Zone Refining of Ultrahigh-Purity Sodium Iodide for Low-Background Detectors

There has been a growing interest in ultrahigh-purity low-background $\mathrm{Na}\mathrm{I}$($\mathrm{Tl}$) crystals for dark-matter direct searches. Past research indicates that zone refining is an efficient and scalable way to purify $\mathrm{Na}\mathrm{I}$. In particular, $\mathrm{K}$ and $\mathrm{Rb}$—two elements with radioisotopes that can cause scintillation backgrounds—can be efficiently removed by zone refining. However, zone refining has never been demonstrated for ultrahigh-purity $\mathrm{Na}\mathrm{I}$, which has become commercially available recently. In this paper, we show that many common metallic impurities can be efficiently removed via zone refining. A numerical model for predicting the final impurity distribution is developed and used to fit the inductively coupled plasma mass spectrometry (ICPMS) measurement data to determine the segregation coefficient and the initial concentration. Under this scheme, the segregation coefficient for $\mathrm{K}$ is estimated to be $0.57$, indicating that zone refining is still effective in removing $\mathrm{K}$ from ultrahigh-purity $\mathrm{Na}\mathrm{I}$. As zone refining tends to move the impurities to one end, elements with concentrations too low to be measured directly in the unprocessed powder can potentially be detected in the end due to the enrichment. We also present an analysis technique to estimate the initial concentrations of impurities with partial data, which effectively enhances the sensitivity of the spectrometer. Using this technique, the initial concentration of ${}^{85}\mathrm{Rb}$ is estimated to be between 5 parts per trillion (ppt) and 14 ppt at the 90% confidence level (CL), at least 14 times lower than the detection limit of ICPMS and 7 times lower than the current most stringent limit set by the DAMA collaboration by direct counting of radioactive ${}^{87}\mathrm{Rb}$. These results imply that zone refining is a key technique in developing next-generation $\mathrm{Na}\mathrm{I}$-based crystal scintillators for dark-matter direct detection.

Figure 1

The $\mathrm{Na}\mathrm{I}$ powder is melted under a ${\mathrm{Si}\mathrm{Cl}}_4$ atmosphere prior to zone refining. The plug on the right is used to introduce ${\mathrm{Si}\mathrm{Cl}}_4$ vapor through the vent hole on the topside while preventing the back flow of the molten $\mathrm{Na}\mathrm{I}$. The plug on the left is used to hermetically seal the crucible once the powder has been treated with ${\mathrm{Si}\mathrm{Cl}}_4$.

Figure 2

Zone refining in progress at the Mellen Company with three zones. The crucible is placed inside a fused-silica preheater tube maintained at $300{}^{\circ }\mathrm{C}$ by a resistive wire wound around the preheater tube.

Figure 3

The ingot is divided into $N$ cells with equal width. Solid blue cells represent solidified sections of the ingot and the dashed red cells represent the molten-liquid zone. Two arrays, $A_j$ and $C_j$, are used to denote the cross-section area and the solute concentration of the $j\mathrm{th}$ cell. When the left boundary of the zone travels from $i$ to $i+1$, cell $i$ solidifies and its solute concentration is given by $k$ times the solute concentration of the molten-liquid zone [Eq. (1)]. As the right boundary advances to ($i+w$)th cell, the solute concentration and total volume of the molten zone are updated based on the volume and the amount of solutes in the newly melted cell [Eqs. (2) and (3)]. To simulate the entire zone-refining process, the molten zone is swept across the entire ingot incrementally and the appropriate boundary relation is applied at each step.

Figure 4

The numerically calculated solute distributions after 1, 5, 10, and 25 zone passes. The segregation coefficient is assumed to be $0.5$ and the zone width 10% of the ingot length. The initial average solute concentration is normalized to 1. As zone refining progresses, more and more impurities are pushed to the end of the ingot.

Figure 5

The distribution of the concentration of ${}^{39}\mathrm{K}$ as a function of the position. The position is measured from the beginning of the ingot where zone refining starts. The geometrical center of each sample is taken as the $x$ coordinate of the data point and the size of the sample as the $x$ error. The solid curve represents the best fit to the data.

Figure 6

The ${}^{39}\mathrm{K}{\chi }^2$ map obtained by grid search in $k$-$C_0$ space. The ${\chi }^2$ map is characterized by a well-defined global minimum, since the ${}^{39}\mathrm{K}$ concentration is above the spectrometer detection limit at three different locations, allowing for simultaneous determination of $k$ and $C_0$. The three contour lines correspond to 1-$\sigma$, 90% CL, and 99% CL.

Figure 7

The pointwise comparison of ${}^{85}\mathrm{Rb}$ data leads to overestimation of $C_0$. ${}^{85}\mathrm{Rb}$ is detected only in the last sample at the end of the ingot after 53 zone passes. Since the concentration varies rapidly near the end, the true concentration-weighed center differs significantly from the geometrical middle of the sample. When the middle of the last sample is used as the $x$ coordinate in a pointwise ${\chi }^2$ computation, the distribution that matches exactly at the last data point is favored. Since the first four data points are all upper limits, $k$ can take an arbitrarily small value at the cost of increased $C_0$, thereby leading to overestimation of $C_0$ (dashed blue line). To treat this case properly, ${\chi }^2$ should be computed using the average of the model distribution (solid orange line).

Figure 8

The ${\chi }^2$ map for ${}^{85}\mathrm{Rb}$ is characterized by a band and a series of local minima, since there is only one sample with a concentration above the detection threshold. If there is one more such data point, $k$ will be constrained from below by the inefficiency of the zone refining and the ${\chi }^2$ map will resemble Fig. 6. The three contour lines correspond to 1-$\sigma$, 90% CL, and 99% CL.

Figure 9

The impurity reduction as a function of the fraction of material kept after zone refining after 10, 25, and 50 zone passes. The zone width is assumed to be 6% of the length of the ingot and the segregation coefficient is set to be 0.57.