus, the BaS system appears to be a good candidate to synthesize this new type of modification in thin films or a bulk phase.

4. ELECTRONIC PROPERTIES OF BARIUM SULFIDE POLYMORPHS After modeling and optimization of the proposed BaS polymorphs on ab initio level, an investigation of their electronic properties was performed, with the goal to elucidate existing theoretical results on BaS and identify possible technological and industrial applications on not yet observed phases. Therefore, band structure and density of states (DOS) calculations were performed using HF, DFT (GGA-PBE), and hybrid (B3LYP) functionals. Our calculations were in very good agreement with previous experimental observations, where such data were available, and can represent the electronic properties of BaS with high accuracy. Previous experimental investigations of BaS have found a relatively large direct band gap of ∼3.9 eV at the Γ point of the Brillouin zone.23,24,101 However, previous theoretical investigations of electronic properties of the NaCl modification in BaS system have shown an indirect band gap along Γ → X direction, ranging in size from 1.83 to 3.54 eV.42,65−70 Our DOS and band structure calculations are represented in Figure 10648


Article

Inorganic Chemistry

Figure 7. Band structure of the CsCl (B2) structure: (a) at 44 GPa showing direct band gap and (b) at 63 GPa exhibiting metallic properties. Calculation performed using GGA-PBE.

Figure 8. Band structure of the (a) TlI type and (b) 5−5 type at the computed equilibrium volume in the BaS system using GGA-PBE method. Note that the labels of the special points in the TlI type correspond to a base-centered orthorhombic lattice and in the 5−5 type to a hexagonal lattice, respectively.

32 GPa.70 However, due to the large spreading of the results, we hope that our results will encourage future high pressure research of BaS. Our calculations show further shrinking of the band gap with increase in pressure up to ∼53 GPa. Figure 7a shows a CsCl structure calculated at 44 GPa using the GGA-PBE method, where we observed a direct band gap at the Γ point. These changes have been observed in previous experimental and theoretical research of BaS at high pressures where CsCl has been shown to become a direct gap semiconductor with a transition at the Γ point.26,36 At 53 GPa, we observe closing of the direct band gap and CsCl modification becoming metallic (see Supporting Information). Figure 7b shows metallic properties of CsCl at 63 GPa, and with further increase in pressure up to 121 GPa, we observed metallic behavior of the CsCl modification for the whole pressure range (see Supporting Information). Metallization of the CsCl structure was also observed with B3LYP and HF calculations, however, at the extreme pressure conditions beyond ∼150 and ∼200 GPa, respectively. Furthermore, we show the band structure calculations for the most relevant alternative BaS modifications within the GGA approximation: the TlI type (Figure 8a), and the 5−5 type [Figure 8(b)]. Our calculations show band gap size of 2.50 eV

in the TlI modification and 3.06 eV in the 5−5 modification, and in both cases an indirect band gap along the Γ-Y and Γ-K points of the Brillouin zone, respectively. Note that the labels of the special points in the equilibrium NaCl (B1) modification correspond to a face-centered cubic lattice, while the labels of the special points in the TlI type correspond to a base-centered orthorhombic lattice and in the 5−5 type to a hexagonal lattice, respectively (for the DOS, see Supporting Information). In addition, we show the band structures and DOS of the NiAs and ZnS modifications in the Supporting Information. We note that the orbital contributions near the band gap in the metastable structures look similar as for the experimentally known stable structures NaCl and CsCl. An important issue is that by using these additional BaS modifications in technological applications, one could tune the band gap, decreasing it by using the TlI (B33) and the CsCl (B2) type of structure, or increasing it by using, e.g., the 5−5 type of structure. This is not a simple task in a complex multiphase systems because electronic band structure is not a simple additive property, i.e., one cannot trivially tune the band gap of mixed phase system by changing the ratio of components by adding the band gaps of the pure phases. Multiphase material is composed of phases with different band structures and in, e.g., polycrystalline materials, it is in fact the 10649


