Phase transitions <ul><li>Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free ener...
Phase transitions in Ferro magnetic shape memory alloy T C T M First order  second order
Ferroelectric BaTiO 3
Ferroelectric domains and P-E loop
Resistivity vs. T for Ba TiO 3  based systems
Experimental procedure <ul><li>The thermo-dielectric effect is the production of electric currents and charge separation d...
<ul><li>These two probes are connected to capacitance meter and temperature controller. </li></ul><ul><li>The capacitance ...
Experimental arrangement
Relation <ul><li>From the measured capacitance (C) values, dielectric function (k) can be measured using the relation </li...
 
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7.curie temperature of a ferroelectric material from temperature dependence of dielectric constant

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curie temperature of a ferroelectric material from temperature dependence of dielectric constant

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7.curie temperature of a ferroelectric material from temperature dependence of dielectric constant

  1. 1. Phase transitions <ul><li>Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free energy as a function of other thermodynamic variables. </li></ul><ul><li>First order phase transitions show discontinuity in the first derivative of free energy </li></ul><ul><li>Ex: Solid-Liquid transition, Liquid-Gas transition </li></ul><ul><li>Second order phase transitions show discontinuity in the second derivative of energy </li></ul><ul><li>Ex: Ferro magnetic to para magnetic transition </li></ul><ul><li>This classification could not explain the case where the derivative of the free energy diverges </li></ul><ul><li>Modern classification: </li></ul><ul><li>First order transitions involves latent heat, exhibits thermal hysteresis, Two phases co-exist. Order parameter shows discontinuity at transition </li></ul><ul><li>Second order transitions do not involve latent heat, no thermal hysteresis. Order parameter varies continuously thro’ transition </li></ul>
  2. 2. Phase transitions in Ferro magnetic shape memory alloy T C T M First order second order
  3. 3. Ferroelectric BaTiO 3
  4. 4. Ferroelectric domains and P-E loop
  5. 5. Resistivity vs. T for Ba TiO 3 based systems
  6. 6. Experimental procedure <ul><li>The thermo-dielectric effect is the production of electric currents and charge separation during phase transition. </li></ul><ul><li>Barium titanate exhibits ferroelectric behavior at low temperature with spontaneous dipole moment in tetragonal phase and becomes Para electric at high temperature in cubic phase with no spontaneous dipole moment. The temperature at which the spontaneous polarization disappears is called the Curie temperature, T C . </li></ul><ul><li>In the experimental set-up, we have two spring loaded probes. They are mounted on a suitable stand, which also holds the sample plate. To ensure the correct measurement of sample temperature, the sensor is embedded in the sample plate just below the sample. </li></ul>
  7. 7. <ul><li>These two probes are connected to capacitance meter and temperature controller. </li></ul><ul><li>The capacitance across the sample is measured as a function of temperature. The temperature is varied with the help of temperature controlled oven. </li></ul><ul><li>Platinum RTD sensor is used for temperature measurement. A Wheatstone bridge and an amplifier are used for signal conditioning. </li></ul><ul><li>Capacitance is measured by using digital capacitance meter, with a range of 50-6000 pf with 1pf resolution. </li></ul><ul><li>Sample used : BaTiO 3 </li></ul>
  8. 8. Experimental arrangement
  9. 9. Relation <ul><li>From the measured capacitance (C) values, dielectric function (k) can be measured using the relation </li></ul><ul><li>Where d is the distance between the plates with area A </li></ul><ul><li>Variation of k is measured as a function of temperature thro’ T C </li></ul>

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