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Expansion of high tech materials

Industrial applications are ever more frequently demanding materials of highest thermal stability. A precision interferometer has been developed in the PTB to exactly measure this property. With this instrument, the change in length can be determined with highest accuracy in an absolute measurement as a function of temperature, time and – if necessary – ambient pressure.

Thermal expansion coefficient (α) of a special glass with extremely low expansion. The progress of α shown here derives from α series of interferometrically measured lengths of a sample with parallel end surfaces as a function of temperature. In this example, there is a point of reversal at approximately 17.5 °C at which the thermal expansion disappears. Below this point, α fall in temperature causes an expansion of the material. The figure (upper left) shows a typical topography of the interference phase, which includes the front surface of the body and α wrung end plate. The averaged phase values within the rectangular areas on the end plate (left/right) and on the front surface of the body (middle), are the basis for the interferometrical length measurement.

Thermally stable materials play an important role in dimensional metrology and in precision manufacturing. The currently highest requirements on the thermal stability of critical components are made in EUV lithography of reflection masks and mirrors. These are, therefore, based on substrates made of high tech glass/ceramics which are to exhibit a very low thermal expansion coefficient α (α < 1 · 10–8 · K–1).

For the precise characterization of gauge-blockshaped measuring objects made of high tech materials, a precision interferometer was developed with the aim of measuring samples of up to 400 mm length with uncertainties in the sub-nanometer range. From such exact measurements of length, it is possible to calculate the thermal expansion coefficient as a function of the temperature with uncertainties of up to 2 · 10–10 · K–1. Furthermore, it is possible to get quantitative statements regarding the homogeneity of the thermal expansion, compressibility, length relaxations and also the long-term stability of samples.

Length measurements with sub-nm uncertainties demand, besides the application of frequencystabilized lasers, the consideration of influences whose uncertainty contributions are difficult to minimize. For this purpose, various methods have been developed in the PTB in the last few years and these have been integrated into the measuring process. A new autocollimation process is cited as an example and this ensures that the lightwaves reach the surfaces of the measuring objects exactly perpendicularly. The so-called cosine error is hereby lowered to under 10–11 · L. Furthermore during the electronic evaluation of the interference pattern, the exact assignment of the sample position to the camera pixel coordinates is considered. This is particularly important when it comes to measuring objects whose end faces are non-parallel and when the influence of small temperature-induced changes of the lateral sample position can be corrected. By taking the temperature-related influence of the deflection of the end plate wrung to the back into consideration, the precision could be increased further. When taking thermal expansion measurements on typical samples, length measurement uncertainties of 0.25 nm are now achieved.

In a recently completed international comparison measurement, the leading position of the PTB in the determination of thermal expansion coefficients was confirmed. The new possibilities for the precise characterization of high tech materials are already being used intensively by companies working in the fields of optics and precision manufacturing.

Contact at PTB:

Phone: +49-531-592-0