Scientific Visualization Project:

Tracks in Mica Detectors

University of Sydney

Vislab

Eva Schlenker and Jeremy Mitchell

Abstract

The aim of this project was to visualize the tracks of particles in mica. Using 3-dimensional images, it should be possible to get an accurate estimate of the relation a- and b-axes of the unit crystal cell of the mica.

1.0 Introduction

1.1 Crystal structure of the mica

The geometry of the tracks contains information about the crystal structure of mica. Mica has a monoclinic structure, that means that the three sides of the unit cell are all of different length, the angles a and b are equal to 90° while g is not equal to 90° . A monoclinic crystal structure is shown in Figure1. Figure 2 shows to which angle a , b and g correspond.

Figure 1: Simple monoclinic structure [1] Figure 2: Unit cell [2]

1.2 Formation of the tracks

The formation of the tracks is due to 238U decaying in the crystal. The half-life of 238U is 4.5 ´ 109 years. Here, the decay is represented by two particles going into opposite directions (conservation of momentum). Possible formations of the tracks are shown in Figure3.

Figure 3: Formation of the tracks [3]

1.3 Geometry of the tracks

The number of geometries available is limited due to the composition of the crystal and the crystal structure. The geometry of the tracks is also related to the extent of the radiation damage at a certain residual range [4]. Two different formations are formed.

If a track starts with a hexagonal shape or a triangular shape depends on the cutting and etching surface.

To be able to see the tracks, the crystal had to be cut and the surface was etched in 40 % hydrofluoric (HF) acid. An image of an etched cone is shown in Figure 4.

Figure 4: Etched cone [3]

2.0 Experimental Procedure

The images were taken using a computer controlled optical microscope (CCOM). Each image taken corresponds to different depth of focus, here the difference was 1 m m. For more detailed information about the CCOM see [6]. The number of images taken is 24. Some of them are shown in Figure 5.

Figure 5a: Tenth image taken. Figure 5b: Seventeenth image taken
The first few pictures appeared kind of blurry. This is due to the fact the microscope was not focused on the surface but a little bit above it. The actual track starts at approximately the fifth image.

2.1 Procedure for Creating the Three Dimensional Data Set

In order to visualize the track, it was necessary to combine all twenty four two dimensional data sets into one three dimension data set. Firstly, the images were viewed using xv, enabling size of each data set to be determined and then saved as bitmaps. Each was found to have 140 ´ 132 pixels, and since they were colour images, each contained 140 ´ 132 ´ 3 bytes, with the amount of red, green and blue light being specified for each point. Since the images were taken using a black and white camera, the values of each colour at a point are identical, so it was necessary only to include the data for one colour.

In Matlab, a 140 ´ 132 ´ 24 array of zeros was created, then each of the twenty four bitmap data sets were read into Matlab as 140 ´ 132 ´ 3 arrays. The first layer of each array (that is, points with coordinates of the form [x, y, 1]) was copied into the appropriate layer of the 140 ´ 132 ´ 24 array, such that the first image was stored in the first layer and so on. When each of the twenty four images had been read in, the resulting three dimensional array was written as the file ff1.dat, which was the data file subsequently visualized using AVS.

The procedure for creating the three dimensional data set outlined above was carried out using the following Matlab code:

>> a='ff1_';

>> b='.bmp';

>> A=zeros(132,140,24);

>> for i=0:23,

c=num2str(i);

d=strcat(a,c,b);

B=imread(d,'bmp');

A(:,:,i+1)=B(:,:,1);

end

>> fid = fopen('ff1.dat','w');

>> fprintf(fid,'%12.8f\n',A);

Once the three dimensional data set had been created, a field file was written to enable the data set to be visualized in AVS. The field file is a simple description of the data set containing information about the data set, specifically that is a uniform and three dimensional, with 140 ´ 132 ´ 3 floats at each position, that it contains no other information other than the data to be visualized, and its location.

2.2 Visualization of the Data Set

As stated earlier, the data set was visualized using AVS. A number of methods were used to display the tracks, the most useful of these for obtaining information about the tracks was the use of the orthogonal slicer module. Three orthogonal slicers were set up, each taking slices perpendicular to the other two, to allow the tracks to be seen from all three dimensions, and at any depth. These were viewed in both gray scale, as the image was originally obtained, and as well as this, the gray scale was replaced by a colour scale for other visualizations. It was found that the addition of a colour scale aided in differentiating between various parts of the image, however, it was necessary to compare results obtained this way with the grayscale images to insure that features we observed were not artifacts created by the gray scale.

