Abstract
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 (cL) indirectly. The performance of this method was verified by simulations. Considering the dependence of cL on temperature (T), we carried out the derivation of the analytical model between cL and T. Based on reasonable constant assumptions in the physical sense, a cL–T exponential model was produced, and some experimental results support this model. Additional experiments were carried out to validate the accuracy of the cL–T exponential model. The studies we conducted indicate that the cL–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.
Highlights
Ultra-low expansion (ULE) glass is a SiO2–TiO2 glass formed by flame hydrolysis and vapor deposition that has found applications in large telescope mirror blanks because of its near-zero coefficient of thermal expansion (CTE) over the 5~35 ◦C temperature range [1,2]
The ultrasonic velocity in ULE glass is proportional to its CTE, a fact that can be utilized to nondestructively assess the absolute and relative CTE of large ULE glass, and its feasibility has been demonstrated by researchers [9,10]
Based on the simulation and experimental investigations, we can draw the following conclusions: 1. The proposed pulse reflection immersion method provides reliable and stable measurements of the ultrasonic echo signal of ULE glass, and the calculation of the signal based on the correlation method can be used to conveniently and accurately extract the ultrasonic time of flight (TOF) of the tested sample and obtain the ultrasonic velocity
Summary
Ultra-low expansion (ULE) glass is a SiO2–TiO2 glass formed by flame hydrolysis and vapor deposition (nominal composition: 93 wt% SiO2 and 7 wt% TiO2) that has found applications in large telescope mirror blanks because of its near-zero coefficient of thermal expansion (CTE) over the 5~35 ◦C temperature range [1,2]. The procedures are time-consuming and expensive, so they are not suitable for the detection of the CTE uniformity of large ULE glass. We use the correlation method to accurately measure the ultrasonic velocity in ULE glass. The use of ultrasonic velocity measurements to characterize the CTE of ULE glass was first discovered by researchers at Corning. The various cumbersome practical steps (including ensuring the constant temperature of the sample to reach thermal equilibrium, removal of the water bath, quick-drying, and ultrasonic velocity measurement [9]) can introduce uncertainty regarding the sample temperature, which, in turn, affects the accuracy of the CTE measurement results. The principle and method of ultrasonic velocity measurement are mathematically stated .
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