The Dependence of Ultrasonic Velocity in Ultra-Low Expansion Glass on Temperature

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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mi mathvariant="normal">L</mi></msub></mrow></semantics></math></inline-formula>) indirectly. The performance of this method was verified by simulations. Considering the dependence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mi mathvariant="normal">L</mi></msub></mrow></semantics></math></inline-formula> on temperature (<i>T</i>), we carried out the derivation of the analytical model between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mi mathvariant="normal">L</mi></msub></mrow></semantics></math></inline-formula> and <i>T</i>. Based on reasonable constant assumptions in the physical sense, a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mi mathvariant="normal">L</mi></msub></mrow></semantics></math></inline-formula>–<i>T</i> exponential model was produced, and some experimental results support this model. Additional experiments were carried out to validate the accuracy of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mi mathvariant="normal">L</mi></msub></mrow></semantics></math></inline-formula>–<i>T</i> exponential model. The studies we conducted indicate that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mi mathvariant="normal">L</mi></msub></mrow></semantics></math></inline-formula>–<i>T</i> 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.