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346) Information for users of CR-39

Ludwik Kowalski
Montclair State University, Montclair, NJ, 07055
April 6, 2008


0) Chemical composition and some proprties of CR-39 are shown at:
http://tinyurl.com/yp6ld5
Last page shows that density is 1.31, refractive index is 1.498, and that 89-91% of light is transmitted.

1) CR39 detectors are likely to play an important role in CMNS research. With this in mind, all researchers should use the same etching conditions, and the same calibration curves. Otherwise it would be difficult to directly compare our experimental results. A calibration curve is a relation between the track diameter and the particle energy (for perpendicular exposures and for a chosen etching protocol). Calibrations experiments were performed by Russian scientists: Andrei Lipson, Alexei Rusetski and Eugeny Saunin, as reported at the 8th International Workshop on Anomalies in Hydrogen/Deuterium Loaded Metals (Catania, October 13-18, 2007).

Their standard etching times (in 6N NaOH at 70 C) are 7hrs, 14 hrs, 21 hrs and 28 hrs. The layers of the CR-39, etched away during these times, can be calculated from the known bulk etching rate of 1.32 microns per hour. Thus etching for 28 hours will make the CR-39 chip about 2*37=74 microns thinner. Note that the range of a 5 MeV alpha particle in CR-39 is approximately 30 microns. Longer etching can be used to reveal tracks due to alpha particles produced inside the CR-39 material.

2) The experimental data for the calibration curves are available for protons between 1 and 2.5 MeV, and for alpha particles between 5 MeV and 13 MeV. What follows are equations which fit experimental data points. Note that x is the energy in MeV while y is the corresponding diameter in microns. Also note that diameters might depend on some difficult-to-control parameters, such as additives added during manufacturing, time of storage, conditions of storage (air versus vacuum), etc. etc. For that reason, relative diameters might be more informative than absolute diameters.

Alpha Particles (5 to 13 MeV)
Etching for 7 hours: y=12.364*x-0.2169
Etching for 14 hours: y=30.556*x-0.3733
Etching for 18 hours: y=81.763*x-0.6785
Etching for 21 hours: y=145.04*x-0.8321

Protons (1 to 2.5 MeV)
Etching for 7 hours: y=7.1395*x-0.3363
Etching for 14 hours: y=9.6093*x-0.5057
Etching for 18 hours: y=12.354*x-0.6143
Etching for 21 hours: y=15.611*x-0.7608

The plots of these eight functions, together with actual data points, can be seen at

http://www.iscmns.org/catania07/RussetskiAanalysisof.pdf

3) It is well known that most alpha-radioactive substances emit particles with energies between about 5 MeV and 8 MeV. For these particles, the diameters, after 7 hrs of etching (in 6 N NaOH at 70 C), should be between about 8.7 and 7.9 microns, for nearly perpendicular incidences. For oblique incidences, tracks are expected to be more or less elliptical and the y would refer to the width of an elongated track. A track whose diameter, or width, is significantly smaller than 7.9 microns could not be attributed to an alpha particle from a natural contaminant. But it can be due to a triton, or to a neutron colliding with a proton. Likewise, a track whose diameter, under the same etching conditions, is larger than 15 microns cannot be attributed to an alpha particle from a natural contaminant. But it can be attributed to a fission fragment, for example, from spontaneous fission of uranium.

4) It is important to keep in mind that these equations should not be used outside the energy ranges specified above. Diameters do not continue to increase with decreasing energies. At some points diameters are known to decrease, rather than to increase, as illustrated in the figure below. That figure, due to Dorschel (1995?), is a calibration curve for alpha particles with data points for energies smaller than 5 MeV. The etching conditions were probably different from those used by Russian scientists. Perhaps the concentration of the NaOH, or etching temperature, or etching time, were higher than those chosen by Lipson et al. I am saiying this because Dorschel’s diameters at 5 MeV and 8 MeV are 13 microns and 11.5 microns, respectively. These values are nearly 50% higher than those calculated from the first equation above. Extrapolations of the equations toward lower energies are likely to result in large systematic errors.


