电子陶瓷教学课件04conductivity

1、Functional ceramics,Properties of Functional ceramics,Functional ceramics,3 Electrical Conduction,The electrical conduction characteristics of ceramics can range from those of superconductors through those of metals to those of the most resistive of materials; in between the extremes are characteris

2、tics of semiconductors and semiinsulators,Conductivity of the various classed of material: shading indicates the range of values at room temperatures,Functional ceramics,Conductivities of some typical ceramics,room temperature,3 Electrical Conduction,Functional ceramics,3 Electrical Conduction,Ceram

3、ics,Measurement of conductivity,Electrodes,Inner diameter D2, cm,Diameter D1, cm,Thickness h, cm,Volume conductivity,Surface conductivity,Functional ceramics,3 Electrical Conduction,Conductivity characteristics of the various classes of materials,Functional ceramics,Carrier type: Metal Electrons Sem

4、iconductor Electrons,holes Ceramic Electrons, holes, ions,3 Electrical Conduction,陶瓷材料的导电机理非常复杂，在不同的温度范围，载流子的种类可能不同。例如，刚玉(a-Al2O3)陶瓷在低温时为杂质离子电导，高温(超过1100oC)时则呈现有明显的电子电导,Functional ceramics,Carrier types of functional ceramics,3 Electrical Conduction,Functional ceramics,Electronic conduction: electro

5、ns, holes, (band conduction) Polarons, (polaron conduction) Ionic conduction: ions,Band conduction,3 Electrical Conduction,Functional ceramics,Band conduction,Schematic electron energy band structures for (a) a metallic crystal and (b) a semiconducting or insulating crystal,3 Electrical Conduction,F

6、unctional ceramics,Band conduction,Band structure with electrons promoted from the valence to the conduction band,Temperature dependence of conductivity in band conduction,2.3,3 Electrical Conduction,Functional ceramics,3 Electrical Conduction,The theory outlined above was developed for group IV sem

7、iconducting elements such as silicon and germanium; some of the compounds of group III and V elements, the III-V compounds, are also covalently bonded and have similar electrical properties which can be described in terms of a band model,The same model can be applied to an ionic solid. In this case,

8、 for the example of MgO: an electron in the conduction band derived from the Mg2+ 3s states and a hole in the valence band derived from the 2p states of the O2- ion. (Eg= 8 eV,Apart from the wider band gaps, electrons and holes in ionic solids have mobilities several orders lower than those in the c

9、ovalent semiconductors. This is due to the variation in potential that a carrier experiences in an ionic lattice,Functional ceramics,One of the most important features of oxide semiconductors is the effect on their behaviour of the external oxygen pressure,Conductivity of undoped BaTiO3 (Ba/Ti=1.000

10、) as a function of pO2 and T. (After Smyth,3 Electrical Conduction,Functional ceramics,Polaron conduction,In some oxides, the electron and hole is regarded as “hopping” from site to site. “Hopping” conduction occurs when ions of the same type but with oxidation differing by unity occur on equivalent

11、 lattice sites and is therefore likely to be observed in transition metal oxides,For example: The addition of Li2O to NiO (fired under oxidizing conditions). The lithium ion Li+ (74pm) substitutes for the nickel ion Ni2+ (69pm), for every added Li+ one Ni2+ is promoted to the Ni3+ state, the lost el

12、ectron filling a state in the oxygen 2p valence band. The lattice now contains Ni2+ and Ni3+ ions on equivalent sites and is the model situation for conduction by polaron hopping, which is more often referred to simply as electron hopping,3 Electrical Conduction,Functional ceramics,Difference betwee

13、n polaron conduction and band conduction: In polaron conduction, the concentration of carriers is determined solely by the doping level and is therefore temperature independent, whereas the carrier mobility is temperature activated,Resistivity of NiO as a function of lithium content,Thus it follows

14、that the temperature dependence of conductivity is similar to that for band conduction, but for different reasons,2.4,3 Electrical Conduction,Functional ceramics,Ionic conduction,Energy barriers to ionic transport in a crystal (a) in the absence of a field and (b) with applied field E,Temperature de

15、pendence of conductivity in ionic conduction,2.5,3 Electrical Conduction,Functional ceramics,Ionic conduction,Extrinsic and intrinsic regimes in the logs versus 1/T relation,Vacancies might also be introduced into the crystal extrinsically by the addition of impurities,High temperature: intrinsic to

16、 create and to move defects Low temperature: extrinsic only to move defects,3 Electrical Conduction,Functional ceramics,Ionic conduction in glasses,Glass formers: SiO2, B2O3, Al2O3 Modifier ions: Li+, Na+, K+ (very mobile) Ca2+, Mg2+ (block the network,Observations: Conductivity s depends upon tempe

17、rature through an exponential term, because mobile need to be activated to squeeze their way past oxygen ions in moving from one site to the next. For a given temperature and alkali ion concentration, s decreases as the size of the mobile ion increases (e.g. sLi+sNa+sK+, where the corresponding size

18、s of the three ion types are in the ratio 1:1.5:2). For a given temperature and mobile ion content, s decreases as the concentration of blocking ions (Ca2+, Mg2+) increasing,3 Electrical Conduction,Functional ceramics,Summary,Electronic conductors (semiconductors), ionic conductors (solid electrolyt

19、es) and mixed electronic-ionic conductors are encountered in ceramics,In all cases the conductivity is likely to vary with temperature according to,Ea, activation energy k, Boltzmann constant T, temperature,2.6,3 Electrical Conduction,Functional ceramics,3 Electrical Conduction,Functional ceramics,4

