Stress-Driven Evolution on Mismatched Ca 2 Co 2 O 5 Oxide Material: From Geometry to the Electronic States

The geometrical structures, phase stabilities, electron energy band structures, electron density of states, and atom recombination together with the electron conduction behaviors of the sandwiched Ca 2 Co 2 O 5 with external stress of 1GPa are intensively studied by the density functional theory method. The studying results show that the symmetry remains undisturbed; the strain to the stress response is anisotropic. The strain of microarchitecture induced by external stress is also anisotropic. There is stronger covalent binding between Co and O. The binding between Co and O within CdI 2 like CoO 2 is very much even covalent, and it is weakened under external stress. But the covalent Co-O binding within the rock salt like CaCoO layer is enhanced. The Ca-O binding strength is insensitive to external stress. An energy gap of 0.1 eV below Fermi level for the spin-up electron band disappears, and the two energy gaps are narrowed for the spin-down electron bands. The p orbital electrons form primarily the bands below Fermi level and the d orbital electrons form primarily the bands above Fermi level. The transitions from p orbital electrons to d orbital electrons produce the conduction. The CdI 2 like CoO 2 layer has been enhanced in terms of participating in the conduction properties with external stress of 1GPa, and the capability of Co is enhanced while the capability of O is decreased.


Introduction
e multioxide framework materials with complicated layered crystal structures such as NaCoO, CaCoO, and BiSrCoO are very much diverse in physical properties, as well as the related sensitivity to structure, spintronics, topology, preparation procedures, and so on [1][2][3][4][5][6]  e family of transitional metal Co-based CaCoO oxide materials which show similar valuable properties are the research focus in recent years. For example, the Ca 2 Co 2 O 5 and Ca 3 Co 4 O 9 type layered oxide materials exhibit especially complex crystal structure, spin topology, preparation variety, and anisotropic transport phenomena [2,3]. ey are similarly composed of rock salts like the CaCoO layer and CdI 2 like the CoO 2 layer that are stacked along c axis with the Sandwich framed crystal structure. e Ca 2 Co 2 O 5 crystalline oxide material was first discovered and reported in terms of its unique sandwiched structure by Vidyasagar et al. in 1984 [4]. Its anisotropic semiconductor conduction and positive temperature-dependent thermopower of 100 μV·K −1 at 100 K were then demonstrated by Funahashi et al. [2,3].
e Ca 3 Co 4 O 9 crystalline oxide material was discovered and reported in terms of its sandwiched structure and anisotropic transport by Shikano and Funahashi in 2003 [5]. e sensitivity of physical properties to preparation procedures was also investigated during the past years. For instance, the grain alignment together with conduction is very dependent on the external stress of preparation. e polycrystalline materials of sandwiched CaCoO oxide have been more widely studied in contrast to their single-crystal materials for the sake of preparation cost, fabrication easiness, product scale, etc. In addition, they have been intensively studied experimentally in terms of the transport properties for the intrinsic as well as the regulated materials in recent years [7][8][9][10][11]. In order to recover the performance of single-crystal materials, some fabrication methods have been adopted. For instance, isostatic pressing is one of these ways. In this way, stress ranging from tens of MPas to several GPas is applied to the crystalline bulk materials when preparing. e resulting bulk materials should then be consolidated and regulated with regard to their density and grain alignment in order to get the bulk texture. We have also reported the stress-dependent transport properties of this sandwiched CaCoO crystalline oxide material. e grain alignment and the transport property thereafter can be regulated by external stress ranging from 30 MPa to 500 MPa [9,12]. e fundamental background physical properties are determined by the geometry structure as well as the electronic states thereafter. e evolution of geometry and electronic states with external stress merits investigation. Unfortunately, a theoretical study in this sandwiched CaCoO crystalline oxide material is moderately lacking. e transitional metal Cobalt has several d orbital electrons where varieties of spin alignments can be configured. We have demonstrated and reported that the antiferromagnetic aligned Ca 2 Co 2 O 5 crystalline oxide material is most stable among the antiferromagnetic phase and ferromagnetic phase [13]. In the present work, the geometrical structures, microarchitectures, stabilities, electron energy band structures, the electron density of states, and species recombination together with the electron conduction properties of the sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa are intensively studied via the density functional theory (DFT) calculational and analyzing method for the first time to our knowledge.

