Bulk Etch Rate and the Activation Energy of the CR-39 Detector using Thickness Difference Method 1

The aim of this paper is to determine the bulk etch rate Vb of the nuclear track detector CR-39 using the method based on measuring the thickness of the layer removed from the surface of the detector (the thickness difference) by the chemical etching, and then studying how to change it with the temperature of the etching solution to extract an empirical relationship between them. The detector samples were etched in a 6 N of NaOH solution at temperatures 80, 70, 60 and 501 o C, and the thickness of the removed layer was determined by successive measuring the detector thickness for etching times of 1-9 h increasing with 1 h intervals. The results showed that the values of Vb range between 2.351-0.605 μm/h for etching temperature 50-80 o C respectively. An exponential relationship was obtained between the bulk etch rate and the etching temperature. It was noted that the results were consistent with that obtained by other studies using the track Length-diameter(Le-D) measurement method. The slight difference in Vb magnitudes between the compared results is due to the slight difference in the concentration of the etching solution in certain cases as well as the difference of the detector origin and the method of measurement.


Introduction
The bulk etch rate V b is one of the basic parameters for studying the track geometry in the SSSNTDs. Due to the significance of V b in controlling the development of the etched track as it is linked to the etch rate ratio V(=V t /V b ), its precise estimation is viewed as an important and decisive issue in studying the track shape and its profile development with the progress of the etching process.
The bulk etch rate is defined as the measure of the material removed from the undamaged areas of the detector surface in the horizontal direction during the etching process. The Various, direct and indirect, methods have been employed for the determination of the bulk etch rate of SSNTD either by irradiating or non-irradiating the detector with the charged particles. One of the methods based on the mass difference of the detector before and after the etching process. This method is known as the gravimetric method [4, 11] and it is restricted to measurement accuracy of no less than the order of 10 -5 . Another method, which is used in this paper, relied on measuring the thickness of the detector before and after etching, and then the thickness difference [12,13]. The most commonly used method is measuring the track diameters of the fission fragments, particularly that from 252 Cf source [2,12]. Recently the L e -D method is used to find V b for the detector CR-39 [13, 14,15]. This method depended on the direct measurement of the track lengths and diameters from the images of the etched track.
The precision of the results is limited by the measurements in the sharp conical phase of the track development [10, 13, 15].
Further methods have been used to determine V b in different SSNTDs. For example, the "masking" method in CR-39 using the atomic force microscope (AFM) [16,17,18], and the "peel-off" method to directly measure the bulk etch rate for the LR115 detector in the light of the investigation of the surface profilometry. A non-destructive method is also used to determine V b relied on measuring the thickness of the removed layer using energy dispersive X-Ray fluorescence (EDXRF) [19], or measuring the thickness of the active layer removed from the LR115 detector using a Fourier Transform Infrared (FTIR) spectroscopy [20].
The aim of the paper is to find the bulk etch rate (V b ) and the activation energy of the bulk etching of the nuclear track detector CR-39 for different etching temperatures and to find an empirical equation for the variation of the V b with the temperature of the etching solution.

Methodology
The TASTRAK plastic CR-39 detector used in the present study was purchased from Track Analysis Systems Ltd (TASL)(Pristol.UK). The original thickness of the detector sheet was 500 m. The CR-39 detector was cut to a size of about 1.5 × 1.5 cm 2 and its thickness It should be noted that the detector was etched from the two sides (i.e. the upper and lower surfaces), and the thickness of the detector before and after etching was measured directly from the images of the detector edges which transferred to the PC by a digital camera (MDCE-5C) installed on the optical microscope (Novel).  and this was in good agreement with that found by [15,21].  Table 1 .      (2) and (3) or other forms [15] in which the activation energy does not clearly appear.

Results and Discussion
So, the activation energy of the detector cannot be calculated according to Eq. (6) in such a case, and if it is calculated, its value will not be accurate.
In light of this discussion, the exponential form of V b given by Eq. (6) which involves the activation energy may not be applied on the TASTRAK PADC plastic CR-39 detector used in the present study, and in contrast the exponential formula in Eq. (2) which have no activation energy term can be used for this detector.
The exponential change pattern of the bulk etch rate with the etching temperature is consistent with the results recorded by [4,15] However, these results seem in good agreement with that found in the present study.

Conclusion
One of the positive aspects of the thickness difference method is that it provides high accuracy results, and it does not need to irradiate the detector with particles and to measure the track diameters and lengths. The effect of the etching temperature is significantly shown on the thickness of the detector and the Bulk etch rate. It was found that increasing the etching temperature by 10 o C leads to an increase of 50-60% in V b . Increasing the temperature of the etching solution leads to a linear increase of the thickness of the layer removed from the surface of the detector and it enhances the bulk etch rate of the detector, which increases exponentially with the temperature according to the exponential formula