Article

Inorganic Chemistry

tions.64,102,103 Therefore, first we computed the phonon spectrum for the NaCl type structure by using the GGA-PBE approach. We recall from the corresponding E(V) and H(p) curves that the NaCl modification is the most stable BaS phase at standard pressure and temperature (corresponding to 0 GPa and 0 K in the ab initio calculations), which is confirmed by experimental and theoretical observations.26,30,36,41−47,67,68 Figure 9a shows the phonon band structure calculations of the NaCl modification at equilibrium. The computed dielectric constant (ε∞) is 4.26, in good agreement with experiment.104 Because all the frequencies are real, the rock salt structure is considered a local minimum, which is kinetically stable. At low frequencies, as expected, the main contribution to the phonon DOS is due to the heavy Ba ions, and at high frequencies, the main contribution is due to the lighter S ions (see the total phonon DOS and the DOS projections in Figure 9b). This trend has been observed in all other calculated metastable structure candidates of barium sulfide. Again, our calculations were in a good agreement with previous experimental and theoretical observations,41,100,104 and phonon bands agree best with the ones in ref 96. For the other structure types (the TlI, the NiAs, the 5−5, and sphalerite), we display the phonon density of states in the Supporting Information. To check the stability with respect to phonon modes with imaginary frequencies, we consider the integral of the phonon DOS for each of the calculated BaS phases from 0 cm−1 onward. The integrated phonon density of states for the BaS structure is normalized to 3*n, where n is number of atoms in the reference unit cell. In the case of the NaCl structure, n = 2, and the integrated DOS amounts to 6, indicating the stability. In the case of the TlI modification, with n = 4, the integrated DOS amounts to 11.99 with the remaining states referring to imaginary frequencies. In the case of the phonon DOS, the NiAs, and the 5−5 structure (n = 4), the integrated DOS amounts to 12, again indicating stability at 0 GPa and 0 K. On the other hand, the sphalerite structure (n = 2) has an integrated DOS of 5.96 only, which indicates instability. However, as stated before, this modification is far away from the range which can be expected to be reached with experimental synthesis. In addition, we calculated thermodynamical properties, including vibrational contributions. Figure 10a shows G(T)

band alignments at the interphase boundaries which start to govern the electronic structure and electronic band gaps. Finally, the summary of the calculated band gaps of the most relevant BaS modifications by using HF, DFT (GGA-PBE), and hybrid (B3LYP) functionals is shown in Table 4 (for additional Table 4. Computed Band Gap Size of the Most Relevant BaS Polymorphsa band gap (eV) structure type

GGA-PBE

B3LYP

HF

ZnS 5−5 NaCl TlI NiAs CsCl

4.29b 3.06 2.55 2.50 2.43b 1.64

5.68b 4.77 4.00 3.83 3.84b 3.03

11.68b 10.41 9.86 9.53 9.66b 8.65

a

Calculations were performed at 0 GPa using Hartree-Fock (HF), DFT (GGA-PBE), and hybrid (B3LYP) functionals. Note that the band gap is expressed in eV units. bCalculations have shown direct band gap at 0 GPa.

band structures and DOS, see Supporting Information). We observe the general trend that the size of the band gap decreases from equilibrium NaCl (B1) modification to the nonequilibrium structures in the high pressure regions regardless of the computational method applied. We note that the NiAs band gap size is a bit larger than TlI type at HF and B3LYP level of calculation. Similarly, we observe the increase in the band gap size from equilibrium NaCl (B1) modification to the nonequilibrium structures at effective negative pressures regardless of the computational method applied (see Table 4). A similar effect has been observed in PbS and ZnO.18,20,59 In addition, we observed an influence of the structure type on the direct or indirect band gap, which is summarized in Table 4. We conclude that our research offers a new possibility of tuning the band gap in pure BaS by employing different barium sulfide modifications.

5. VIBRATIONAL AND THERMODYNAMICAL PROPERTIES OF BAS Finally, to further investigate the thermodynamical stability of the calculated phases, we performed phonon calcula-

Figure 9. (a) Phonon band structure and (b) phonon density of states of the NaCl (B1) modification at equilibrium volume. Calculation was performed using GGA-PBE. 10650


Article

Inorganic Chemistry

Figure 10. (a) Gibbs free energy and entropy versus temperature of BaS using GGA-PBE: (a) G(T) curves and (b) S(T) curves calculated for the most relevant structure types. Note that the Gibbs free energy is given in E h (AU)/cell, entropy is given in J/mol K, while temperature is in K.

hypothetical BaS modification in the experiment using BaO as a template. The TlI structure type is also energetically very close but found to be metastable due to imaginary phonon frequencies. Finally, the BaS system appears to be a good candidate to synthesize the 5−5 type of modification in thin films or as a bulk phase. Furthermore, we investigated the electronic, vibrational, and thermodynamical properties of BaS modifications on ab initio level, and our calculations were in very good agreement with previous experimental and theoretical observations where such data were available. We show the electronic properties of barium sulfide at standard and high pressures, and in particular the metallization of BaS. Therefore, we offer new possibilities of the band gap engineering in barium sulfide, which can have great applications in optical and electrical technologies.

