PMIC IAS 17023:2005 Accredited
Precision Measurements and Instruments Corporation
3665 SW Deschutes Street • Corvallis, Oregon 97333-9285
Ph: (541) 753-0607 • Fax: (541) 753-0610
PMIC Testing Services

Thermal Expansion

Coefficient of Thermal ExpansionCTE – is defined as the fractional increase in strain per unit rise in temperature. It can be defined at a precise temperature or over a temperature range.

PMIC uses a variety of techniques to measure the thermal expansion of materials, components and structures. These are principally Michelson interferometry and quartz dilatometry. The normal temperature range is -253°C (20K) to 1100°C (1373K). PMIC also uses optical telescopes, optical levers and diffraction techniques to measure at higher temperatures.

Michelson Interferometry (ASTM E289)PMIC employs Michelson laser interferometry to measure real time thermal expansion/contraction of materials with a low coefficient of thermal expansion (CTE). The CTE uncertainty is typically on the order of 10 parts per billion/K (10-8/ºC). Each shift in a fringe pattern corresponds to a change in specimen length of one-half the laser wavelength (12.456 micro-inches for a He-Ne laser in vacuum). Precision optics, photodetectors and interpolation techniques allow length resolution to about a nanometer. PMIC expertise contributed to the modification of the ASTM Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry to include Michelson, as well as Fizeau and other interferometers (ASTM 289-95).

A unique feature of this technique is little restriction on sample size or shape. Thin films, plates, sandwich structures, tows and tubes up to 3m long have been tested. Multi-directional strains can be determined simultaneously, e.g., for composite components or structures.

Figure 1 shows a step in the process of optics alignment

Figure 1
Fig. 1 – Optics Alignment Process

Figure 2 illustrates the basic features of PMIC Michelson laser Interferometer

Figure 2
Fig. 2 – Basic Illustration of the Michelson Laser

Continuous strain and temperature data are normally plotted as shown in Figure 3. The slope of the strain/temperature curve at a given temperature is the instantaneous coefficient of thermal expansion. In addition, the average slope over a finite temperature range can be obtained to give an average CTE.

Fig. 3 – High Resolution Thermal Expansion Measurement

Figure 3
Fig. 3 – High Resolution Thermal Expansion Measurement

Quartz Dilatometry (ASTM E228 and ASTM D696) – The Quartz Dilatometer, ASTM E228 and D696, is used with materials that have a large expected CTE and when higher temperatures are required. Minute changes are recorded, in real-time, over variable temperature ranges with high accuracy and resolution down to 0.05 ppm/ºC.

Fig. 4 – Basic Dilatometer configuration

Figure 4
Fig. 4 – Basic Dilatometer configuration

A unique feature of this technique is little restriction on sample size or shape, and multiple specimens can be tested at one time. Thin films, plates, sandwich structures, circuit boards, IC chips and specimens up to 20cm have been tested. Longer specimen sizes can be accommodated using a custom LVDT setup.

In Figure 5, Continuous strain and temperature data are normally plotted in real time. The slope of the strain/temperature curve at a given temperature is the instantaneous coefficient of thermal expansion. The average slope over a finite temperature range can be obtained to give an average CTE.

Fig. 5 – Thermal Expansion Measurement

Figure 5
Fig. 5 – Thermal Expansion Measurement

Thermal Cycling – All PMIC thermal expansion techniques include real time strain measurement and thermal cycling instrumentation. CTE changes with time and temperature may be caused by microcracking, phase changes, glass transition temperatures, moisture diffusion and/or plastic flow, as with metal matrix composites. Such data permit accurate extrapolation to extended lifetime projections.

Linear Thermal Expansion (CTE) by Optical Diffraction Techniques – Highly precise CTE measurements are made at PMIC by various interferometric techniques such as Michelson interferometry. For temperatures above 1000°C (1273K), however, there are limitations, such as stability of reflecting surfaces. PMIC has developed a technique based on laser diffraction between sample edges and a refractory thin edge (such as alumina) which can measure CTE in any atmosphere and any temperature up to the sample melting point. It was described at the ITCC 27/ITES15 symposia in 2003 (Knoxville, TN, Destech publishers)

Volumetric CTE – The total volume change of crystals, liquids, and many composites is usually measured by mercury based systems over limited temperature ranges. PMIC has examined the sample induced displacements of organic and metallo-organic liquids in quartz capillaries over the temperature range -70 to ~200°C (200 to 473K). This work has been described at the ITCC28/ITES 16 in New Brunswick, June 2005.
(See www.thermalconductivity.org).

Strain Gage CTE – Strain gages are ideal for finding localized strain in populated and unpopulated circuit boards and other odd shaped materials such as composite tubes. Due to the complex structure inherent in PCBs, measuring the bulk CTE does not always provide a clear picture of the strain at circuit concentration locations or at solder junctions. By using strain gages, we can determine the strain at specific locations on the PCB. The circuits can then be mounted and retested to determine the effect mounting the circuits have on the bending of the PCB. Combining strain gages with bulk measurements from our Dilatometer, provide a very clear and accurate strain representation of your PCB. This method can also be done “in-situ” for a real-time understanding of your PCB.

Please contact us for your Thermal Expansion requirements.