## 3 Measurement Tests
### Test Results and Analysis  
The tests in this article used a gas ionization counter. The model number of the test instrument is UltraLo-1800 Alpha Particle, manufactured by XIA. The background can be as low as 0.0005 \(\alpha\)/(cm\({}^{2}\)-h) [21]. The instrument consists of an ionization chamber, an electrical signal amplifier, and a receiver. The instrument determines the location of signal generation by intentionally increasing the geometry of the emission signals of alpha particles emitted from different surfaces, and then the reduction of background effects is achieved by actively shielding the signal from the surface of the ionized room. This ensures the reliability of the test results. The flow of the test is as follows:  
(1) Before the test, the instrument and the non-radioactive tray for the test is cleaned and background tested to ensure that the emissivity of the instrument is lower than 0.002 \(\alpha\)/(cm\({}^{2}\)-h) and the measured background emissivity is \(\epsilon_{0}\). (2) The tin sphere is placed on the test tray in the test area (A1) after the test into the ionization chamber, the closure of the ionization chamber for vacuum and argon filling, the test mode selection \"wafer\" (test area of A\({}_{0}\) = 707 cm\({}^{2}\)), the test obtained the emissivity of \(\epsilon_{1}\). (3) Background clipping: The actual test area of the sample is generally different from the instrumental test area, and the instrument displays the average surface emissivity of the \(\alpha\)-particles under the actual test area rather than the average surface emissivity of the sample's own area, so it is necessary to process the test results, i.e., bottom clipping, at the end of the test. The formula for background clipping is:  
\[\epsilon=\frac{\epsilon_{0}A_{0}-\epsilon_{1}\cdot\left(1-\frac{A}{A_{0}} \right)}{A} \tag{1}\]  
The surface \(\alpha\)-particle emissivity of the Sn\({}_{63\%}\)Pb\({}_{37\%}\) tin sphere, Sn\({}_{10\%}\)Pb\({}_{90\%}\) tin sphere, and SAC305 tin sphere are given in Table 3. From the table, it can be seen that: (1) the surface \(\alpha\)-particle emissivity of the Sn\({}_{63\%}\)Pb\({}_{37\%}\) tin sphere is about one order of magnitude lower than that of the Sn\({}_{10\%}\)Pb\({}_{90\%}\) tin sphere, and the \(\alpha\)-particle emissivity of the SAC305 tin sphere is the lowest of the three, which is reduced by about 55.6% compared to the emissivity of the Sn\({}_{63\%}\)Pb\({}_{37\%}\) tin sphere. (2) The surface \(\alpha\)-particle emissivity of the low \(\alpha\) tin sphere is reduced by thousands or even tens of thousands of times. According to the \(\alpha\)-particle emissivity grade classification method in Table 4, some samples have reached the level of ultra-low emissivity grade. \begin{table}
\begin{tabular}{l l l l} \hline
**Group** & **Sample Composition** & **Ball Diameter** & **Densities (g/cm\({}^{3}\))** \\ \hline
1\# & Sn\({}_{10\%}\)Pb\({}_{90\%}\) & 0.1 mm & 10.7 \\
2\# & Sn\({}_{63\%}\)Pb\({}_{37\%}\) & 0.1 mm & 7.34 \\
3\# & Sn\({}_{63\%}\)Cu\({}_{0.5\%}\) & 0.1 mm & 8.84 \\
4\# & Low\(\alpha\)Sn\({}_{10\%}\)Pb\({}_{90\%}\) & 0.1 mm & 10.7 \\
5\# & Low\(\alpha\)Sn\({}_{63\%}\)Cu\({}_{0.5\%}\) & 0.1 mm & 7.34 \\
6\# & Low\(\alpha\)Sn\({}_{63\%}\)Pb\({}_{37\%}\) & 0.1 mm & 8.84 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of samples to be measured. Figures 1 and 2 show the \(\alpha\)-particle energy spectra emitted by the Sn\({}_{10\%}\)Pb\({}_{90\%}\) tin sphere and Sn\({}_{63\%}\)Pb\({}_{37\%}\) tin sphere obtained from the tests and the Gaussian function to fit the curve. As seen from the figure, the \(\alpha\)-particle spectra of the two kinds of tin spheres show similar characteristics:  
(1) The test results show that the peak of the spectra is located between 5.3 MeV and 5.5 MeV and the peak of the curve fitted by Gaussian function is 5.38 MeV. (2) There is a relatively single peak.