MSE 452 Study Guide
MSE 452 Study Guide MSE 452
Popular in Functional properties of materials II
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This 6 page Study Guide was uploaded by Quinn Haynie on Thursday February 19, 2015. The Study Guide belongs to MSE 452 at University of Washington taught by Dr. Cao in Fall. Since its upload, it has received 220 views. For similar materials see Functional properties of materials II in General Engineering at University of Washington.
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Date Created: 02/19/15
MSE 452 Midterm Study Guide Dielectrics paraelectrics 0 large polarization 0 dipole moment is charge times distance u q 6 so x E 0L E O polarization sum of u over volume P Z P Z N pi Z Nico xi E Z N on E 0 Electronic polarization ue q 6 ae E 80 xe E o q the number of charges 0 so permittivity of vacuum 8854e12 Fm o xe the electric susceptibility 0 ae polarizability I For applied field 1e6 Vm ue quot39 1e15 m I Total PeNue o N number of atoms per unit space I Outer she electrons 10e15 Hz I No temperature dependence 0 Ionic polarization pi q 6 a E I Shift of ions relative to sub lattice 10e13 Hz I No temperature dependence 0 Dipolar molecular polarization um q 6 am E I Polarization P Num 2 am cos 6 theta is bond angle I Molecules vibrating 10e10 Hz I Temperature dependent 0 Space chargeinterfacial polarization us q 6 as E I Diffusion of electrons and charged defects 10e3 Hz I Temperature dependent o Polarizability Larger atoms have larger polarizability 1e4O sz 0 Electron valence directly related to polarizability o Capacitance 0 Energy stored E5CV2 I Maximize by increasing V but limit is VB see dielectric strength 0 Charge density surface chargearea 39 qQA 0 Field between plates applied voltagedistance EVh O For vacuum QQo qqoQoA I Q q free surface charge free surface charge density C Cmz I Capacity CoeoAh 39 QoEoVAh oAhVCoV qoQoAeoVh oE O Fora dielectric Qt Qo Qb eoVAh eoxVAh so 1xAh V CV I Capacity in Farads C so 1 x Ah 0 Dielectric constant er K K OO 0 Direct relationship to total surface charge density qt I qtQtAQoAQbAqoqb soVh soxVh so 1x Vh so 1x E soer s E I Er 1 x s so Dqo qtqo QtQo CCo I sr sre sri sr0 srS electronicionicdipolarspace Dielectric permittivity s Fm Bound surface charge density qo P Solid high K quot39 150 gt Solid low K quot39 10 gt Liquid polar quot39 25 gt Liquid nonpolar quot39 225 gt Gas quot39 1 Water quot39 811 Vacuum 1 Low K dielectric lt 2 I Electronic polarization only carbon backbone molecules I Dipolar polarization is rare I Electronic and ionic polarization in high 2 elements high valence ions amp perovskites 0 Gate HfOZ ZrOZ Ta205 o Ferroelectric BaTi03 SrTi03 I Highly porous inorganics Complex dynamic and static relaxation I Complex dynamic and static dielectric constant described by Debye equations I Relaxation time is TAeBkT I For to 0 DC bias 5 ES Ern0 I w 9 N Err Em Ern0 I For0ltwltoo ops4 858 I Resonance at w mm relaxation time 1 I ColeCole plot can be used to determine s5 s 0 Plot s vs s left intercept is s right intercept is sS Electric displacement O O D P qo qt E D P are all vectors s 0L and x are orientation dependent material properties Real vs Ideal capacitor 0 O 0 Real energy loss overlap in current and voltage during charging surface charge increases instantaneously then continues to increase at a decreasing rate until saturation Current leads voltage by an angle 90 6 6 delay angle work done is nonzero I Pt P Pr t Ideal The exact opposite of all those things I Pt PM polarization at optical frequency electronic ionic polarization Loss tangent tan 6 loss factor sr tan 6 Dielectric AC conductivity 6Ac S m Electrical impedance 0 Dielectric materials can be modeled as a system with dielectric conductivity and dielectric displacement O The system can be simplified using a RLC analog circuit equivalent I ZZ jZquotRjCDLjCDC I Many dielectrics can be further simplified by expression as an RC circuit 0 Impedance plot is created by plotting 2 vs Z and the response function is tan 6 Z Z 1 mRiCi 0 Model is useful in understanding AC circuits in DC bias impedance resistance I For AC circuit presents a significant loss that is dependent on the input frequency I Alternating magnetic fields produce loss by inductive reactance I AC bias on a capacitor allows fewer surface charges to collect than with DC and decreases with increasing frequency capacitive reactance O Impedance spectroscopy I Info on intrinsic properties 0 Behavior of charges 0 Molecular relaxation