Copper contraction coefficient

Figure 8-10 The shrinkage process model for copper and ceramic during firing (Sea- ceramic contraction coefficient. So, copper contraction coefficient).

Figure 8-7 The relationship between copper content in the substrate and contraction coefficient.

In order to reduce the amount of mismatch in the contraction between the two materials, adding alumina or other additives to the copper paste has been suggested. Since alumina powder does not change at the firing temperatures of LTCCs, it can increase the contraction coefficient of copper while it is also effective in strengthening interface adhesion with its anchor effect and by preventing expansion due to foaming. 

In ammonia synthesis, copper was the preferred material for use with steel or low alloy flanges. Copper expands and contracts 9 times faster than steel. Leakages were found due to the large differences of the thermal expansion coefficients between the metals. 

The dielectric laminate expands and contracts during heating and cooling of the product during assembly and applications in the field. The coefficient of thermal expansion (CTE) is a measure of the expansion in parts per million (PPM) per degree of temperature change. For example copper expands at approximately (15.5-17 PPM) / °C. Many of the dielectric and fiber systems are designed to have an expansion rate approximately equal to copper since copper is the most widely used conductor material in printed circuit boards. 

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