Miscibility and ordered structures of MgOZnO alloys under high pressure.  
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The MgxZn1xO alloy system may provide an optically tunable family of wide band gap materials that can be used in various UV luminescences, absorption, lighting, and display applications. A systematic investigation of the MgOZnO system using ab initio evolutionary simulations shows that MgxZn1xO alloys exist in ordered groundstate structures at pressures above about 6.5 GPa. Detailed enthalpy calculations for the most stable structures allowed us to construct the pressurecomposition phase diagram. In the entire composition, no phase transition from wurzite to rocksalt takes place with increasing Mg content. We also found two different slops occur at near x = 0.75 of Egx curves for different pressures, and the band gaps of high pressure groundstate MgxZn1xO alloys at the Mg concentration of x > 0.75 increase more rapidly than x < 0.75. 
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Fubo Tian; Defang Duan; Da Li; Changbo Chen; Xiaojing Sha; Zhonglong Zhao; Bingbing Liu; Tian Cui 
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Type: Journal Article Date: 20140721 
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Title: Scientific reports Volume: 4 ISSN: 20452322 ISO Abbreviation: Sci Rep Publication Date: 2014 
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Created Date: 20140721 Completed Date:  Revised Date:  
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Journal Information Journal ID (nlmta): Sci Rep Journal ID (isoabbrev): Sci Rep ISSN: 20452322 Publisher: Nature Publishing Group 
Article Information Download PDF Copyright © 2014, Macmillan Publishers Limited. All rights reserved openaccess: Received Day: 26 Month: 03 Year: 2014 Accepted Day: 01 Month: 07 Year: 2014 Electronic publication date: Day: 21 Month: 07 Year: 2014 collection publication date: Year: 2014 Volume: 4Elocation ID: 5759 PubMed Id: 25044101 ID: 4104395 Publisher Item Identifier: srep05759 DOI: 10.1038/srep05759 
Miscibility and ordered structures of MgOZnO alloys under high pressure  
Fubo Tian1  
Defang Duan1  
Da Li1  
Changbo Chen1  
Xiaojing Sha1  
Zhonglong Zhao1  
Bingbing Liu1  
Tian Cuia1  
1State Key Laboratory of Superhard Materials, College of physics, Jilin University, Changchun 130012, P. R. China 

acuitian@jlu.edu.cn 
To realize highperformance ZnObased optoelectronic devices, two important requirements are necessary: one is ptype doping of ZnO, and the other is modulation of the band gap (E_{g})^{1}^{, 2}. ZnO can alloy with MgO to form the ternary compound Mg_{x}Zn_{1−x}O to extend the energy band gap, and therefore the detection spectrum into the shorter wavelength region. While ptype doping of ZnO is studied intensively, the latter has been demonstrated by the development research on Mg_{x}Zn_{1−x}O allowing modulation of band gap in a wide range, from 3.34 to 7.8 eV^{3}. Although the topic of ZnO has been extensively researched, less is known concerning the detailed structures of the Mg_{x}Zn_{1−x}O alloy system.
Fabrication and characterization of Mg_{x}Zn_{1−x}O alloy are important from the viewpoint of band gap modulation as well as of p–n junction. Mg_{x}Zn_{1−x}O thin films and nanostructures that include nanocrystals as well as coreshell structures have recently been studied with the objective of achieving a viable alloy family with tunable band gap and luminescence at the UV range^{4}^{, 5}^{, 6}^{, 7}^{, 8}^{, 9}^{, 10}^{, 11}^{, 12}^{, 13}^{, 14}^{, 15}^{, 16}^{, 17}^{, 18}^{, 19}^{, 20}^{, 21}. Sans et al.^{4} investigated the dependence of the phase transition on the hydrostatic pressure and found that the wurtzite to rocksalt transition pressure is observed to decrease from 9.5 ± 0.2 pure (ZnO) to 7.0 ± 0.2 GPa (for x = 0.13), with an almost linear dependence on the Mg content. Difficulties for the growth of high quality Mg_{x}Zn_{1−x}O films are partly from the fact that MgO (cubic) and ZnO (hexagonal) have different crystal structures at normal conditions.
