Modeling the Thermal and Electrical Properties of Different Density Sintered Binder Jetted Copper for Verification and Revision of The Wiedemann-Franz Law

Abstract

There is a link between the thermal and electrical properties of metal. The equation which links these two properties is called the Wiedemann-Franz Law. Also there is an emerging technology within Additive Manufacturing called Binder Jet Printing which can print high purity copper without heat stress within the material. Due to the Binder Jet Printings ability to print high resolution prints without any print through, this makes future use of this technology a necessity for future electrical and thermal components within computers . However a thermal and electrical conductivity analysis of binder jetted copper has never been performed, and needs to be for simulation with this material. Therefore within this thesis the relationship of the thermal and electrical properties of printed binder jetted copper part will be researched.

To find the electrical resistivity of binder jetted copper, three sets of 2mm diameter rods where printed and then placed within a modified four wire resistance method test. For the thermal conductivity measurements a laser flash diffusivity machine was used, and three sets of 11 copper disks of approximately 1cm diameter by 1mm where printed.

The data shows a strong linear trend linking electrical resistivity to the density ratio of the copper. Within the thermal conductance measurement, a lot more variability was seen within the three different prints. The 70% density ratio prints saw a large 13% spread in density ratios throughout the prints, which is believed to be caused by improper sintering due to temperature gradients near the door of the kiln. The 82% density prints saw better grouping of density ratios by placing the specimens in the back of the kiln. Lastly, the 92% prints saw the best density ratio grouping but the largest thermal conductivity variance. Even though the scatter plot for the thermal conductivity measurements are not as precise as the electrical resistivity measurements, it still shows a linear trend which matches the NASA data from 1971. Overall, these linear trends can be modeled and compiled into a new form of the Wiedemann-Franz law, which accounts for the density ratio of the binder jetted print.