DIELECTRIC PROPERTIES OF INSULATING MATERIALS 523 



strength of the binding forces may vary widely amongst the types of 

 polarization which have an infinite-frequency conductivity. An ion 

 will be regarded as bound if its potential energy increases when it is 

 displaced from an equilibrium position by an applied field. ^ 



Included among the infinite-frequency conductivities which depend 

 upon the presence of ions in the dielectric is a type for which macro- 

 scopic inhomogeneities in the dielectric are responsible; for example, 

 a two-layer or multiple layer laminated dielectric, or a dielectric in 

 which space-charges ^° form because of spatial variations in its re- 

 sistivity or because of a transition layer of high resistance at the contact 

 between dielectric and electrode. Examples of the infinite-frequency 

 conductivity due to this type of mechanism are given in Items dia, b, 

 c and d of Table I. 



This type of infinite-frequency conductivity is of little interest in 

 principle, but in practice there may be many instances in which the 

 measurement of the infinite-frequency conductivity provides a con- 

 venient means of determining the conductivities of the constituents of 

 these non-homogeneous systems. For example, when one layer of a 

 two-layer dielectric has a much higher conductivity than the other, 700 

 assumes a value which is related simply to the free ion conductivity 

 of the layer which has the higher conductivity (see Item 3b, Table I). 

 If the dielectric constants of the two layers are equal, 700 is equal to 

 one-quarter of the conductivity of the high-conductivity layer. The 

 conductivities 71 and 72 of the two layers are considered in the present 

 connection to be free ion conductivities. A more complicated situation 

 is possible where 71 and 72 are in part polarization conductivities due 

 to polar molecules or bound ions. 



The special case of a space-charge caused by a thin layer of high 

 resistance at one or both of the electrodes is of interest in connection 

 with the methods recommended by Joffe for the measurement of the 

 true conductivity of crystals. This will be discussed in more detail 

 later but for the present it may be noted that the infinite-frequency 



^ It is necessary to confine the application of the last statement to direct voltages 

 or to frequencies lower than those for which 7' is equal to 7co. When the frequency is 

 high enough for the latter condition to prevail the amplitude of displacement of the 

 ion becomes so small that the applied field produces no appreciable increase in the 

 average potential energy of the ion; this is illustrated in Fig. 3 at C. 



'" The external effects of a space-charge occurring in a dielectric because of spatial 

 variations in its resistivity' may be reproduced by a uniformly distributed polarization 

 of suitably adjusted magnitude and relaxation-time. Several different polarizations 

 of different magnitudes and relaxation-times would in some instances be required. 

 In referring to such a space-charge as a polarization we may think of the term as 

 applying to the uniform distribution of polarization which could replace the space- 

 charge in its external effects. 