20、 Charge displacement processes,When an electric field is applied to an ideal dielectric material there is no long-range transport of charge but only a limited rearrangement such that the dielectric acquires a dipole moment and is said to be polarized,Atomic polarization , which occurs in all materia

21、ls, is a small displacement of the electrons in an atom relative to the nucleus; in ionic materials there is, in addition, ionic polarization involving the relative displacement of cation and anion sublattices,4.1. Dielectric in static electric fields,4.1.1 macroscopic parameters,Functional ceramics

22、,Atomic polarization and ionic polarization,4 Charge displacement processes,Functional ceramics,Dipolar materials, such as water, can become polarized because the applied electric field orients the molecules,Space charge polarization involves a limited transport of charge carriers until they are sto

23、pped at a potential barrier, possibly a grain boundary or phase boundary,4.1.1 macroscopic parameters,4 Charge displacement processes,Functional ceramics,Dipolar polarization and space charge polarization,4 Charge displacement processes,Functional ceramics,The role of the dielectric in a capacitor,I

24、n situation (a) (separated by a vacuum,Electric field,4 Charge displacement processes,Functional ceramics,In situation (b) (with a dielectric,Electric field,Dielectric displacement vector,2.8,2.9,4 Charge displacement processes,Functional ceramics,where the dimensionless constant ce is the electric

25、susceptibility. In general, ce is a tensor of the second rank. Unless otherwise stated it will be assumed in the following discussions that P and E are collinear, in which case ce is simply a scalar,It follows from (2.9) and (2.10) that,If the dielectric is linear,2.10,2.11,4 Charge displacement pro

26、cesses,Functional ceramics,In which QT is the total charge on the capacitor plate. Therefore the capacitor is,Since D=sT,The capacitor C0 of an empty parallel-plate capacitor is,2.12,2.13,2.14,4 Charge displacement processes,Functional ceramics,Where,If the space between the plates is filled with a

27、dielectric of susceptibility ce, the capacitor is increased by a factor 1+ce,and er is the relative permittivity (or dielectric constant) of the dielectric,2.15,2.16,4 Charge displacement processes,Functional ceramics,The local field in a dielectric,4.1.2 From induced elementary dipoles to macroscop

28、ic properties,Ea applied external field Em internal macroscopic field Edp depolarizing field,2.17,4 Charge displacement processes,Functional ceramics,An individual atom or ion in a dielectric is not subjected directly to an applied field but to a local field EL, which has a very different value,Loca

29、l field EL differs from Em since the latter is arrived at by considering the dielectric as a continuum,In reality the atomic nature of matter dictates that the local field, which is also known as the Lorentz field, must include contributions from the adjacent, individual dipoles. Furthermore, the lo

30、cal field arises from the charges in their displaced positions, and because it is also doing the displacing, calculation of it is by no means straightforward,4 Charge displacement processes,Functional ceramics,Lorentz calculated EL in the following way,Ep can be shown to be P/3e0, but Ed must be cal

31、culated for each particular site chosen and for each dielectric material,In which Ep is the contribution from the charges at the surface of the spherical cavity (imaging for the moment that the sphere of material is removed) and Ed is due to the dipoles within the boundary,2.18,4 Charge displacement

32、 processes,Functional ceramics,For certain crystals of high symmetry and glasses it can be shown that Ed=0, and so for these cases,In which g is the internal field constant,In the more general case it is assumed that,2.19,4 Charge displacement processes,Functional ceramics,The dipole moment p induce

33、d in the entity can now be written,If it is assumed that all entities are of the same type and have a density N, then,In which a is the polarizability of the entity, i.e. the dipole moment induced per unit applied field,or,2.20,2.21,2.22,4 Charge displacement processes,Functional ceramics,In the par

34、ticular case for which g=1/3e0 rearrangement of the previous equation leads to the Clausius-Mosottie relationship,Using the cgs system the Clausius-Mosottie relationship becomes,2.23,2.24,This form has been widely used in calculating polarizabilities,4 Charge displacement processes,Functional cerami

35、cs,For equation,ce as Nag1, and this implies that under certain conditions lattice polarization produces a local field which tends to stabilize the polarization further a feedback mechanism. This points to the possibility of spontaneous polarization, i.e. lattice polarization in the absence of an ap

36、plied field,a) Non-polar array; (b), (c) polar arrays. The arrows indicate the direction of spontaneous polarization Ps,4 Charge displacement processes,Functional ceramics,Such spontaneously polarized materials do exist, ferroelectrics constitute an important class among them,Ferroelectric behaviour

37、 is limited to certain materials and to particular temperature ranges for a given material,Of the 32 crystal classes, 11 are centrosymmetric and non-piezoelectric. Of the remaining 21 non-centrosymmetric classes, 20 are piezoelectric and of these 10 are polar,4 Charge displacement processes,Function

38、al ceramics,Local,2.2 Charge displacement processes,A limited number of pyroelectric materials have the additional property that the direction of the spontaneous polarization can be changed by an applied electric field or mechanical stress. Where the change is primarily due to an electric field the

39、material is said to be ferroelectric; when it is primarily due to a stress it is said to be ferroelastic,The piezoelectric crystals are those that become polarized or undergo a change in polarization when they are stressed; conversely, when an electric field is applied they become strained. The 10 polar crystal types