ionic conductivity and solid electrolytes - ychzhu/solid_state_chemistry/04-2-ionic...ionic...

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  • 1

    Ionic Conductivity and Solid Electrolytes

    Ceramic insulators

    The primary function of insulation in electrical circuits is physical separation of conductors and regulation or prevention of current flow between them.

    Other functions are to provide mechanical support, heat dissipation, and environmental protection for conductors.

    Ceramic materials which in use these functions are classified as ceramic insulators.

    They include most glasses, porcelains, and oxide and nitride materials.

    The advantage of ceramics as insulators is their capability for high-temperature operation.

    Insulation Resistance

    Conductivity

    = d/(R A) and 1/ = = (R A)/d

    Or in terms of the material parameters

    = nq

    where is the electrical resistivity (m), R () the sample resistance, A is area (m2), and d thickness (m).

    If more than one type of charge carrier being present, the

    resultant conductivity can be defined as the sum of component

    conductivities (I) as follows:

    = i ni (ez)i i = i i

    Insulation Resistance

    Depending on which charge carriers predominate, the solid may be classified as primarily an

    electronic (n or p type) or

    ionic conductor.

    However, mixed conduction is

    = electronic + ionic

    Insulation Resistance

    For an ionic solid, mobility is related to the diffusion coefficient D (cm2/sec) by the Einstein relationship

    = ezD/kT

    Diffusion and conductivity are related by the Nernst-Einstein equation:

    = n(ez)2D/kT

    Since both diffusion and N (number of defects generated) are activated processes, where

    N = n exp(-w/2kT)

    Insulation Resistance

    D = Do exp(- /kT) Then = o exp(-E/kT) and E = w/2 +

    Where w and are activation energies for defect generation and migration.

    For extrinsic conduction w=0 and E=; that is, the ionic mobility becomes the controlling factor in the conduction.

  • 2

    Ionic Conduction

    What is an ion? An ion is a positive or negative loaded atom caused by electron deficiency or electron excess.

    This electron deficiency/excess arises at the reaction of two atoms (ionic connection).

    Positive loaded ions are called cations and negative loaded ions are called anions.

    In ionic crystal, the individual lattice atoms transfer electron between each other to form positively charged cations and negatively charged anions.

    Ionic Conduction

    The binding forces between ions are electrostatic in nature and thus very strong.

    The RT conductivity of ionic crystals is much lower than the conductivity of typical metallic conductors.

    The large difference in conductivity can be understood by realizing that the wide bandgap in insulators allows only extremely few electrons to become excited from the valence band into the conduction band.

    Ionic Conduction

    Ionic conduction is caused by the movement of some negatively (or positively) charged ions which hop from lattice site to lattice site under the influence of an electric field.

    This ionic conductivity: (1)

    Nion is the number of ions per unit volume that can change their position under the influence of an electric field

    ion is the mobility of these ions.

    ionionion eN

    Ionic Conduction

    In order for ions to move through a crystalline solid, they must have sufficient energy to pass over an energy barrier (see schematic).

    Thus, Nion in eq.(1) depends on the vacancy concentration in the crystal (i.e., on the number of Schottky defects).

    Ionic Conduction

    d

    Q

    E

    distance

    (a) E

    distance

    (b)

    Figure: Schematic representation of a potential barrier, which an ion ( )

    has to overcome to exchange its site with a vacancy ( ).

    (a) Without an external electric field, (b) with an external electric field. d =

    distance between two adjacent, equivalent lattice sites, Q = activation

    energy.

    Ionic Conduction

    The D varies with temperature; this dependence is commonly expressed by an Arrhenius equation:

    (2)

    Where Q is the activation energy , Do is a pre-exponential factor that depends on the vibrational frequency of the atoms and some structural parameters.

    Tk

    QDD

    B

    o exp

  • 3

    Ionic Conduction

    Combining (1) through (2) yields,

    (3)

    Equation (3) is shortened by combining the pre-exponential constant:

    (4)

    Taking the natural logarithm yields:

    (5)

    Tk

    Q

    Tk

    DeN

    BB

    oion

    ion exp

    2

    Tk

    Q

    B

    oion exp

    Tk

    Q

    B

    oion

    1lnln

    Ionic Conduction

    If plotted ln ion vs. 1/T,

    a straight line with a

    negative slope would

    result. (See figure).