In the last decade, there are numerous theoretical studies on the MgOZnO alloys^{22}^{, 23}^{, 24}^{, 25}^{, 26}^{, 27}^{, 28}^{, 29}^{, 30}^{, 31}^{, 32}^{, 33}^{, 34}^{, 35}^{, 36}^{, 37}^{, 38}^{, 39}^{, 40}. Sanati et al.^{22} showed that isostructural MgOZnO alloys are stable under certain conditions using the cluster expansion (CE) method, but they also concluded that if MgO and ZnO can adopt their own crystal structures (B1 and B4, respectively), the alloy is predicted to phase separate. This means that Mg_{x}Zn_{1−x}O alloys are not thermodynamically stable, consistent with a rather low observed solid solubility limit for Mg in ZnO. The clusterexpansion method was also used by Seko et al.^{23} for investigating phase transitions, including vibrational effects through lattice dynamics calculations. Very recently, combining the CASPCE with a systematic set of firstprinciples total energies, Liu et al.^{24} exhaustively searched for the groundstate structures of MgOZnO alloys, and found a few structures as yet unreported. Several groups^{25}^{, 26}^{, 27}^{, 28}^{, 29} reported their theoretical studies in which the random Mg_{x}Zn_{1−x}O alloy have been simulated using special quasirandom structures (SQS) approach^{41}^{, 42}. There exist other theoretical studies^{30}^{, 31}^{, 32}^{, 33}^{, 34}^{, 35}, in which alloying of ZnO and MgO proceeds by substituting Mg atoms by Zn atoms in the cubic rocksalt structure or vice versa in the hexagonal wurtzite structure, and also exist several theoretical reports^{36}^{, 37}^{, 38} on MgZnO_{2} in various model systems. An extensive systematic study of structural properties of Mg_{x}Zn_{1−x}O was performed by Fan et al.^{39} using a supercell approach within the localdensity approximation. In another theoretical study^{40}, alloying of MgO and ZnO is described within coherentpotential approximation (CPA)^{43}.
Bulk and undoped ZnO prefers the hexagonal wurtzite (B4) structure under normal conditions and transforms into a cubic rocksalt (B1) structure at a pressure in the vicinity of 9 GPa reported by some experiments^{44}^{, 45}^{, 46}, while MgO adopts the cubic rocksalt structure up to the highest pressure of 227 GPa^{47}. Generally, a large crystal structure difference between the wurtzitehexagonal ZnO (B4) and the rocksaltcubic MgO (B1) can cause unstable phase mixing^{6}^{, 48}, as reported by Sanati et al.^{22}. The same conclusions are made by Seko et al.^{23} and Malashevich et al.^{30}, who both get that the formation energy of Mg_{x}Zn_{1−x}O is positive. Are there any stable structures of Mg_{x}Zn_{1−x}O alloy when ZnO and MgO adopt the same structure (B1) at pressures greater than 9 GPa? However, for the ordered structures of Mg_{x}Zn_{1−x}O under high pressure, few theoretical studies have been reported to the best of our knowledge. Therefore, a firstprinciples calculation is very interesting to investigate the high pressure stable structures of Mg_{x}Zn_{1 − x}O, because they are the basis of all properties in theoretical studies and can also provide valuable information for experimental synthesis.
Here, we investigate the possible stability of MgOZnO alloys under high pressure using the firstprinciples calculations, and the structures are obtained from a recently developed evolutionary algorithm for the prediction of crystal structures^{49}^{, 50}. We also analyse the band gaps of these alloys.
