Architecture of RER reference device (RERRD)

Ambient air pressure influences radon migration, and the pressure gradient causes seepage [18]. Thus, dense and low-permeability double-layer plate materials were used as the diffusion media for the reference device, and an air pressure balance device was designed to reduce the influence of ambient air pressure.

As shown in Fig. 1, the RERRD comprises five parts. A 0.6 L cylindrical solid radon source chamber was located at the bottom of the RERRD. A solid radon source with a high emissivity coefficient, manufactured by the University of South China, was sealed inside a solid radon source chamber. This solid radon source had an emanation coefficient of 96±2% under an ambient temperature of 10–45°C and relative humidity of 40%–90%[19-21]. The upper part of the solid radon source chamber was connected to an inverted radon accumulation chamber with a volume of 57.9 L. A pressure balance device containing a 95% saltwater mixture was installed at the bottom right of the radon accumulation chamber. For maintaining constant pressure inside and outside the RERRD, a U-shaped transparent organic glass tube connected the radon accumulation chamber to the ambient environment. The shifting effects of the radon accumulation chamber and external pressure during the migration process were due to the setting of the blue line on the surface of the glass tube. The diffusion of radon through the liquid into the environment was successfully stopped using a highly concentrated saltwater mixture. The high-humidity environment created at the mouth of the gas cylinder maintained a certain level of saltwater mixture concentration in the U-shaped tube, which reduced the diffusivity of radon through the water body. The upper part of the radon accumulation chamber was designed with two crossbar support frames that could bear a load of approximately 300 kg. Diffusion media were placed on the upper part of the support frames. The high-density wooden board (thickness = 30 mm) and plasterboard (thickness = 60 mm) comprised cylindrical diffusion media with an inner diameter of 800 mm and an effective exhalation area of 0.5024 m². A stainless steel sheet was stamped and welded into one piece to form the shell of the device, with a total height of 0.6 m and a surface smoothness of less than 2 mm. The manufacturing company tested the airtightness of the device during factory delivery, and the device passed the test with satisfactory airtightness.

Fig. 1Full-screen View

Schematic of the RERRD

The radon accumulation chamber was formed as an inverted cone, and the diffusion media (plasterboard and high-density wooden board) were shaped into cylinders to guarantee a one-dimensional upward direction of radon diffusion. The plasterboard, created by an artificial combination of solidification and drying, had well-developed, unevenly distributed internal pores [22]. The high-density wooden board was fabricated using the high pressure of machines, and small and regular interior pores were formed. There is a crucial small pore between the plasterboard and the high-density wooden board. After the radon diffused through the plasterboard, it was evenly distributed in the pores. The radon evenly distributed in the pores diffuses to the surface through the high-density wooden board and finally forms a uniform RER. The plasterboard and high-density wooden board were combined at a specific thickness to ensure the stability and uniformity of the RER on the media surface. Surface moisture has a significant impact on the uniformity of the RERRD. The emulsion paint exhibited excellent waterproofing ability. The high-density wooden board coated with the paint emulsion was essentially moisture-free. The radon in the accumulation chamber was highly concentrated, and a concentration gradient existed between the upper and lower surfaces of the diffusion medium. Therefore, the radon exchange in the media occurs via active diffusion.

Principle of radon diffusion in a two-layered media

Radon exists as a single-atom gas at normal environmental temperatures, and its migration occurs via atomic thermal motion and convection. Because of the porous nature of the media, radon atoms can move freely through the connecting pores inside the media and diffuse out of the surface. The diffusion motion of radon in porous media obeys Fick's first law [23] is as follows: $J=-D\cdot \nabla C,$ (1) where J is the RER on the surface of the RERRD (Bq·m^-2·s^-1), D is the radon diffusion coefficient in the media (cm²·s^-1), and ∇C is the radon concentration gradient in the media.