for the most relevant structure types of BaS. The energetically lowest structure up to 1500 K is the NaCl modification. None of the calculated modifications crosses at any temperature, which indicates the metastability of all calculated phases at elevated temperatures. We note that the sphalerite modification is the most unstable, while TlI, 5−5, and NiAs modifications are more likely to be experimentally feasible. The NiAs phase is closest in energy to the NaCl modification at any temperature. The S(T) plot (Figure 10b) shows that all phases have similar entropy contribution at large temperature scale, although the NiAs and TlI type have slightly higher entropies. Furthermore, we calculated the heat capacity of the most relevant phases, presented in the Supporting Information. Again, our calculations were in good agreement with previous experimental and theoretical observations.41,104 Finally, we highlight the importance of the BaS compound at elevated temperatures105−109 and that the presented results of the thermodynamical properties can support a significant step forward in future scientific, industrial, and technological applications.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01617. Full list of structure candidates for barium sulfide, E(V) and H(p) curves calculated using B3LYP and Hartree− Fock approximation, calculated DOS of the TlI type and the 5−5 type, calculated DOS and band structures of the NiAs and the sphalerite type, band structures of the CsCl structure at 53 and 121 GPa, calculated phonon DOS of the TlI, NiAs, sphalerite, and 5−5 types, and calculated heat capacity of the most relevant phases (PDF)

6. CONCLUSION We performed ab inito modeling of barium sulfide under pressure using three different computational approaches: Hartree−Fock, GGA-PBE, and hybrid B3LYP. Our calculations show good agreement with previous experimental and theoretical results involving the equilibrium NaCl (B1) and high pressure CsCl (B2) phase. When comparing the methods, the calculated cell parameters and atomic positions using the GGA-PBE functional are closest to the experimental values. Furthermore, our calculations show that the experimentally observed modification of BaS is the energetically lowest and thermodynamically most stable one at ambient conditions regardless of the computational approach applied. We predict new BaS polymorphs which have not yet been synthesized or calculated in the BaS system, e.g. we found the TlI type modification as a metastable structure, which might be observed at elevated pressures and/or temperatures, possibly with the decompression of the CsCl structure. The calculated E(V) curves showed NiAs type as a promising structure candidate at elevated temperatures regardless of the computational approach, and it might be possible to observe this

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Dejan Zagorac: 0000-0002-3102-852X Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by Grants 45012 and 171001 from the Ministry of Education, Science and Technological Develop10651


