Elastic properties can be determined by dynamic methods, e.g. based on resonant frequency measurements (including the impulse excitation technique) or methods based on ultrasound wave propagation (e.g., the pulse echo technique). Since the elastic constants are intimately related to the sound velocities (in particular, the two independent elastic constants of isotropic porous ceramics can be transformed into the sound velocities of transverse and longitudinal sound waves), models for the porosity dependence of elastic constants can be used to predict the porosity dependence of sound velocities and vice versa. This opens a way to predict the porosity dependence of sound wave velocities by models that are fundamentally different from the semi-empirical or purely empirical ones that have been proposed in the previous literature.
In this contribution we first explain the predictive models that are available for predicting the porosity dependence of transverse and longitudinal sound waves [1]. These are based on the Maxwell-Mori-Tanaka model, the self-consistent model, the differential model / power-law relation, the exponential relation and a benchmark relation obtained by fitting numerical results calculated for computer-generated model microstructures based on monosized spherical particles undergoing partial sintering. Secondly, we present results of sound velocity measurements (both for longitudinal and transverse waves) by the ultrasonic method (pulse echo technique) and the subsequent calculation of the elastic constants of various oxide and silicate ceramics. These ceramics were prepared by uniaxial pressing followed by conventional sintering in air (from 1000 to 1600 °C depending on the material) or by spark plasma sintering (SPS) in vacuum (from 1000 to 1400 °C depending on the material). Different sintering temperatures were used to obtain a broad range of porosities by partial sintering. Alumina and zirconia ceramics (the latter doped with either 3 mol.% Y₂O₃ or 8 mol.% Y₂O₃) as well as alumina-zirconia composite ceramics, titania ceramics and mullite- and kaolin-based silicate ceramics were prepared by conventional sintering, while titania ceramics and mullite ceramics were prepared also by spark plasma sintering (SPS). Experimental results obtained via the ultrasound method were compared to data obtained via the impulse excitation technique. Both methods have been found to be reliable and to provide very consistent results. Last but not least, the experimental data obtained in this work are compared to the aforementioned theoretical predictions, the models for which best agreement is found are emphasized and the correlation of longitudinal and transverse sound velocities is discussed. 

References: [1] Šimonová P., Pabst W.: The porosity dependence of sound velocities in ceramic materials, J. Eur. Ceram. Soc. 2023, 43 (4), 1597-1604.
Acknowledgement: Project GA22-25562S, funded by the Czech Science Foundation (GA?R), and project A1_FCHT_2023_005 (specific university research).