Aging models and parameters of quartz crystal resonators and oscillators

For practical applications of quartz crystal resonators, accurate estimation of the aging pattern and adoption of appropriate correction procedure will be important in ensuring the precise operating condition and maintaining their optimal performance. There are two generally accepted aging models for the prediction of long-term behavior of quartz crystal resonators. The Arrhenius model is universally accepted for aging of most materials in engineering applications under a physical process, while the Mattuschka model is an empirical formula from quartz crystal device industry based on the long-term measurement of quartz crystal resonators. In this study, quartz crystal samples from major producers in different countries are collected and a common testing standard was adopted. From the statistical analysis of measurement data, it is found that the Arrhenius model has a much better agreement. Different products and measurements are consistent with the general trend of aging patterns from the Arrhenius model but the key parameters are different from products.