IONIC POLARIZATION AND DIELECTRIC RESONANCE-By Tahmid Rongon,Electrical Properties Of Matarials
- 1. Prepared by Md.Mostak Tahmid Rongon
- 2. IONIC POLARIZATION AND DIELECTRIC RESONANCE
- 3. Polarization Polarization is the separation of positive and negative charges in a system so that there is a net electric dipole moment per unit volume.
- 4. IONIC POLARIZATION Ionic polarization is polarization caused by relative displacements between positive and negative ions in ionic crystals. This type of polarization occurs in ionic crystals such as NaCl, KCl etcs.
- 5. DIELECTRIC RESONANCE Dielectric resonance occurs when the frequency of the applied ac field is such that there is maximum energy transfer from the ac voltage source to heat in the dielectric through the alternating polarization and depolarization of the molecules by the ac field.
- 6. Derivation of the dielectric dispersion relation between the relative permittivity, due to ionic polarization and the frequency of the electric field.
- 7. Consider two oppositely charged neighboring ions Na+ and CI–, which experience forces QE in opposite directions where Q is the magnitude of the ionic charge of each ion as shown in Figure. The bond between the ions becomes stretched and the two ions become displaced from the equilibrium separation r0 to a new separation r0 + x as depicted in Figure.
- 8. The force F= QE of the applied field is the polarizing force, which causes the relative displacement. We take F to be along the x direction. The applied force is resisted by a restoring force Fr that is due to the stretching of the bond (Hooke's law) and is proportional to the amount of bond stretching, that is- Fr = - βx ……………………………….① Where, β is the spring constant associated with the ionic bond the negative sign ensures that Fr is directed in the opposite direction to the applied force.
- 9. The ions are oscillated by the applied force. They couple some of the energy in the applied field to lattice vibrations and this energy is then lost as heat in the crystal. energy loss through a coupling mechanism can be represented as a frictional force,Floss (force associated with losses) that acts against the effect of the applied force.
- 10. This frictional force is proportional to the velocity of the ions or dx/dt , so it is written as Floss = -γ (dx /dt)………………..② Where, γ is a proportionality constant that depends on the exact mechanism for the energy loss from the field the negative sign ensures that it is opposing the applied field.
- 11. So the total (net) force on the ions is, …………….③ Normally we would examine the equations of motion (Newton's second law) under forced oscillation for each ion separately.
- 12. An equivalent procedure (as well known in mechanics) is to keep one ion stationary and allow the other one to oscillate with a reduced mass Mr , which is Mr = (M+ + M-)/(M+ + M- ) where M+ and M- are the masses of Na+ and Cl- ions respectively.
- 13. For example, we can simply examine the oscillations of the Na+ -ion within the reference frame of the Cl- ion and attach a reduced mass Mr to Na+ as depicted in Figure. Then Newton's second law gives- …………….④
- 14. It is convenient to put Mr and β together into a new constant w1 which represents the resonant or natural angular frequency of the ionic bond. when the applied force is removed. Defining w1 = ( β+ M+)1/2 and ϒ1 as ϒ per unit reduced mass. That is - • ϒ = ϒ1 / Mr
- 15. ………④ …………⑤ This equation is called the forced oscillator equation. The solution to Equation will give the displacement x = x0 exp(jwt), which have the same time dependence as E but phase shifted; that is, x0 will be a complex number.
- 16. The relative displacement of the ions from the equilibrium gives rise to a net or induced polarization Pi=Qx. Thus this equation can be multiplied by Q to represent the forced oscillations. When we divide Pi by the applied field E, we get the ionic polarizability- …………⑦ Equation is also called the Lorentz dipole oscillator model.
- 17. when ω = 0,under dc conditions, the ionic polarizability a i (0) from Equation, ………………………………⑧ The dc polarizability is a real quantity as there can be no phase shift under dc conditions. We can then write the ionic polarizability in Equation 7 in terms of the normalized frequency (ω/ ω 1) as- …………………………………………⑨
- 18. The dependences of the real and imaginary parts of ai , on the frequency of the field are shown on the Figure. In terms of the normalized frequency (ω/ω1 ) for one particular value of the loss factor, γ1 = 0.1 ω1
- 19. At high frequencies, well above ω1 ,the ions cannot respond to the rapidly changing field and the coupling between the field and the ions is negligible. The peak in the ai ’’ versus ω behavior around ω = ω1. which is called the dielectric resonance peak and in this particular case it is called the ionic polarization relaxation peak and is due to the strong coupling of the applied field with the natural vibrations of the ionic bond at ω = ω1 .
- 20. The resulting relative permittivity єr can be found from the Clausius-Mossotti equation. But we also have to consider the electronic polarizability a e of the two types of ions since this type of polarization operates up to optical frequencies (ω » ω1), which means that ……………………………………⑩ where Ni is the concentrations of negative and positive ion pairs.
- 21. We can express Equation ⑩ differently by noting that at very high frequencies, co » al. = 0, and the relative permittivity is the denoted as єrop . Equation ⑩ then becomes- This is called the dielectric dispersion relation between the relative permittivity, due to ionic polarization, and the frequency of the electric field.
- 22. summary • Polarization • ionic polarization • Dielectric resonance • the dielectric dispersion relation between the relative permittivity due to ionic polarization • Finding the value of ionic resonance absorption frequency