Calcium peroxide from ambient to high pressures

Structures of calcium peroxide (CaO2) are investigated in the pressure range 0-200 GPa using the ab initio random structure searching (AIRSS) method and density functional theory (DFT) calculations. At 0 GPa, there are several CaO2 structures very close in enthalpy, with the ground-state structure dependent on the choice of exchange-correlation functional. Further stable structures for CaO2 with C2/c, I4/mcm and P21/c symmetries emerge at pressures below 40 GPa. These phases are thermodynamically stable against decomposition into CaO and O2. The stability of CaO2 with respect to decomposition increases with pressure, with peak stability occurring at the CaO B1-B2 phase transition at 65 GPa. Phonon calculations using the quasiharmonic approximation show that CaO2 is a stable oxide of calcium at mantle temperatures and pressures, highlighting a possible role for CaO2 in planetary geochemistry. We sketch the phase diagram for CaO2, and find at least five new stable phases in the pressure/temperature ranges 0


Introduction
The typical oxide formed by calcium metal is calcium oxide, CaO, having Ca and O in +2 and À2 oxidation states respectively. Calcium and oxygen can also combine to form calcium peroxide, CaO 2 , a compound which enjoys a variety of uses in industry and agriculture. Calcium peroxide is used as a source of chemically bound but easily evolved oxygen in fertilisers, for oxygenation and disinfection of water, and in soil remediation. 1,2 At ambient pressure bulk calcium peroxide decomposes at a temperature of about 620 K. 2,3 Early X-ray diffraction (XRD) experiments assigned a tetragonal 'calcium carbide' structure of space group I4/mmm to CaO 2 . 4 This same structure was already known to be formed by heavier alkaline earth metal peroxides. 5,6 Recently, Zhao et al. 7 used an adaptive genetic algorithm and density functional theory (DFT) calculations to search for structures of CaO 2 , finding a new orthorhombic ground state structure of Pna2 1 symmetry, which is calculated to be close to thermodynamic stability at zero pressure and temperature. The simulated XRD pattern from this structure is in good agreement with the available experimental data. 7 Thermodynamic stability in this case means stability against decomposition via We are interested in the stabilities of structures of CaO 2 from zero pressure up to 200 GPa, and temperatures up to 1000 K. Calcium and oxygen have high abundances in the Earth's crust and mantle and, because they also have high cosmic abundances, stable compounds formed from these elements at high pressures are key (exo)-planetary building blocks. Understanding the structures of such compounds allows insight into the composition of planetary interiors, including exoplanets. To date, almost no work has been performed investigating CaO 2 as a stable oxide of calcium at high pressures. Some previous work has explored the effect of low pressures (o10 GPa) on the bond lengths and lattice parameters of I4/mmm-CaO 2 . 5 We therefore employ DFT calculations to explore the behaviour of CaO 2 at pressures in the GPa range. DFT calculations provide an excellent avenue for investigating materials properties under pressure, both at pressures accessible to diamond anvil cells 8 and at terapascal pressures. 9,10 To explore the stability of CaO 2 , we search for new crystal structures of this compound at a variety of pressures in the range 0-200 GPa.
respectively. We use the Perdew-Burke-Ernzerhof (PBE) 13 form of the exchange-correlation functional with a plane-wave basis cutoff of 800 eV. A k-point sampling density of 2p Â 0.03 Å À1 is used for our CaO and CaO 2 phases. For our oxygen phases, we use a denser k-point sampling of 2p Â 0.02 Å À1 . Bulk modulii are calculated by fitting static lattice pressure-volume data to the third-order Birch-Murnaghan equation of state.
The electronic density of states is calculated using the OPTADOS code. [14][15][16] Calculations of phonon frequencies are performed with the CASTEP code and a finite-displacement supercell method, using the quasiharmonic approximation. 17,18 To search for new phases of CaO 2 , we use the ab initio random structure searching (AIRSS) technique. 19 AIRSS proceeds by generating random starting structures containing a given number of formula units. Of these, structures which have lattice parameters giving reasonable bond lengths and cell volumes at a particular pressure are then relaxed to an enthalpy minimum, and the lowest enthalpy structures are selected for refinement. AIRSS has proved to be a very powerful tool in predicting new structures, several of which have subsequently been found experimentally. AIRSS searches have for example uncovered high pressure phases of silane, 20 and correctly predicted high pressure metallic phases in aluminium hydrides. 21 In this study, we perform structure searching at pressures of 0, 10, 20, 50, 100, 150 and 200 GPa. The bulk (about 60%) of our searches use cells with 2 or 4 formula units of CaO 2 , and we have also performed searches with cells containing 1, 3, 5, 6 and 8 formula units. Not all combinations of pressures and formula unit numbers are searched; further detailed information on the AIRSS searches is given as ESI. † In total, we relax over 25 000 structures in our CaO 2 searches. We supplement our AIRSS searches by calculating the enthalpies of five known alkaline earth metal peroxide structures taken from the Inorganic Crystal Structure Database (ICSD), 22 and other authors. 7,23,24 The relevant alkaline earth metal is replaced with calcium where appropriate.