Computational Methods and Details
e sandwiched Ca 2 Co 2 O 5 crystalline oxide material is composed of rock salts like the CaCoO sublayer and CdI 2 like the CoO 2 sublayer along c axis with space group of P1M1. e rock salt like CaCoO and CdI 2 like CoO 2 has the same lattice parameters along b and c axis; their sublattices are mismatched along a axis. e cell angles α, β, and c are 90°, 90°, and 98.13°, the a, b, and c of the cell are 4.56Å, 9.66Å, and 10.84Å, respectively [2][3][4].
e schematical crystal structure of this sandwiched Ca 2 Co 2 O 5 crystalline oxide material and the projections onto several planes are shown in Figures 1 and 2. e present study was carried out based on the platform which is implemented in the Serial Total Energy Package (CASTEP, Cerius2, Molecular Simulation, Inc.) code within the DFT framework [12,14]. is packaged code is established within the DFT framework which has been successfully applied within the areas of solid states and material sciences for several years [12][13][14]. e DFT framework has been verified to be one of the most accurate strategies for the solutions of the electronic eigenvalues of solid states [15]. In this work, the deep valance electrons together with the atomic core were treated as Coulombic cores, and the Coulomb interactions of valance electrons with their cores of Ca, Co, and O were herein described by Vanderbilt pseudopotential function. e wave functions of electrons were represented by plane wave functions. e configurations of valence electrons for Ca(3s 2 3p 6 4s 2 ), Co(3d 7 4s 2 ), and O(2s 2 2p 4 ) were selected. e generalized gradient approximation (GGA) scheme and revised Perdew-Burke-Ernzerhof (RPBE) function within the scheme were used to describe the exchange-correlation relation between these electrons. e Hubbard energy revision of 2.5 eV was used to represent the on-site Coulomb effect of Co d electrons. e antiferromagnetic aligned Ca 2 Co 2 O 5 has previously been verified to be most thermally stable among their ferromagnetic phase and antiferromagnetic phase [13]. For the antiferromagnetic phase, the spin state of Co d within the CoO 2 layer was set as contrary as that of Co d within the CaCoO layer for the unpaired electron. In addition, the computational result of the magnetism is well in consistent with the initial settings of the antiferromagnetic phase. In the ground state total energy calculational process, the convergence tolerance of displacement during the self-consistent calculations was set as 0.0005Å, and the maximum force tolerance was set as 5 × 10 −6 eV/atom. e cutoff energy for  Table 1 shows the lattice parameters, total energy E t , formation enthalpy E f , and magnetism of sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa, these values for the counterpart Ca 2 Co 2 O 5 are also provided, and the ratios of these parameters are also deduced for comparison. e α, β, and c keep invariant. e initial lattice symmetry type is not influenced, and the space group remains undisturbed within the externally applied stress range. It can be seen from Table 1 that a, b, c, and cell volume exhibit decreasing trends. is is corresponding to the positive shrinkage expansion of this type of material under external stress. However, it is worth noting that the ratios of a, b, and c between counterpart cells and that under external stress are distinctively different. For example, the ratio of a is 0.997, and the ratio of b and c is 0.998 and 0.999, respectively, corresponding to the disproportionate ratio of the volume of 0.994. It is an indication that the strain induced by external stress is very much anisotropic. Specifically, it can be seen that the strain to the stress response of geometry is sensitive along a direction and insensitive along b c direction for the sandwiched Ca 2 Co 2 O 5 crystalline oxide material. In addition, this is another indication that the bindings within the sandwiched Ca 2 Co 2 O 5 crystalline oxide material are very much different, in terms of the binding nature, binding type, binding length, and binding strength.

