Ab initio investigation of CaO-ZnO alloys under high pressure

CaxZn1–xO alloys are potential candidates to achieve wide band-gap, which might significantly promote the band gap engineering and heterojunction design. We performed a crystal structure search for CaO-ZnO system under pressure, using an ab initio evolutionary algorithm implemented in the USPEX code. Four stable ordered CaxZn1–xO structures are found in the pressure range of 8.7–60 GPa. We further constructed the pressure vs. composition phase diagram of CaO-ZnO alloys based on the detailed enthalpy calculations. With the increase in Ca concentration, the CaO-ZnO alloy first undergoes a hexagonal to monoclinic transition, and then transforms back to a hexagonal phase. At Above 9 GPa, there is no cubic structure in the alloys, in contrast to the insostructural components (B1-B1). The band gap of the CaxZn1–xO alloy shows an almost linear increase as a function of the Ca concentration. We also investigated the variation regularity of the band gap under pressure.

Scientific RepoRts | 5:11003 | DOi: 10.1038/srep11003 Ca x Zn 1-x O alloy under high pressure using first principles calculations. We examine the stability, structural and electronic properties of the Ca x Zn 1-x O alloys with different Ca concentrations. These structural and electronic properties are crucial for hetero-structural design and optimized growth of the related quantum wells and superlattices.

Results and discussion
In this work, we report four stable ground state structures of Ca x Zn 1-x O. The formation enthalpy of Ca x Zn 1-x O alloy is calculated using a fractional representation of Ca x Zn 1-x O (0 ≤ x ≤ 1) with respect to its decomposition into CaO and ZnO, as where x is the concentration of CaO. B1− CaO transits to B2 at 58 GPa in our calculation, similar to previous results 24,29 . In the condition of ZnO, the transition from B4 to B1 takes place at 9 GPa in our calculation, consistent with the experimental findings P t ≈ 8.7 GPa 30 , P t ≈ 9.1 GPa 31 , or P t ≈ 10 GPa 32 and first-principles calculations P t = 8.8 GPa 12 . Thus, when pressure is below 9 GPa, B4 phases are considered, and above 9 GPa B1-ZnO is considered for the lowest energy. Similarly in the case of CaO, B1 phases below 58 GPa, and above 58 GPa, B2 phases are considered. The relative energetics of CaO-ZnO alloys from 10 to 60 GPa are summarized in the convex hull plots shown in Fig. 1. The formation enthalpies were evaluated as the difference in the enthalpy of the predicted CaO-ZnO alloys with respect to CaO and ZnO at the selected pressures. Structures lying on the convex hull are either thermodynamically stable or metastable, and can be synthesized in principle. Figure 1 reveals that CaZn 6 O 7 is the first stable alloy below 10 GPa, which has the most negative enthalpy of formation. In Fig. 2 Fig. 3. More alloy structures with higher Ca-concentration appear with further increase in pressure. However, the structures can only be stable when the Ca-concentration is no more than 50%, even if pressure is increased over 60 GPa.
These detailed calculations for stable structures allow us to construct a P-x phase diagram of CaO-ZnO alloys, as shown in Fig. 3. There is a tendency for the number of Ca x Zn 1-x O alloys to increase with pressure, similar to Mg x Zn 1-x O alloys 12 . However, with pressure increasing, more Mg-rich structures appeared in the MgO-ZnO case, but more Zn-rich structures appear in our study. CaO, ZnO, and MgO all exhibit cubic structures under pressure; and the ionic radii of Ca, Zn and Mg is 1, 0.74, and 0.72 Å, respectively 33 . In this case, the element with the smaller ionic radius trend to turn into higher component in the alloys.
For all the predicted structures shown in Fig. 4, the corresponding structural information is listed in Table 1. We calculated the phonon dispersions under pressure, and found them to be dynamically stable ( Supplementary Fig. S2). We also calculated the phonon dispersions and elastic constants of the four predicted structures under 0 GPa, as shown in Supplementary Fig. S3 and Table S1, which show the structures are mechanically and dynamically stable at 0 GPa. So we think our predicted alloys can be synthesized at high pressure and reserved at ambient conditions.  Previous studies suggest that the symmetry of component structures is important in alloys of ZnO with other group-II metal oxides 6,18,26,27,34 . Most of these structures were created using the substitution method, where Zn was replaced with Ca in the wurtzite supercell or Ca was replaced with Zn in the rocksalt supercell. However, our current study shows that the stable CaO-ZnO alloys undergo a transition from hexagonal to monoclinic, and back to hexagonal structure, with the increase in the Ca concentration. At 8.7 to 9 GPa, the CaZn 6 O 7 alloy made from the nonisostructural components (wurtzite + rocksalt) is stable through both dynamics and thermodynamic analysis. At above 9 GPa, more structure became stable, however, none of the alloys have the rocksalt structure, without even the cubic symmetry adopted, although they were made from the isostructural components (rocksalt + rocksalt). In our previous study, we found similar results in the MgO-ZnO alloys 12 , where the alloys have a hexagonal structure    were found using our USPEX calculations. In contrast to previous views, the symmetry of component structure shows little impacts on the alloy structure here.
Band gap (E g ), which denotes the required energy of an electron from valence band maximum (VBM) to conduction band minimum (CBM), is an important parameter to determine the optoelectronic properties of semiconductors. The band gap of ZnO increases with pressure, and that of CaO decreases with pressure, as shown in Supplementary Fig. S3. Therefore, it is interesting to observe the pressure effects on band gaps of CaO-ZnO alloys. These band gaps are graphed in Fig 5(b) as a function of Ca composition for ground-state Ca x Zn 1-x O structures under high pressure. The band gap increases with pressure and also increases in an almost linear fashion with Ca concentration, when the pressure increases from 10 to 60 GPa. The more CaO mixing with ZnO, the wider band gap of alloy will be formed. In our previous theoretical study 12 , we also found the band gap linearly increases with Mg content in the Mg x Zn 1-x O alloys, which is consistent with the experimental results 35 .
As shown in Fig. 5(b), band gaps of all alloys increase with pressure except CaZnO 2 , whose band gaps have different variation rules for pressure. Calculated electronic band structures are graphed in Fig. 5 We further analyze whether the different concentrations of alloys lead to a variation in the electronic band structures. Firstly, when Ca concentration is less than 0.5, the band gap increases with pressure, and the CBM is always located at the Γ point. Band gaps are plotted as a function of pressure in Supplementary Fig. S4. However, CaZnO 2 displays some extraordinary properties. The band gap of CaZnO 2 first increases and then decreases with pressure, as shown in Fig. 6. The CBM of CaZnO 2 under 40 GPa is located at the Γ point (0, 0, 0), and the band gap at Γ point increases with pressure, similar to the behavior in B1-ZnO. Meanwhile, the CBM of CaZnO 2 from 40 to 60 GPa is located at the M point (0, 1/2, 0), and the gap at the M point reduces slowly with pressure, same to CaO at the X point (1/2, 0, 1/2). Using qualitative analysis, we keep the lattice constants unchanged, remove Ca or Zn atoms, respectively, and analyze the band structures of the broken crystal. The CBM of CaZnO 2 without Ca atoms located at the Γ point, and without Zn locates at the M point, which reveals that the conduction band at the Γ point basically comes from ZnO, and at the M point comes from CaO. Thus, with the increase in pressure, the CaO band-gap is more significant than the ZnO one.
Furthermore, other than the above-mentioned four stable structures, we find a metastable structure when Ca concentration is 0.75, as shown in Fig. 7(a). There is no imaginary frequency in Fig. 7(c), so the Ca 3 ZnO 4 structure is dynamically stable. Although the formation enthalpy (with respect to ZnO and CaO) is negative as shown in Fig. 1 above 40 GPa, the enthalpy respect to CaZnO 2 and CaO is always positive, which indicates a tendency to segregate into CaZnO 2 and CaO. From the calculated electronic band structures in Fig. 7(b), the CBM of Ca 3 ZnO 4 alloy is located at M the point. The band gap of this metastable structure is represented by the purple dotted line in Supplementary Fig. S4. The band gap of those large Ca-concentration structure decreases with pressure, while the low Ca-concentration structure exhibit the opposite behavior. In view of the band structure of all of these alloys, and considering the effects of pressure on band gap, the effect of Ca-concentration is also significant. In summary, the band gap of CaO-ZnO alloy depends on a fine interplay between concentration and pressure.

