A route to possible civil engineering materials: the case of high-pressure phases of lime

Lime system has a chemical composition CaO, which is known as thermodynamically stable. The purpose here is to explore further possible phases under pressure, by means of variable-composition ab initio evolutionary algorithm. The present investigation shows surprisingly new stable compounds of lime. At ambient pressure we predict, in addition to CaO, CaO2 as new thermodynamically stable compound. The latter goes through two phases transition from C2/c space group structure to Pna21 at 1.5 GPa, and Pna21 space group structure to I4/mcm at 23.4 GPa. Under increasing pressure, further compounds such as CaO3 become the most stable and stabilize in P-421m space group structure above 65 GPa. For the necessary knowledge of the new predicted compounds, we have computed their mechanical and electronic properties in order to show and to explain the main reasons leading to the structural changes.

. However, apart of this, much is still to be known about its fundamental properties as well as its behavior under pressure effect.
In the present study, we aim to investigate the new thermodynamically stable compounds based on Ca-O composition. To this end, we will explore all stable compositions from Ca-O system and their crystal structures at high pressures using the variable and fixe composition ab initio evolutionary algorithm 10 . Besides, we will discuss their different structures, phase transitions, elastic properties and chemical bonding.
In order to find all possible phases of lime and their corresponding structures, we used the ab initio evolutionary algorithm (USPEX) [10][11][12] , which has a capability to simultaneously find stable stoichiometries and the corresponding structures in multicomponent systems. In our calculations, we allowed all possible compositions in our studied system with structures containing up to 10 atoms in the unit cell. The calculations were performed at zero Kelvin and pressures of 1 atm, 50 GPa, 70 GPa and 100 GPa. The initial generation consisted of 120 structures, and all subsequent generations have 40 structures. Stable structures and their compositions were determined using the convex hull construction. A compound is thermodynamically stable if the enthalpy of its decomposition into any other compound is positive 10 .
The present investigation results a surprisingly new stable compounds of lime. While we reproduce stability of CaO in the whole pressure range investigated here, new stable compounds are predicted. In Fig. 1, we display the convex hull of Ca-O system at high pressure. The enthalpies of formation of the predicted structures are shown as well. It can be clearly seen that in addition to CaO, CaO 2 is thermodynamically stable at high pressure.
At 70 GPa, convex hull diagram shows that a new compound, namely CaO 3 , becomes thermodynamically stable. The latter remains thermodynamically stable up to 100 GPa (Fig. 1). The latter have never been reported before.
Thereafter, we explore all our results of stable compounds for lime, using fixe composition evolution algorithm, in order to determine the possible phase change under pressure. The structure prediction runs for CaO and CaO 2 compound were performed at 1 atm, 20 GPa, 50 GPa, 70 GPa and 100 GPa, for CaO 3 at 70 GPa, all at zero Kelvin. The phase diagram and crystal structures of the newly predicted compounds are remarkable. The pressure-composition phase diagram is shown in Fig. 2. We may see that CaO phase transition occurs at around 65 GPa. It is stable below 65 GPa in Fm-3 m space group structure. Above 65 GPa, the structure of Pm3m space group becomes more stable. This is in good agreement with both experimental and theoretical data [5][6][7] . On the other hand, calcium peroxide, CaO 2 , stabilize in C2/c space  Table 1.
In order to confirm the stability of the obtained structures at different pressures, we list in Table 2 the enthalpies per formula unit of each compound with the one of oxygen. For instance, the enthalpy of the decomposition reaction ∆E of CaO 2 , from a reaction CaO + 1/2 O 2 − > CaO 2 , is defined as: Mechanically, the elastic constants of a material describe its response to an applied stress or, conversely, the stress required to maintain a given deformation. These properties are obviously directly related to the mechanical stability of a given system. The criteria of the mechanical stability of a monoclinic crystal are as follows 13 : and of tetragonal crystal are 13 : 0  3   44  66  11  12  11  12  33  13  2 The calculated elastic constants of CaO 2 , CaO 3 , at 1atm, 65 GPa respectively are listed