In this work, we report a few stable ground state structures of Mg_{x}Zn_{1 − x}O. The phase stabilities of MgOZnO systems are investigated by calculating the formation enthalpy of various Mg_{x}Zn_{1−x}O alloys at different pressures. The formation enthalpy of Mg_{x}Zn_{1−x}O is calculated by using fractional representation Mg_{x}Zn_{1−x}O (0 ≤ x ≤ 1) with respect to the decomposition into MgO and ZnO, as
where the enthalpies H for Mg_{x}Zn_{1−x}O are obtained for the most stable structures as searched at the desired pressures. For MgO, the known structure B1 at our studied pressure is considered. For ZnO, transition from B4 to B1 takes place at 8.8 GPa as suggested by our enthalpy calculation (see Supplementary Fig. S1), which is in good consistency with the experimental findings p_{t} ≈ 8.7 GPa^{44}, p_{t} ≈ 9.1 GPa^{45}, or p_{t} ≈ 10 GPa^{46} and firstprinciples calculations p_{t} = 9.3 GPa^{51}. It can also be seen that the B3 phase is slightly higher in energy than the B4 phase of ZnO. So, the enthalpies H for ZnO below 8.8 GPa, B4, B3 and B1 phases are all considered, for the reason of the lowest energy, lower energy and cubic structure, and B1MgOlike structure, respectively, and above 8.8 GPa, only B1ZnO is considered for the lowest energy and B1MgOlike structure. The formation enthalpies of MgOZnO alloys under conditions of high pressure are depicted in Fig. 1 and Fig. 2. From Fig. 1 we noticed that MgZn_{3}O_{4}, MgZnO_{2}, and Mg_{3}ZnO_{4} made from B1MgO and B1ZnO are thermodynamically stable at zero pressure because of their negative formation enthalpy, which is consistent with the results reported by Liu et al.^{24} While in the case of B4ZnO (or B3ZnO) and B1MgO, the formation enthalpies of all Mg_{x}Zn_{1−x}O alloys we got are positive below 6.5 GPa (or 5.9 GPa), indicating the tendency for segregation of the ZnO and MgO, in agreement with the calculated results at ambient pressure of previous theoretical studies^{22}^{, 23}^{, 40}.
Further detailed calculations above 8.8 GPa found a number of Mg_{x}Zn_{1−x}O stable against decomposition into the constituent oxides (B1ZnO, B1MgO, or Mg_{x}Zn_{1−x}O). The formation enthalpies are shown in Fig. 2 for pressures of 10, 40, 60, and 80 GPa, and detailed enthalpy calculations for the most stable structures allowed us to construct the Px phase diagram of the MgOZnO alloys (see Fig. 3). When the pressure reaches 10 GPa or higher, the formation enthalpies of all Mg_{x}Zn_{1−x}O alloys we predicted become negative. This is interesting trend for the number of Mg_{x}Zn_{1−x}O alloy to increase with increasing pressure. In this direction, high pressure is obviously the right tool to widen the range of compositions in which the stable structures can be obtained. To the contrary, the structures of Mg_{2}ZnO_{3} and Mg_{3}ZnO_{4} become metastable when pressure is increased above about 50 GPa. This resulted in a confirmation of the following structures as DFT predicted ground states under different pressures: MgZn_{3}O_{4} (Pm3m, I4/mmm), MgZnO_{2} (P4/mmm, I4_{1}/amd), Mg_{3}Zn_{2}O_{5} (C2/m), Mg_{2}ZnO_{3 }(Cmcm), Mg_{3}ZnO_{4} (Pm3m, I4/mmm), Mg_{4}ZnO_{5} (I4/m)_{,} Mg_{7}Zn_{2}O_{9} (C2/m), and Mg_{6}ZnO_{7} (R3). For all the predicted structures as shown in Fig. 4 we computed phonon dispersions (see Supplementary Fig. S2) in the pressure range of 0–80 GPa, and found them to be dynamically stable.