    The slopes in Arrhenius

    plots are utilized to

    calculate the activation

    energy, Q or Ea.

    Tk

    Q

    B

    oion

    1lnln

    Ionic Conduction

    Slope = - Q/k

    For SiO2 from graph:

    Slope = (ln 10-7 ln 10-14)/(1.5x10-3 2.55x10-3)

    = [ln (10-7/10-14)]/(-1x10-3)

    = ln 107/(-1x10-3) = - 1.612x104

    From Slope = - Q/k

    Q = (1.612x104)x(1.3806x10-23) = 2.225x10-19 J

    Q = 1.39 eV (1 eV = 1.6x10-19 J)

    Ionic Conduction

    800 600 400

    ln

    1/T

    T(oC)

    Sometimes,

    ln vs. 1/T plot will

    give us two (2) line regions representating of two different Q values. Figure: Schematic representation of ln

    versus 1/T for Na+ ions in NaCl.

    (Arrhenius plot).

    Ionic Conduction

    At low T, the Q is small, the thermal energy is just sufficient to allow the hopping of ions into already existing vacancy sites. This T range is commonly called the extrinsic region.

    At high T, the thermal energy is large enough to create additional vacancies.

    The related Q is thus the sum of the Q for vacancy creation and ion movement. This T range is called the intrinsic region.

    High Conducting Ceramics

    Ceramics are generally classified as electronic conductors, ionic conductors, mixed (electronic/ionic) conductors, and insulators.

    The electronic conductors include superconductors, and semiconductors.

    Ionic conductors generally exhibit conductivities in the range 10-1 to 100 S m-1 that increase exponentially with temperature.

    Insulators such as high-purity alumina are at the lower extreme of the conductivity of 10 -13 S m-1.

  • 4

    Temperature Sensitive Resistor

    Some ceramic resistors exhibit high value of the temperature coefficient of resistance (TCR) and they may be negative (NTC) or positive (PTC).

    Temperature Sensitive Resistor

    In a ceramic a large temperature coefficient of resistivity can arise from 3 causes:

    The intrinsic characteristic.

    A structure transition which accomponied by a change in the conduction mechanism from semiconducting to metallic.

    A rapid change in dielectric properties in certain ceramics which affects the electronic properties in the intergranular region to give rise to a large increase in resistivity with temperature over small temperature range.

    The 3rd Mechanism has led to important TCR devices.

    Typical resistance-temperature response for various sensor materials

    NTC Thermistor

    The TCR of a semiconductor is expected to be negative. In each case the resistivity depends on temperature according to

    where is approximately independent of T and B is a constant related to the energy required to active the electron to conduct.

    Differentiating this equation leads to TCR value R:

    T

    BT exp)(

    2

    1

    T

    B

    dT

    dR

    NTC Thermistor

    The most NTC materials are based on solid solutions of oxides with spinel structure, e.g. Fe3O4-ZnCr2O4 and Fe3O4-MgCr2O4.

    A series that gives favorable combinations of low resistivity and high coefficients is based on Mn3O4 with a partial replacement of Mn by Ni, Co and

    Cu.

    PTC Thermistor

    PTC thermistors exhibit an increase in resistance at a specified temperature.

    PTC resistor could be classified as critical temperature resistors because, in the case of the most widely used type

    The positive coefficient is associated with the ferroelectric Curie point.

  • 5

    PTC Thermistor

    Most PTC has the negative resistivity-temperature characteristic up to about 100oC and above about 200oC.

    While between these temperatures there is an increase of several orders of magnitude in resistivity.

    The PTC effect is exhibited by specially doped and processed (eg. BaTiO3).

    Application of PTC Thermistor

    The are two main groups:

    Applications such as temperature measurement, temperature control, temperature compensation and over-temperature protection.

    The second group includes applications such as over-current protection, liquid level detection and time delay.

    Voltage-dependent Resistors (Varistors)

    There are a number of situations in which it is valuable to have a resistor which offers a high resistance at low voltages and a low resistance at high voltages.

    Such a devices can be used to protect a circuit from high-voltage transients by providing a path across the power supply that

    takes only a small current under normal conditions but takes large current if the voltage rises abnormally,

    thus preventing high-voltage pulses from reaching t

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