Electrically Based Non-Destructive Microstructural Characterization of All Classes of Materials
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resistivity measurements always come to mind. However, in spite of their long usage in this field, they have often been found to not be sensitive enough to detect small changes caused by the presence of defects, grain boundary layers or cracks. In this paper, the advantages of using impedance and/or dielectric spectroscopy for the detection of microstructural features at all length scales in several materials is presented. Many more examples of potential microstructural features which may be detectable by electrical measurements can be found in two previous MRS proceedings books[ 1, 2]. While impedance data acquisition can easily be obtained using a variety of commercially available equipment, data interpretation can be complex. Therefore, some theoretical background is necessary. Theoretical Background The simplest model of a two-phase material is given by the two-layer condenser model originally proposed by Maxwell and Wagner[3]. Given two materials with dielectric constants (KI and K 2) and conductivities (a, and a 2), it is possible to obtain the effective dielectric constant of the composite with the following equation:
93 Mat. Res. Soc. Symp. Proc. Vol. 5910 2000 Materials Research Society
d/ IKcomp
o
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(di/KI + d 2/K 2) where c, = 8.854 x 10-12 F/m and d, d, and d 2 are the thicknesses of the two layer condenser, layer one and layer two respectively. Likewise, the steady state conductivity of the composite may be determined from d / co a•comp-
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(di 01 +d2/a 2) From these two equations, the two unknowns di and d2 can then be calculated and lead us to an estimate of the volume fraction of phase 1 with respect to 2. It should be noted that d, and d 2 can each be subdivided into equal sized sublayers and the results are expected to remain the same[3]. However, if the electric field is applied parallel to the layers instead of perpendicular to them, a completely different electrical response would result[4]. The above equations assume that there is no frequency dependence in either the conductivity or the dielectric permittivitty equations. This is in fact the case, when the material is mostly a conductor or an insulator respectively[5]. However, in many materials, the difference between the electrically detectable phases is large and the frequency dependences need to be considered. The best method for detecting frequency dependences associated with microstructural features is commonly known as impedance spectroscopy[6]. Impedance spectroscopy is a technique that allows the measurement of the voltage, current and their phase anfle difference over many frequencies. Most commercial instruments span frequencies from 10- to 107 Hz[6]. These instruments were originally developed for use with electrochemical systems and are thus best suited for measuring materials that have impedances between 1 x 10-3 and 2 x 106. Nevertheless, one can obtain reliable data for the properties of more insulating or more conducting samples over narrower frequency ranges than the equipment specifications indicate. The eff
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