This curve was posted by a researcher on our Internet discussion list. But I also found it (in a slightly different form) in C. Brun, M. Fromm, M. Jouffroy, P. Meyer, J.E. Groetz, F. Abel, A. Chambaudet, B. Dorschel, D. Hersmdorf, R. Bretschneider, K. Kander, and H. Kuhne; “INTERCOMPARATIVE STUDY OF THE DETECTION CHARACTERISTICS OF THE CR-39 SSNTD FOR LIGHT IONS: PRESENT STATUS OF THE BESANCON DRESDEN APPROACHES,” Radiation Measurements, vol 31, (1999), pp 89-99.

5) The next figure shows the range-energy relation for alpha particles in polymers (plotted by me a long time ago) is shown below.




6) To convert ranges from mg/cm2 to microns one must know the density of a particular material. The density of CR-39 is 1.3 g/cm3. That is why the range of 5 MeV alpha particles is close to 30 microns. For a material of density 1.0 the number of microns would be ten times larger than the number of mg/cm 2. That is a good rule of thumb for crude estimates, even when densities are slightly different from unity.

7) Ranges of alpaha particles in air (at 20 C and 1 atm) are shown in the table below.

Here is a table showing how energies depend on distances between the CR-39 and the source of 5.5 MeV alphas, in air at 1 atm and 20 C. This table was constructed on the basis of 1966 data. I am certain that these data are reliable, but I will try to produce a similar table on the basis of more recent data.

Energy (MeV) . . . . . Range(cm)
1.0 . . . . . . . . . . . . . . 0.50
2.0 . . . . . . . . . . . . . . 1.00
3.0 . . . . . . . . . . . . . . 1.68
4.0 . . . . . . . . . . . . . . 2.60
5.0 . . . . . . . . . . . . . . 3.63
6.0 . . . . . . . . . . . . . . 4.78
7.0 . . . . . . . . . . . . . . 6.02
8.0 . . . . . . . . . . . . . . 7.35
9.0 . . . . . . . . . . . . . . 8.77

Suppose an 241Am source (initial energy is 5.5 MeV) is used to calibrate a detector. How does the energy of alpha particles depend on the thickness of air between the source and the detector. The answer is shown in the next table. It was produced on the basis the above data.

distance . . . . . . energy

0.5 cm . . . . . . . 5.0 MeV
1 cm . . . . . . . . . 4.5 MeV
2 cm . . . . . . . . . 3.6 MeV
3.5 cm . . . . . . . 1.3 MeV
3.75 cm . . . . . . 0.8 MeV
3.9 cm . . . . . . . 0.5 MeV

Here are two usedul equations to calculate energy from distance, or vice versa.

E =5.416 - 0.5646 * d - 0.1790 * d^2

d = 4.092 - 0.31705 * E - 0.07847* E^2

Each of them is a reasonable fit for the data in the above table.

Appended on 4/28/08
8) Looking for something else I found an interesting paper. The title is "Variation of alpha-particle track diameters in CR-39 as a function of residual energy and etching   conditions." The authors are A.H. Khayrat and S.D. Durrani. The paper  was published in February 1999 (Radiation Measurements, vol. 30, Issue 1, pages 15-18). Can the track diameter be used for [rough] energy spectrometry [in the energy region between ~1 MeV and ~ 5 MeV]? The authors explore conditions under which this should be possible. They used a source of alpha particles whose initial energies were 5.5 MeV. Energies of particles entering the detector, E, were controlled by the amount of air between the source and the detector. These energies were actually measured by using a calibrated surface barrier detector, connected to a multichannel analyzer. Collimating tubes were used to make sure that angles of incidence were small. In other words alpha particles were entering detectors nearly perpendicularly. The etching solution was 6 M NaOH at 70 C.

9) The bulk etching speed, Vb, in CR-39, was measured by using a 252Cf source of fission fragments. Presumably, it is well known, that for fission fragments the track diameter, D, is directly proportional to the etching time (D=2*Vb*t). In other words Vb was determined by measuring D and t for several tracks. The track etching rate, Vt, was determined by authors by measuring the etch-cone length, Le, after the etching tile t. The used relation was Le=(Vt-Vb)*t . The Le seems to be the depth of the track. But the method for measuring it is not specified. Ranges of alpha particles of different energies in CR39, were calculated using a computer program based on old Henke and Benton’s data. How do ranges plotted in their Figure 2, differ from those I plotted above? The answer is in the following table (numbers read from their Figure 2):

Alpha energy . . . Range in CR-39

5.5 MeV . . . . . . . . 33 microns
4.0 MeV . . . . . . . . 20 microns
2.4 MeV . . . . . . . . 10 microns
1.6 MeV . . . . . . . . 7 microns
0.8 MeV . . . . . . . . 3 microns
0.0 MeV . . . . . . . . 0 microns

10) Figure 3, in their paper, shows how the values of dE/dx (in MeV per g/cm^2) depend on energies of alpha particles.

