The loss tangent

Definition and measurement.

Drilling down: the origins of dielectric loss.

Further reading.

 

Definition and measurement.  The loss tangent and the loss factor take a little more explanation.  An oscillating field drives the charge back and forth between two alternative configurations.  This charge-motion is like an electric current that – if there were no losses – would be 90o out of phase with the voltage.  In real dielectrics this current dissipates energy, just as a current in a resistor does, giving it a small phase shift,  (Figure 1).  The loss tangent, , also called the dissipation factor, , is the tangent of the loss angle.  The power factor, , is the sine of the loss angle.  When  is small, as it is for the materials of interest here, all three are essentially equivalent:

               

More useful, for our purposes, is the loss factor L, which is the loss tangent times the dielectric constant:

               

It measures the energy dissipated by a dielectric when in an oscillating field.  If you want to select materials to minimize or maximize dielectric loss, then the measure you want is L.

         When a dielectric material is placed in a cyclic electric field of amplitude  and frequency  power  is dissipated and the field is correspondingly attenuated.  The power dissipated is

               

where, as before,  is the dielectric constant of the material and tan is its loss tangent.  This power appears as heat and is generated uniformly through the volume of the material.  Thus the higher the frequency or the field strength, and the greater the loss factor , the greater is the heating and energy loss.  This dielectric loss is exploited in processing – for example, in radio frequency welding of polymers.

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Drilling down: the origins of dielectric loss.  Polarization (see Dielectric constant) involves the small displacement of charge (electrons, ions) or of molecules that carry a dipole moment when an electric field is applied to the material.  An alternating field makes the charge swash back and forth: when the upper plate of Figure 2 is negative, the displacements are in the direction shown at (a).  When its polarity is reversed, it is the negative ions that are displaced upwards, the positive ions downwards as at (b); in an oscillating field, the ions oscillate.  If their oscillations were exactly in phase with the field, no energy would be lost, but this is never exactly true, and often the phase shift is considerable.  Materials with high dielectric loss usually contain awkwardly shaped molecules that themselves have a dipole moment – the water molecule is an example.  These respond to the oscillating field by rotating, but because of their shape they interfere with each other (you could think of it as molecular friction) and this dissipates energy that appears as heat – that is how microwave heating works.  As the last equation shows, the energy that is dissipated depends on the frequency of the electric field; generally speaking, the higher the frequency, the greater the power dissipated (because power is work-per-second, and the more times the molecules shuttle, the more is lost), but there are peaks at certain frequencies that are characteristic of the material structure.

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Further reading.

Author

Title

Chapter

Ashby et al

Materials: Engineering, Science, Processing and Design

14

Askeland

The Science and Engineering of Materials

19

Budinski

Engineering Materials: Properties and Selection

7, 8

Callister

Materials Science and Engineering: An Introduction

18

Callister & Rethwisch

Fundamentals of Materials Science and Engineering: An Integrated Approach

12

Further reference details

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