The temperature coefficient of resistance change can be explained by a platinum resistance thermometer element. (This interpretation is also true for thick-film and thin-film platinum resistance thermometers.) Assume that the overlay on the mandrel and platinum wire has the same coefficient of thermal expansion. A continuous, void-free and crack-free base is formed. Platinum wire is buried inside. Platinum resistance thermometer components are usually cold drawn platinum wire around. Before use, the element is heated to a temperature above 400 ° C to anneal the platinum wire, which theoretically falls to zero at the annealing temperature. While platinum is buried in the device, the coefficient of thermal expansion of the vaporized aluminum is smaller than that of platinum, and when the device is cooled down from the annealed state, the shrinkage of the platinum wire is smaller than normal due to the obstruction of the ceramic substrate. This generates tensile stress in the platinum wire, which tensile stress increases with decreasing temperature. The resistance increases by tens of thousands of tensile strains, so the resistance decreases when the component cools down as much as the non-strained platinum wire, so the value of a is lower. Conversely, if the ceramic matrix surrounding the platinum wire has a higher coefficient of thermal expansion than when it is hot, the platinum foil will be compressed upon cooling, resulting in a higher a value than unstrained platinum.
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