Scope:

ASTM E289 – 04 test method covers the determination of linear thermal expansion of rigid solids using either a Michelson or Fizeau interferometer. Rigid solids require detailed preconditioning and specific thermal test schedules for correct evaluation of linear thermal expansion behavior for some material applications and applicable to the approximate temperature range −150 to 700°C.

Test Procedure:

In this test method, a specimen is given polished reflective ends or placed between two flat reflecting surfaces (mirrors). The mirrors consist of flat-uniform thickness pieces of silica or sapphire with the surfaces partially coated with gold or other high reflectance metal. Light, either parallel laser beam or from a point monochromatic source, illuminates each surface simultaneously to produce a fringe pattern. As the specimen is heated or cooled, expansion or contraction of the specimen causes a change in the fringe pattern due to the optical path length difference between the reflecting surfaces. This change is detected and converted into length change from which the expansion and expansion coefficient is determined.

FIGURE 1. Typical Low-Temperature Cryostat

Specimen size:

A cylindrical specimen with a radius of curvature of the hemispherical ends is 3mm or less, and the diameter is uniform to 61 m rad

Data:

Calculate the linear thermal expansion for each temperature interval as follows:

Fizeau and Single Pass Michelson:

Double Pass Michelson:

Where measurements are carried out at helium or other gas pressures above 1.33 kPa, allowance should be made for the effects of pressure and temperature on the index of refractions of the gas.

As an example, for the Fizeau types:

and

At the 288 k and 100 kPa reference conditions, for air n_r = 1.0002771 (yellow line helium) or 1.0002779 (green line of mercury). For helium n_r = 1.000036. For helium at a pressure of 1.33 kPa or less, the overall effect is less than ±6 nm and may be neglected.