Assignment 1 TC

Assignment 1 (EBT427 SEM1 20182019)
Conductivity of Sm doped CeO2 in the temperature range of 400 oC –1000 oC is tabulated in

Table 1.
1) Complete the table below.
TEMPERATURE TEMPERATURE CONDUCTIVITY CONDUCTIVITY T ln σT 10³ / T

(C°) (K) (Ω¯¹m¯¹) (Ω¯¹cm¯¹) (Ω¯¹cm¯¹K) (Ω¯¹cm¯¹K) (K¯¹)
400 673 0.07 0.0007 0.4711 -0.752684893 1.485884101
450 723 0.1785 0.001785 1.290555 0.255072358 1.383125864
500 773 0.3651 0.003651 2.822223 1.037524872 1.293661061
550 823 0.8465 0.008465 6.966695 1.941140937 1.215066829
600 873 1.4052 0.014052 12.267396 2.506945011 1.145475372
650 923 2.2833 0.022833 21.074859 3.048080813 1.083423619
700 973 2.897 0.02897 28.18781 3.338889615 1.027749229
750 1023 4.1946 0.041946 42.910758 3.759122564 0.977517107
800 1073 6.0639 0.060639 65.065647 4.175396714 0.931966449
850 1123 8.0976 0.080976 90.936048 4.51015649 0.89047195
900 1173 10.1479 0.101479 119.034867 4.77941645 0.852514919
950 1223 13.776 0.13776 168.48048 5.126819897 0.817661488
1000 1273 14.9784 0.149784 190.675032 5.250570576 0.785545954
2) Based on the experimental data, using excel draw an Arrhenius plot (ln σT versus 103/T)
from temperature range of 400 –650 OC and 650 oC -1000 oC. Use conductivity in unit Ω-
1cm-1
Graph of ln σT versus 10³ /T

6
5
ln σT,(Ω¯¹cm¯¹K)
4
3
2 400°C-650°C
1 650°C-1000°C
0
-1 0.7 0.9 1.1 1.3 1.5
-2
10³ / T,(K¯¹)
3) Describe the effect of temperature on conductivity of the material.
At higher temperature ionic conductivity depends only on Em because all the clusters are
dissociated and mobile. Lower than transition temperature, conductivity depends on Em +
E0, leading to a steep slope in Arrhenius plots. In other words, there is conductivity drop
or discrepancy compared with extrapolated line of higher temperature plot to lower
region, reflecting the E0. The discrepancy equals zero at temperature region higher than
transition temperature, and it becomes larger with decreasing temperature. So, when
temperature is increased, molecules starts to vibrate more due to thermal energy. This
increase in vibration decreases the mean free path of molecules and therby its electrons.
Now in case of conductors there are many more free electrons than semi conductors so
when lattice vibration takes place all these electrons have their mean free path reduced
there by reducing conductivity. Where as there are way less free electrons in a
semiconductor than the conductor and increase in temperature will make the mean free
path less but conductivity will altogether increase as valence electrons will move up to
free electrons. So the increase in the number of valence electron to free electron is more
in semi conductor than the conductor. So collision is less in semiconductor than
conductors.
4) Find activation energy for each temperature range in 2) in unit eV.
5) Describe activation energy.
Activation energy is the energy which must be available to a chemical or nuclear[1]

system with potential reactants to result in: a chemical reaction[2], nuclear reaction[3], or
various other physical phenomena. The activation energy (Ea) of a reaction is measured
in joules (J) and or kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol).[6]
Activation energy can be thought of as the magnitude of the potential barrier (sometimes
called the energy barrier) separating minima of the potential energy surface pertaining to
the initial and final thermodynamic state. For a chemical reaction, or division [7] to
proceed at a reasonable rate, the temperature of the system should be high enough such
that there exists an appreciable number of molecules with translational energy equal to or
greater than the activation energy.
Catalyst
A substance that modifies the transition state to lower the activation energy is termed a
catalyst; a catalyst composed only of protein and (if applicable) small molecule cofactors
is termed an enzyme. It is important to note that a catalyst increases the rate of reaction
without being consumed by it. In addition, while the catalyst lowers the activation
energy, it does not change the energies of the original reactants or products. Rather, the
reactant energy and the product energy remain the same and only the activation energy is
altered (lowered).
6) Explain each activation energy found in 3).
From the gradient of Arrhenius plot, activation energy, Ea can be determined based
on the Arrhenius equation which is given by, σT ¼ σ0 expð−Ea=kTÞ ð1Þ where σ0 is
pre-exponential factor, σ is ionic conductivity, T is absolute temperature, and k is
Boltzmann constant. In general, there are two energies that contribute to ionic
conduction, i.e. charge carrier migration energy, Em and ion-defect clusters dissociation
energy, E0. In wide temperature range, transition temperature appears where gradient
change in Arrhenius plot can be observed. At higher temperature ionic conductivity
depends only on Em because all the clusters are dissociated and mobile. Lower than
transition temperature, conductivity depends on Em + E0, leading to a steep slope in
Arrhenius plots. In other words, there is conductivity drop or discrepancy compared with
extrapolated line of higher temperature plot to lower region, reflecting the E0. The
discrepancy equals zero at temperature region higher than transition temperature, and it
becomes larger with decreasing temperature.
A possible explanation for this finding is that reduction in activation energy is

attributed to the absorbed MMW energy which becomes one of energy contributor in
conduction process apart from thermal energy. Numerous studies in regards to the
enhancement of mass transport and solid state reaction rates in microwave processing
have been reported. The researchers mostly explain the observation of reduction in
activation energy as the result of microwave non-thermal effect that leads to enhancement
in the process involved. Similar to the present study, in conventional heating, the only
energy source for conduction process to occur originates from thermal energy.
Meanwhile, in MMW heating, an additional energy absorbed from MMW plays
important part to facilitate the charge carriers transport, thus resulted in lower apparent
activation energy.

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Assignment 1 (EBT427 SEM1 20182019)

Conductivity of Sm doped CeO2 in the temperature range of 400 oC –1000 oC is tabulated in

1) Complete the table below.

TEMPERATURE TEMPERATURE CONDUCTIVITY CONDUCTIVITY T ln σT 10³ / T

Graph of ln σT versus 10³ /T

Activation energy is the energy which must be available to a chemical or nuclear[1]

6) Explain each activation energy found in 3).

A possible explanation for this finding is that reduction in activation energy is

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