Fig. 6: Designation of bonding through charge density plots of RE2SnFeO6 (RE =Ca,Ba) in (110) plane.
3.5 Thermoelectricity :
Energy in nowadays is a big requirement and due to its scarcity is one of the prime factor to resolve it. The loss of heat releasing from automotive exhausts, industrial processes and residential heating are the leading sources. The main aim to carry this study work is to determine the thermoelectric applicability of these materials which could recapturate the unwanted heat into useable electric power. Thermoelectric materials for their potential in exchanging the energy conversion have studied much interms of their efficiency known as figure of merit (ZT) which corresponds to its intrinsic properties can be expressed as: (2)
the terms in the commonly used equation describes S the Seebek coefficient, σ means the electrical conductivity, T is the operation temperature and defines lattice thermal conductivity [40-49]. Here, in this comprehensive report we have made an attempt to simulate the materials within the instructions of density functional theory. So far as RE2SnFeO6 (RE=Ca, Ba) alloys are concerned the understanding of transport mechanism within semi-classical Boltzmann theory under constant relaxation time approximation [50,51] is addressed. Since, the characterization of these materials supports the half-metallic character from both oxide based alloys, therefore the quantities in two spin phases (spin-up as well as spin-dn) plots are assembled in single plots as designated in Fig. 7 (a-f) . Now insighting various temperature dependent parameters on observing Seebeck coefficient (S) first labels the thermoelectric mechanism as well as thermoelectric sensitivity to the temperature gradient. The description from the graphical plot of S shown inFig. 7 (a) descripts the metallic behavior in the up-phase due to increasing value of Seebeck corresponding to temperature. The increasing value of Seebeck is seen in the spin-majority channel from a lower temperature value of 50 K with an approximate value of 1.23 μVK-1 to 7.43 μVK-1 at 800 K. Mean while, for the down spin-minority channel the decreasing trend is reflected from a low temperature of 50 K to high temperature 800 K with a value of -979.56 μVK-1 to -234.38 μVK-1 respectively. Similarly for Ba2SnFeO6 Seebeck coefficient shown inFig. 7 (b) follows the same trend but the value increases from -5.67 μVK-1 at 50 K to -21.40 μVK-1 at 800 K in the spin-up channel. The negative sign reflects the electrons are majority transporters for heat conduction. While in spin-down semicoducting channel the value of S declines from 977.74 μVK-1 to 256.10 μVK-1 along the linearily increasing value of temperature. The turnout value of large S comes out due to the presence of flat conduction band (CB) parallel Г to X direction, as seen from all the band structures of both these perovskite alloys. Next we have graphically plotted in Fig. (c, d) (σ/τ) over the relaxation time τ = (1.5×10-15) of RE2SnFeO6 (Re=Ca,Ba) against temperature which portrays a decreasing pattern in both the up-spin phases. The decrease in electrical conductivity is attributed due to its metallic behavior and electron scattering processes that describes the main reason of decreasing the value of electrical conductivity. The value eventially decreases from 2.14×1018 Ω-1m-1s-1 (6.45×1018Ω-1m-1s-1) to 1.89×Ω-1m-1s-1 (1.11 × Ω-1m-1s-1) in the temperature range of 0-800 K. However the increase in σ/τ is visualized at a lower temperature value from a small value at 50 K to 1.11 Ω-1m-1s-1 (1.09 Ω-1m-1s-1) for Ca2SnFeO6 and (Ba2SnFeO6) at higher temperatures respectively. The increasing nature is due to its negative temperature coefficient of resistance i.e; with increase in temperature electrical conductivity increases .Hence the overall investigation from the spin dependent electrical conductivities in both the spin phases owes its occurrence of perfect half-metallic nature. Also, we have calculated the total Seebeck coefficient as shown graphically in Fig. (e) for both the oxide materials which aids the generation of thermopower within these materials. With the help of two current model the total Seebeck coefficient computed for ReSnFeO6 (Re=Ca, Ba) is given by the formula: S= (3)
.In order to see the lattice thermal conductivity (κl) displayed in Fig 7(f), we have taken the use of Slack’s equation [52,53] which accounts the phononic contribution in containing these crystal lattices and is written in a mathematical way as: Kl (4)
In equation (9) (A = 3.04×10−8, M, θD) in the numerator hand signifies physical constant, average mass and Debye temperature. The terms on the denominator side (γ, n, T) is Grüneisen parameter, no of atoms in the primitive unit cell and temperature respectively. The graphical representation of lattice thermal conductivity of Ca2SnFeO6 shows exponential decreasing trend from a higher value of 60.95 κ (W/mK) at 50K to 3.38 κ (W/mK) at 800K. Similar results are reflected for Ba2SnFeO6 with a decreasing value of 40.30 κ (W/mK) to 2.34 κ(W/mK). The diminishing value of lattice thermal conductivity over a wide range of temperatures of both these alloys projects better stand in imminient thermoelectrics and other application purposes
Fig. 7 (a, b) : Graphical representation of Seebeck coefficient (S) against temperature for RE2SnFeO6 (RE=Ca,Ba) double perovskites
Fig. 7 (c, d) : Graphical representation of electrical conductivity (σ/τ) against temperature for RE2SnFeO6 (RE=Ca,Ba) double perovskites.
Fig. 7 (e, f) : Graphical representation of total Seebeck coefficient (S) and lattice thermal conductivity (κ) against temperature for RE2SnFeO6 (RE=Ca,Ba) double perovskites.