1Dielectric behaviorTopic 9Reading assignment• Askeland and Phule, The Science and Engineering of Materials, 4thEd., Sec. 18-8, 18-9 and 18-10.• Shackelford, Materials Science for Engineering, Sec. 15.4.• Chung, Composite Materials, Ch. 7.Insulators and dielectric properties• Materials used to insulate an electric field from its surroundings are required in a large number of electrical and electronic applications. • Electrical insulators obviously must have a very low conductivity, or high resistivity, to prevent the flow of current.• Porcelain, alumina, cordierite, mica, and some glasses and plastics are used as insulators.Dielectric strength• Maximum electric field that an insulator can withstand before it loses its insulating behavior• Lower for ceramics than polymers• Dielectric breakdown - avalanche breakdown or carrier multiplication2Polarization in dielectrics• Capacitor – An electronic device, constructed from alternating layers of a dielectric and a conductor, that is capable of storing a charge. These can be single layer or multi-layer devices.• Permittivity - The ability of a material to polarize and store a charge within it.• Linear dielectrics - Materials in which the dielectric polarization is linearly related to the electric field; the dielectric constant is not dependent on the electric field.• Dielectric strength - The maximum electric field that can be maintained between two conductor plates without causing a breakdown.Polarization mechanisms in materials:(a) electronic, (b) atomic or ionic, (c) high-frequency dipolar or orientation (present in ferroelectrics), (d) low-frequency dipolar (present in linear dielectrics and glasses), (e) interfacial-space charge at electrodes, and (f ) interfacial-space charge at heterogeneities such as grain boundaries. ©2003 Brook s/Cole, a division of T homson Learning, Inc. T homson Learning™is a tradema rk used herein under license.A charge can be stored at the conductor plates in a vacuum (a). However, when a dielectric is placed between the plates (b), the dielectric polarizes and additional charge is stored.3, AQ = Do, dV = ∑Do= εoΣεo= 8.85 x 10-12C/(V.m), dAdAVQC = Slopeoooεε=ΣΣ==4, AQD =Domκκ=Dm= κεoΣ = εΣ, CdAdAVQ = Cooomκκεκεκ==ΣΣ=P = Dm− Do= κεoΣ−εoΣ= (κ−1) εoΣE5, 1 = QQQ−−κκ, P 1= oΣ=−εκχ(bound charge)d = (κ−1) Qd, PA1)Q(Ad1)Qd( = VolumemomentDipole=−=−κκmCQ = VκκQ = DmA = εΣAxAxA = Comεκε=xxAA = V Σ=Σεε6Table 7.6 Values of the relative dielectric constant κ of various dielectric materials at 1 kHz (Data from Ceramic Source ’86, American Ceramic Society, Columbus, Ohio, 1985, and Design Handbook for DuPont Engineering Plastics).3.6Polyester3.7Nylon-66 reinforced with glass fibers4.1-5.3Cordierite6.7BeO (99.5%)9.8Al2O3(99.5%)___κ__MaterialΣ =(),sinicosˆeˆtittωωω+= ΣΣDm= ()()[],)tsin(itcosDˆeDˆmtimδωδωδω−+−=−(),eˆeDˆtitimωδωεΣ=−(),sinicosˆDˆeˆDˆmi-mδδεδ−==ΣΣ, ofpart Real ofpart Imaginary tanκκδ−=7, dtdvCdt dQic==ν = V sin ωt, T2f2ππω==, cosCVdtdvCictωω== cosC1/Vtωω=⎟⎠⎞⎜⎝⎛+2sinπωt 2sincos2cossinπωπωtt +=, cos tω=, 2sinC1/Vic⎟⎠⎞⎜⎝⎛+=πωωt, sinRVRiRtων==, 2sinC1/Vic⎟⎠⎞⎜⎝⎛+=πωωt, sinRVRiRtων==, CR1CVV/Rtanωωδ==8Energy stored =, di0C∫τνt, dcossinCV02tttωωωτ∫=, d2sin2CV02tt∫=τωω[], 2cos4CV02τωωωt−=(), 12cosCV412−−=ωτMaximum energy stored = ½ CV2This occurs when cos 2ωt = -1Energy loss per cycle due to conduction through the resistor REnergy loss = dsinsinRV/202ttt∫ωπωω()() d2cos121RV202ttωωωπ∫−= 2sin2121RV202πωωω⎥⎦⎤⎢⎣⎡⎟⎠⎞⎜⎝⎛−= tt() 000221RV2⎥⎦⎤⎢⎣⎡+−−=πω. RV2ωπ=9The smaller is R, the greater is the energy loss. 2/CV2R/Vstoredenergymaximum2cycleperlostEnergy22πωππ=×δωtan CR1==10Frequency dependence of polarization mechanisms. On top is the change in the dielectric constant with increasing frequency, and the bottom curve represents the dielectric loss.Quartz – polarization only under stress11©2003 Brook s/Cole, a division of T homson Learning, Inc. T homson Learning™is a tradema rk used herein under license.(a) The oxygen ions are at face centers, Ba+2 ions are at cube corners and Ti+4 is at cube center in cubic BaTi03.(b) In tetragonal BaTi03 ,the Ti+4 is off-center andthe unit cell has a net polarization.12Different polymorphs of BaTiO3and accompanying changes in lattice constants and dielectric constants.Table 7.3 Contribution to dipole moment of a BaTiO3unit cell by each type of ion.Total = 17 x 10-304.2 x 10-30-0.13(10-10)(-2)(1.6 x 10-19)O2-(top and bottom of cell)6.4 x 10-30-0.10(10-10)2(-2)(1.6 x 10-19)2O2-(side of cell)6.4 x 10-30+0.10(10-10)(+4)(1.6 x 10-19)Ti4+00(+2)(1.6 x 10-19)Ba2+Dipole moment (C.m)Displacement (m)Charge (C)Ion330230m103.984.03C.m1017−−×××=P= 0.27 C.m-213-Ec E14(b) single crystal.c) Polycrystalline BaTiO3 showing the influence of the electric field on polarization.The effect of temperature and grain size on the dielectric constant of barium titanate. Above the Curie temperature, the spontaneous polarization is lost due to a change in crystal structure and barium titanate is in the paraelectric state. The grain size dependence shows that similar to yield-strength dielectric constant is a microstructure sensitive property.Effect of grain sizeFerroelectric domains in polycrystalline BaTiO3.15E,ttlogruuu12112=−Piezoelectric aging rate rDepolingu : parameter such as capacitancet: number of days after polarizationFerroelectric -A material that shows spontaneous and reversible dielectric polarization.Piezoelectric – A material that develops voltage upon the application of a stress and develops strain when an electric field is applied.16©2003 Brook s/Cole, a division of T homson Learning, Inc. T homson Learning™is a tradema rk used herein under license.The (a) direct and (b) converse piezoelectric effect. In the direct piezoelectric effect, applied stress causes a voltage to appear. In the converse effect (b), an applied voltage leads to development of strain.Direct piezoelectric effectReverse (converse) piezoelectric effect17E E18P = dσ∂P = d ∂σσκε∂∂Σ=odd: Piezoelectric coupling coefficient (piezoelectric charge coefficient)Direct piezoelectric effectTable 7.1 The piezoelectric constant d (longitudinal) for selected materials80 x