The Force-Frequency Characteristics of Quartz Wafers under a Cantilever Beam Structure.

This study investigated the force-frequency characteristics of quartz wafers inside a cantilever beam frame. Firstly, the force-frequency coefficient formula of quartz wafers with fixed ends under axial force was analyzed. Firstly, the formula for the force-frequency coefficient of quartz wafers with fixed ends under axial force was analyzed. A force-frequency coefficient formula suitable for cantilever beam structures was derived by considering the changes in surface stress and stiffness of quartz wafers with fixed ends and one end under force on the other. Subsequently, the formula's accuracy was verified by experiments, and the accuracy was more than 92%. In addition, strain simulation analysis was performed on three different shapes of quartz wafers, and experimental verification was carried out on two of them. The results revealed that trapezoidal quartz wafers and cantilever beam structures exhibited superior stress distribution to rectangular chips. Furthermore, by positioning electrodes at various locations on the surface of the quartz chip, it was observed that, as the electrodes moved closer to the fixed end, the force-frequency coefficient of the rectangular quartz chip increased, along with an increase in chip strain under the cantilever structure. In summary, this study provides a new approach for designing cantilever quartz resonator sensors in the future.

Correlating micro/meso pore evolution and chemical structure variation in a mild thermal treatment of a subbituminite.

This work investigates the evolution of micro/meso pores during a mild thermal treatment of subbituminous coal based on the observation of coal structure changes with the gradual detachment of organic matter from the coal. Pores in coal can be described as super-micropores (d < 1 nm), micropores (1 nm < d < 2 nm) and mesopores (2 nm < d < 50 nm). The decomposition of the carboxyl group at 200 °C decreases the super-micropore volume. A mild and sustained reaction takes place at 300 °C to gradually change the aromaticity and CH2/CH3 ratio of the treated coal. The amount of micropore structure sharply decreases in the early stages of heating, while the amount of mesopore structure continuously decreases during the whole process. A dramatic reaction takes place at 400 °C to sharply change the aromaticity and CH2/CH3 ratio of the treated coal, while the detachment of volatile compounds from the coal matrix caused an evident variation in the mesopore structure of the coal. The aromaticity and CH2/CH3 ratio of coal organics are found to correlate with the volumes of super-micropores and mesopores, respectively. The super-micropores are identified as comprising the inter-layer distance between stacks of aromatic rings, and mesopores are the spaces between macromolecular aromatic rings which are inter-connected via aliphatic chains.