The most important aspect of using orthogonal slices is that the dimensions of parts of the track can be obtained quite easily via this method. The easiest way of obtaining these dimensions is to select the slice showing an appropriate image, and to use the probe module to determine the coordinates of particular points, and then find the distance between these points using Pythagoras’ theorem. This method gives lengths in units of pixels, however this does not cause any difficulties since the size of the image in terms of micrometres is known, and so values in units of pixel length can easily be converted to more conventional units if required. On the other hand, such conversions did not prove to be necessary since the values we wished to obtain were ratios of lengths, and therefore dimensionless.

Many other methods of visualization were used besides these, the most important and useful of which were displaying the track using isosurfaces (Figure 7), displaying as scatter dots, and using volume rendering. Interpreting the images obtained using isosurfaces required some thought, as they were potentially misleading if not properly understood, since it is easy to misinterpret an isosurface as the shape of track. While the similarity between some isosurfaces and the track shape, for others, although hints of the shape were often present, in many cases important features were missing. Nonetheless, this method was useful in examining the features of the track which were of the same colour (which corresponds to the amount of interference).

Visualization using volume rendering and scatter dots enabled viewing the track as a three dimensional object, which proved useful in studying its geometry. In order to utilize these modules effectively, the data needed to be sufficiently downsized not only to decrease the computation time required to create these images, but also to allow desired areas of the image to be viewed more directly. The clamp module is also useful in this respect.

3.0 Results Obtained by the Visualization

It was noted that approximately the first five or six images (viewed using the orthogonal slicer) are slightly more blurred than the others. An interpretation of this is that these images were taken with the microscope focused above the cleave layer, the fifth or sixth slice is an image of approximately the cleave surface. In the next eleven or twelve slices, a hexagram is clearly the dominant feature of the image, corresponding to high energy disruptions to the crystal structure. From these images (slice 10), a ratio for a/b, which corresponds to the ratio of two sides of the unit cell for the mica crystal, was obtained, specifically, a/b = 0.57 which compares well with the accepted value of 0.577. Beyond these slices, a region in which triangles are the dominant feature is encountered, due to low energy disruptions to the crystal. The triangle remains the dominant feature for the remaining six or seven slices.

The hexagonal and triangular structures in the track are also very easily observed using the scatter dots and volume render modules (Figure 6). One of the most interesting results obtained by volume rendering was the presence of a second triangle. (That is, what seemed like a single triangle was actually two, one slightly bigger than the other. This difference in size is explained by the amount of energy dumped into the crystal by the daughter atom of the decaying uranium isotope. As this atom travels through the mica, its energy decreases, since energy is expended in damaging the crystal lattice. At various points, the rate of change of energy in the atom, corresponding to the amount of energy dumped into the crystal, is not continuous, but jumps to a smaller value. For instance, it moves from a high rate of change, producing hexagons (more generally, producing various polygons in various crystals), to a lower rate of change, producing triangles, and then possible to even lower rates of change producing smaller and smaller triangles.

It is possible to find an estimate of the energy of the initial energy of the daughter atom by comparing the length of the triangular section of the track with the hexagonal section, however calculation this was not able to be completed in time.

Figure 6: Image obtained using volume rendering Figure 7: Image obtained using isosurfaces

4.0 Conclusion

In this project, we successfully created a three dimensional image of tracks in a mica detector. We used various techniques to visualize the image, and determine properties of the crystal structure.

5.0 Acknowledgements

We would like to thank Dr. S.R. Hashemi-Nezhad for his help during our project and Mr. Marek Dolleiser for providing us with the images.

6.0 References

[1] www.its.caltech.edu/~ecfit/bravais.html

[2] www.its.caltech.edu/~ecfit/bravais.html

[3] P.B. Price and R. L. Fleischer, Ann. Rev. Nuc.Sci., 21, 289 (1971)

[4] S.R. Hashemi-Nezhad, Nucl. Instr. and Meth. in Phys. Research B 142 (1998), 98

[5] S.R Hashemi-Nezhad, Radiat. Measurem. Vol. 28, Nos 1-6, pp 167-170,(1997)

[6] S.R Hashemi-Nezhad and M. Dolleiser, Radiat. Measurem. Vol. 28, Nos 1-6, pp. 839-844,(1997)