20241027_report_on_sands.md

Emissivity measurements on sand

T. Echániz and I. Urcelay-Olabarria

October 26, 2024

1 Introduction

We report normal emissivity measurements at room temperatures of differents sand-samples: ST1, ST2, ST3, ST4 and ST5.

2 Experimental details

The emissivity of different sand-samples has been investigated at room-temperature. The directional-hemispherical total reflectance was measured with an integrating sphere at an incident angle of $13^{\circ}$. This integrating sphere has a diameter of 75 mm and is equipped with a DLaTGS detector. The usual comparison measurement method has been used, by comparing the radiance reflected by the sample to that reflected by an Infragold reference $\left(R_{r e f}=0.95\right)$. The reflectivity of the sample, $R_{s}$, is obtained as following:

$$ R_{s}=\frac{S_{s}}{S_{r e f}} \times R_{r e f} $$

being $S_{s}$ and $S_{\text {ref }}$ the measured sample signal and the reference signal, respectively. For each measurements we have done 10 scans and calculated the mean value together with the corresponding standard deviation for the sample as for the reference. In order to calculate the error of the measurement, it has been considered as a combination of the misalignment (smaller than 2%),....

The standard uncertainty is taken as the combination of uncertainties due to signal noise in the sample and reference reflectance measurements. It is small $2 %$ in the $\lambda<10 \mu \mathrm{~m}$ range, but increases quickly at longer wavelengths due to the low signal emitted by the source in that range.

Finally, the emissivity, $\epsilon$ is calculated as

$$ \epsilon=1-R_{s} $$

The emissivity of a material depends strongly on its surface conditions. Since the sample is already very irregular, with different sand-grains oriented in different directions, two different measurements were carried out to see if the conditions of the surface of the samples affected the measurements. In the first experiment, the surface of the sand-sample was smoothed, whereas for the second measurement, the surface was very irregular. The result shown in Fig. 1 show that the emissivity measurements barely change due to surface conditions. In fact, in all the cases both curve collapse at low wavelengths, as observed in the insets. Small deviations can be observed at high wavelengths, where the experimental errors are relatively bigger. Thus, these measurements suggest that the intrinsic characteristics (grain size and arbitrary orientation) of the sand the limiting factors for this experiment. From now on, all the presented results will correspond to those samples with smoothed surface.

Falta cometar algo sobre el comportamiento de los materiales ceramicos. Y sobre el angulo.

With the aim of comparing the behavior of the five samples, the data has been plotted in Fig. 2. The emissivity of all the samples is very close to 0,9 for wavelengths between 3 to $18 \mathrm{~cm}^{-1}$. At lower values of $\lambda$ the emissivity decreases down to about $0,6 \pm 0,1$. There are two intermediate regions where there is a significant decrease of the emissivity: from $3,5 \mu \mathrm{~m}$ to $5 \mu \mathrm{~m}$ and from $8 \mu \mathrm{~m}$ to $10 \mu \mathrm{~m}$. This could be due to the absorption of .... . Moreover, it is in those regions where the different sand-samples present the biggest deviations. So far, we suggest carrying out a more rigorous characterization of the samples to determine the origin of these effects.

Figure 1: Emissivity measurements of sand samples: (a) ST1, (b) ST2, (c) ST3, (d) ST4 and (e) ST5. For each samples measurements were carried out in two different conditions: The red curve corresponds to the sample with smoothed surface, whereas the blue one corresponds to the same sample with rough surface. The details at low wavelengths are shown in the inset.

Figure 2: Emissivity measurements of ST1, ST2, ST3, ST4 and ST5 sand-samples represented in black, red, green, blue and pink lines, respectively. The inset shows the areas where the emissivity of the samples exhibit slightly unequal behavior.