DIELECTRICS PARAELECTRICS FERROELECTRICS ADVANCED CERAMICS MAT-SCI PH0102 UNIT-2 PART-2 DIELECTRICS PARAELECTRICS FERROELECTRICS ADVANCED CERAMICS

Dielectric materials are also called : insulators. In dielectric materials, all the electrons are tightly bound to their parent molecules , hence there are no free charges to conduct electricity. The energy band gap (g.) for dielectric materials is more than 3eV. It is not possible for the electrons in the valence band to excite to the conduction band, by crossing the energy gap, even with normal voltage or thermal energy. Dielectrics are non-metallic materials of high specific resistance and negative temperature coefficient of resistance like semiconductors Ms-ph0102-u-2p-2-1

Active and Passive Dielectrics The dielectric materials can be classified into active and passive dielectric materials . a. Active dielectrics If a dielectric material placed in an external electric field actively accepts the electricity, then it is called as active dielectric material. Thus, active dielectrics are the dielectrics, which can easily adapt themselves to store the electrical energy in them. Examples: piezo-electrics , ferro-electrics etc. b. Passive dielectrics Those dielectrics, which restrict the flow of electrical energy in them are called passive dielectrics. So, these dielectrics act as insulators. Examples: All insulating materials such as glass, mica, rubber , ceramics etc., Ms-ph0102-u-2p-2-2

Basic Definitions in Dielectrics Electric Field E : The region around the charge within which its effect is felt or experienced is known as electric field. The electric field is assumed to consist of imaginary electric lines of force. These lines of force are assumed to originate from the positive charge and terminate on the negative charge . Electric field strength or electric field intensity (E) Electric field strength at any point is defined as the force experienced by an unit positive charge placed at the point. It is denoted by ‘E’ and defined as: E= f/q , where ‘q’ - magnitude of the charge in coulombs ‘f’ - force experienced by that charge in Newton. . Its unit is Newton / Coulomb (or) volt / metre. Ms-ph0102-u-2p-2-3

Electric flux density or electric displacement vector (D) It is defined as the total number of electric lines of force passing through a given area in the electric field. (Emanated from the positive charge) [Unit: Coulomb] Electric flux density or electric displacement vector (D) It is defined as the number of electric lines of force passing normally through an unit area of cross section in the field. Its unit is Coulomb / m2 Permittivity Permittivity is defined as the ratio of electric displacement vector (D) in a dielectric medium to the applied electric field strength (E). Mathematically the permittivity is, D=  E .Its unit is Farad /metre The permittivity indicates the degree to which the medium can resist to the flow of electric charge. It is always greater than unity. Dielectric Constant The dielectric constant r or relative permittivity of a material determines its dielectric characteristics. It is the ratio of the permittivity of the medium to the permittivity of free space i.e. r = /0 Ms-ph0102-u-2p-2-4

Electronic Polarization: Consider an atom. It is electrically neutral as well as the centres of the negative charge of the electrons coincides with the positive charge of the nucleus . which means that the atom has no net dipole moment. When this atom is placed in an external electric field, the centres of positive and negative charges are displaced with respect to each other. Therefore electric dipoles are created in all the atoms under the effect of external electric field. This is called electronic polarization. This is an induced effect alike to diamagnetism Polarizability (): When the electric field strength ‘E’ is increased, the strength of the induced dipole is also increased. Thus, the induced dipole moment is proportional to the intensity of the electric field. The induced dipole moment µ = eE where e = electronic polarizability. Polarization vector :The dipole moment per unit volume of the dielectric material is called polarization vector. [Unit: Coulomb / metre square] P = 0 e E , where e is called the electrical susceptibility Ms-ph0102-u-2p-2-5

Fig. (a) Without field (b) With field Orientation Polarization The orientation polarization arises due to the presence of polar molecule in the dielectric medium. Net Polarization is Zero B- dipoles are Aligned along Electric field a- random orientation Of dipoles Fig. (a) Without field (b) With field Explanation: In the case of a CH3Cl molecule, the positive and negative charges do not coincide. The Cl- has more electro negativity than hydrogen. Therefore, the Cl atoms pull the bonded electrons towards them more strongly than H atoms. Therefore, even in the absence of external electric field, there exists a net dipole moment. Such molecules are called as Polar molecules. Water (H2O )molecule is also a polar molecule. Under the applied field, positive end align along the electric field and negative end align opposite to the electric field. This kind of polarization is called as ‘orientation polarization’. Ms-ph0102-u-2p-2-6

Possess Centre of Symmetry Centro-Symmetric Possess Centre of Symmetry

The electromechanical Coupling factor is defined as: k.k = electrical energy converted into mechanical energy / Input electrical energy OR = Mechanical energy converted into electrical energy / Input mechanical energy

What is Ferroelectric? Ferroelectrics are materials which possess a “spontaneous” electric polarization Ps which can be reversed by applying a suitable electric field E. This process is known as “switching”, and is followed by “hysteresis”. Ferroelectrics are electrical analogues of “ferromagnetics” (P-E and M-H relations). PE FM

Ferroelectric Characteristics “Anomalous” properties (i.e. ferroelectricity disappears above a temperature Tc known as “Curie Point” Above Tc, the anomaly is frequently of the “ Curie-Weiss” form: (Curie-Weiss Relation) e = C / (T-T0) C ~ Curie-Weiss constant T0 is called “Curie-Weiss Temperature” T0 < Tc in materials with first-order transitions T0 = Tc in materials with second-order transitions !! Some materials do not follow Curie-Weiss Relation !!