The second-order differential Eq. [24] for the diffusion and migration of radon through the medium is expressed by Eq. (2). $\frac{\partial C\left(x,t\right)}{\partial t}=D\frac{{\partial }^{2}C\left(x,t\right)}{\partial x^2}-\lambda C\left(x,t\right),$ (2) where x denotes the coordinate of the axis normal to the surface of the medium (m).

The radon diffusion coefficient expresses the degree of radon diffusion in a medium. The relationship between the RER of the medium and the diffusion coefficient [25] is expressed by Eq. (3). $J=-D\frac{\partial C}{\partial x}.$ (3)

When there is no pressure gradient in the surrounding space, the radon transport within the double-layer media is purely diffusion transport. Based on radon diffusion theories, when the radon concentration reaches a stable equilibrium state in space, the differential equation for radon diffusion in double-layer media is $｛\begin{array}{c}{D}_1\frac{{\text{d}}^2{C}_1}{\text{d}{x}^2}-\lambda C_1=0\\ D_2\frac{{\text{d}}^2{C}_2}{\text{d}{x}^2}-\lambda C_2=0\end{array},$ (4) where C₁ is the radon concentration in the plasterboard (Bq·m^-3), C₂ is the radon concentration in the high-density wooden board (Bq·m^-3), D₁ is the radon diffusion coefficient of the plasterboard (cm²·s^-1), D₂ is the radon diffusion coefficient of the high-density wooden board (cm²·s^-1), and λ is the radon decay constant (s^-1).

The ratio (k) between the RER on the lower surface of the plasterboard and that on the upper surface of the high-density wooden board was obtained as follows: $k=\frac{J_1}{J_2},$ (5) where $J_1$ is the RER on the lower surface of the RERRD plasterboard, and $J_2$ is the RER on the upper surface of the high-density wooden board.

Methods for measuring RER

2.3.1

Instruments selection

Various instruments were used in the experiments. The radon monitor used was an FYCDY-P30 produced by Hubei Fangyuan Environmental Protection Technology Co., Ltd. The constant air pump was manufactured by Schauenburg Technology. The radon collection hood, an integrated and forged cylindrical stainless steel plate, had a steel plate thickness of 2 mm, an inner diameter of 280 mm, a capacity of 5.85 L, and a bottom area of 0.06 m² (Fig. 2). The activated carbon boxes, made by the Beijing Institute of Metrology, were flat aluminum cylindrical boxes containing 80 g activated carbon. The thickness of the carbon layer was 2.5 cm and was covered with a metal screen and sealing cap. The sampling area of the activated carbon boxes was 3.848×10^-3m². The high-purity germanium gamma spectrometer was manufactured by the company ORTEC.

Fig. 2Full-screen View

Schematic of connection using open-loop method

2.3.3

Activated carbon-γ spectrum method for measuring the RER

The activated carbon-γ spectrum method [27] was used to measure the RER from the surface of the reference device. The activated carbon boxes were placed upside down on the surface of the exhalation medium to collect the radon exhaled by the RERRD during sampling. A high-purity germanium gamma spectrometer was used to measure the intensities of the characteristic peaks of the radon daughters in the activated carbon. Finally, the activated carbon-γ spectrum method was used to obtain the RER. The selected coconut shell-activated carbon had significant radon adsorption properties. Therefore, the impact of leakage and counter-diffusion was minimal [28].

First, the activated carbon boxes were sealed immediately after sampling. In this case, the short-lived daughters of radon (²¹⁴Pb and ²¹⁴Bi) reached radioactive equilibrium with ²²²Rn [29]. This study used a high-purity germanium gamma spectrometer to measure the full energy peak area of the distinctive rays of the radon daughters; subsequently, the RER was calculated [10]. The 609 keV γ-rays from the decay of ²¹⁴Bi exhibited the highest branching ratio, the best energy peak shape, and least interference from other nuclides; thus, 609 keV γ-rays are generally used for experimental measurements [30].