Results and Discussion
It can be seen from Table 1 that the counterpart sandwiched Ca 2 Co 2 O 5 crystalline oxide material without external stress has a total energy of −12556.6 eV for the cell, while the total energy of −12556.5 eV for the cell under external stress is slightly larger than it. Although the difference is negligible, it indicates that the counterpart sandwiched Ca 2 Co 2 O 5 crystalline oxide material without external stress is more thermally stable. In order to verify the stability of the sandwiched Ca 2 Co 2 O 5 crystalline oxide material under different external stress, the formation enthalpy is applied. e formation enthalpy ΔH MN of materials with specific molecular equation x M y N can be deduced by where E t is the total energy of the molecular, E M and E N are the averaged energy of element M and N, and x M and y N are the quantity of element M and N of the molecular equation. e thermal stability should be higher for material with a smaller formation enthalpy value and it is easier to be formed. It can be seen from Table 1 that the counterpart sandwiched Ca 2 Co 2 O 5 crystalline oxide material has a formation enthalpy of −6.221 eV, which is slightly lower than that under external stress of 1 GPa with −6.220 eV. e counterpart sandwiched Ca 2 Co 2 O 5 crystalline oxide material should be easier to be formed according to the formation enthalpy values. is is in agreement with the total energy that has been discussed above. It is convinced herein that the total energy as well as the formation enthalpy can be applied Advances in Condensed Matter Physics 3 jointly for analyzing the thermal stability of materials; it turns out to be reasonably reliable. e Ca-O binding strength is insensitive to external stress and strain within the applied range. Figure 4 shows the full energy range spin electron band structures of the sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa, the Fermi energy level is relatively set to be 0 eV, and other energy levels are determined thereafter by comparing with Fermi energy level. Figure 5 shows the full energy range spin electron density of states of the sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa. It is true that the bands are anisotropic, especially for a band near the Fermi energy level. It can be seen that the spin-up valence electrons of Ca 2 Co 2 O 5 form five bands within the whole energy range; they locate near −38.5 eV, −19.5 eV, −17 eV, Fermi energy level, and 5 eV. e spin-down valence electrons of Ca 2 Co 2 O 5 form six bands within the whole energy range, and the new band near 1.5 eV can be detected. It can also be observed from Figure 4 that the deep valence bands far from the Fermi level are heavier and the conduction bands are lighter for both of the spin-up and spin-down electrons [13,14]. ere is an obvious band concentration near −19.5 eV, and a strong interaction between electrons can be observed near −2.5 eV, as shown in Figure 5. Figure 6 shows the spin electron band structures near the Fermi energy level of the sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa. Figure 7 shows the spin electron density of states near the Fermi energy level of the sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa. For the spin-up electron band structure, a band valley locates at 4.0485 eV and a band peak locates at 1.9680 eV, and there is an indirect energy gap of 2.0805 eV. It has been investigated within our former study that the spin-up band has an energy gap of 2 eV above Fermi level and an energy gap of 0.1 eV below Fermi level for the counterpart Ca 2 Co 2 O 5 crystalline oxide material. e energy gap of 0.1 eV below Fermi level disappears for the Ca 2 Co 2 O 5 crystalline oxide material under external stress of 1 GPa. For the spin-down electron band structure, the band valleys   It can be seen from Figure 7 that the density of states below Fermi energy level is largely contributed by p orbital electrons and the density of states above Fermi energy level is largely contributed by d state electrons. e p orbital electrons form primarily the bands below Fermi energy level, and the d state electrons form primarily the bands above Fermi energy level. In addition, it can be said that the transitions from p orbital electrons to d orbital electrons should produce the conduction process, and they should be responsible for the electron heat capacity part for this kind of Ca 2 Co 2 O 5 crystalline oxide material. Figure 8 shows the detailed density of states of the rock salt like CaCoO and CdI 2 like CoO 2 layer near Fermi energy level of the sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa. Figure 9 shows the density of state values on the Fermi energy level for the sandwiched Ca 2 Co 2 O 5 , the rock salt like CaCoO, and CdI 2 like CoO 2 layer, as well as species that form these layers. e values marked with number 1 are for the sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa, and the values marked with number 0 are for the intrinsic sandwiched Ca 2 Co 2 O 5 crystalline oxide material with no  31. e proportion of density of states for this layer is decreased from 84% down to 82%. e electronic properties of metallic solids are determined by electrons near Fermi energy; the capability of determining the