The coefficient of thermal expansion (CTE) is an important property of ultra-low expansion (ULE) glass, and the ultrasonic velocity method has shown excellent performance for the nondestructive measurement of CTE in large ULE glass. In this method, the accurate acquisition of the ultrasonic velocity in ULE glass is necessary. Herein, we present a correlation method to determine the ultrasonic TOF in ULE glass and to further obtain the ultrasonic longitudinal wave velocity ($c_{\mathrm{L}}$) indirectly. The performance of this method was verified by simulations. Considering the dependence of $c_{\mathrm{L}}$ on temperature (T), we carried out the derivation of the analytical model between $c_{\mathrm{L}}$ and T. Based on reasonable constant assumptions in the physical sense, a $c_{\mathrm{L}}$–T exponential model was produced, and some experimental results support this model. Additional experiments were carried out to validate the accuracy of the $c_{\mathrm{L}}$–T exponential model. The studies we conducted indicate that the $c_{\mathrm{L}}$–T exponential model can reliably predict the ultrasonic velocity in ULE glass at different temperatures, providing a means for the nondestructive CTE measurement of large ULE glass at a specified temperature.

Herein, Pb_0.95Ba_0.01Sr_0.04(Zr_0.53Ti_0.47)O₃ piezoelectric ceramics comprising 0.25 wt% MnCO₃, 1 wt% LiBiO₂ and 0.06 wt% CuO (PBSZT-LBCu-Mn ceramics, abbreviated as Mn0.25) were prepared via a conventional method at a low firing temperature of ∼900 °C. The phase structure and temperature-dependent electrical properties were systematically investigated. The product composition possesses the following properties: normalised strain (d₃₃*) ∼362 pm/V, Curie temperature (T_c) ∼336 °C, mechanical quality factor (Q_m) ∼568, loss factor (tan δ) ∼0.0058 and relative dielectric constant (ϵ_r) ∼872. The remnant polarisation (P_r), maximum polarisation (P_max) and coercive field (E_c) slightly decreased as a function of increasing temperature, while the strain (S_pol) was observed to increase. Additionally, d₃₃* values of 362 and 411 pm/V were achieved at 25 °C and 120 °C, respectively, with a change ratio <14%. The Mn0.25 ceramics exhibit low ϵ_r and tan δ values, leading to small average power dissipation, which is beneficial for high-frequency actuator applications.

The coefficient of thermal expansion (CTE) of ultra-low-expansion (ULE) glass is critical to the development of precision optical systems. Herein, an ultrasonic immersion pulse-reflection method is proposed to characterize the CTE of ULE glass. The ultrasonic longitudinal wave velocity of ULE-glass samples with significantly different CTE values was measured using a correlation algorithm combined with moving-average filtering, which can achieve 0.2 m/s precision with a contribution to the ultrasonic CTE measurement uncertainty of 0.47 ppb/°C. Furthermore, the established ultrasonic CTE measurement model predicted the 5°C–35°C mean CTE with a root-mean-square error of 0.9 ppb/°C. Notably, a complete uncertainty analysis methodology was established in this paper, which can provide directional guidance for the subsequent development of higher-performance measurement devices and the improvement of relevant signal processing procedures.

Li₂O–Al₂O₃–SiO₂ (LAS) glass–ceramics are widely used in many fields owing to their ultra-low coefficient of thermal expansion (CTE). The ultrasonic velocity method shows potential as an effective method for the nondestructive measurement of the CTE and CTE homogeneity of large LAS glass–ceramics. To further improve the precision of ultrasonic velocity (c_L) measurements of LAS glass–ceramics and reveal the effect of the temperature (T) on c_L, an improved correlation method to rapidly determine the time of flight (TOF) in LAS glass–ceramics is proposed. The proposed method significantly reduces the calculation time by a factor of 100 for LAS glass–ceramics with a thickness of 50 mm. Furthermore, the TOF results obtained by this method were compared with those obtained by the commonly used peak and zero-crossing methods. The proposed correlation method showed better TOF repeatability precision (0.69 ns). Considering the effect of T on the precision of the c_L measurement, a c_L–T exponential model was developed based on the theoretical c_L–T analytical model. The accuracy of the c_L–T exponential model was experimentally verified. The root-mean-square error was within 0.30 m/s, which shows that the developed exponential model can reliably predict the c_L values of LAS glass–ceramics at different temperatures. The two meaningful findings mentioned above provide methodological and modeling support for high-precision nondestructive CTE testing of large LAS glass–ceramics at specific temperatures.

The existence of bubble defects in ultra-low expansion quartz glass will affect the optical properties and mechanical strength of the material. The present paper proposes a novel defect characterization method based on ultrasonic nondestructive testing. The simulation model of bubble defect detection in ultra-low expansion quartz glass was established using numerical simulation technology, and experimental verification was carried out. The propagation mechanism of the ultrasound and its interaction with bubble defects were then analyzed. The results showed that the shape of the reflected wave was similar to that of the corresponding defect, and the scattering of the reflected wave was different due to the different curvature radius of the defect interface. The acoustic scattering characteristics of the circular defect were more obvious than those of the elliptical defect. Finally, an analysis of the interaction between different depth defects and different size defects and the ultrasound was conducted, leading to the conclusion that the relative amplitude of the defect echo corresponding to a 6 mm probe diameter shows a monotonic decreasing relationship with the defect depth, and there is also a monotonic corresponding relationship between the relative amplitude of the defect echo and the size of bubble defect. Therefore, it can be concluded that the relative amplitude of the defect echo can be used to characterize the size of the bubble defect. This study not only analyses the interaction between defects and ultrasound but also provides a quantitative characterization of defects using the proposed method.