STRUCT. & PROP. I
STRUCT. & PROP. I MATRL 100A
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This 5 page Class Notes was uploaded by Miss Alberto Prohaska on Thursday October 22, 2015. The Class Notes belongs to MATRL 100A at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 59 views. For similar materials see /class/226930/matrl-100a-university-of-california-santa-barbara in Material Science and Engineering at University of California Santa Barbara.
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Date Created: 10/22/15
Materials 100A Class 13 Electrical Properties ll Ram Seshadri MRL 2031 x6129 seshadri mrliucsbiedu httpwwwimrliucsbleduNseshadriteachihtml Capacitance and Ferroelectrics A voltage V applied across a capacitor of caacitance C allows a quantity Q of charge to be stored Then 7Q 0 The units are CoulombsVolt or Farad In a parallel plate capacitor if the area of the plates in A the separation between them l then if there is a vacuum in the capacitor between the plates the capacitance is obtained from Ceo where 60 is the permittivity of vacuum a constant having the value 885 X 10 12 Fmi If a dielectric material is inserted into this region then the equation modi es to Ce where e is the dielectric constant of the mediumi It is convenient to consider the relative dielectric constant e ereo The relative dielectric constants of different media typically vary between 1 and 100 Water is about 80 Certain special materials such as relaxor ferroelectrics have 6T running into the 1000s The dielectric constant is usually frequency dependent see Callisteri If an electric eld 5 is applied on a sphere of dielectric constant 6 then the surface charge density D of the sphere is D 605 73 Where P is the electric polarization 7 the number of electric dipoles per unit volume Crystals comprising cations and anions can be classi ed into four types according to their polar behavior Materials 100A Class 13 Electrical Properties ll cation Oanion applied eld 4 T gt TC T lt Tc T lt Tc pyroelectric ESE m antipolar we 3966 O O O O O O O O O Piezoelectric materials There is coupling between electrical and mechanical energies For example an applied stress results in the generation ofpolarization Pyroelectric materials A material With a temperature dependent polarization This requires a unique polar axis Ferroelectrics A subgroup of pyroelectric materials in Which the spontaneous polarization can be reoriented between equilibrium states by applying an electric eld All ferroelectrics are both pyroelectric and piezoelectric The possibility of inorganic crystals being polar pyroelectric or piezoelectric is strictly a function of their point group symmetry 1 i The ferroelectric phase transition for example in Ple03 is character ed by the I of a A zero eld polarization changes in the dielectric constant and crystal structural changes Materials 100A Class 13 Electrical Properties ll P Cml W T K T K cell pmmems i T K At the origins of such a phase transition are developments of a dipole Within the unit cell7 due to the centers of positive and negative charges not coinciding PbTiOg ijm PbTiOg P4mm In the particular case of PbTiOg7 the phase transition from the cubic7 paraelectric phase to the tetragonal ferroelectric phase a displacive phase transition is associated With the freezing of a phonon mode that is referred to as the soft modelll Phonon modes are speci c vibrational modes of the crystal lattice In the case of PbTiOg7 this phonon mode is associated With the Ti atom in the center of the octahedron Materials 100A Class 13 Electrical Properties ll hm meV frozen Ti Vibrating Ti The frequency energy of the soft mode goes to zero as the phase transition is approached Ferroelectric materials are also characterized by hysteresis of the polarization below the ferroelectric To just as are ferromagnets are characterized by a hysteresis of the magnetization P As is true for ferromagnets7 the hysteretic behavior is a consequence of the presence of domains in the materiall Some materials undergo an orderdisorder phase transition from the paraelectric phase to the ferroelectric phasel An example is NaNOg sodium nitrite Materials 100A Class 13 Electrical Properties ll Room temperature ferroelectric structure of NaNOg projected on 001 The rigid NO groups have been shown as little cheVrons7 and the Na ions as circles Hatching indicates that the atoms are at a height of 1 2 Above the phase transition at 438 K7 the structure is nonpolar and has the Immm space group Below this temperature7 the material is ferroelectric and has the space group ImZm the ferroelectric structure is displaye l The dipole moment is lost in the high temperature structure because of disorder Half the cheVrons point to the left and half to the right7 and correspondingly the Na ions also occupy two different sites at randoml Antiferroelectrics These are usually characterized by antiparallel dipole moments in the unit cell The formation of antiparallel moments as in antiferro magnetic systems results in the formation of larger unit cells
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