Alpha energy . . . . . dE/dX

5.5 MeV . . . . . . . . . . 800
4.0 MeV . . . . . . . . . . 1000
2.4 MeV . . . . . . . . . .1400
1.6 MeV . . . . . . . . . . 1780
0.8 MeV . . . . . . . . . . 2000
0.4 MeV . . . . . . . . . . 2200
0.1 MeV . . . . . . . . . . 1900
0.0 MeV . . . . . . . . . . . 0

11) It is convenient to think about dE/dx as an indicator density of ionization, or as degree of damage created by the particle in the CR-39 material. Note that dE/dx reaches a maximum when the particle is nearly stopped. The fact that dE/dx decreases rapidly when particles slow down can easily be explained. At the end of their ranges alpha particles catch two electrons (one after another), and turn into neutral atoms of helium. The dependence of dE/dx on E is after called Bragg’s curve.

Note that If diameters of tracks were proportional to dE/dx, at corresponding energies, then diameters of tracks due to alpha particles of ~ 1 MeV would be two times larger that diameters of tracks due to alpha particles of 5.5 MeV. The authors did measure diameters of alpha particles at different energies and results are shown in their Figure 5. According to that figure, the diameter for 5.5 MeV particles was found to be close to 4.5 microns while diameter of 1 MeV particles was found to be close to 7 microns. For 3 MeV particles diameters are close to 6 microns while diameters below 1 MeV quickly decrease to zero, just like the values of dE/dx. It is important to emphasize that these results were obtained with etching times of 2 hours. The ratios of diameters at longer etching, for example, at 5.5 MeV versus 1 MeV, are usually much smaller, as illustrated by Dorschel’s calibration curve (see my Figure at point 4 above).

12) The main point of this study is to show that it is possible to estimate energies of alpha particles on the basis of track diameters, provided etching times are very short. The slope of their curve in Figure 5 (track diameter versus the energy above 1 MeV) is approximately 0.6 microns par MeV. Suppose a CR-39 chip is exposed to alpha particles of 1.5 and 5.5 MeV. Then diameters of tracks due to low energy particles will exceed diameters of tracks due to high energy particles by 4*0.6 = 2.4 microns. This is measurable, under high magnification. Yes, the energy resolution offered by CR-39 detectors is not as high as that offered by silicon detectors. But ability to distinguish low energy alpha particles whose energies differ by two ot three MeV might be appreciated in applications in which only CR-39 can be used.

13) Why did I not say anything about Figure 4, and text describing it? Because this part is not clear to me, except for they way of etching. Instead of etching for only two hours, the chips were etched for times t=R/Vt, where R is the range of alpha particles. In other words chips exposed to alpha particles of higher energies were etched longer than chips exposed to alpha particles of lower energy. The dependence of diameters on energies of alpha particles is plotted as curve (a) in Figure 4. The rate at which diameters increase with energy is high, about 10 microns per MeV, for E>4 MeV. But how much of the slope is due to longer etching times (at higher energies) and how much (if anything) is due to other factors? The authors are trying to answer this question but I cannot understand them.

Appended on 4/29/08
14) According to my Unit #347, SPAWAR team works under the hypothesis that nuclear tracks, produced during their electrolysis experiments, are due to alpha particles of ~1 MeV. Referring to this I posted the following message on the Internet discussion list for CMNS researchers.

“ Here is an idea based on that paper of Khayrat and Durrani. What would I do to confirm Pam's hypothesis -- that tracks produced during electrolysis are due to alpha particles of about one MeV?

a) First I would try to replicate the experiment of Khayrat and Durrani (using alpha particles of at least three energies: 5.5, 3 and 1 MeV and etching for two hours only). Suppose my results also showed  that tracks due to alpha particles of ~1 MeV   are nearly two times larger than those due 5.5 MeV.

b) In that case I would start testing the hypothesis. First one corner of a CR-39 chip would be irradiated by alpha particles from 241Am. Then I would conduct a codeposition experiment, using that chip,  as described in SPAWAR last paper (*). But instead of etching the chip for 9 hours, I would etch it for 2 hours.