CaO
CaO undergoes a transition from the rocksalt (Fm% 3m) to the CsCl (Pm% 3m) structure (the B1-B2 transition) around 60-65 GPa. Diamond-anvil-cell experiments indicate a transition pressure of 60 AE 2 GPa at room temperature, 25 while DFT calculations give a transition pressure of 65-66 GPa. 26,27 We find a pressure of 65 GPa in the present study, and we therefore use the Fm% 3m rocksalt structure below 65 GPa and the CsCl structure at higher pressures. The bulk modulus of Fm% 3m-CaO has been measured to be 104.9 GPa, 28 while our static-lattice DFT calculations give a value of 108.5 GPa. To exclude the possibility that CaO might have a different, more stable structure (other than Fm% 3m or Pm% 3m) over the pressure range 0-200 GPa, we also perform AIRSS on CaO at pressures of 50, 100 and 200 GPa. We do not find any new low-enthalpy structures for CaO at these pressures.

Solid oxygen
Structure searching over the pressure range 0-200 GPa has already been performed for solid oxygen, 29,30 and we use the lowest enthalpy structures found therein. We also examine the enthalpies of the experimentally-determined a and d oxygen phases at low pressures. 31 Choosing the lowest-enthalpy oxygen structure at each pressure, we find that d-O 2 is stable between 0 and 1.2 GPa, after which an insulating phase with space group Cmcm 31 is stable up to 41 GPa. A phase of symmetry C2/m 30 then becomes stable, remaining so up to 200 GPa. Our spin-polarised calculations show no discernable difference in enthalpy between a d-O 2 phase with antiferromagnetic spin ordering, and the experimentally-determined ferromagnetic spin-ordering for d-O 2 . 32 These results are not in accord with low-temperature experiments on solid oxygen, which predict a-O 2 to be stable between 0 and about 5 GPa, d-O 2 to be stable between about 5 and 10 GPa, followed by the 'e-O 2 ' phase between 10 and 96 GPa, with a further isostructural phase transition around 100 GPa. [33][34][35] Our DFT calculations do not yield a-O 2 ; optimising its structure at low pressures simply gives the d-O 2 structure. The aforementioned C2/m oxygen phase is however very similar in structure to e-O 2 (which is also of C2/m symmetry), and is within 50 meV per f.u. of that phase in enthalpy over the pressure range 0-200 GPa. Any higher enthalpy structure for oxygen over the pressure range being explored here would only increase the calculated stability of CaO 2 , so we proceed with the lowest enthalpy DFT phases for oxygen.