Article

Inorganic Chemistry

(19) Zagorac, D.; Schön, J. C.; Jansen, M. Energy Landscape Investigations Using the Prescribed Path Method in the ZnO System. J. Phys. Chem. C 2012, 116, 16726−16739. (20) Zagorac, D.; Schön, J. C.; Zagorac, J.; Jansen, M. Theoretical investigations of novel zinc oxide polytypes and in-depth study of their electronic properties. RSC Adv. 2015, 5, 25929−25935. (21) Zagorac, J.; Zagorac, D.; Zarubica, A.; Schön, J. C.; Djuris, K.; Matovic, B. Prediction of possible CaMnO3 modifications using an ab initio minimization data-mining approach. Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. 2014, 70, 809−819. (22) Rosić, M.; Zagorac, D.; Milivojević, D.; Paunović, N.; Zagorac, J.; Dohčević-Mitrović, Z.; Branko, M. Theoretical and experimental study of octahedral tilting of Ca1−xGdxMnO3 (x = 0.05, 0.1, 0.15, 0.2) nanometric powders. J. Alloys Compd. 2016, 678, 219. (23) Zollweg, R. J. Optical Absorption and Photoemission of Barium and Strontium Oxides, Sulfides, Selenides, and Tellurides. Phys. Rev. 1958, 111, 113−119. (24) Kaneko, Y.; Morimoto, K.; Koda, T. Optical Properties of Alkaline-Earth Chalcogenides. II. Vacuum Ultraviolet Reflection Spectra in the Synchrotron Radiation Region of 4−40 eV. J. Phys. Soc. Jpn. 1983, 52, 4385−4396. (25) Nakanishi, Y.; Ito, T.; Hatanaka, Y.; Shimaoka, G. Preparation and luminescent properties of SrSe: Ce thin films. Appl. Surf. Sci. 1993, 66, 515−519. (26) Cervantes, P.; Williams, Q.; Côté, M.; Rohlfing, M.; Cohen, M. L.; Louie, S. G. Band structures of CsCl-structured BaS and CaSe at high pressure: Implications for metallization pressures of the alkaline earth chalcogenides. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, 9793. (27) Grzybowski, T. A.; Ruoff, A. L. Band-Overlap Metallization of BaTe. Phys. Rev. Lett. 1984, 53, 489−492. (28) Heng, K. L.; Chua, S. J.; Wu, P. Prediction of Semiconductor Material Properties by the Properties of Their Constituent Chemical Elements. Chem. Mater. 2000, 12, 1648−1653. (29) Holleman, A. F.; Wiberg, E.; Wiberg, N. Inorganic Chemistry; Academic Press: San Diego, 2001. (30) Yamaoka, S.; Shimomura, O.; Nakazawa, H.; Fukunaga, O. Pressure-induced phase transformation in BaS. Solid State Commun. 1980, 33, 87. (31) Holgersson, S. Die Struktur der Sulfide von Mg, Ca, Sr und Ba. Z. Anorg. Allg. Chem. 1923, 126, 179−182. (32) Petzel, T. Ü ber die Darstellung von CaS, SrS und BaS aus den Metallen und Schwefelwasserstoff in flüssigem Ammoniak. Z. Anorg. Allg. Chem. 1973, 396, 173−177. (33) Rad, H. D.; Hoppe, R. Ü ber Thiomercurate. 2. Zur Kenntnis von Ba2HgS3. Z. Anorg. Allg. Chem. 1981, 483, 7−17. (34) Gü ntert, O. J.; Faessler, A. Präzisionsbestimmung der Gitterkonstanten der Erdalkalisulfide MgS, CaS, SrS und BaS. Z. Kristallogr. 1956, 107, 357−361. (35) Grzybowski, T. A.; Ruoff, A. L. High-pressure phase transition in BaSe. Phys. Rev. B: Condens. Matter Mater. Phys. 1983, 27, 6502. (36) Weir, S. T.; Vohra, Y. K.; Ruoff, A. L. High-pressure phase transitions and the equations of state of BaS and BaO. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 33, 4221. (37) Lai, W. H.; Haynes, A. S.; Frazer, L.; Chang, Y. M.; Liu, T. K.; Lin, J. F.; Liang, I. C.; Sheu, H. S.; Ketterson, J. B.; Kanatzidis, M. G.; Hsu, K. F. Second Harmonic Generation Response Optimized at Various Optical Wavelength Ranges through a Series of Cubic Chalcogenides Ba6Ag2.67+4δSn4.33−δS16−xSex. Chem. Mater. 2015, 27 (4), 1316−1326. (38) Vilciauskas, L.; Beganskiene, A.; Kareiva, A.; Gibson, K.; Ziegler, P.; Meyer, H. J. Superconductivity in the Y-Ba-Ca-Cu-O system. J. Mater. Sci. 2006, 41, 579−581. (39) Sturza, M.; Allred, J. M.; Malliakas, C. D.; Bugaris, D. E.; Han, F.; Chung, D. Y.; Kanatzidis, M. G. Tuning the Magnetic Properties of New Layered Iron Chalcogenides (BaF)2Fe2−xQ3 (Q = S, Se) by Changing the Defect Concentration on the Iron Sublattice. Chem. Mater. 2015, 27, 3280−3290.

ment of the Republic of Serbia. The authors thank M. Rosic, K. Djuris, B. Babic, and V. Maksimovic for valuable discussions. The authors thank Prof. R. Dovesi and Crystal Solutions for software support. The authors thank the Max Planck Institute for Solid State Research, Stuttgart, Germany, for collaboration and providing computational support.

