Recording processes for swift charged particles in muscovite mica.
F M Russell
April 2013
Abstract. Crystals of muscovite can record the tracks of swift charged particles and also the tracks of energetic
nonlinear mobile excitations of the lattice. The tracks are recorded and made observable by local deposition of
magnetite. This is a chemical process and so the recording process must involve local changes of chemical
potentials. This is consistent with the observed discrimination between the recording of particles with positive or
negative charge. It is also consistent with the recording of uncharged mobile lattice excitations involving large
amplitude, nonlinear, motion of atoms from their equilibrium positions that cause transient changes in local
crystal potentials. These effects are not unique to muscovite. The internal structure of most rocks and minerals
could be modified by the constant flux of swift charged particles.
Introduction.
The discovery that crystals of muscovite can record transient disturbances to the lattice caused by the
passage of high energy charged particles gives information about the recording process.[1] The tracks are
delineated by the deposition of magnetite in close proximity to the tracks.[2] Although this effect has not been
reproduced in a laboratory the general principles underlying the process can be deduced from basic principles.
The necessary conditions for this process to operate require the growth of large single crystals containing an
impurity of iron up to about 2 atomic percent and for the crystals to have cooled slowly. Crystals of the mineral
muscovite require both high pressure and temperature to form, typically, greater than 5km underground and at
up to ~650oC.[3] At such depths the direct muon component of cosmic rays is greatly attenuated, leaving the
background of neutrino created muons. In addition, there are secondary protons and neutrons, gamma rays and
the products from radioactive decay of potassium 40K in the crystal and radioactive elements in the surrounding
rock matrix. None of these cause significant long term damage to the crystal. Finally, there is spontaneous
fission of Uranium and Thorium impurities in the crystals, which causes persistent massive damage to the
crystal structure. This massive damage is exploited for dating of rocks.[4]
The occurrence of imperfections in the form of black or red patterns, sometimes called staining, in the
(001)-plane of easy cleavage in muscovite was known in antiquity. An example is shown in Figure 1. In some
civilisations such crystals were treasured, as evidenced by their forming part of burial goods.[5] The
development of electrical equipment and especially electronic valves led to rapid expansion of the mining of
muscovite for use as an electrical insulator. It is relatively chemically inert, can be split in to thin but strong
sheets, and can be manipulated and machined easily. In particular, it is stable under high vacuum, has excellent
insulating and surface tracking resistance and has a high decomposition temperature. For these reasons good
quality crystals of muscovite without staining were in great demand and led to careful selection of material at
the mines.[6] This was because some forms of the staining are electrical conductors. There was little interest in
the cause and growth of the staining other than to identify the minerals involved and their habit.[7] Partly, this
was due to the thermal stability of the staining, which prevented upgrading of such material by thermal cycling.
The development of micro-analytical techniques for studying minerals and inclusions allowed analysis of the
decorated tracks of charged particles that are responsible for much of the staining.[8] However, this has not led
to a deeper understanding of the underlying solid-state processes involved in the recording and decorating of the
tracks. Here, an attempt is made to identify basic aspects of the recording process, starting with a review of the
interaction of swift charged particles propagating in crystals of muscovite.
Detectors.
The behaviour of swift charged particles moving through crystals has been studied for over a hundred
years but still there are unresolved aspects. This is partly because there are no tools for studying the motion and
energy state of individual atoms inside a crystal. It is for this reason that computer-based molecular dynamics is
important in studies of staining although this technique has not yet been applied to the recording process. In the
study of the properties and interactions of high energy particles various types of detectors have been developed.