As can be seen from Fig. 2, at 10 GPa, the energetically “deepest” structures occur at x = 0.25, x = 0.5 and x = 0.75, which have been extensively studied by many authors^{22}^{, 23}^{, 24}^{, 25}^{, 26}. Two structures were found respectively at the three compositions under pressure bellow 80 GPa, and the enthalpies difference are depicted in Fig. 5. It should be pointed out that the enthalpy differences are only within a few meV/formula. At 6.5 (or 5.9 GPa for B3ZnO considered) to 21 GPa, Mg_{3}ZnO_{4} is stable in the Pm3m structure (L1_{2}type, as reported in Ref. ^{25}), and then transforms into a tetragonal I4/mmm structure (D0_{22}type), which is the same as that reported in Refs.^{22}^{, 24}. For MgZn_{3}O_{4}, the cubic Pm3m and tetragonal I4/mmm phases are found to be the most stable in pressure ranges of 8.5 (or 7.9 GPa for B3ZnO considered)68 and 68–80 GPa, respectively. The Pm3m MgZn_{3}O_{4} (L1_{2}type) is the same as that reported in Refs^{24}^{, 25}. MgZnO_{2} is stable in the P4/mmm structure (same as that in Ref. ^{25}) at 7.7 GPa (or 7.1 GPa for B3ZnO considered), and transforms into a tetragonal I4_{1}/amd structure (same as “40”type reported in Ref.^{24}) at 38 GPa, which is stable up to at least 80 GPa. Fig. 5(b) shows that both of the MgZnO_{2} structures are more stable rather than in chalcopyrite structure^{37}^{, 38}. It is emphasized that the structural researches of Refs^{22}^{, 24}^{, 25} are all performed at atmospheric pressure.
Detailed calculations and analysis of the other structures under higher pressure are performed and show other five stable MgOrich MgOZnO alloys made from isostructural components (B1MgO and B1ZnO): Mg_{2}ZnO_{3} (Fig. 4(f); space group Cmcm), stable in a pressure range of 28–53 GPa; and Mg_{7}Zn_{2}O_{9} (Fig. 4(i); space group C2/m), Mg_{4}ZnO_{5} (Fig. 4(j); space group I4/m), Mg_{3}Zn_{2}O_{5} (Fig. 4(e); space group C2/m), and Mg_{6}ZnO_{7} (Fig. 4(k); space group R3), which are stable above 23 GPa, 41 GPa, 48 GPa, and 60 GPa, respectively. Among the five phases of Mg_{x}Zn_{1−x}O alloy, the C2/m Mg_{7}Zn_{2}O_{9} is the same as R1Mg_{7}Zn_{2}O_{9} (C2/m) reported in Ref.^{24}. For the MgOrich side of the phase diagram, we predict a stable hexagonal R3 Mg_{6}ZnO_{7}, which confirms the possibility that Mg_{x}Zn_{1−x}O crystallizes in a hexagonal structure at high concentrations x, as recently reported by Shimada et al.^{35}. This is a very interesting case due to the point that Mg_{x}Zn_{1−x}O alloy with high concentrations x have long been thought to adopt rocksalt (cubic) structures. Especially, the MgOZnO alloys more should be B1like structure since both MgO and ZnO are stable in B1 phase above 8.8 GPa. In addition, our calculated formation enthalpy data of metastable C2/mMg_{4}Zn_{3}O_{7} is slightly above the convex hull up to 80 GPa, which is different from their report on R2Mg_{4}Zn_{3}O_{7} (C2/m) as one of groundstate structures^{24}.
Figure 6 illustrates the calculated band gaps as a function of Mg composition using the the local density approximation (LDACAPZ)^{52}^{, 53} functional and screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE06)^{54}^{, 55} for the groundstate Mg_{x}Zn_{1−x}O structures under high pressure. From Fig. 6(a), it can be clearly seen that the gap increases with increase in the Mg content at the same pressure and increases with pressure increased at the same concentration. In addition, two different slops occur at about x = 0.75 of E_{g}x curves for different pressures, which agrees with the findings reported in previous works^{40}^{, 56}^{, 57}^{, 58}, in which the change of slope near one composition value has been attributed to structural phase from wurtzite to cubic with Mg content increased. Our calculated results show that no phase transition from wurzite to cubic or vice versa takes place at the point where the slope changes, and we consider that the band gaps of Mg_{x}Zn_{1−x}O strongly dependent on the Mg content. The HSE06 functional results are depicted in Fig. 6(b), which show the same trend as the LDA values, with the difference of 0.5–1.0 eV higher value at the same pressure.
