two electrical conductivity terms have cancelled out and so Sign convention The sign is made explicit in the following expression: Thus, if S is positive, the end with the higher temperature has the lower voltage, and vice versa. The voltage gradient in the material will point against the temperature gradient. The Seebeck effect is generally dominated by the contribution from charge carrier diffusion (see below) which tends to push charge carriers towards the cold side of the material until a compensating voltage has built up. As a result, in p-type semiconductors (which have only positive mobile charges, electron holes), S is positive. Likewise, in n-type semiconductors (which have only negative mobile charges, electrons), S is negative. In most conductors, however, the charge carriers exhibit both hole-like and electron-like behaviour and the sign of S usually depends on which of them predominates. Relationship to other thermoelectric coefficients According to the second Thomson relation (which holds for all non-magnetic materials in the absence of an externally applied magnetic field), the Seebeck coefficient is related to the Peltier coefficient by the exact relation where is the thermodynamic temperature. According to the first Thomson relation and under the same assumptions about magnetism, the Seebeck coefficient is related to the Thomson coefficient by The constant of integration is such that at absolute zero, as required by Nernst's theorem. Measurement Relative Seebeck coefficient In practice the absolute Seebeck coefficient is difficult to measure directly, since the voltage output of a thermoelectric circuit, as measured by a voltmeter, only depends on differences of Seebeck coefficients. This is because electrodes attached to a voltmeter must be placed onto the material in order to measure the thermoelectric voltage. The temperature gradient then also typically induces a thermoelectric voltage across one leg of the measurement electrodes. Therefore, the measured Seebeck coefficient is a contribution from the Seebeck coefficient of the material of interest and the material of the measurement electrodes. This arrangement of two materials is usually called a thermocouple. The measured Seebeck coefficient is then a contribution from both and can be written as: Absolute Seebeck coefficient Although only relative Seebeck coefficients are important for externally measured voltages, the absolute Seebeck coefficient can be important for other effects where voltage is measured indirectly. Determination of the absolute Seebeck coefficient therefore requires more complicated techniques and is more difficult, but such measurements have been performed on standard materials. These measurements