(*) Mosier-Boss, P., Szpak, S., Gordon, F., Forsley, L, "Use of CR-39 in Pd/D Co-deposition Experiments," European Physical Journal, Applied Physics , Vol. 40, p. 293–303, (Dec. 13, 2007)

c) After that I would compare sizes of tracks due to 241Am with sizes of tracks created during electrolysis. Suppose sizes of tracks created during electrolysis were nearly twice as large as those due to 241Am. That would be a confirmation of their hypothesis.

Does this make sense? I am assuming that tracks, attributed to nuclear particles, are nearly always produced in at least one kind of SPAWAR experiment. That seems to be the case, according to their publications.”

15) In subsequent message, on the same forum, I wrote: “Suppose the following question is asked. Why are tracks due to ~ 1MeV alpha particles nearly twice as large as tracks due to 5.5 MeV particles, after 2 hours of etching, while at much longer etching (for example, ~7 hrs) sizes of tracks are nearly the same (according to Dorschel)?

I already tried to answer this question.But here is a simpler answer. It is well known that the degree of damage created by an alpha particle in CR-39, is higher near the end of the latent track. The range of alpha particles of ~ 1 MeV is close to 4 microns while the range of 5.5 MeV particle is close to 30 microns. Two hours of etching is enough to reach the bottom of a latent track of a 1 MeV particle but not enough to reach the bottom of the latent track of a 5.5 MeV particle. The highly damaged region, of the 5.5 latent track, is not etched and that is why the track is not as large as it would be after etching for 6 or 9 hours.

This probably captures the essence of the explanation without addressing many details. I would very much like to know if simulated tracks, after 2 hours virtual etching, agree with experimental data of Khayrat and Durrani.”

18) About etching rates, Vb (often assumed to be 1.2 microns per hour) and Vt
Also from: C. Brun, M. Fromm, M. Jouffroy, P. Meyer, J.E. Groetz, F. Abel, A. Chambaudet, B. Dorschel, D. Hersmdorf, R. Bretschneider, K. Kander, and H. Kuhne; “INTERCOMPARATIVE STUDY OF THE DETECTION CHARACTERISTICS OF THE CR-39 SSNTD FOR LIGHT IONS: PRESENT STATUS OF THE BESANCON DRESDEN APPROACHES,” Radiation Measurements, vol 31, (1999), pp 89-99. According to authors, Vt, the etching rate along the track, can be calculated from the easily measurable Vb, the bulk etching rate (both in microns per hour).

Vt = [1 +0.00155 * (LET-100)] * Vb <----- for 7 M NaOH at 60 C

and

Vt = [1 +0.00267 * (LET-100)] * Vb <----- for 8 M NaOH at 70 C

And what if LET (Linear Energy Transfer) is less than 100? In such cases Vt = Vb. The LET, in these formulas, is in MeV/cm. The coefficients 0.00155 and 0.00267 would have to be changed if LET were expressed different units, such as MeV per micron or MeV per (mg/cm^2). This is obvious because the term between square brackets must be dimensionless, like the Vt / Vb ratio.

LET is a parameter describing ionization density, dE/dx , in a given material. The general rule is that LET increases when the particle energy decreases, except when the kinetic energy becomes smaller than about 1 MeV/amu. For very low energies LET decreases when energies become smaller. In principle, the value of LET, in any given material, and for any given particle, such proton, deuteron, triton or alpha, can be calculated when its kinetic energy is given. The LET for alpha particles of 6 MeV, in CR-39, is said to be 3000 MeV/cm (in the caption of Figure 5, of the above reference). Note that LET=3000 MeV/cm is the same as 3000 / 1300 = 2.31 MeV per (mg/cm^2); 1300 is density of CR-39 is mg/cm^3. LET can also be expressed in terms of number of primary ions per unit length. It is well know, for example, that it takes about 30 eV of energy to create a pair of primary ions in air. Thus 3000 MeV/cm = 300 MeV/mm, implies that 10^7 ions are formed along the path segment of 1 mm. Some references provide LET in terms of MeV*cm^2/mg, instead of MeV/cm.