Photographic films were of great importance, even though these only gave evidence of past events at some place
and the location of the events was grossly smeared out in the developing of the films.[9] Bubble chambers and
cloud chambers gave better spatial and temporal location of particles but only in liquid or vapour targets. To
extract information from these detectors optical images had to be recorded and then analysed, which introduced
1
time delays. Multiple wire proportional counters, based on ionization of gases, traded positional for temporal
information and often were used in conjunction with huge magnets. These detectors were designed to delineate
the paths of particles regardless of the origin of the particles. The recent development of charge coupled
detectors, such as used in cameras, has increased the accuracy of spatial and temporal information on flight
paths but gives no information about the originating interactions in target materials. Probably the best tool for
studying interactions within a solid target is the electron microscope yet even this has severe limitations on field
of view and resolution. Nevertheless, it was the tool used to observe for the first time the massive damage done
by high energy fission fragments crashing through a crystal of mica.[10] Later, the technique of chemical
etching of massive damage tracks in solids to reveal their location by optical methods was developed. The
sensitivity of this etching method is illustrated by the particle with the least ionizing power that can be seen in
muscovite, namely, 2 MeV 20Ne ions, where the rate of energy loss is ~2GeV/cm or ~2x10 5 eV/micron.[11]
This contrasts starkly with the least ionizing particle recorded in muscovite by the natural recording process,
namely, 1.4MeV positrons, with a rate of energy loss of about 1eV/micron - a factor of 105 more sensitive. The
necessary conditions of high pressure at high temperature for this process to occur have hindered its study in a
laboratory.
Decay of potassium nuclei. It is fortuitous that muscovite contains potassium atoms, of which 1 in 8,000 is the
radioactive 40K isotope with a half life of 1.3x109 years. There are three decay channels of which the most
frequent gives 40Ca with ejection of an electron. The least frequent channel, by a factor of about 1:105, leads to
40
A with ejection of a positron. A third channel involves internal electron capture with no ejected particle. In
each cubic centimetre of muscovite ~1300 positrons and ~1.3x108 electrons are emitted per year, or ~4 decays
per second. The electron and positron channels are three body decays involving emission of a neutrino. As a
result the electrons and positrons are emitted over a range of energies up to the maximum values of 1.3MeV and
1.5MeV, respectively. The maximum energy occurs when the neutrino takes minimum kinetic energy, the
emitted particle and recoiling nucleus then going in nearly opposite directions. The ejected particles are
isotropic in space. In an amorphous material of the same average atomic weight as muscovite the maximum
range of positrons is ~2mm. However, the crystalline structure of muscovite dramatically influences the
propagation of the emitted electrons and positrons. This is due in part to their quantum mechanical properties
but also their opposite charge. The most important effects are enhanced range due to channelling of positrons
and diffraction scattering by the lattice. Channelling is when a charged particle moves through the spaces
between atoms in a crystal and is strongest for positively charged particles moving in principal crystal
directions. Diffraction scattering is the manifestation of the wave-like properties of elementary particles. These
two effects discriminate strongly against electrons. For positrons of near maximum energy emitted in a direction
close to a principal crystal direction in the (001)-plane of potassium atoms, i.e. an atomic chain direction, the
range or flight path can reach ~120mm. One such track is shown in Figure 2. The strong discrimination against
electrons and the increase in range of positrons assists in identification of positron tracks. The emission of
positrons from a potassium nucleus in the monatomic sheet of potassium atoms leads to a unique angular
distribution of their tracks, dominated by Fresnel diffraction scattering by the nearest neighbour potassium atom
in the direction of flight from the point of emission. The positively charged nucleus acts as an opaque disc for
positrons moving in that direction. The unique feature of the angular distribution is a central maximum of
probability for a positron that lies exactly on the axis of the atomic chain flanked by symmetrical diffraction
wings. This distribution is shown in Figure 3. The narrowness of the central spike is limited by measurement
error. The central peak is independent of the de Broglie wavelength and thus of the energy of the particles.
