TEMPERATURE MEASUREMENT UNCERTAINTY

Temperature measurement is very important for the evaluation of results of the in-situ SXRD experiment. The aim of this section is to investigate the uncertainty of the temperature value measured by the thermocouples, as well as the uncertainty in the temperature stamps assigned to the diffraction images acquired during the thermomechanical cycles.

The thermocouples for the experiment were made from R-type wires, i.e. pure platinum for one conductor and an alloy of platinum containing 13% rhodium for the other. To make a thermocouple the wires are melted together to produce a bead, which subsequently is spot-welded to the surface of the specimen. Although the thermocouples were fabricated following a standard procedure, they were made manually, which means that there were potential differences in the size of the bead, the quality of the contact between the thermocouple wires and the quality of the contact between the thermocouple bead and the surface of the specimen. All these factors produce uncertainty in the temperature measurement. In addition, the temperature stamps assigned to the SXRD images can have another sources of error, such as the distance between the thermocouple and the X–ray beam, and delay in temperature logging.

The variability in the measured phase transformation temperature was used to evaluate the extent of these uncertainties. If identical Zircaloy-2 samples are heat treated under the same conditions (heating/cooling rate, load), the measured transformation temperature should not differ between samples. The transformation temperatures were evaluated in two different ways: (1) performing resistivity measurements during the

 phase transformation in similar thermomechanical cycles, and (2) analysing diffraction images acquired during the synchrotron experiment.

Resistivity Measurements

Numerous samples were subjected to thermal cycles without applied load, similar to those applied to sample T1, in order to determine the phase transformation temperatures by means of resistivity measurements. These tests were carried out at The University of Manchester, in an ETMT of similar characteristics to the one at the ESRF, with exception of the absence of inert gas atmosphere, i.e. the surface of the samples was subjected to oxidation. The resistivity measurements were not direct. Two platinum wires were spot-welded to the samples, as close as possible to the thermocouple bead, and the electrical potential difference (voltage) between these two connectors was logged along with the temperature, current, and load. The resistivity was calculated from instantaneous data of current and voltage.

Figure 4.5 shows the resistivity obtained in four different samples during heating. All these samples were thermally cycled starting in the as-rolled condition, and using a

Texture Evolution during -quenching of a Zirconium Alloy 137 heating rate of 10Cs^-1. The absolute resistivity values differ between samples, due to differences in cross-section and in the distance between the conductors measuring the voltage. The resistivity trace obtained during cooling (at 50Cs^-1) is shown for one of the samples (R1) to illustrate the hysteresis of the phase transformation. All the results exhibit some degree of noise in the signal, which is a major obstacle to determine accurately the transformation temperatures. The noise in the resistivity signals comes from oscillation of the electrical current applied to the sample to control the temperature. Nevertheless, the start and the end of the  phase transformation are evident, marked by changes in the gradient of the resistivity.

In order to approximate the transformation temperatures, the signals shown in Figure 4.5 were normalised and fitted to a Gaussian peak as implemented in (O'Haver 2009).

An example of the results is shown in Figure 4.6, and the transformation temperatures for the four samples are shown in Table 4.2. According to these results, the variation in measured transformation temperature ranges between 6 and 9C.

Figure 4.5 Resistivity measurements during thermal cycling of as-rolled samples

Figure 4.6 Example of peak fitting of resistivity measurements, corresponding to the first transition observed during heating in sample R1.

Table 4.2 Transformation temperatures according to resistivity measurements SAMPLE α → α+β (°C) α+β → β (°C)

R1 834 919

R2 821 907

R3 821 899

R4 826 910

Texture Evolution during -quenching of a Zirconium Alloy 139 With the aim of isolating the effect of changing thermocouples, an additional set of tests was carried out. This time one single sample was used, maintaining the wires to measure the voltage, so the effect of cross section and location/attachment of the wires was minimised. The thermal cycle on this sample was applied using a current cycle: the current was increased from 0 to 32A with a rate of 0.25As^-1 and then decreased at a rate of 1.50 As^-1. This cycle emulates one of the temperature-controlled -quenching cycles, taking the sample to a peak temperature of 1100C with mean heating and cooling rates of ~9Cs^-1 and ~40Cs^-1 respectively. This cycle was repeated five times (RC-1 to RC-5), and then the thermocouple was changed, before repeating the cycle another five times (RC-6 to RC-10). Sections of the temperature profiles obtained are shown in Figure 4.7, while the maximum temperatures measured are listed in Table 4.3.

Figure 4.7 Temperature profiles obtained from sample TC in different cycles.

Cycle Max. Temperature (°C)

For this sample, it is clear that in addition to the effect of the thermocouple, the sample undergoes physical changes, which makes difficult to evaluate temperature uncertainty quantitatively. However, some useful observations can be made:

 The temperature profile of the first run (RC-1) showed more variability than runs RC-2 to RC-4. This may be explained by stabilisation of the thermocouple and the spot weld. Conversely, the second thermocouple seems to deteriorate, runs RC-7 to RC-10 show significantly less stable temperature profiles than run RC-6.

 The temperature measured increased from run RC-2 to run RC-5. This would indicate that after -quenching the first time, the resistivity of the material increases slightly with each new -quench. This may be related to an accumulated oxidation in the surface with each cycle, given that these samples were heat treated in air.

 Regarding the effect of the thermocouple, minimising the physical changes in the sample, one can compare the results between run RC-5 and RC-6, i.e. the last run of the first thermocouple and the first run of the second thermocouple. The differences in measured temperature between these two runs, for the same value of current, range between 20 and 40C with an average of ~33C. This large difference could

Texture Evolution during -quenching of a Zirconium Alloy 141 be explained by the difficulty of attaching a second thermocouple in a surface that was already oxidized.

Analysis of Diffraction Images

According to results that will be presented in the next section (4.1.4), there are three main events occurring during heating of cold-rolled Zircaloy-2 samples, which are detectable in the diffraction images: (1) start of recrystallization, (2) start of the 

phase transformation, and (3) end of the  phase transformation (-transus). During the first stage of the in-situ synchrotron experiment, i.e. where temperature stamps were logged with each individual diffraction image, two pairs of samples were subjected to identical heating to samples T2 and T3 in the experimental matrix, and their diffraction images were acquired using the same parameters (frequency and exposure).

Table 4.4 lists the temperatures at which recrystallization and phase transformation were observed in the diffraction images for these two pairs of samples, according to the corresponding temperature stamps. As a reference, resistivity measurements carried out by Gey et al. in Zircaloy-4 (Gey et al. 2002a) detected the start and the end of the phase transformation at 834C and 938C respectively. The differences with respect to these results and to the resistivity measurements may be attributed to a delay in the macroscopic response of the resistivity variations (depending on the size of the sample), and the differences in composition between Zircaloy-2 and Zircaloy-4.

SAMPLE HEATING transition temperatures. The transformation temperatures observed in the two samples heated at 2Cs^-1 are similar to each other, as are the ones of the group heated at 10Cs^-1. However, there is a consistent difference between the two groups, with lower transition temperatures obtained in the slow heated samples. This effect could be attributed to a consistent delay between the time at which the diffraction image is saved, and the time at which the temperature is logged. Although the number of data points for this analysis is limited, the data in the table suggests that the temperature uncertainty ranges between 5C and 8C, which is close to the results obtained from the resistivity measurements carried out in similar conditions. This uncertainty was taken into account when analysing the results of the following sections.