To compare the results of multiple measurements, we selected a fixed area to measure the RER on the RERRD surface. Nineteen activated carbon boxes were evenly arranged in concentric circles on the surface of the exhalation media. Furthermore, these activated carbon boxes were used for measurements and distributed uniformly over the surface of the exhaled media. A schematic of the points on the activated carbon boxes is shown in Fig. 3. The activated carbon boxes were dried at 120 °C for 8 h before the experiment. The background counting rate of the activated carbon boxes was measured after cooling, and the boxes were inverted equally on the surface of the exhaling media. The borders of the activated carbon boxes were sealed with plastic and stored for 24 h. The high-purity germanium gamma spectrometer was used to measure the net count rate after 3 h. The RERs were measured three consecutive times and calculated using Eq. (9). $J=\frac{\left(n_{\text{r}}-n_{\text{b}}\right)\lambda \cdot e^{\lambda T}}{K\cdot S\left(1-e^{-\lambda \cdot T_{\text{s}}}\right)}$ (9) where J is the RER on the surface of the media to be measured (Bq·m^-2·s^-1), K is the scale factor of the high-purity germanium gamma spectrometer for 609 keV energy gamma rays (the scale factor was applied to the standard source scale before use) (0.007 cps∙Bq^-1), n_r is the full energy peak area (net count rates) of the characteristic 609 keV gamma rays (cps), n_b is the background counting rate of the activated carbon before the sampling rate (cps), S is the bottom area of the activated carbon boxes (m²), T_s is the sampling time (h), λ is the decay constant of radon (s^-1), and T is the time interval between stopping sampling of the activated carbon boxes and the start of the high-purity germanium gamma spectrometer measurement (h).

Fig. 3Full-screen View

Schematic of the points of activated carbon boxes

The uncertainty of the gamma spectrometry of the activated carbon-γ spectrum method mainly originates from the detection efficiency of the high-purity germanium gamma spectrometer and the uncertainty in the production process of the standard source. The high-purity germanium gamma spectrometer was calibrated using a 230 Bq standard source before use. The relative uncertainty of the spectrometer was approximately 5%, and the uncertainty in the production process of the standard source was approximately 3%. Because of the uncertainty of the experiment, the overall uncertainty of this method can be controlled within 10% [10].

Methods for measuring the media radon diffusion coefficient

A miniaturized reference device was used to measure the radon diffusion coefficient of the medium (Fig. 4). The type of diffusion medium could be changed arbitrarily. The volume of the radon accumulation chamber was V₁ (m³); the radon concentration in the radon accumulation chamber was C₁ (Bq·m^-3); and the change in radon concentration exhaled from the media was measured continuously using the open-loop method. The volume of the radon collection hood was denoted as V₂ (m³)_; the radon concentration in the radon collection hood was denoted as C₂ (Bq·m^-3); the bottom area of the radon collection hood was denoted as S (m²); and the thickness of the media was denoted as H (m).

Fig. 4Full-screen View

Schematic of miniaturized reference device

Then, $\frac{C_2}{C_1}=\frac{S\cdot D}{\lambda \cdot H\cdot V_1}\left[1+2{\displaystyle \sum _{n=1}^{\infty }{\left(-1\right)}^n}\times \frac{1}{1+\frac{n^2{\pi }^{2}D}{\lambda \cdot H^2}}\right],$ (10)

When D/H² is sufficiently large, Equation (10) can be simplified to $D=\frac{\lambda \cdot H\cdot V_1\cdot C_2}{S\cdot C_1}.$ (11)

The radon diffusion coefficients of the plasterboard and high-density wooden board can be calculated using Eq. (11).

