Editing Precision Thermocouple Based Temperature Measurement System (section)

== 4. Results (Thermoelectric Characterisation of Undoped ZnO Pellet) ==

=== 4.1. Output Voltage Response to Applied Temperature Difference ===

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[[File:1.jpeg|thumb|500px|Graph-1]]
[[File:2.jpeg|thumb|500px|Graph-2]]
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[[File:3.jpeg|thumb|500px|Graph-3]]
[[File:4.jpeg|thumb|500px|Graph-4]]
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The thermoelectric response of the synthesized undoped ZnO pellet was examined by measuring the output voltage (Vout) generated across the pellet at varying temperature differences (ΔT), using the Keysight B2901A Source Measure Unit. The temperature gradient was established by stepping the heater input voltage (Vin) was stepped between 2.0 V and 3.0 V, producing temperature differences in the range of 1°C to 14°C across the pellet. At every ΔT step, four consecutive voltage readings were recorded and averaged to reduce the effect of short-term fluctuations. Before each of the four independent runs, silver paste was freshly applied at both contact points to ensure reliable electrical coupling between the measurement leads and the pellet surface.

Throughout all four runs, the output voltage was negative at every measured temperature difference, with values lying between −59 μV and −80 μV across the different runs. The Vout versus ΔT data for all four runs are presented in Graphs 1 through 4.

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! Slope (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

The mean Seebeck coefficient extracted across the four runs is S = −0.934 ± 0.094 μV/K. The negative sign reflects the consistently negative output voltage observed throughout all measurements, confirming that electrons are the dominant charge carriers and that the undoped ZnO pellet behaves as an n-type semiconductor.The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the variation that came with reapplying the silver paste contacts between each run.

=== 4.3. Anomalous Behaviour Beyond ΔT = 14°C ===
[[File:anomaly.jpeg|thumb|center | 800px]]

Within the primary measurement window of ΔT = 1°C to 14°C, the output voltage increased monotonically from approximately −71 μV toward less negative values with increasing temperature difference, consistent with the linear thermoelectric response characterised in Section 4.2. At ΔT = 14°C, the output voltage reached a maximum of approximately −61.5 μV.
Beyond this point, a departure from the established trend was observed. At ΔT = 16°C, the output voltage reversed direction, falling back to approximately −63.5 μV rather than continuing to increase. This behaviour was reproduced consistently across repeated measurements conducted under identical conditions, confirming that the reversal is a systematic feature of the pellet's response and not attributable to instrumentation noise, contact instability, or measurement artefact. The onset of this anomalous behaviour at ΔT = 14°C therefore defines the practical upper limit of the linear operating window for this measurement configuration. All primary data used for Seebeck coefficient extraction were accordingly restricted to ΔT ≤ 14°C. The physical mechanisms underlying this behaviour are examined in Section 5.3.