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In some metals such as Platinum Seebeck coefficient is taking for 0 conditionally. https://en.wikipedia.org/wiki/Seebeck_coefficient#Seebeck_coefficients_for_some_common_materials Or graphite. How it is possible to explain it physically? Why exactly it is "0"?

The Seebeck coefficient of pristine graphite is nearly zero, because the number of electrons and the number of holes are almost equal. https://www.jim.or.jp/journal/e/pdf3/50/07/1607.pdf

I wanted to receive an explanation in terms of a charge carriers behavior. Some sources claim that in materials with zero Seebeck coefficient both electrons and holes are equally mobile and when you heat one end of the metal rod an equal amount of electrons and holes flow to the cold end. What I wish to know whether electrons and holes recombine at the cold end. If yes, does it mean such thing as carriers recombination can happen in metals?

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This is explained in the very same article that you linked. The absolute Seebeck coefficient is simply difficult to measure because the voltage probes with which you measure also experience a temperature gradient. Hence, the measured voltage is influenced by both the Seebeck coefficient of the sample material and the Seebeck coefficient of the electrode material. By defining one reference material, platinum in your case, the difference of the Seebeck coefficients is used as an easy-to-measure quantity. You just have to use the same setup to measure platinum and all the materials that you are interested in. If you want to obtain the absolute Seebeck coefficients you just need to determine the Seebeck coefficient of platinum, and not for all the materials that you measured.

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