Method for rapidly establishing equilibrium radon concentration in radon accumulation chamber

Radon in the accumulation chamber was generated from solid radon sources, which required an excessively long time to reach equilibrium. As shown in Fig. 1, to rapidly establish the equilibrium radon concentration in the radon accumulation chamber, a method was adopted wherein the radon accumulation chamber was filled with a flowing gas–solid radon source in the initial state. The flowing gas–solid radon source must be emptied before use. The radon accumulation chamber was filled using an air pump after accumulation for a certain period. The variation in the radon concentration in the accumulation chamber is expressed by Eq. (12). $\frac{\text{d}C}{\text{d}t}=\frac{\lambda \cdot \eta \cdot A_0}{V}-\frac{J_1\cdot S}{V}-\lambda \cdot C,$ (12) where A₀ is the activity of the flowing gas solid radon source (Bq), V is the volume of the radon accumulation chamber (m³), C is the radon concentration in the radon accumulation chamber (Bq·m^-3), J₁ is the RER on the lower surface of the plasterboard (Bq·m^-2·s¹), S is the effective exhalation area (m²), η is the solid radon source jet coefficient, and λ is the radon decay constant (s^-1).

When the radon concentration reaches the equilibrium state, the left side of Eq. (12) is equal to zero; thus, the initial radon concentration, denoted C_e, is obtained.

As J₁ = k ∙ J₂. Equation (12) is reduced to $C_e=\frac{1}{V}\left(\eta \cdot A_0-\frac{k\cdot J_2\cdot S}{\lambda }\right).$ (13)

According to Equation (13), when the activity of the solid radon source and the RER on the surface of the media are known, the initial radon concentration in the radon accumulation chamber can be obtained. The time required to attain equilibrium was reduced by the rapid filling of the radon accumulation chamber with a flowing gas solid radon source. Increasing the speed of the formation of a stable RER on the RERRD is feasible.

Methods for measuring uniformity and stability of RERRD

Relationship between RERs on upper and lower surfaces of diffusion component

The diffusion coefficient of radon indicates its ability to migrate in media. After the radon concentrations in the radon accumulation chamber and the radon collection hood reached a dynamic equilibrium state, the diffusion coefficients of the media were calculated using Eq. (11). The radon diffusion coefficients of the plasterboard and high-density wooden board displayed in Table 1 are closely related to the RER on the upper and lower surfaces of the diffusion component.

As the diffusion coefficient decreased, the ability of radon to migrate in the medium weakened. As shown in Table 1, the diffusion ability of radon on the plasterboard was lower than that on the high-density wooden board. Therefore, a high-density wooden board was placed atop the plasterboard in the double-diffusion media in the design of the RERRD.

On the basis of the data in Table 1, the radon diffusion coefficient of the plasterboard was denoted as D₁ (2.94×10^–9m² s^–1), the radon diffusion coefficient of the high-density wooden board was denoted as D₂ (1.42×10^–8 m² s^–1), the thickness of the plasterboard was denoted as h₁ (0.06 m), the thickness of the high-density wooden board was denoted as h₂ (0.03 m). We analyzed k. By substituting D₁, D₂, h_1, and h₂ into Eq. (18), we obtained $k=\frac{1}{14\frac{C_{h_1+h_2}}{C_{h_1}}+1}.$ (18)

The radon concentration exhaled from the RERRD on the surface of the high-density wooden board is much lower than that in the radon accumulation chamber, namely, C_h1+h2 / C_h1 ≈ 0; therefore, k ≈ 1 and J₁ ≈ J₂. The radon in the radon accumulation chamber was exhaled into the environment through the plasterboard and high-density wooden board. The RERs from the lower surface of the plasterboard and the upper surface of the high-density wooden board were approximately equal. In this case, a solid radon source with different activities and RER can be rapidly obtained based on the initial radon concentration in the radon accumulation chamber by using Eq. (11). The time required for the RERRD to reach equilibrium can be reduced considerably from 28 d to approximately 2 d, which fulfills the requirements of experimental measurements rapidly.