Approximate LET values can be calculated from the range-energy data. Let me illustrate this by using the already shown data for air, at 20 C.

Energy (MeV) . . . . . Range(cm)
1.0 . . . . . . . . . . . . . . 0.50
2.0 . . . . . . . . . . . . . . 1.00
3.0 . . . . . . . . . . . . . . 1.68
4.0 . . . . . . . . . . . . . . 2.60
5.0 . . . . . . . . . . . . . . 3.63
6.0 . . . . . . . . . . . . . . 4.78
7.0 . . . . . . . . . . . . . . 6.02
8.0 . . . . . . . . . . . . . . 7.35
9.0 . . . . . . . . . . . . . . 8.77

Looking at the last two rows, we see that a layer of air of 8.77-7.35 = 1.42 cm reduces the energy of alpha particles by 9 - 8 = 1 MeV. In other words the average rate at which energy is lost is 1/1.42 = 0.70 MeV/cm. I can assign this value of LET to alpha particles of 8.5 MeV. Likewise, the first two lines allow me to estimate LET of alpha particles of 1.5 MeV. The value is 1/0.5 = 2 MeV. In the same way LET = 1.09 MeV/cm at 3.5 MeV, etc. The LET versus E curve, with 8 data points, can be plotted on the basis of the above table. Note that density of air is about 1.3 mg/cm*3, Thus LET = 2 MeV/cm is the same thing as LET = 1.54 MeV*cm^2/mg. The values of LET for CR-39 can also be estimated (in MeV/micron and then in MeV*cm^2/mg) on the basis of the range-energy data for CR-39 (shown earlier in this unit).

Appended on 5/11/08
a) I found an interesting paper in Review of Scientific Instruments (78, 013304, 2007, pages 1-14). The title is “Study of saturation of CR39 nuclear track detectors at high ion Ŗuence and of associated artifact patterns.” The authors are: by  S. Gaillarda, J. Fuchs, N. Renard-Le Galloudec and T. E. Cowan.

b) Is it possible that our so-called "chopped meat" structures (in SPAWAR type experiments) results from extremely high fluence of nuclear  particles? Below is a brief summary of what is new and interesting to me.

c) A CR-39 chip is exposed to an Am-241 source (activity 4 micro-curies) for 20 seconds, from a distance of 2 mm. Then the chip is etched for 30 minutes only. The source diameter was 4 mm and the track density was found to be essentially gaussian, along the diameter of the irradiated spot . Tracks were tiny and their overlappings were rare. The track density, in the center, turned out to be 0.010 tracks per square micron. Most tracks were confined to a circle whose diameter was about 9 mm, as shown in their Figure 2.

d) The purpose of this preliminary step was to learn how to control fluence (particles/cm^2) in the central region by changing the exposure time. Note that track density of 0.010 per square micron translates into 10^6 tr/cm^2. For ten times shorter exposure the fluence would be 10^5; for ten time longer exposure, it would be 10^7 particles/cm^2.

e) Experiments with a mylar filter were performed to show that CR-39 is not at all sensitive to X-ray photons, or to photoelectrons they produce. This was done by using a mylar filter that was thick enough to stop all alphas but negligibly thin for ~60 keV photons emitted by Am-241).

f) Saturation is defined as a situation in which overlapping of tracks is common, as illustrated in Figure 3c and 3c.’ Saturation can be caused by excessive fluence (particles/cm^2). For short etching times (when the layer of the etched away CR-39 is thinner than the range of particles) saturation starts to play a role when fluence exceeds ~10^6 particles per cm^2. The range, R, for alpha particles of 5.5 MeV, is 30 microns. Thus, assuming Vt=3 microns/hr, one can say that the etching time is short when it does not exceed R/Vt=30/3=10 hrs. I think that the term “saturation” is appropriate for some regions of SPAWAR data. During the 2007 Catania conference, two scientists referred to these regions as “chopped meat.”

g) Figure 5 (pit diameters along the y axis and fluence along the x axis) is presented to show when tracks are saturated and when they are directly countable. Commenting on gray and white regions (on that figure), the authors write: “The valid region, shown in gray [lower left corner], can supply quantitative information (in terms of Ŗuence), since the track diameter is below the track saturation diameter and the particle Ŗuence remains low. In the zone left in white, the detector is saturated, since the tracks are too big and/or the Ŗuence is too high. CR39 cannot be relied upon anymore to extract any quantitative information, but if carefully processed and analyzed, qualitative information (in terms of angular distribution of the ion beam) may still be extracted. Figure 5 is valid for any type of particle, since it represents the track diameter as a function of Ŗuence. . . .