Structure searching and static lattice results
Our structure searching is carried out by minimising the enthalpy at a given pressure within the static-lattice approximation. We discuss these results first before presenting our calculations of the Gibbs free energy. Fig. 1 shows the enthalpy-pressure curves for nine phases of CaO 2 . The first five of these, labelled with their space group symmetries I4/mmm, Pa% 3, Pna2 1 , Cmmm and I4/mcm in Fig. 1, are known alkaline earth metal peroxide structures as mentioned in Section 2. The other four, with space group symmetries C2/c and P2 1 /c, are new CaO 2 structures. These are the lowest-enthalpy phases that turned up during our AIRSS searches. The dotted line in Fig. 1 shows the enthalpy of CaO + 1 2 O 2 , calculated using the lowest-enthalpy phases of CaO and O 2 at each pressure. Any CaO 2 phase below this dotted line is stable against decomposition in the manner of eqn (1).
We find the following sequence of phase transitions for CaO 2 by considering the lowest enthalpy structure at each pressure: with the transition pressures between each structure as indicated by the arrows. The P2 1 /c-L phase is then predicted to be stable up to at least 200 GPa. At 0 GPa, our structure searching reveals a number of CaO 2 phases which are very close (within 10 meV per f.u.) in enthalpy. Within the present approximations (DFT with PBE exchange-correlation), a phase of C2/c symmetry ('C2/c-I') is lowest in enthalpy at 0 GPa. This phase is 8.4 meV per f.u. lower in enthalpy than the proposed Pna2 1 -symmetry ground state structure of Zhao et al., 7 which we note also turned up in our AIRSS searches. Our searches also uncover a second C2/c-symmetry phase ('C2/c-II') which is slightly higher in enthalpy than Pna2 1 at 0 GPa. The enthalpies of these three phases at low pressures are shown in more detail in the lefthand panel of Fig. 1.
We find that the calculated XRD patterns for the C2/c-I, C2/c-II and Pna2 1 structures share many similar features with available experimental data, 23 although this XRD data is best fitted by the Pna2 1 structure. The XRD patterns are provided as ESI. † The enthalpy differences between the C2/c-I, -II and Pna2 1 phases at 0 GPa are dependent on the choice of exchangecorrelation functional. In Table 1, we show the enthalpies of the Pna2 1 and C2/c-II phases relative to the C2/c-I phase using a variety of different functionals. We find differences in calculated equilibrium volumes as well: for C2/c-I at 0 GPa, the LDA gives a volume of 35.8 Å 3 per f.u., while the PBE functional gives 39.1 Å 3 per f.u. The LDA typically overbinds in DFT calculations, with PBE instead underbinding, so these two volumes likely bracket the true volume of the C2/c-I phase at 0 GPa. Given that dP/dV is about À2.3 GPa Å À3 for this phase at 0 GPa, this volume difference (due to functional choice) corresponds to a pressure uncertainty in the neighbourhood of AE3 GPa. In light of this uncertainty, C2/c-I, C2/c-II and Pna2 1 are all reasonable candidates for the structure of CaO 2 at 0 GPa.
The C2/c-I, -II and Pna2 1 phases exhibit very similar structures. Looking down the b-axis of each phase, calcium atoms form a nearly-hexagonal motif, and we note that the monoclinic angle b is close to 1201 for C2/c-I and C2/c-II. For the C2/c-I and -II phases, the peroxide ion axes are almost coplanar, as can be seen in Fig. 2. In C2/c-II, the axes of peroxide ions in the same plane are parallel, while in C2/c-I, they alternate in orientation in the same plane. We use red and blue colouring in Fig. 2 to show peroxide ions with parallel axes. We provide as ESI † further discussion and illustrations of the C2/c-I, -II and Pna2 1 phases, to highlight their similarities and differences.
AIRSS searches also reveal a second phase for CaO 2 with P2 1 /c symmetry ('P2 1 /c-H'). As can be seen in the right-hand panel of Fig. 1, our static-lattice calculations show that this is not a stable phase for CaO 2 over the pressure range 0-200 GPa. However around 38 GPa, the enthalpy of this phase lies within 10 meV per f.u. of the I4/mcm and P2 1 /c-L phases, opening up the possibility this phase could become stable once we take temperature into account. We consider this further in Section 3.4. The I4/mcm phase reported here is also predicted for MgO 2 above 53 GPa. 24 We provide lattice parameters and bulk modulii for the C2/c-I, C2/c-II, I4/mcm, P2 1 /c-H and P2 1 /c-L phases at 0, 20, 30 and 50 GPa in Table 2.

Bonding and electronic structure
The bandstructure of the P2 1 /c-L phase at 50 GPa is shown in Fig. 3. The insulating nature of this phase is evident, with a calculated thermal bandgap of 2.4 eV and optical bandgap