We have performed a systematic theoretical investigation of the compositions and structures of the MgOZnO alloys and identified the stable groundstate structures as well as a number of metastable structures at 0–80 GPa over a wide range of Mg concentrations. Our results show that stable ordered groundstate Mg_{x}Zn_{1−x}O alloys only occur at high pressure. As well as recognizing the previous theoretically observations for the MgZn_{3}O_{4} (Pm3m), MgZnO_{2} (P4/mmm, I4_{1}/amd), Mg_{3}ZnO_{4} (Pm3m, I4/mmm), and Mg_{7}Zn_{2}O_{9} (C2/m) at atmospheric pressure as high pressure stable phases, the new stable alloys MgZn_{3}O_{4} (I4/mmm), Mg_{3}Zn_{2}O_{5} (C2/m), Mg_{2}ZnO_{3} (Cmcm), Mg_{4}ZnO_{5} (I4/m), and Mg_{6}ZnO_{7} (R3), have been predicted in the ground state under different pressure ranges. Among these structures, only Mg_{6}ZnO_{7} with a high Mg content crystallizes in the hexagonal structure under high pressure, and for the entire alloy composition of Mg_{x}Zn_{1−x}O, there is no phase transition from wurzite to cubic or vice versa takes place. Moreover, the band gaps of MgOZnO alloys with high MgO content increase more rapidly than low MgO content.
The high pressure groundstate and metastable structures are all metastable at ambient pressure and may be synthesized under certain conditions (e.g., at high temperature).
The ground state structures of Mg_{x}Zn_{1−x}O below 80 GPa are predicted by the ab initio evolutionary algorithm USPEX^{49}^{, 50}. We have performed variablecomposition simulation through the USPEX code in the range of 0–80 GPa for (MgO)m(ZnO)n system (n + m ≤ 30), and determined the compositions of the Mg_{x}Zn_{1−x}O. To confirm this and to obtain the most accurate results, we then renewed our structure search of stoichiometric Mg_{m}Zn_{n}O_{m + n} with m and n values fixed by the USPEX code.
The structural optimizations, electronic structure, phonon dispersion, and energy calculations for selected structures are performed with CASTEP code^{59}. The local density approximation (LDACAPZ)^{52}^{, 53} approaches of exchangecorrelation functional is employed. The normconserving pseudopotentials^{60} with cutoff energy of 700 eV are used, and a kmesh of 0.03 × 2π Å^{−1} within the MonkhorstPack scheme for sample the Brillouin zone, which ensures the error bars of total energies are less than 1 meV/atom. The hybrid functional HSE06^{54}^{, 55} implemented in the CASTEP code, together with normconserving pseudopotentials, and a cutoff energy of 600 eV, are used to calculate the band gaps of the stable structures at 10 GPa and 80 GPa.
F.B.T. and T.C. conceived the research. F.B.T. carried out the calculations. F.B.T., T.C., D.F.D., D.L., C.B.C., X.J.S., Z.L.Z., B.B.L. analyzed the data. F.B.T. and T.C. wrote the paper.
Supplementary information
Click here for additional data file (srep05759s1.doc)
This work was supported by the National Basic Research Program of China (No. 2011CB808200), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1132), National Natural Science Foundation of China (Nos. 11074090, 51032001, 11104102, 10979001, 51025206, 11204100), National Found for Fostering Talents of basic Science (No. J1103202), and Specialized Research Fund for the Doctoral Program of Higher Education (20110061120007, 20120061120008). Part of calculations were performed in the High Performance Computing Center (HPCC) of Jilin University.
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