■

REFERENCES

(1) Schön, J. C.; Jansen, M. First Step Towards Planning of Syntheses in Solid-State Chemistry: Determination of Promising Structure Candidates by Global Optimization. Angew. Chem., Int. Ed. Engl. 1996, 35, 1286−1304. (2) Verwer, P.; Leusen, F. J. Computer Simulation to Predict Possible Crystal Polymorphs J. Rev. Comput. Chem. 1998, 12, 327−365. (3) Draznieks, M. C.; Newsam, J. M.; Gorman, A. M.; Freeman, C. M.; Férey, G. De Novo Prediction of Inorganic Structures Developed through Automated Assembly of Secondary Building Units (AASBU Method). Angew. Chem., Int. Ed. 2000, 39, 2270−2275. (4) Price, S. L. From crystal structure prediction to polymorph prediction: interpreting the crystal energy landscape. Phys. Chem. Chem. Phys. 2008, 10, 1996−2009. (5) Woodley, S. M.; Catlow, C. R. A. Crystal structure prediction from first principles. Nat. Mater. 2008, 7, 937−946. (6) Schön, J. C.; Doll, K.; Jansen, M. Predicting solid compounds via global exploration of the energy landscape of solids on the ab initio level without recourse to experimental information. Phys. Status Solidi B 2010, 247, 23−39. (7) Jansen, M.; Doll, K.; Schön, J. C. Addressing chemical diversity by employing the energy landscape concept. Acta Crystallogr., Sect. A: Found. Crystallogr. 2010, 66, 518−534. (8) Wales, D. J. Energy Landscapes; Cambridge University Press: Cambridge, 2003. (9) Jiang, N.; Woodley, S. M.; Catlow, C. R. A.; Zhang, X. Applying a new interatomic potential for the modelling of hexagonal and orthorhombic YMnO3. J. Mater. Chem. C 2015, 3, 4787−4793. (10) Schön, J. C.; Pentin, I. V.; Jansen, M. Ab initio computation of low-temperature phase diagrams exhibiting miscibility gaps. Phys. Chem. Chem. Phys. 2006, 8, 1778−1784. (11) Nađđerđ, L.; Davidović, M.; Davidović, D.; Milošević, M.; Jordanov, D.; Stanković, S.; Prvanović, S. A possible improvement of the determination of 133Ba activity and detection efficiency by the sum-peak method, by inclusion of the previously neglected transitions. Nucl. Instrum. Methods Phys. Res., Sect. A 2013, 698, 60−65. (12) Oganov, A. R.; Chen, J.; Gatti, C.; Yanzhang, M.; Yanming, M.; Glass, W. C.; Liu, Z.; Yu, T.; Kurakevych, O. O.; Solozhenko, V. L. Ionic high-pressure form of elemental boron. Nature 2009, 457, 863− 867. (13) Pickard, C. J.; Needs, R. J. Metallization of aluminum hydride at high pressures: A first-principles study. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 144114. (14) Doll, K.; Schön, J. C.; Jansen, M. Structure prediction based on ab initio simulated annealing for boron nitride. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 144110. (15) Kulkarni, A.; Doll, K.; Prasad, D. L. V. K.; Schön, J. C.; Jansen, M. Alternative structure predicted for lithium at ambient pressure. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 172101. (16) Farrow, M. R.; Chow, Y.; Woodley, S. M. Structure prediction of nanoclusters; a direct or a pre-screened search on the DFT energy landscape? Phys. Chem. Chem. Phys. 2014, 16, 21119−21134. (17) Doll, K.; Jansen, M. Ab Initio Energy Landscape of GeF2: A System Featuring Lone Pair Structure Candidates. Angew. Chem., Int. Ed. 2011, 50, 4627−4632. (18) Zagorac, D.; Schön, J. C.; Zagorac, J.; Jansen, M. Prediction of structure candidates for zinc oxide as a function of pressure and investigation of their electronic properties. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 075201. 10652