P-E Hysteresis loops in FE materials

Curie temperature This temperature is termed the Curie temperature, Tc, in light of the analogy with the transition temperature between ferromagnetism and paramagnetism. Above the Curie temperature, ferroelectrics behave as non-polar dielectrics, sometimes termed a paraelectric phase. Some ferroelectrics do not have a Curie temperature .

Polarisation hysteresis

Polarisation vs. E-field Suppose we start with a material where there are many domains which are aligned randomly. What is the initial polarisation? It must be zero

Polarisation vs. E-field If we apply a small electric field, such that it is not able to switch domain alignments, then the material will behave as a normal dielectric: PE As E is increased, we start to flip domains and rapidly increase P. When all domains are switched, we reach saturation. What happens if the E-field is now removed?

Polarisation vs. E-field The value at zero field is termed the remnant polarisation. The value of P extrapolated back from the saturation limit is the spontaneous polarisation. Reversal of the field will eventually remove all polarisation The field required is the coercive field. Further increasing the reverse field will completely reverse the polarisation, and so a hysteresis loop is formed…

Polarisation vs. E-field The value at zero field is termed the remnant polarisation. The value of P extrapolated back from the saturation limit is the spontaneous polarisation. Reversal of the field will eventually remove all polarisation The field required is the coercive field. Further increasing the reverse field will completely reverse the polarisation, and so a hysteresis loop is formed…

DIELECTRIC LOSS: If a dielectric is subjected to an electric field, the electrical energy is absorbed by the dielectric . Certain amount of this energy is dissipated in the form of heat. This is known as the dielectric loss. The dielectric loss can occur both in case of DC or AC electric fields. Power loss in a capacitor: The capacitance of air filled parallel plate capacitor is given by: C0 = ϵ0 A/d [farad , F ] where A= area of the plates and d is the separation between the plates. The permittivity of air is assumed to be equal to the permittivity of free space ϵ0 . ϵ0 = 8.85.10-12 F m-1 If a dielectric is filled in between the plates the capacitance becomes C given by: C = ϵ A/d [farad , F ] ,where ϵ is the permittivity of the dielectric. C/ C0 = ϵ / ϵ0  ϵr ϵr is called the relative permittivity or dielectric constant of the dielectric. TO DO : Calculate the capacitance of a parallel plate capacitor whose plates are circular with diameter of 2cm and are separated by 0.87 mm. If the capacitance after inserting PZT between the plates becomes 25 nF calculate the dielectric constant of PZT. Ms-ph0102-u-2p-2-15

If δ is small Sin δ = δ  Tan δ Ideal capacitor δ Lossy capacitor Current I leads to voltage V by 90 degree Ø V V Case-b Case-a case –a: Power Loss PL = V.I.Cos Ø  Zero since current leads by 90 degrees i.e. Ø = 90 Case-b: PL = V.I.Cos Ø and Ø = 90 - δ PL = V.I.Cos (90- δ) V.I.Sin ( δ ) If δ is small Sin δ = δ  Tan δ For a Capacitor :Xc= 1/2 π νC and V/I = Xc Hence , PL = 2 π νCV2 Tan δ Tan δ is called loss tangent or loss factor of the dielectric of the capacitor. It depends on frequency ν of the applied voltage

Question : Calculate the power loss in the 10 micro Farad capacitor if an AC voltage of 100 V and frequency 50 CPS is applied to it. The loss tangent for the capacitor is 0.02. What will be the power loss if the AC voltage of 10 V at 10 mega hertz is applied? Find the ratio of the power losses in the two cases.

What is Piezoelectricity? Piezoelectrics are materials which acquire electric polarization under external mechanical stresses (Direct Effect), OR materials that change size or shape when subject to external electric field E (Converse Effect). ! (Piezo ~ Pressure or Stress) ! Many piezoelectric materials are NOT ferroelectric All ferroelectrics are piezoelectric Above T0, some ferroelectrics are STILL piezoelectric

Piezoelectric effect The application of an electric field induces a geometrical change. Alternatively, a distortion of the material induces a potential difference. Used in many electrical devices, e.g. sound-to-electricity

Piezoelectric Gas lighter.  

Schematic of piezoelectric actuator Ms-ph0102-u-2p-2-10

FE & Piezo-Electric Materials

Numericals Q2.1 A magnetic material has a magnetization of 2000 A/m. If it produces a flux density of 3 mT ( milli tesla) , calculate the magnetizing force and the relative permeability of the magnetic material. Q 2.2 A paramagnetic material with susceptibility equal to 0.000037 has a magnetic field intensity of 10000 A/m. Calculate the magnetization and flux density in the material. Q2.3 The saturation magnetic intensity for iron is 1.6 x 10 **6 A -turn/m and saturation magnetization is 17.12x10**6 A/m. Find the permeability , relative permeability and flux density at saturation. [ Mu=1.48x10**-5 H/m mur= 11.7, B=23.68 T] Ki= Ms/Hs= 17.12/1.6 10.7 ;mur ki+1=11.7 & mu= mu0xmur ; but mu0=4pix10**-7 hence mu= 1.48x 10**-5 ;now Bs= muxHs23.68 T