Charged particles travelling through any medium in any direction will experience multiple small
deviations from straightness in the flight path due to scattering by atoms. This does not conflict with
channelling, which occurs when particles move in specific crystal-related directions. Even particles that are
channelling can be scattered by imperfections such as dislocations and interstitials. The magnitude of a single
scattering varies from minute to large, even to reversal of direction of flight. For high energy or relativistic
particles the scattering is random, giving a Gaussian distribution of scattering angles. At moderate to low
energies the scattering distribution departs from Gaussian and follows a unique distribution known as the
Rutherford sin4( ) law. There is no known alternative cause for this distribution curve. The measured
distribution curve for tracks in muscovite identified as caused by positrons is shown in Figure 4. Also shown is
the distribution curve for positron tracks recorded in photographic emulsion. The results confirm the unique
distribution expected for positrons emitted from potassium nuclei. Of the other types of charged particles that
could be present in the muscovite the muons have far too high energy to follow the Rutherford law and alpha
particles have orders of magnitude shorter range. That leaves protons but these are rare and loose energy at a far
greater rate than positrons. The advantage of this test for charged particles is that it does not rely on any
particular property of the scattering material.
2
The small mass of positrons means that they mainly lose energy via electronic excitation and occasional
ionization of atoms in close proximity to their flight path as opposed to nuclear scattering of heavier subatomic particles like protons. The occasional ionization events leave positively charged ions on the flight path
and electrons, the delta-rays, which migrate away. Low energy positrons seldom produce delta-rays. The
variation of rate of loss of energy as a charged particle slows down in an amorphous material is known. It
increases steadily with decreasing speed as the moving charge spends more time near atoms it passes, reaches a
maximum and then rapidly falls to zero as it stops. If the recording process in muscovite is based on local
changes of the electronic states of atoms, which is a reasonable assumption as it must have a chemical
basis, then the amount of impurity deposited should follow the change in rate of loss of energy along a flight
path. The staining in muscovite almost invariably takes the form of deposits in the plane of easy cleavage in the
(001)-plane, which results from weak van der Waal’s forces. These deposits tend to be of nearly uniform
thickness of nanometre order. Variations in the amount of material deposited per unit length of flight path then
shows as variation of width. This variable is easily measured. The measured variation of width of tracks with
residual distance to coming to rest is shown in Figure 5, together with the predicted variation based on
proportionality of deposited material to the rate of energy loss. An example of such a track is shown in Figure 6,
where the tadpole shape is clear, which shows the direction of flight of the charged particle and assists in
identification of particle tracks.
The emission of a positron leaves a residual negative charge at the point of origin of the track, which
does not attract decoration. As a positron slows down the probability for annihilation with an electron to give a
gamma ray increases and will certainly occur at the end of the track. This annihilation will result in a residual
positive charge, which is equivalent to an ionisation event. The resulting positive charge will encourage
decoration with magnetite. Conversely, the emission of an electron will give a residual positive charge that
should show up as an isolated decoration dot. However, in both of the emissions the nucleus will recoil to create
a quodon. The isolated decoration dot of the electron emission case will then form the starting end of the
decorated quodon track.
Basis of recording.
It is clear that iron ions must be present in the crystals to delineate the tracks. It is also evident from the
nature of the dendrite-like decoration of tracks that there is an excess of iron beyond that required simply to
delineate the tracks. The processes of recording and subsequent decoration must overlap but it is likely that the
recording stage ceases before the decoration ceases because the extent of decoration often is relatively uniform
in a given crystal and vastly greater than that of tracks with minimum decoration. Measurements show the
number of tracks recorded per unit volume of crystal decreases at high iron concentrations. It is not yet known if
all the iron in a crystal finally accretes in the decoration but the lack of colour or darkening between decorated
tracks suggests this is possible. The recording process appears not to function if the iron concentration is less
than about one iron ion per 200 unit cells. The maximum concentration is expected to occur when Fe +2 replaces
the octahedrally coordinated aluminium, up to about two iron ions per unit cell. However, Fe+3 can also replace
silicon that, significantly, is closer to the potassium layer in which the positrons propagate. The relative
positions of atoms in the muscovite lattice are illustrated in Figure 7.
Clearly, movement of iron ions from the lattice to form the staining is energetically favourable.