Article

Inorganic Chemistry (40) Panella, J. R.; Chamorro, J.; McQueen, T. M. Synthesis and Structure of Three New Oxychalcogenides: A2O2Bi2Se3 (A = Sr, Ba) and Sr2O2Sb2Se3. Chem. Mater. 2016, 28, 890−895. (41) Tuncel, E.; Colakoglu, K.; Deligoz, E.; Ciftci, Y. O. A firstprinciples study on the structural, elastic, vibrational, and thermodynamical properties of BaX (X = S, Se, and Te). J. Phys. Chem. Solids 2009, 70, 371−378. (42) Bouhemadou, A.; Khenata, R.; Zegrar, F.; Sahnoun, M.; Baltache, H.; Reshak, A. H. Ab initio study of structural, electronic, elastic and high pressure properties of barium chalcogenides. Comput. Mater. Sci. 2006, 38, 263−270. (43) Jha, P. K.; Sakalle, U. K.; Sanyal, S. P. High Pressure Structural Phase Transition in Alkaline Earth Chalcogenides. J. Phys. Chem. Solids 1998, 59, 1633−1637. (44) Durandurdu, M. Pressure-induced phase transformation of BaS: An ab initio constant pressure study. Chem. Phys. 2010, 367, 80−82. (45) Potzel, O.; Taubmann, G. The pressure induced B1−B2 phase transition of alkaline halides and alkaline earth chalcogenides. A first principles investigation. J. Solid State Chem. 2011, 184, 1079−1084. (46) Min, T.; Xinhua, H. Phase transition and thermodynamic properties of BaS: An Ab initio study. Wuhan Univ. J. Nat. Sci. 2011, 16, 33−37. (47) Zhou, X.; Roehl, J. L.; Lind, C.; Khare, S. V. Study of B1 (NaCl type) to B2 (CsCl type) pressure-induced structural phase transition in BaS, BaSe and BaTe using ab initio computations. J. Phys.: Condens. Matter 2013, 25, 075401. (48) Rino, J. P. An interaction potential for barium sulfide: A molecular dynamics study. Comput. Mater. Sci. 2014, 92, 334−342. (49) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; DArco, P.; Llunell, M. CRYSTAL14 User’s Manual; University of Torino: Torino, 2009. (50) Dovesi, R.; Orlando, R.; Civalleri, B.; Roetti, C.; Saunders, V. R.; Zicovich-Wilson, C. M. CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals. Z. Kristallogr. Cryst. Mater. 2005, 220, 571−573. (51) Doll, K.; Saunders, V. R.; Harrison, N. M. Analytical Hartree− Fock gradients for periodic systems. Int. J. Quantum Chem. 2001, 82, 1−13. (52) Doll, K. Implementation of analytical Hartree−Fock gradients for periodic systems. Comput. Phys. Commun. 2001, 137, 74−88. (53) Doll, K.; Dovesi, R.; Orlando, R. Analytical Hartree−Fock gradients with respect to the cell parameter for systems periodic in three dimensions. Theor. Chem. Acc. 2004, 112, 394−402. (54) Doll, K.; Dovesi, R.; Orlando, R. Analytical Hartree−Fock gradients with respect to the cell parameter: systems periodic in one and two dimensions. Theor. Chem. Acc. 2006, 115, 354−360. (55) Doll, K. Analytical stress tensor and pressure calculations with the CRYSTAL code. Mol. Phys. 2010, 108, 223−227. (56) Civalleri, B.; D’Arco, P.; Orlando, R.; Saunders, V. R.; Dovesi, R. Hartree-Fock geometry optimization of periodic systems with the CRYSTAL code. Chem. Phys. Lett. 2001, 348, 131−138. (57) Becke, A. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648−5652. (58) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (59) Zagorac, D.; Doll, K.; Schön, J. C.; Jansen, M. Ab initio structure prediction for lead sulfide at standard and elevated pressures. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 045206. (60) Mian, M.; Harrison, N. M.; Saunders, V. R.; Flavell, W. R. An ab initio Hartree-Fock investigation of galena (PbS). Chem. Phys. Lett. 1996, 257, 627−632. (61) Zagorac, D.; Doll, K.; Schön, J. C.; Jansen, M. Structure Prediction for PbS and ZnO at Different Pressures and Visualization of the Energy Landscapes. Acta Phys. Pol., A 2011, 120, 215−220. (62) Hay, P. J.; Wadt, W. R. Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals. J. Chem. Phys. 1985, 82, 299−310.

