Ultrasonic velocity and reduction of surface area during solid-state sintering

We studied the relationships between the ultrasonic velocity and the reduction of specific surface area during solid-state sintering and addressed three questions: (1) What must be the correlation between ultrasonic velocity and specific surface area reduction during the solid-state sintering of monosize spheres? (2) How is this correlation affected by the particle-size distribution and/or changes in packing coordination? (3) How do the answers to these questions help us improve the use of ultrasonic measurements to monitor sintering kinetics and microstructure evolution? From both a theoretical and experimental basis, we found a general power law that describes the relationship between ultrasonic velocity and the reduction of specific surface area during solid-state sintering: VP/VB∝(ΔS/So)x. The power-law exponent x depends on three possible scenarios: (1) x<1 for ideal packing of monosize spheres; (2) x=1 for random packing of monosize spheres where the average, particle coordination number changes upon sintering; and (3) x>1 for specimens containing a broad distribution of particle sizes. We also demonstrated that this power law could be used with ultrasonic velocity measurements to obtain reasonable values of the activation energy for solid-state sintering. The power-law relationship is useful to characterize microstructure evolution during solid-state sintering and is useful to classify different materials in a ceramic manufacturing setting. It is also a simple modeling tool that opens the way to optimize control of the sintering process.