However, since the staining does not occur at random in a dispersed form there must exist an inhibiting potential
energy barrier. The existence of the tracks shows that swift charged particles facilitate the rearrangement of
atoms by lowering this potential energy barrier. Thus a logical and plausible basis for the recording process is
provided by the electronic energy loss of positrons contributing to the required lowering of the potential
energy barrier inhibiting formation of the staining. The close proximity of the moving positrons to the iron
and oxygen in the silicate layers should be an advantage. Probably the only way that details can be revealed of
the movement of charges and atoms that occur in the recording process is by computer simulation. Although this
model of the recording process provides a possible recording mechanism it does not give a complete description
for the formation of the observed tracks. This is because the average rate of energy loss per unit length of track
for the fastest positrons is too small to significantly influence the local chemical potentials related to the
potential energy barrier.
In reality, charged particles loose energy in discrete steps at random scatterings by changing the
electron energy levels in atoms or occasionally by ionizing them. Hence, the flight path of a positron will be
delineated by occasional excited atoms, some of which could trigger the recording process locally. It is not
known exactly where in the lattice the pinning of iron occurs. This topic will be revisited below. Once the
accretion of iron and oxygen to form Fe3O4 begins then the lattice will be strained locally. The behaviour of
muscovite under local stress is observed easily via percussion and pressure figures.[12] These show the weakest
3
directions in the (001)-plane lie in atomic chain directions. Hence, it is energetically favourable for the
accretions to grow in these weakest directions and could lead to linking up of accretion sites. This linking
process should assist the delineation of the longest positron tracks, which lie in chain directions because of
channelling and diffraction scattering - an example of simultaneous particle-like and wave-like properties of
particles. For tracks laying in other directions in the recording plane the linking process would result in a
widening of the decorated track. In most crystals this widening is not obvious because of the extent of
decoration of the initial track path delineation.
As a result of the nature of quodons and kink-like pulses they are inevitably restricted to propagation
and thus to being recorded in the (001)-plane. The effect of channelling and diffraction on charged particles also
tends to restrict them to propagation in the (001)-plane but not exclusively. High energy charged particles can
also pass through the crystals in directions that intersect the (001)-plane. If these paths deviate only slightly
from the (001)-plane then it is sometimes possible to follow their paths as they are recorded in adjacent sheets.
An example is shown in Figure 8, where the grazing angle of incidence is 6x10-3 degree. Successive ionisation
events have led to large accretions of magnetite forming dots in adjacent sheets with the track between the dots
being visible in some cases. Usually, however, continuity between dots due to ionisation events in different
sheets is not clear, often because of the large number of overlapping tracks and dots.
The fact that positrons from 40K decay are recorded in the potassium sheet does not show that other
positively charged particles also are recorded in the same sheets. This question is resolved by observation of the
tracks left by charged particles that, when propagating at an angle to the K-sheets, change direction to move in a
K-sheet by scattering off a potassium atom. In this process a quodon is generated. If the charged particle is later
scattered out of the K-sheet then a second quodon is generated. This sequence leads to two parallel quodon
tracks that are joined by the track of a charged particle that is not parallel to the quodon tracks, as shown in
Figure 9.
For many practical purposes and for simplicity of presentation the recording process can be described
by the following simple model. During crystal growth iron atoms can be incorporated in to the structure. To
delineate the tracks the iron must be able to migrate. The recording of electron-positron showers in muscovite
shows that the recording process starts after the crystals have formed, as the crystals cool. Cooling will bring the
mobile iron to saturation point and further cooling to a supersaturated state. Precipitation of the mobile Fe would
then occur at nucleation sites created by passage of swift charged particles, as seen in cloud chambers. The
recording process will stop when mobile iron is no longer available. Since the precipitation and accretion
processes are exothermic the recording stage cannot be recreated by thermal cycling of the crystals.
Delineation with epidote.
