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The impact of Pb on the environment and human health and recent restrictions on its use in electronic devices are generating demand for Pb-free piezoelectric materials. Examples are now available commercially, but the full elastic-piezoelectric-dielectric (EPD) matrices needed for device design, including over a range of operating conditions, have not yet been published. The standard IEEE EPD matrix measurement method needs four sample geometries, making it inconvenient and increasing errors. Here, we present an alternative method combining resonant ultrasound spectroscopy with optimization algorithms to measure the EPD matrix from a single exact cube sample. The Levenberg–Marquardt (LM) and Nelder–Mead (NM) optimizations are compared in refining the independent parameters. Both give convergent solutions, but the LM algorithm is more accurate and efficient. The single-sample approach was used to obtain results from Pb-free Na1/2Bi1/2TiO3 (PIC 700, PI Ceramics, Lederhose, Germany) piezoceramic (∞ mm sample symmetry) characterized with the standard IEEE method at ambient temperature and with the single-sample method at ambient temperature and additionally up to 80 °C. The results are validated with the laser Doppler vibrometry via mode shape reconstruction and comparison with finite-element analysis (FEA). They demonstrate that convenient measurement of the EPD matrix of Pb-free materials with temperature dependence is possible, providing a crucial capability for the adoption of these materials in devices. [ABSTRACT FROM AUTHOR]

We analyse the temporal and regional structure in mortality rates related to COVID-19 infections, making use of the openly available data on registered cases in Germany published by the Robert Koch Institute on a daily basis. Estimates for the number of present-day infections that will, at a later date, prove to be fatal are derived through a nowcasting model, which relates the day of death of each deceased patient to the corresponding day of registration of the infection. Our district-level modelling approach for fatal infections disentangles spatial variation into a global pattern for Germany, district-specific long-term effects and short-term dynamics, while also taking the age and gender structure of the regional population into account. This enables to highlight areas with unexpectedly high disease activity. The analysis of death counts contributes to a better understanding of the spread of the disease while being, to some extent, less dependent on testing strategy and capacity in comparison to infection counts. The proposed approach and the presented results thus provide reliable insight into the state and the dynamics of the pandemic during the early phases of the infection wave in spring 2020 in Germany, when little was known about the disease and limited data were available., (© 2020 The Authors. Biometrical Journal published by Wiley-VCH GmbH.)