# Study of the Precipitation Process in Aging Steel Pipeline Weldments by Thermoelectric Power Means
## 2 Thermoelectric Technique  
The thermoelectric methods are based on the Seebeck effect, which is commonly used in thermocouples to measure temperatures. Figure 1 shows the schematic diagram of the hot tip thermoelectric measurement as most are often performed for the characterization of materials. One of the reference electrodes is heated by electrical means to a preset temperature (\(T_{h}\)), which acts essentially as the tip of a temperature-stabilized soldering iron, while the other electrode is left to be 'cold' at room temperature (\(T_{c}\)). The measurement is obtained quickly in a few seconds to ensure that the hot reference electrode is not noticeably cooled down by the specimen and that the rest of the specimen beyond the close vicinity of the contact point is not perceivably warmed up. After this, the measured thermoelectric voltage due to the Seebeck effect is given by:  
\[V=\int\limits_{T_{c}}^{T_{h}}[S_{S}(T)-S_{R}(T)]dT=\int\limits_{T_{c}}^{T_{h}} S_{SR}(T)dT \tag{1}\]  
where \(T\) is the temperature; and \(S_{S}\) and \(S_{R}\) denote the absolute thermoelectric powers of the specimen and the reference electrode, respectively. Any variation in the material properties can affect the measured thermoelectric voltage via \(S_{SR}=S_{S}-S_{R}\), which is the relative thermoelectric power of the specimen that is tested with respect to the reference electrode. In most cases, the temperature-dependence of the thermoelectric power can be neglected over the range of operating parameters used and the thermoelectric voltage can be approximated as \(V\approx\left(T_{h}-T_{c}\right)\)\(S_{SR}\). Ideally, regardless of how high the temperature difference between the junctions is, only the thermocouples made of different materials, or more precisely materials of different thermoelectric powers, will generate a thermoelectric signal.  
This unique feature makes the simple thermoelectric tester one of the most sensitive material discriminators that are used in nondestructive inspection. Figure 1b shows the thermal gradient produced inside the sample by using the _hot tip method_. Some advantages of the above-described thermoelectric method are: localized TEP measurements and thus, ability to detect heterogeneities; possibilities to measure the 2D TEP map of massive materials; adjustment of the measured zone by  
Figure 1: Schematic diagram of the (**a**) hot tip thermoelectric method and the (**b**) thermal gradient inside the sample.  
changing the tip size; possibility of Non-Destructive Testing (NDT) directly on massive materials (in-situ measurements). The most important parameters affecting the thermoelectric measurements are those associated with volumetric and contact effects. The volumetric effect is closely related to the thermoelectricity phenomena due to the kinetics of the diffusion of electrons throughout the material. This effect is mainly affected by chemical composition, different heat treatment, precipitation process, grain boundaries, texture and fatigue of the material [3; 4; 5]. The contact effects are related to the imperfect contact between the test sample and the reference probe/block, amount of pressure applied to the probe/block, temperature of hot and cold junctions and probe/block material.