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.