in Table 3. The above mentioned criteria are satisfied in our case, indicating that CaO 2 , CaO 3 are mechanically stable at the corresponding conditions. For comparison, the values of the elastic properties of CaO are presented as well, and we notice the excellent agreement with the reported data. We may also underline that calcium oxide is more rigid and more resistant to shear deformation than calcium peroxide at the ambient conditions. Moreover, the Pugh modulus ratio 14 k = G/B is also reported in Table 3 to show the ductile-brittle behavior of high pressure lime phases. For brittle materials, G/B is higher than 0.571, whereas, for the ductile ones, it is lower than 0.571. It follows that CaO and CaO 3 are brittle; while CaO 2 is ductile. According to the following equation of hardness 15 : The Vickers hardness H of CaO, CaO 2 , and CaO 3 are 13.75, 4.28 and 16.88 GPa respectively, suggesting that the harder phase is CaO 3 and the less hard is CaO 2 .   In order to better understand the bonding behaviors, a Bader charge analysis 16   the band gap value of CaO (3.65 eV), which is in perfect agreement with previous work 7 . The obtained band gap value of CaO 2 , CaO 3 is 2.78 eV and 2.48 eV respectively. Additionally, magnetic calculation is performed for CaO 3 compound. The calculation shows that there is no magnetic moment on all atoms of this compound, what means that CaO 3 is non-magnetic.
In the studied pressure range, calcium peroxide knows two phase transitions at 1.5 GPa and at 23.4 GPa. The most stable CaO 2 at ambient conditions corresponds to the space group C2/c. Zhao et al. found that CaO 2 stabilizes in Pna2 1 space group structure 8 . However, the last structure becomes stable above 1.5 GPa of pressure. After duplicating both structures, we may notice that those structures are very similar as shown in Fig. 2. In Table 4, we compare the atomic distances between the obtained structure and the one of Zhao. We can see that the atomic distances are very close.
Calcium peroxide goes through a second phase transition from Pna2 1 space group structure (Fig. 3b) to I4/mcm space group structure (Fig. 3c) at 23.4 GPa. The tetragonal structure with unit cell parameters a = 5.01 Å and c = 5.92 Å is observed experimentally at a temperature of 550 °C (823 K) by Mumtaz et al. 9 . The corresponding lattice parameters are very similar with our findings. Additionally, we notice that the discovered MgO 2 stabilizes also in the same structure with I4/mcm space group structure above 500 GPa 17 .
In order to understand the main reasons behind CaO 2 phase transition, let us analyze in the bonding character through the electronic charge density. Figure 6 represents the electronic charge density of CaO 2 compound at 1 atm and 20 GPa in the (1 1 1) plane, which contain the maximum Ca and O atoms. We can remark that the electronic structure change between 1atm and 20 GPa. Consequently, new bond between calcium and oxygen are formed at 20GPa leading to a new phase. This explains and justifies the main reasons behind the transitions.
In summary, we have explored new phases of lime through variable-composition ab initio evolutionary algorithm. At ambient pressure we predicted, in addition to CaO, CaO 2 as new thermodynamically stable compound under two transitions at 1.5 GPa and at 23.4 GPa. Further compounds have been predicted such as CaO 3 above 65 GPa.
For the more complete knowledge on the new predicted compounds, we have investigated various kinds of properties including mechanical, electronic and bonding to explain the main reasons leading to the transitions giving the new class of materials from the simple lime system.

Methods summary
We use here the "Universal Structure Predictor: Evolutionary Xtallography" (USPEX) code [10][11][12] . The latter is based on approach features global optimization with real-space representation and physically motivated variation operators. To generate every candidate structure, we use first-principles structural relaxation, based on density functional theory within the GGA functional 17 for solids 18,19 . We used the projector-augmented wave (PAW) 20 with Ca [3s 2 3p 6 4s 2 ] and O [2s 2 2p 4 ] cores (core radii 2.00 a.u. and 1.5 a.u., respectively). The plane-wave kinetic-energy cutoff is 600 eV, and the k-point mesh resolution in reciprocal space is 2 * 0.06 A −1 . These settings enable excellent convergences of the energy differences, stress tensors, and structural parameters. The predicted structure calculation was performed with fixed composition. The plane-wave kinetic-energy cutoff is also 600 eV, and the k-point mesh resolution in reciprocal space is 2 * 0.03 A −1 .