Uniformity measurement result of the RER of the RERRD

The uniformity of the RER at any point on the surface of the diffusion medium is a crucial index for measuring the uniformity of the RERRD. The radon accumulation chamber of the RERRD was filled with two different solid radon sources with activities of 1.0×10⁵ and 2.0×10⁵ Bq. The RER of the RERRD was measured thrice using the activated carbon-γ spectrum method. The measurement results are presented in Fig. 5.

Fig. 5Full-screen View

(a) Uniformity of RER after placing a 1.0×10⁵ Bq solid radon source; (b) uniformity of RER after placing a 2.0×10⁵ Bq solid radon source.

The mean RERs at the 19 points were 197.78±2.32 and 399.26±5.99 mBq·m^-2·s^-1, and their relative standard deviations were 1.17% and 1.50%, respectively. The different points exhibited a uniformity of greater than 5%. The RERs measured at the points of the inner circle (2–7) swung up and down below the average. However, the RERs measured at points outside the circle (8–19) were higher than the average. The low efficiency of the high-purity germanium gamma spectrometer and the statistical errors in the measurement cannot be ignored. Another factor to consider is the latex paint sprayed on the surface of the high-density wooden board to eliminate the effects of moisture. Manual spraying could not ensure consistency in the thickness of the latex paint layer at each spot. The points with a thin latex paint layer had higher RERs than the other points did.

Short-term stability measurement results of the RER of the RERRD

The short-term stability of the RER characterizes whether it is affected by changes in ambient air pressure, environmental temperature, relative humidity, and other conditions. The two solid radon sources with activities of 1.0×10⁵ and 2.0×10⁵ Bq, respectively, were placed in the radon accumulation chamber. The radon collection hood was sampled and measured in the middle of the medium surface by using the open-loop method. The effects of the ambient pressure, environmental temperature, and relative humidity on the RER were studied.

3.3.1

Stability of the RER of the RERRD under various ambient air pressure

The temperature inside the room was controlled via air conditioning and maintained at 20 °C. The dehumidifier stabilized the relative humidity of the room at 40%. The hourly ambient air pressure and the RER were measured thrice using the open-loop method. The daily variation curves of ambient air pressure and the RER are shown in Fig. 6.

Fig. 6Full-screen View

Variation in ambient air pressure and RER with time. (a) Daily variation curves of ambient air pressure and RER after placing a solid radon source with an activity of 1.0×10⁵ Bq; (b) Daily variation curves of ambient air pressure and RER when placing a solid radon source with an activity of 2.0×10⁵ Bq.

The ambient air pressure changed daily, with high values between 9 and 11 am and low values between 3 and 5 am [31]. By contrast, the RERs resulting from the solid radon sources of 1.0×10⁵ and 2.0×10⁵ Bq on the surface of the media of the RERRD varied little within 1 d, with daily relative standard deviations of 2.54% and 3.65%, respectively. Therefore, the short-term stability of the RERRD was greater than 4%. The pressure balance device of the RERRD can reduce the effects of ambient air pressure on radon migration. Internal changes in the pressure in the radon accumulation chamber were maintained at all times. We calculated the correlation coefficient between the ambient air pressure and the radon exhalation rate and found that the correlation between these two factors was weak (Fig. 6 (a):0.42; Fig. 6 (b):0.35). The results revealed that the ambient air pressure had almost no effect on the RER of the RERRD.

3.3.2

Stability of the RER of the RERRD under various environmental temperatures

The environmental relative humidity was stabilized at 40% with a dehumidifier while imposing different environmental temperatures via air conditioning. As shown in Fig. 6, the influence of ambient air pressure on the RER, although nonsignificant, should be eliminated as much as possible. The open-loop method was used to conduct the experiment from 9:00 to 11:00 am daily. The relationship between the environmental temperature and the RER of the RERRD was measured thrice using the open-loop method (Fig. 7).