transport properties is reduced for this layer. It can also be seen that the total density of states value below Fermi energy of this layer is largely composed by p orbital electrons, and the total density of state value above Fermi energy of this layer is largely composed by d orbital electrons. It can be seen that the total density of state value for CdI 2 like CoO 2 layer at Fermi level is 0.5093; it contributes 18% to the total density of state value of 2.8836. Nevertheless, for the intrinsic counterpart Ca 2 Co 2 O 5 , the total density of state value for this same layer at Fermi level is 0.83; it contributes 16% to the total density of state value of 5.31. e proportion of density of states for this layer is increased from 16% to 18%. It is seen that this layer has been enhanced in determining the electronic properties. It can also be seen that the total density of states value below Fermi energy of this layer is largely composed by p orbital electrons; the total density of state value above Fermi energy of this layer is largely composed by d orbital electrons.   Advances in Condensed Matter Physics Figure 10 shows the detailed density of states of Ca, Co, and O within the rock salt like CaCoO near Fermi energy level of the sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa. It is observed that the total density of state values of Ca, Co, and O at Fermi level is 0.0197, 0.565, and 1.7465; they contribute 0.8%, 24%, and 75.2% to the total density of state value of 2.3742 of this layer. Nevertheless, for the counterpart Ca 2 Co 2 O 5 , the total density of state values of Ca, Co, and O at the Fermi level is 0.09, 2.08, and 2.30; they contribute 2%, 47%, and 51% to the total density of state value. It can be indicated that the capability of contributing to electronic properties of Ca and Co is decreased; the capability of contributing to electronic properties of O is enhanced. It can be concluded from Figures 9 and 10 that the total density of states of the CaCoO layer at the Fermi energy level is mainly composed of the orbital electrons of Co d and O p. is is the same as the counterpart Ca 2 Co 2 O 5 . It is inferred that these two kinds of orbital electrons within this layer contribute to the conduction process. Figure 11 shows the detailed density of states of Co and O within the CdI 2 like CoO 2 layer near Fermi energy level of the sandwiched Ca 2 Co 2 O 5 crystalline oxide material with external stress of 1 GPa. It is observed that the total density of state values of Co and O at the Fermi level is 0.1854 and 0.3237; they contribute 36% and 64% to the total density of state value of 0.5093 of this layer. However, for the counterpart Ca 2 Co 2 O 5 , the total density of state values of Co and    same as the counterpart Ca 2 Co 2 O 5 . It is inferred that these two kinds of orbital electrons within this layer contribute to the conduction process.

Conclusions
In conclusion, the geometrical structures, microarchitectures, phase stabilities, electron energy band structures, electron density of states, species recombination, and the electron conduction properties of the sandwiched Ca 2 Co 2 O 5 with external stress of 1 GPa are intensively studied within the framework of density functional theory calculational and analyzing method. e symmetry type is not influenced, and the space group remains undisturbed.
e strain-to-stress response of geometry is sensitive along a direction; it is insensitive along the c direction. e strain induced by external stress of microarchitecture is anisotropic, indicating the different binding characteristics. e distances between Ca and O are larger than those between Co and O in common, and there is stronger covalent binding for the Co and O. e bindings between Co and O within CdI 2 like CoO 2 are very much covalent than those between Co and O within the rock salt like CaCoO layer. e covalent Co-O binding within the rock salt like CaCoO layer is enhanced; nevertheless, the covalent Co-O binding within the CdI 2 like CoO 2 layer is weakened under the external stress. e Ca-O binding strength is insensitive to external stress. e intrinsic sandwiched Ca 2 Co 2 O 5 is more stable. An energy gap of 0.1 eV below Fermi level for spin-up electron band disappears, and the two energy gaps are decreased to 1.1089 eV and 0.6047 eV for the spin-down electron bands, respectively. e p orbital electrons form largely the bands below Fermi energy level and the d state electrons form largely the bands above Fermi energy level. e transitions from p orbital electrons to d orbital electrons produce the conduction process. e CdI 2 like CoO 2 layer has been enhanced in terms of involving the transport properties with external stress of 1 GPa. Nevertheless, the rock salt like the CaCoO layer exhibits contrary characteristics. For the CdI 2 like CoO 2 layer, the capability of contributing to transport properties for Co is enhanced, but the capability of contributing to transport properties for O is decreased. For the rock salt like the CaCoO layer, the capability of contributing to transport properties for Ca and Co is decreased; the capability of contributing to transport properties for O is enhanced.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare no conflicts of interest.