3.2 Elasto-mechanical properties:
The elastic constants supplies an authunticate understanding about the response of the material to external stresses within the elastic limit and hence aids their performance in various technological and industrial based purposes. The number of elastic constants are directly related to symmetry of the crystal structure. This means more symmetric the material is, lesser no of elastic constants are examined. To estimate them, we have used the rhombohedral and tetragonal distortions on the cubic lattice under volume conserving constraints. Thus, the elastic constants obtained via first principle approach are used to reproduce the other elastic parameters which determines the mechanical strength and nature of material characteristics. To show mechanical stability, the cubic crystal in its fcc phase must obey the Born-Haung stability criterion i.e; C11 > 0, C12 > 0, C44 > 0, C11+ 2C12 > 0, C11 − C12 > 0 [31-33] and are quoted as well as enlisted in Table 3 . These constants completely satisfies the above conditions indicating that both RESnFeO6 (RE=Ca,Ba) are elastically stable. The polycrystalline mechanical constants were estimated using the Voigt (V), Reuses (R) and Hill (H) formula [34,35]. The bulk modulus measures resistance of volumetric change caused by the external pressure of a given material. The calculated value of B from the elastic parameters of both oxides are 142.67 and 135.25 GPa respectively are relatively large signifying strong bonding strength of atoms involved in such type of materials. On the contrary, change of shape in a solid largely depends on its shear modulus G, which also shows a crucial role in predicting the material’s hardness. The forecasting value of G is presented and shown inTable. 3 . Also, Young’s modulus (Y) being ratio of stress to strain provides a better evidence about the stiffness of the material. In addition to this, for most of the practical applications a material is needed to identify ductile or brittle. To estimate the materials charactericteritics, Pugh’s ratio [36] defined as B/G of index value 1.75. According to this formula, a material acts as a ductile if the value of Pugh’s ratio surpasses the critical value and below it supports the brittle character. The calculated values of the Pugh’s ratio confirms the the brittle nature of both the compounds. Furthermore on accomplishing Cauchy,s descrepancy (C12−C44) [37] catagorises the nature of the materials. If the value of Cauchy pressure is negative, the material is labelled as brittle, otherwise positive value hints the ductile feature. Since, C’=(C12 −C44) is negative potrays brittleness in these alloys. Lastly the universal anisotropic index, denoted by AU is an another indicator which is also used in a practice to clearify the ductile and brittle nature of crystals. When AU = 0, the material is perfectly isotropic or otherwise anisotropic [38]. The values of AU for both the complex alloys are 1.06 and 1.43 respectively refers to brittle character in these alloys. Therefore, the compounds RE2SnFeO6 (RE=Ca,Ba) in accordance with the below mentioned parameters shows brittle characteristics. In addition, by using the ground state parameters, we have established their chemical stability using the cohesive energy ECoh analysis. The depiction of large cohesive energy values tenders the stability as well as retention of ground state structure upon the implementation of external forces on these materials.