(63) Piskunov, S.; Heifets, E.; Eglitis, R. I.; Borstel, G. Bulk properties and electronic structure of SrTiO3, BaTiO3, PbTiO3 perovskites: an ab initio HF/DFT study. Comput. Mater. Sci. 2004, 29, 165−178. (64) Zagorac, D.; Doll, K.; Schön, J. C.; Jansen, M. Sterically Active Electron Pairs in Lead Sulfide? An Investigation of the Electronic and Vibrational Properties of PbS in the Transition Region Between the Rock Salt and the α-GeTe-Type Modifications. Chem. - Eur. J. 2012, 18, 10929−10936. (65) Pourghazi, A.; Dadsetani, M. Electronic and optical properties of BaTe, BaSe and BaS from first principles. Phys. B 2005, 370, 35−45. (66) Mishra, K. C.; Johnson, K. H.; Schmidt, P. C. A comparative study of electronic structure of alkaline earth sulfides as hosts for phosphors. Mater. Sci. Eng., B 1993, 18, 214−219. (67) Kalpana, G.; Palanivel, B.; Rajagopalan, M. Electronic structure and structural phase stability in BaS, BaSe, and BaTe. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 12318. (68) Lin, G. Q.; Gong, H.; Wu, P. Electronic properties of barium chalcogenides from first-principles calculations: Tailoring wide-bandgap II-VI semiconductors. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 085203. (69) Feng, Z.; Hu, H.; Lv, Z.; Cui, S. First-principles study of electronic and optical properties of BaS, BaSe and BaTe. Cent. Eur. J. Phys. 2010, 8, 782−788. (70) Carlsson, A. E.; Wilkins, J. W. Band-overlap metallization of BaS, BaSe, and BaTe. Phys. Rev. B: Condens. Matter Mater. Phys. 1984, 29, 5836−5839. (71) Baima, J.; Ferrabone, M.; Orlando, R.; Erba, A.; Dovesi, R. Thermodynamics and phonon dispersion of pyrope and grossular silicate garnets from ab initio simulations. Phys. Chem. Miner. 2016, 43, 137−149. (72) Ferrero, M.; Rérat, M.; Orlando, R.; Dovesi, R. The calculation of static polarizabilities of periodic compounds. The implementation in the CRYSTAL code for 1D, 2D and 3D systems. J. Comput. Chem. 2008, 29, 1450−1459. (73) Hundt, R. KPLOT, A Program for Plotting and Analyzing Crystal Structures; Technicum Scientific Publishing: Stuttgart, Germany, 2016. (74) Momma, K.; Izumi, F. VESTA: a three-dimensional visualization system for electronic and structural analysis. J. Appl. Crystallogr. 2008, 41, 653−658. (75) Zagorac, D.; Schön, J. C.; Jansen, M. Identification of promising chemical systems for the synthesis of new materials structure types: An ab initio minimization data mining approach. Process. Appl. Ceram. 2013, 7, 37−41. (76) Schön, J. C.; Jansen, M. Determination of candidate structures for simple ionic compounds through cell optimization. Comput. Mater. Sci. 1995, 4, 43−58. (77) Schön, J. C. Enthalpy Landscapes of the Earth Alkaline Metal Oxides. Z. Anorg. Allg. Chem. 2004, 630, 2354−2366. (78) Cancarevic, Z.; Schön, J. C.; Jansen, M. Stability of Alkali Metal Halide Polymorphs as a Function of Pressure. Chem. - Asian J. 2008, 3, 561−572. (79) Mudring, A. V. Thallium Halides − New Aspects of the Stereochemical Activity of Electron Lone Pairs of Heavier Main-Group Elements. Eur. J. Inorg. Chem. 2007, 2007, 882−890. (80) Lowndes, R. P.; Perry, C. H. Molecular structure and anharmonicity in thallium iodide. J. Chem. Phys. 1973, 58, 271. (81) Chattopadhyay, T. K.; von Schnering, H. G.; Grosshans, W. A.; Holzapfel, W. B. High pressure X-ray diffraction study on the structural phase transitions in PbS, PbSe and PbTe with synchrotron radiation. Physica B+C 1986, 139, 356−360. (82) Grzechnik, A.; Friese, K. Pressure-induced orthorhombic structure of PbS. J. Phys.: Condens. Matter 2010, 22, 095402. (83) Wang, S.; Zhang, J.; Zhang, Y.; Alvarado, A.; Attapattu, J.; He, D.; Wang, L.; Chen, C.; Zhao, Y. Phase-Transition Induced Elastic Softening and Band Gap Transition in Semiconducting PbS at High Pressure. Inorg. Chem. 2013, 52, 8638−8643. (84) Li, Y.; Lin, C.; Xu, J.; Li, G.; Li, X.; Liu, J. Structures of two intermediate phases between the B1 and B2 phases of PbS under high pressure. AIP Adv. 2014, 4, 127112. 10653


Article

Inorganic Chemistry

Properties, Thermal and Thermodynamic Properties, and Lattice Properties); Springer Verlag: Heidelberg, 2014. (105) Kobayashi, T.; Morita, K.; Sano, N. Thermodynamics of Sulfur in the BaO-MnO-Si02 Flux System. Metall. Mater. Trans. B 1996, 27, 652−657. (106) Sohn, H. Y. Thermodynamics of a New Cyclic Reaction System Involving BaS and BaSO4 for Converting Sulfur Dioxide to Elemental Sulfur. Ind. Eng. Chem. Res. 2003, 42, 5946−5948. (107) Khritohin, N. A.; Andreev, O. V.; Mitroshin, O. V.; Korotkov, A. S. Thermodynamics of Phase Changes in Systems BaS-Ln2S3 (Ln = Pr, Sm, Gd, Tb, Er, Lu). J. Phase Equilib. Diffus. 2004, 25 (6), 515− 519. (108) Sohn, H. Y.; Savic, M.; Padilla, R.; Han, G. A novel reaction system involving BaS and BaSO4 for converting SO2 to elemental sulfur without generating pollutants: Part I. Feasibility and kinetics of SO2 reduction with BaS. Chem. Eng. Sci. 2006, 61, 5088−5093. (109) Medvedev, D.; Lyagaeva, J.; Plaksin, S.; Demin, A.; Tsiakaras, P. Sulfur and carbon tolerance of BaCeO3-BaZrO3 proton-conducting materials. J. Power Sources 2015, 273, 716−723.