o Polarization I Info on interfaces 0 Solid to liquid or solid to solid interactions 0 Diffusionadsorption o Electrochemistry I Single frequency stimuli 0 Provides interference produced by material electrical properties 0 Composite dielectrics can be modeled by using parallel and series combinations 0 Parallel CC1C2 e 1y1 Ezyz 0 Series 1C ViEi O Mixture In em SUMmi1 y ln s 0 Local field 0 Macro external depolarizing field Em Ee E1 0 Micro Eloc Ee E1 E2 E3 3r 2E3 I 1 2 3 are discrete depolarizing electric fields within an atom I Microscopic equations use Eloc instead of E otherwise the same I Dielectric constant at visible light freq square of index O 800 n2 I homogeneous materials Sr1sr 2 NOL380 I LorentzLorenz eq n21n2 2 Nae380 0 Temp dependence 0 Dielectric constant increases with increase in Temp I At high frequencies effect is less pronounced 0 Dielectric strength 0 Lattice is able to absorb and dissipate kinetic energy by a threshold number of electrons impacting from an applied field Above that threshold lattice atoms are ionized bonds broken and avalanche occurs I DS VBd kVmm breakdown voltage thickness I Thinner materials however will have fewer defects present so will typically have a higher DS Ferroelectrics dielectric piezoelectric subset o Spontaneous polarization 0 Arising from displacement of ions in noncentrosymmetric unit cells 0 Reversible at field lt DS 0 Applied field is greater than energy barrier ions are able to move to lower energy 0 Coercive field 0 High Ec hard ferros 0 Low Ec soft ferros o Antiferroelectric O No domains cells polarize to cancel charges 0 Ferrielectric O Ferroelectric hysteresis in one direction antiferroelectric in perpendicular direction 0 Hysteresis loop 0 Resulting from domain wall switching ED 40 E El E 23 Eglow E E E quot 1I39 Ti EEED are E39 r A 4o Gpwmgf 53 7 an HEDiHlDD m a mmtnoquot eon Ei Electric fielid RENEW AB Initial linear response fully reversible 00 BC Domain switch remnant polarization irreversible leading to minor loop C All domains are aligned CD linear response due to induced polarization I Intercept on y axis is spontaneous polarization Ps DE Decreasing field leads to remanent polarization PR 0 F coercive field Ec to reduce polarization to zero 000 G saturation with opposite alignment 0 After poling the only way back to A is by thermal processing 0 Domains 0 Single crystals do not form domains act as a single dipole I Large hysteresis more square 0 Ceramicpoly structures form domains many unit cells contribute to domain dipole I Separated by domain walls location where switching originates 0 Walls are abrupt 0 180 abutting walls 0 90 is not favored for low symmetry crystals I Domain polarization determined by internal crystal arrangement 0 Temperature effects 0 Tc Curie temperature below which material is ferroelectric I Dielectric constant maximum at Tc 0 To CurieWeiss temperature close to To epsilon becomes very large I Tc quot39 To second order phase transition 0 No latent heat of transformation reciprocal susceptibility continuous I Tc gtgt T0 or Tcltlt To first order phase transition 0 T vs Reciprocal susceptibility shows discontinuity at Tc 0 Ordered structure 0 Noncentrosymmetric unit cell I Perovskites o AB03 o A corner large cation 0 B body center 0 O face center 0 Below curie temp show ferro props from symmetry lowering o Tetragonal 6 facecentered loading on 100 o Orthorhombic 12 edge loading on 110 o Rhombohedral 8 corner loading on lt111gt o No closepacked oxygen anion lattice 0 Grain size effect I Large grains each form multiple internal domains high permittivity I Small grains each form single domains switching is poor at grain boundaries lower permittivity 0 Corner sharing oxygen octahedral have high stability high frequency high Tc 0 Perovskites tungsten bronze types bismuth oxide layer structured o Doping 0 Small radius B site dopants allow higher polarization I Vanadium low processing temp increases Tc increases epsilon r increases hysteresis size and squareness decreases coercive field 0 Energy diagram Energy vs Displacement 0 Energy barrier and width of displacement determine characteristics of response I Polarization from displacement lowering overall energy 0 32 Point groups 0 Understand HermannMauguin notation will not be tested directly on derivation I Rotational symmetry numbers n 360angle I Dihedral symmetry underlines inversion center I Mirror symmetry m m parallel perpendicular 0 3m gm are rhombo
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