7 Application of CR-39 Solid State Nuclear Track Detectors …
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7.2.3 Determination of the Range of an Ion in an SSNTD
The range of an ion can be determined by the growth behaviour in the spherical phase
of the etch pit, so-called rounded out, in which the etching exceeds the range of an
ion. Figure 7.5 shows the etch pit profiles in the conical and spherical phases, i.e.,
before and after being rounded out, with dashed and solid lines, respectively. The
depth of the etch pit l never changes before and after being rounded out. The lengths
of the triangle ABC are described as follows:
AB = G − R 0 ,
(7.15)
BC = r,
(7.16)
C A = G − (R 0 − l)
(7.17)
Applying the Pythagorean theorem to the triangle ABC, r
2 and R 0 can be derived as
follows:
r
2
= 2lG − 2R 0 l + l
2
,
(7.18)
R 0 = G +
1
4
dr
2
dG
−
r
2
dr 2
dG
(7.19)
From (7.18), therefore, the growth curve of the squared radius in the spherical phase
is linear. The range R 0 can be determined from the slope of the linear function, i.e.,
dr
2
/dG = 2l, using (7.19).
Fig. 7.5 Schematic
cross-sectional view of the
etch pit profiles in the
conical and spherical phases.
The dotted line shows the
original surface. The dashed
and solid lines show the
conical and spherical etch pit
profiles, respectively