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.