Stability of CaO 2
As can be seen in Fig. 1, our low-enthalpy phases for CaO 2 show remarkable stability against decomposition as pressure increases. We predict CaO 2 to be most stable at the B1-B2 CaO phase transition pressure of 65 GPa. There, the decomposition enthalpy (eqn (1)) of CaO 2 is +0.64 eV per unit of CaO 2 (+62 kJ mol À1 ). One implication of the stability of CaO 2 is that it may be preferentially formed over CaO in an oxygen-rich environment under pressure, through the reverse of eqn (1). For example, the pressure in the Earth's lower mantle, at a depth of around 1550 km, is about 65 GPa, 25 close to our predicted peak stability pressure for CaO 2 . The formation of MgO 2 in this way has also been discussed, 24 although much higher pressures (4116 GPa) are needed before MgO 2 is stable against decomposition, whereas CaO 2 is stable from around 0 GPa. The mantle temperature in the Earth at 65 GPa is in the neighbourhood of 2500 K, and our phonon calculations show that under these conditions, DG = +0.54 eV per f.u. for the reaction of eqn (1). Hence, CaO 2 is a thermodynamically stable oxide at temperatures and pressures encountered in planetary interiors.
Reactions of the form X + O 2 -Y for species X and Y, such as the reverse of eqn (1) We highlight the fact that the pressures at which these different CaO 2 phases are predicted to become stable are amenable to experimental study in diamond anvil cells. Very few pressure-induced phase transitions for A[B 2 ] compounds are experimentally known, 36 although at least one example already occurs among the alkaline earth metal peroxides, in BaO 2 . 36 Equivalently, it would be interesting to test the reactivity of CaO and O 2 under conditions of excess oxygen, as our results suggest that CaO and O 2 are reactive at high pressures. The formation of CaO 2 may require laser heating in a diamond anvil cell to overcome the likely high potential barriers between phases. High pressure phases of CaO 2 could be recoverable at lower pressures, although possibly not at ambient or zero pressure.

Lattice dynamics
In addition to our static-lattice calculations, we calculate the phonon free energies of our lowest-enthalpy CaO 2 phases, namely those with Pna2 1 , C2/c-I/II, I4/mcm, P2 1 /c-H and P2 1 /c-L symmetries. We encounter no imaginary phonon frequencies over the pressure ranges relevant to these phases, indicating that they are dynamically stable. The relevant thermodynamic potential is now the Gibbs free energy, which includes the phonon pressure. Selecting the lowest Gibbs free energy structure from these six structures gives rise to the T-P phase diagram given in Fig. 5. We note that the upper-left (low-P, high-T) part of the phase diagram is representative only, because at ambient pressures CaO 2 decomposes at temperatures around 620 K. 2,3 We find that the small enthalpy difference between the I4/mcm and P2 1 /c-H phases seen in our static-lattice calculations ( Fig. 1) closes with increasing temperature, and we see the emergence of P2 1 /c-H as a stable phase for CaO 2 at 37.7 GPa and for T 4 281 K. The free energy difference between the I4/mcm and P2 1 /c-H phases does remain quite small however, around 20 meV per CaO 2 unit at the most over the temperature range 0-1000 K.
At room temperature (300 K), we therefore predict a different sequence of phase transitions than those given in Section 3.1 for our static-lattice calculations. We find that, with PBE exchangecorrelation: C2=c-I ! 2:2 GPa Pna2 1 ! 2:6 GPa C2=c-II ! 28:3 GPa I4=mcm ! 37:4 GPa P2 1 =c-H ! 37:9 GPa P2 1 =c-L; with the arrows labelled by the predicted transition pressures. We also provide the equation of state for CaO 2 for our static lattice calculations and at 300 K with our phonon calculations in the ESI. † The phase diagram of Fig. 5 does not extend all the way to 200 GPa. However, we expect P2 1 /c-L to continue to be the most stable phase at high pressures. This is because our structure searching results (which use static-lattice enthalpies) show that the next most stable structure for CaO 2 over the pressure range 100-200 GPa is at least 45 meV per unit of CaO 2 higher in enthalpy. This was not the case at low pressures, where our searches reveal quite a few structures (such as P2 1 /c-H) that are close to becoming stable and may therefore do so at high temperatures. Structural changes in CaO 2 under pressure have been explored over the pressure range 0-200 GPa at temperatures up to 1000 K. CaO 2 remains insulating up to pressures of at least 200 GPa. Structure searching and DFT calculations reveal six stable phases for CaO 2 over these pressure and temperature ranges, of which five are reported for the first time in this study. Calculations of the phonon frequencies of these new structures confirms their dynamical stability. The lowest-enthalpy phase of CaO 2 at 0 GPa is dependent on the choice of DFT exchangecorrelation functional. At pressures above 40 GPa, a phase of P2 1 /c symmetry ('P2 1 /c-L') emerges for CaO 2 which is predicted to be stable up to 200 GPa, and at mantle pressures and temperatures. CaO 2 is a very stable oxide of calcium at high pressures, and may be a constituent of exoplanet mantles. The pressures at which these CaO 2 phases become stable are readily attainable in diamond anvil cells.