A Measure of Energy Density to Quantify Progress in Pb-free Piezoelectric Material Development

Publication Name

IEEE International Ultrasonics Symposium, IUS


The negative environmental impact of Pb has led to an increased demand for Pb-free electronics. This is particularly important in ultrasonic transducers where Pb-based piezoelectric materials, primarily ceramic PZT, are the dominant choice. Naturally for Pb-free materials to become a viable option, the performance must match that of the current standard. However, present comparison methods and figures of merit for piezoelectric materials are based on specific use cases which can lead to disparate results. In the work described here, a new measure is developed for the performance of a piezoelectric material, based on its energy density. This was achieved by developing a generalized electromechanical coupling factor derived from first principles and defined at zero frequency. It encompasses all conversion mechanisms allowed by symmetry and so avoids any resonance/geometry effects which obscure the pure material response. Comparison between Pb-free materials using this new coupling factor are made within the con of PZT and high performance piezocrystal and were validated using finite element analysis. Whilst no Pb-free materials currently match the level of PZT/single crystal by this method, it is shown that the new figure of merit is independent of geometry and other spatial effects and thus allows a fully unbiased comparison between materials. Hence it defines a universal measure against which Pb-free material development may be traced.

Open Access Status

This publication is not available as open access

Funding Number


Funding Sponsor

Engineering and Physical Sciences Research Council



Link to publisher version (DOI)