(85) Demiray, F.; Berber, S. Ab initio investigation of B16(GeS), B27(FeB) and B33(CrB/TlI) phases of lead chalcogenides. Phys. Scr. 2013, 88, 015603. (86) Wang, J.; Zhang, Y. Topologic connection between 2-D layered structures and 3-D diamond structures for conventional semiconductors. Sci. Rep. 2016, 6, 24660. (87) Sponza, L.; Goniakowski, J.; Noguera, C. Confinement effects in ultrathin ZnO polymorph films: Electronic and optical properties. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 195435. (88) Schön, J. C. Nanomaterials - What energy landscapes can tell us. Process. Appl. Ceram. 2015, 9, 157−168. (89) Tusche, C.; Meyerheim, H. L.; Kirschner, J. Observation of Depolarized ZnO(0001) Monolayers: Formation of Unreconstructed Planar Sheets. Phys. Rev. Lett. 2007, 99, 026102−026106. (90) Pueyo, C. L.; Siroky, S.; Landsmann, S.; van den Berg, M. W. E.; Wagner, M. R.; Reparaz, J. S.; Hoffmann, A.; Polarz, S. Molecular Precursor Route to a Metastable Form of Zinc Oxide. Chem. Mater. 2010, 22, 4263−4270. (91) Martınez-Boubeta, C.; Botana, A. S.; Pardo, V.; Baldomir, D.; Antony, A.; Bertomeu, J.; Rebled, J. M.; Lopez-Conesa, L.; Estrade, S.; Peiro, F. Heteroepitaxial growth of MgO(111) thin films on Al2O3(0001): Evidence of a wurtzite to rocksalt transformation. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 041407. (92) Rempel, A. A.; Valeeva, A. A.; Sato, K.; Kozhevnikova, N. S. Positron annihilation sites in nano lead sulfide powders. J. Phys.:Conf. Series 2013, 443, 012013. (93) Trejo, O.; Roelofs, K. E.; Xu, S.; Logar, M.; Sarangi, R.; Nordlund, D.; Dadlani, A. L.; Kravec, R.; Dasgupta, N. P.; Bent, S. F.; Prinz, F. B. Quantifying Geometric Strain at the PbS QD-TiO2 Anode Interface and Its Effect on Electronic Structures. Nano Lett. 2015, 15, 7829−7836. (94) Thiele, G.; Franzke, Y.; Weigend, F.; Dehnen, S. {μ-PbSe}: A Heavy CO Homologue as an Unexpected Ligand. Angew. Chem., Int. Ed. 2015, 54, 11283−11288. (95) Knox, K. R.; Bozin, E. S.; Malliakas, C. D.; Kanatzidis, M. G.; Billinge, S. J. L. Local off-centering symmetry breaking in the hightemperature regime of SnTe. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 014102. (96) Xiong, Y.; Yao, S.; Karni, M.; Kostenko, A.; Burchert, A.; Apeloig, Y.; Driess, M. Heavier congeners of CO and CO2 as ligands: from zero-valent germanium (‘germylone’) to isolable monomeric GeX and GeX2 complexes (X = S, Se, Te). Chem. Sci. 2016, 7, 5462− 5469. (97) Ihanus, J.; Hänninen, T.; Hatanpäa,̈ T.; Aaltonen, T.; Mutikainen, I.; Sajavaara, T.; Keinonen, J.; Ritala, M.; Leskelä, M. Atomic Layer Deposition of SrS and BaS Thin Films Using Cyclopentadienyl Precursors. Chem. Mater. 2002, 14, 1937−1944. (98) Ihanus, J.; Hänninen, T.; Hatanpäa,̈ T.; Ritala, M.; Leskelä, M. Electroluminescent SrS and BaS Thin Films Deposited by ALD Using Cyclopentadienyl Precursors. J. Electrochem. Soc. 2004, 151, 221−225. (99) Ni, J. E.; Case, E. D.; Khabir, K. N.; Stewart, R. C.; Wu, C. I.; Hogan, T. P.; Timm, E. J.; Girard, S. N.; kanatzidis, M. G. Room temperature Young’s modulus, shear modulus, Poisson’s ratio and hardness of PbTe-PbS thermoelectric materials. Mater. Sci. Eng., B 2010, 170, 58−66. (100) Gokoglu, G. First principles study of barium chalcogenides. J. Phys. Chem. Solids 2008, 69, 2924−2927. (101) Saum, G. A.; Hensley, E. B. Fundamental Optical Absorption in the IIA-VIB Compounds. Phys. Rev. 1959, 113, 1019−1022. (102) Lazewski, J.; Jochym, P. T.; Piekarz, P.; Parlinski, K. Quasiharmonic approach to a second-order phase transition. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 104109. (103) Grabowski, B.; Ismer, L.; Hickel, T.; Neugebauer, J. Ab initio up to the melting point: Anharmonicity and vacancies in aluminum. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 134106. (104) Strauch, D.; Rössler, U., Eds. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Condensed Matter, Vol. 44, Semiconductors, Subvolume G, New Data and Updates for several IIa-VI Compounds (Structural 10654


Barium Sulfide under Pressure: Discovery of Metastable Polymorphs

Recommend Documents