Surprisingly, there is a second route by which tracks can be recorded in muscovite. It results in the
formation of thin ribbons of the mineral epidote. Study of this process shed light also on the recording process
leading to formation of magnetite. This second process was identified in connection with the recoil of potassium
nuclei during radioactive decay of 40K. It was found that at the start of a high energy positron track laying in a
chain direction and delineated with magnetite there was a collinear track that started at the position of the
recoiling atom and extended exactly in the opposite chain direction. Figure 10 shows the junction between the
two parts and how the width varies along the tracks. These tracks were found to be composed of the mineral
epidote. These tracks were of constant width over their entire length but the width varied slightly on different
tracks and in different crystals. In some crystals containing an intermediate concentration of Fe there were
portions of these uniform width tracks that were decorated with magnetite. In crystals with moderate to high
concentrations of iron the lengths of positrons tracks were much reduced due to increased scattering by the iron,
either by local distortion of the lattice or by interstitial atoms of iron. Under these conditions the tracks resulting
from recoiling atoms were decorated only with magnetite.
It was shown that the tracks moving in the opposite direction to the positrons were due to the creation
of a mobile, highly localised, nonlinear lattice excitation called a quodon.[13] The reality of quodons has been
demonstrated in the laboratory. In these quodons adjacent atoms on a chain execute large amplitude oscillations
in near anti-phase motion, while the envelope of the quodon moves along the chain at slightly sub-sonic speed.
The kinetic energy in a quodon can exceed 50eV, with most of this energy carried by less than five atoms. The
maximum range of quodons is limited only by the size and degree of perfection of the crystal. Most of the
energy in a quodon is carried by atoms on a single chain, with atoms on adjacent chains moving only slightly.
No evidence was found for quodons carrying an electric charge. It follows that the delineation of quodon tracks
by magnetite is not due to ionization. The only known cause for triggering the recording process is the highly
4
localised, large magnitude, variations in local chemical potentials of the potassium atoms within a quodon. The
relative motion of adjacent atoms in a chain due to the passage of a kink-like pulse can be studied using
molecular dynamics. Figure 11 shows the variation of atomic spacing between adjacent atoms in a metal,
expressed as the ratio of the displacement from equilibrium position to the average spacing. Each plot is a
snapshot at equal intervals of time in a sequence. The plots show that a kink-like pulse pushes atoms closer
together at the front of the pulse followed by an immediate increase of spacing in the tail as the disturbance
fades, indicated by the shaded part. It is suggested that the region of increased spacing could be the site for
pinning of mobile iron ions as a nucleation site for development of magnetite decoration. Molecular dynamic
studies of the muscovite lattice have shown that large amplitude displacements of potassium atoms from their
equilibrium positions can create a secondary potential well.[14] This is illustrated in Figure 12. In a similar way
large amplitude oscillations of atoms in a quodon modifies the local crystal potentials in such a way that the
potential energy barrier inhibiting movement of iron ions is either increased or reduced, the latter permitting
pinning of the iron, in a similar manner to that proposed for the delineation of charged particles.
Discussion.
Since the paths of both charged particles and quodons can be recorded and decorated with magnetite
the recording mechanism must respond to highly localised transient variations in the chemical potentials. This is
an obvious comment because the recording process is clearly a chemical one. The sign of the charge on the swift
particles is important because the recording process only responds to positive charges. This is consistent with
the concept of a potential energy barrier inhibiting the deposition of iron. Negative charge increases the barrier
height and positive charge reduces it. As a result ionisation events have a charge dependent effect on the
recording mechanism. Positive ions encourage decoration but free electrons discourage it. The persistence of
ionisation in insulating muscovite would be expected to cause stronger deposition of magnetite than that
resulting from only a transient reduction of the barrier by moving disturbances. This corresponds to what is seen
in the decorated tracks, especially in the tracks resulting from electron/positron showers.