Fig. 7Full-screen View

Variation in RER with environmental temperature. (a) Relationship between RER and environmental temperature after placing a solid radon source with an activity of 1.0×10⁵ Bq; (b) Relationship between RER and environmental temperature after placing a solid radon source with an activity of 2.0×10⁵ Bq.

Figure 7 shows the relationship between the RER and environmental temperature at a relative humidity of 40% and essentially unchanged ambient air pressure. Because the adjustable range of the air conditioning is 16–30 ℃, the temperature was set to 16, 20, 25, and 30 °C, respectively; for a solid radon source with an activity of 1.0×10⁵ Bq, the short-term stabilities were 1.02%, 0.76%, 1.52%, and 2.08%, respectively; by placing a solid radon source with an activity of 2.0×10⁵ Bq, the short-term stability was 2.56%, 1.90%, 2.49%, and 4.14%, respectively. The short-term stability of the RERRD was within 5%. The environmental temperature had little effect on the RER of the RERRD.

3.3.3

Stability of the RER of the RERRD under various environmental relative humidity

First, the indoor air conditioning stabilized the temperature at 20 °C. Subsequently, a cloudy and rainy day (with high relative humidity in the environmental air) was selected. The relative humidity of the indoor air was controlled using a dehumidifier. To consider the influence of ambient air pressure, we used the open-loop method to conduct the experiment from 9:00 to 11:00 am. The effect of the environmental relative humidity on the RER of the RERRD is presented in Fig. 8.

Fig. 8Full-screen View

(a) Relationship between RER and environmental relative humidity after placing a solid radon source with an activity of 1.0×10⁵ Bq; (b) Relationship between RER and environmental relative humidity after placing a solid radon source with an activity of 2.0×10⁵ Bq.

The environmental temperature was 20 °C, and the ambient air pressure was essentially unchanged. The relationship between the RER and environmental relative humidity is shown in Fig. 8. When placing a solid radon source with an activity of 1.0×10⁵ Bq, the relative humidity was set to 40%, 50%, 60%, 70%, 80%, and 90%; the short-term stabilities were 1.97%, 1.78%, 2.54%, 2.40%, 2.37%, and 2.59%, respectively; for a solid radon source with an activity of 2.0×10⁵ Bq, the short-term stabilities were 2.70%, 2.27%, 1.48% 1.61%, 3.29% and 3.10%, respectively. The relative standard deviation and short-term stability of the RER of the RERRD were within 4% at T = 20 °C. The environmental relative humidity had little effect on the RER measurement, and it had almost no effect on subsequent measurements using the RERRD.

Relationship between activities of diffusion solid radon sources and the RER of the RERRD

The studied RERRD can create different levels of uniform and stable RERs on the surface of the media by changing the activities of the solid radon sources. The existing activities of the solid radon sources in the Radon Laboratory of the University of South China were 3.0×10³, 8.5×10³, 1.7×10⁴, 1.0×10⁵, and 2.0×10⁵ Bq. They were placed separately in the accumulation chamber of the RERRD, and the RER was rapidly brought to a steady state by filling the accumulation chamber with a predetermined amount of radon. The activated carbon-γ spectrum method was used to measure the RER by placing solid radon sources with different activities at the midpoint of the medium. The results are shown in Fig. 9.

Fig. 9Full-screen View

Relationship between RERs and activities of solid radon sources

As shown in Fig. 9, a linear fitting equation between the RERs of the RERRD and the activities of the solid radon sources was obtained by linear fitting of the data as follows: $J=0.002A_0-\mathrm{5.854.}$ (19)

Because the minimum activity of the solid radon source used in our experiment was 3000 Bq, Equation (19) is valid when A₀ ≥ 3000.

R² was 0.99. If the activity of a radon source placed in the RERRD is known, the RER of the RERRD can be rapidly obtained using Eq.(19). This finding provides a reference activity for a solid radon source for high RER levels and improves the experimental efficiency.