Table of Contents
International Journal of Spectroscopy
Volume 2014, Article ID 538206, 7 pages
Research Article

Graphical Conversion between Compliance and Modulus, Permittivity and Electric Modulus, and Impedance and Admittance

Department of Applied Physics, The Hebrew University of Jerusalem, Bergman Building, Givat Ram, Jerusalem 91904, Israel

Received 11 September 2014; Revised 2 November 2014; Accepted 5 November 2014; Published 25 November 2014

Academic Editor: Akihide Wada

Copyright © 2014 Masahiro Nakanishi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Spectrometries probing relaxation and retardation phenomena, such as dielectric, mechanical, and impedance spectroscopies, often require the analyses with both susceptibilities spectra and its reciprocals (e.g., complex permittivity and electric modulus, mechanical compliance and mechanical modulus, and impedance and admittance). In the present paper, the geometric relation between and is derived and the procedure to convert into on a Cole-Cole diagram is proposed. This method helps us to relate them intuitively and yields clearer understanding on their interrelations. Moreover, it opens the new route for the geometric approach to derive many mathematical properties of spectra. The relation between peak position of spectrum and that of spectrum and the shape of spectra are discussed on the basis of this method.