Although it is clear iron can migrate in muscovite crystals exactly what happens at the atomic level is
unknown. Staining is obviously a lower energy state for crystals that follow the normal route of growth at high
temperature followed by slow cooling. The most common mineral comprising staining is magnetite but hematite
can also form. Under the artificial conditions induced by irradiation from cosmic rays and radioactivity,
including the violent nonlinear vibrations of atoms in quodons and kinks, the minerals epidote and more rarely
glauconite also can form. Staining with glauconite appears to be restricted to the vicinity of the transition of
decoration of tracks between magnetite and epidote. The slow cooling rate of crystals within pegmatites allows
ample time for migration of impurities. Migration and the annealing of small defects will be fastest when the
crystals are at high temperature, the rate decreasing rapidly as the temperature drops. However, they will
continue to be assisted by the continuous creation of quodons and kinks throughout the remaining life of the
crystals.
It is expected that iron would be incorporated in to a crystal in an essentially uniform way during
crystal growth. Migration would also tend to reduce any local variations in concentration. However, when
splitting stained sheets it is evident that many adjacent layers to a stained layer are depleted of iron. This
strongly suggests that iron can migrate easily in the direction normal to the (001)-plane.
Conclusion.
It is likely that the staining often seen in crystals of muscovite is the result of a common phenomenon
that allows a crystal lattice to relax to lower energy states as it slowly cools after growth. In common with other
materials that have variable composition this relaxation process results in separation in to phases or crystals of
simpler composition. Again in common with other multi-phase systems spontaneous separation is inhibited by a
potential energy barrier in absence of nucleation sites. It is the transient lowering of this barrier by swift charged
particles or by the violent motion of atoms in quodons and kinks that allows the creation of more persistent
nucleation sites that, in turn, allow progressive accretion of a second phase of material to render tracks
observable. The unique features of the staining in muscovite arise from its propensity to form large single
crystals, its ease of cleavage, transparency of thin sheets, it being a good electrical insulator and opacity of the
precipitated second phase. In combination these features allow the tracks of swift charged particles and
energetic, nonlinear, mobile lattice excitations to be recorded and rendered visible. It is unlikely that this
combination of features can be found in other natural systems. This suggests that muscovite mica offers a
unique opportunity to study the formation and recording of tracks in crystals. The high sensitivity, long
recording time and permanency of record also suggest muscovite crystals would be a good place to look for very
rare events that might be caused by the action of dark matter. Most rocks and minerals are good electrical
5
insulators and are constantly bombarded by swift particles, which can create quodons and kinks in addition to
nucleation sites by ionisation. Thus, it is probable that both during and after growth their internal structure could
be modified by these disturbances to the structure.
Acknowledgement.
It is a pleasure to acknowledge helpful discussions with Prof. G Fitton on various aspects of the genesis and
properties of muscovite mica.