On the other hand, in the region limited by the dotted counter, which represents a zone for which the detectors are saturated, qualitative information can only be obtained in terms of beam distribution. Outside of these two zones, the detectors are in saturation and therefore do not provide trustworthy data anymore. At this point, optical ring structures start forming. The region with the dashed contour corresponds to a highly saturated zone, in which bull’s eye structures appear. The region limited by a dot-dash contour corresponds to a region for which a clumping pattern (see below) forms in the central region of the detector (including the white ring region).”

h) Figure 6 shows about 100 small pictures obtained when etched CR-39 chips were placed on the flatbed scanner whose resolution was 1200 dpi (21 microns between pits). That seems to be an appropriate way of examining saturated regions. Each picture is identified in terms of two known parameters, the fluence (between 5*10^6 and 5*10^10) and the etching time (between 18 min and 78 min). It would be desirable to see that, for a given etching time, an optical parameter, such as mean grayness, were proportional to the fluence. Unfortunately, this is not the case. The dependence of the mean grayness on the fluence is not even monotonic. This is illustrated in Figure 8.

i) Another technique used to study saturation regions was Atomic Force Microscopy. Such instruments are described, for example, at

http://en.wikipedia.org/wiki/Atomic_force_microscope

j) The second half of the paper reports on what was observed via microscopic examination of saturated regions. Some of the figures resemble what I observed in the examination of etched CR-39 detector from our The Galileo Project experiment. But my etching time was 6 hours while this paper is based on experiments in which etching times were less than 1.5 hours. This, however, does not exclude a possibility that fluences in SPAWAR-type experiments are much higher than what one measures by counting tracks in the non-saturated regions? Perhaps fluences were high enough to be compatible with reported amounts of helium produced diring excess heat experiments.

P.S.
k) According to http://en.wikipedia.org/wiki/Fluence,

“In physics, fluence [F1] or integrated flux is defined as the number of particles that intersect a unit area.” But the authors seem to use this term differently. Perhaps their fluence, F2, should be multiplied by a large factor, M, to obtain F1. Suppose they identify F2 with the number of tracks per cm^2, in the preliminary experiment (when tracks do not overlap). If this is so, then particles whose angle of incidence are larger than 22 degrees are ignored. This would make F2 considerably smaller than F1. To estimate the order of magnitude of M, defined as F1/F2, let me assume that the source diameter is large (much larger than 4 mm). In that case the source area could be treated as a set of point sources. For each point source, the factor M is nothing else but 4*Pi (total solid angle) divided by the solid angle A, within the half-angle of 22 degrees. In this case:

A=2*pi*[1-cos(22 degr)] = 6.28*0.0728 = 0.45 stereoradian.

Within my approximation, M =12.56 / 0.45 = 27.5. Thus if F2 is specified as 10^8 p/cm^2, then F1= 2.7*10^9 p/cm^2. This is for an ideal situation (well defined geometry, etc.)

l) What we are interested in is the total number of particles emitted during an experiment. Some of these particles are emitted in the direction of the cathode. They are not intercepted by the CR-39 detector. The source itself is not thin and a very large fraction of particles, emitted toward the detector, is absorbed in the source. Likewise, a very large fraction of particles, emitted toward the CR-39, is absorbed in the electrolyte. For that reason, an estimation of the total number of particles, emitted during an experiment, is not going to be easy. Only Monte Carlo simulations can help us in this task, even if F2 could be accurately determined, for example, on the basis of the mean grayness. But reliability of such simulations cannot be higher then reliability of assumptions one must make. One think is clear; the estimated number of tracks produced during electrolysis is likely to be a tiny fraction of one percent of all particles emitted during a SPAWAR-type experiment.

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