Conclusion
We investigate the composition and structure of the CaO-ZnO alloys at high pressure using USPEX codes. In a range of 0-60 GPa, four stable alloy structures with different Ca concentrations have been found. With increasing pressure, more alloys with higher Ca concentrations appear. However, the structure can only be stable when the Ca-concentration is no more than 50%, with pressure up to 60 GPa. When the Ca concentration increases, the stable structures of CaZn 6 O 7 , CaZn 5 O 6 , CaZn 3 O 4 and CaZnO 2 undergo a hexagonal to monoclinic transition, and then transforms back to a hexagonal phase. We find that ground-state structures of the alloys do not share the cubic nature of ZnO and CaO, indicating the symmetry of component structures has little impact on the alloy structure. Through detailed analysis of band structure, we note an almost linear increase in band gap as a function of Ca-concentration at the selected pressure. When the concentration is below 50% the band gap increases with pressure. The band gap of CaZnO 2 first increases with pressure up to 40 GPa, and then starts to decrease with pressure.

Methods
To search for the stable and low-enthalpy structures of CaO-ZnO alloy, an ab initio evolutionary algorithm (EA), which has been designed to find the most stable structure for a given chemical composition range at given external conditions as implemented in the USPEX code, is employed [36][37][38] . In this work, evolutionary crystal structure prediction calculations were performed at 0, 20, 40 and 60 GPa for (CaO) m -(ZnO) n system (m + n ≤ 20), all at zero temperature. We performed ab initio calculations with the Local Density Approximation (LDA) 39 as implemented in the Vienna ab initio simulation package (VASP) code 40 , which is based on density functional theory. The electron-ion interaction was described by the projector augmented wave (PAW) scheme 41 . The electron configurations 10d2p, 6p2s and 4p2s were treated as valence for Zn, Ca, and O, respectively. During structural relaxation, a tested energy cut off of 550 eV was used for the plane wave basis sets, and a k-point resolution of 0.03 Å-1 in the reciprocal space was used for all structures to minimize error from the k-point meshes. The atomic positions, lattice parameters, and cell volume were fully relaxed until the force on each atom was less than 1 meV/Å. Phonons were calculated with the supercell method implemented in the PHONOPY program.