References
1. M Russell, Identification and selection criteria for charged lepton tracks in mica. Nucl. Tracks Radiat. Meas.
15, (1988) 41-44
2. F M Russell, Decorated track recording mechanisms in muscovite mica. Nucl. Tracks Radiat. Meas., 19, 1-4,
(1991) 109-113
3. W A Deer, R A Howie, J Zussman, Rock-forming minerals, Vol 3, Longmans, (1965) 1-20
4. R L Fleischer, P B Price, Charged particle tracks in glass, J. Appl. Phys., 34, (1963) 2903-2904
5. G Hancock, Fingerprints of the Gods, p. 188-9, Arrow, (1998)
6. D F Hugo, Ph.D. Thesis, 1995, History Discipline, Northern Territory University, Australia.
7. D A Richards, Magnetite inclusions in mica. Proc. Phys. Soc., Vol. 63, Pt. 8, (1950) p 852-855
8. J W Steeds, F M Russell, W J Vine, Formation of epidote fossil positron tracks in mica, Optik, 92, 4,(1993)
149-154
9. C B Childs, L M Slifkin, Delineating of tracks of heavy cosmic rays and nuclear processes within large
crystals of silver chloride, Rev. Sci. Instr. 34,(1963) 101-104
10. E C H Silk & R S Barnes, Examination of fission fragment tracks with an electron microscope, Phil.Mag. 4,
(1959) 970-971
11. R L Fleischer, P B Price & R M Walker, Nuclear tracks in solids, Uni, Cal. Press, (1975) p 19,
12. R H Jahns & F W Lancaster, Physical characteristics of commercial sheet muscovite in the south-eastern
united states, Geol. Survey Prof. Paper 225, (1950) 6-7
13. F M Russell & D R Collins, Lattice-solitons in radiation damage. Nuc. Insts. and Meth. B, 105(1995) 30-34
14. F M Russell & D R Collins, Lattice-solitons and non-linear phenomena in track formation. Rad. Meas. 25,
1-4 (1995) 67-70.
6
FIGURES
Figure 1. Contact print of sheet of muscovite mica showing many lines that are parallel to principal crystal
directions. These are due to mobile lattice excitations called quodons, which propagate along chains of atoms.
Also visible are several tracks due to charged particles that are not parallel to the quodon tracks.
7
Figure 2. A contact print of a positron of ~1.5MeV energy emitted from a 40K nucleus. The width of the track
increases as the positron slows down, when it annihilates and leaves a positive residual charge. These processes
give rise to a tadpole shape for the tracks. There are many other tracks of lower energy positrons visible that lie
in other atomic chain directions.
Figure 3. Plot of the angular distribution of
tracks of positrons from 40K decays. The
central spike and symmetrical wings are the
result of diffraction scattering of positrons
by the lattice.
8
Figure 4. Plot of the scattering distribution
function for relatively low energy positrons
from of 40K decays. D2 is the second
difference of coordinates of a track at equal
intervals along the track and D2 bar is the
mean. The distribution follows the
Rutherford scattering law, which is unique
to the scattering of charged particles.
Figure 5. Plot of the variation of width of positron tracks as a function of the residual path length before coming
to rest. The dashed lines are the theoretical predictions for different energy regimes as particles slow down.
9
Figure 6. Contact prints of several positron tracks, showing the characteristic tadpole shape. The maximum
range of 1.5 MeV positrons in an amorphous material of the same atomic composition as muscovite is 2mm.
10
Figure 7. Diagram showing the
structure of muscovite. Iron can
substitute for silicon in the sheets
adjacent to the potassium sheets, so
they will feel changes in crystal
potentials caused by large amplitude
motion of potassium atoms and
passage of swift positively charged
particles in K-sheets.
Figure 8. Diagram showing sections of the track of a swift charged particle moving at grazing angle relative to
the (001)-plane in muscovite. Thin layers of the crystal were stripped off using selotape. The thickness of the
layers was determined by optical interference colours.
11
Figure 9. Contact prints of swift charged particles that scatter in to the recording layer, move some distance in
that layer and then scatter out of the layer. A quodon is created at each scattering event, giving rise to the
characteristic dog-leg pattern of two parallel quodon tracks joined by a section of track due to a particle moving
in a random direction.
Figure 10. Diagram
showing the different
types of decoration of
tracks for a positron
and quodon simultaneously created in a
40
K decay. The black
decoration with magnetite shows variable
width along the track
whereas the quodon
track part decorated
with
epidote
has
uniform width.
12
Figure 11. Plots of the ratio of
separation of potassium atoms relative
to their equilibrium separation as a
kink-like pulse moves along a chain of
atoms. The different plots are for equal
intervals of time for a single pulse on
one chain. The shaded parts indicate
where atoms are more widely spaced
than normal. It is energetically
unfavourable for an interstitial atom or
a nearby atom to insert in to the chain
when atoms are closer together than
normal.
13
Figure 12. Plot of the defect energy of a potassium atom when it is moved away from its equilibrium position in
the K-sheet. In this plot the other atoms in the lattice are held fixed, corresponding to rapid motion of the
displaced atom.
14